%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP206^3 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:28 AM UTC 2026
% Result : Theorem 28.44s 7.23s
% Output : Refutation 28.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 197 ( 92 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 408 ( 49 ~; 38 |; 1 &; 293 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 205 ( 204 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3626 (3623 usr; 116 con; 0-5 aty)
% Number of variables : 100 ( 5 ^; 95 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(type_def_6,type,
int: $tType ).
thf(type_def_8,type,
set_int: $tType ).
thf(type_def_9,type,
set_Pr958786334691620121nt_int: $tType ).
thf(type_def_10,type,
set_nat: $tType ).
thf(type_def_11,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(type_def_12,type,
set_se7855581050983116737at_nat: $tType ).
thf(type_def_13,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(type_def_14,type,
set_se5479201105039950375at_nat: $tType ).
thf(type_def_15,type,
set_Pr7459493094073627847at_nat: $tType ).
thf(type_def_16,type,
code_integer: $tType ).
thf(type_def_17,type,
nat: $tType ).
thf(type_def_18,type,
set_o: $tType ).
thf(type_def_19,type,
set_Product_prod_o_o: $tType ).
thf(type_def_20,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(type_def_21,type,
set_Pr7995236796853374141at_int: $tType ).
thf(type_def_22,type,
num: $tType ).
thf(type_def_23,type,
set_Pr6200539531224447659at_num: $tType ).
thf(type_def_24,type,
set_Pr4105333604307423337at_rat: $tType ).
thf(type_def_25,type,
set_num: $tType ).
thf(type_def_26,type,
set_Pr8218934625190621173um_num: $tType ).
thf(type_def_27,type,
set_Co4375521073081744395nteger: $tType ).
thf(type_def_28,type,
produc8923325533196201883nteger: $tType ).
thf(type_def_29,type,
set_Co726186806682698383nteger: $tType ).
thf(type_def_30,type,
set_int_int: $tType ).
thf(type_def_31,type,
set_int_nat: $tType ).
thf(type_def_32,type,
set_int_num: $tType ).
thf(type_def_33,type,
set_in6154042108061588260nt_int: $tType ).
thf(type_def_34,type,
product_prod_int_int: $tType ).
thf(type_def_35,type,
set_in7748886932685137004at_nat: $tType ).
thf(type_def_36,type,
product_prod_nat_nat: $tType ).
thf(type_def_37,type,
set_in3169746454734514176um_num: $tType ).
thf(type_def_38,type,
product_prod_num_num: $tType ).
thf(type_def_39,type,
set_li2168235667650531768at_nat: $tType ).
thf(type_def_40,type,
list_nat: $tType ).
thf(type_def_41,type,
set_nat_o: $tType ).
thf(type_def_42,type,
set_nat_nat: $tType ).
thf(type_def_43,type,
set_na7251125088705586816nt_int: $tType ).
thf(type_def_44,type,
set_na8845969913329135560at_nat: $tType ).
thf(type_def_45,type,
set_ra518564293221149304nt_int: $tType ).
thf(type_def_46,type,
set_ra2113409117844698048at_nat: $tType ).
thf(type_def_47,type,
set_ch6383161263842509759nt_int: $tType ).
thf(type_def_48,type,
char: $tType ).
thf(type_def_49,type,
set_ch7978006088466058503at_nat: $tType ).
thf(type_def_50,type,
product_unit: $tType ).
thf(type_def_51,type,
set_Code_integer: $tType ).
thf(type_def_52,type,
set_ref_a: $tType ).
thf(type_def_53,type,
ref_a: $tType ).
thf(type_def_54,type,
heap_e7401611519738050253t_unit: $tType ).
thf(type_def_55,type,
set_list_nat: $tType ).
thf(type_def_56,type,
set_Pr1133966238863718811t_unit: $tType ).
thf(type_def_57,type,
produc7812382424243267045t_unit: $tType ).
thf(type_def_58,type,
set_rat: $tType ).
thf(type_def_59,type,
set_char: $tType ).
thf(type_def_60,type,
produc101387210554329899nteger: $tType ).
thf(type_def_61,type,
product_prod_o_o: $tType ).
thf(type_def_62,type,
product_prod_o_nat: $tType ).
thf(type_def_63,type,
product_prod_nat_o: $tType ).
thf(type_def_64,type,
product_prod_num_nat: $tType ).
thf(type_def_65,type,
produc723880050079548563nteger: $tType ).
thf(type_def_66,type,
product_prod_int_nat: $tType ).
thf(type_def_67,type,
product_prod_nat_int: $tType ).
thf(type_def_68,type,
product_prod_nat_num: $tType ).
thf(type_def_69,type,
product_prod_num_o: $tType ).
thf(type_def_70,type,
produc3843707927480180839at_nat: $tType ).
thf(type_def_71,type,
set_Pr8415741480598773322nteger: $tType ).
thf(type_def_72,type,
produc2963269191615333738nteger: $tType ).
thf(type_def_73,type,
set_Pr49084382684228242at_int: $tType ).
thf(type_def_74,type,
produc859450856879609959at_nat: $tType ).
thf(type_def_75,type,
produc4196048018000912732at_int: $tType ).
thf(type_def_76,type,
set_o_o: $tType ).
thf(type_def_77,type,
set_o_nat: $tType ).
thf(type_def_78,type,
set_Product_unit: $tType ).
thf(type_def_79,type,
set_o_Product_unit: $tType ).
thf(type_def_80,type,
set_int_rat: $tType ).
thf(type_def_81,type,
set_nat_int: $tType ).
thf(type_def_82,type,
set_rat_o: $tType ).
thf(type_def_83,type,
set_rat_nat: $tType ).
thf(type_def_84,type,
set_rat_Product_unit: $tType ).
thf(type_def_85,type,
set_char_o: $tType ).
thf(type_def_86,type,
set_char_nat: $tType ).
thf(type_def_87,type,
set_ch7814610555394875923t_unit: $tType ).
thf(type_def_88,type,
produc1319942482725812455at_nat: $tType ).
thf(type_def_89,type,
set_he8644174446132254637t_unit: $tType ).
thf(type_def_90,type,
option_num: $tType ).
thf(type_def_91,type,
produc6271795597528267376eger_o: $tType ).
thf(type_def_92,type,
set_int_int_o: $tType ).
thf(type_def_93,type,
set_int_o: $tType ).
thf(type_def_94,type,
set_nat_nat_o: $tType ).
thf(type_def_95,type,
set_nat_num_o: $tType ).
thf(type_def_96,type,
set_Pr8049984349381595834_int_o: $tType ).
thf(type_def_97,type,
set_Pr5582243495563764594_nat_o: $tType ).
thf(type_def_98,type,
set_Pr7010166363911110284_nat_o: $tType ).
thf(type_def_99,type,
set_se9180647916752606350_nat_o: $tType ).
thf(type_def_100,type,
set_se7255092946006855566_nat_o: $tType ).
thf(type_def_101,type,
set_set_o: $tType ).
thf(type_def_102,type,
set_set_int: $tType ).
thf(type_def_103,type,
set_set_nat: $tType ).
thf(type_def_104,type,
set_se6260736226359567993nt_int: $tType ).
thf(type_def_105,type,
set_se4826145725398303499at_num: $tType ).
thf(type_def_106,type,
set_se6425085446898223655at_nat: $tType ).
thf(type_def_107,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(type_def_108,type,
set_se7592288975875140775at_nat: $tType ).
thf(type_def_109,type,
set_set_Product_unit: $tType ).
thf(type_def_110,type,
set_set_rat: $tType ).
thf(type_def_111,type,
set_set_char: $tType ).
thf(type_def_112,type,
set_se4612898379794543757t_unit: $tType ).
thf(type_def_113,type,
produc8126358835630522215t_unit: $tType ).
thf(type_def_114,type,
produc5288414631154139675_ref_a: $tType ).
thf(type_def_115,type,
product_prod_o_int: $tType ).
thf(type_def_116,type,
product_prod_o_num: $tType ).
thf(type_def_117,type,
produc1799199577659733785_ref_a: $tType ).
thf(type_def_118,type,
set_Pr4111642102156807771nteger: $tType ).
thf(type_def_119,type,
set_Pr4811707699266497531nteger: $tType ).
thf(type_def_120,type,
set_Pr3280342998896498603um_nat: $tType ).
thf(type_def_121,type,
set_Pr5564308138774400199at_nat: $tType ).
thf(type_def_122,type,
heap_Heap_ref_a: $tType ).
thf(type_def_123,type,
heap_H6156071679106078628t_unit: $tType ).
thf(type_def_124,type,
heap_Heap_a: $tType ).
thf(type_def_125,type,
a: $tType ).
thf(type_def_126,type,
literal: $tType ).
thf(type_def_127,type,
produc4675096598859438275atural: $tType ).
thf(type_def_128,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(type_def_129,type,
set_Pr6671815714118170108t_unit: $tType ).
thf(type_def_130,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(type_def_131,type,
set_Pr4334478416066269672t_unit: $tType ).
thf(type_def_132,type,
set_Pr5464989305201766866unit_o: $tType ).
thf(type_def_133,type,
set_Pr1763845938948868674it_nat: $tType ).
thf(type_def_134,type,
set_Pr5094982260447487303t_unit: $tType ).
thf(type_def_135,type,
sum_sum_nat_nat: $tType ).
thf(type_def_136,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(type_def_137,type,
pred_Product_unit: $tType ).
thf(type_def_138,type,
set_Pr3798168094891919931at_nat: $tType ).
thf(type_def_139,type,
set_int_char: $tType ).
thf(type_def_140,type,
set_nat_rat: $tType ).
thf(type_def_141,type,
set_nat_char: $tType ).
thf(type_def_142,type,
set_rat_rat: $tType ).
thf(type_def_143,type,
set_rat_char: $tType ).
thf(type_def_144,type,
set_char_rat: $tType ).
thf(type_def_145,type,
set_char_char: $tType ).
thf(type_def_146,type,
set_Pr2926629348867340898t_char: $tType ).
thf(type_def_147,type,
set_Pr3594552606344371909at_int: $tType ).
thf(type_def_148,type,
set_Pr6084635751276098665at_nat: $tType ).
thf(type_def_149,type,
set_Pr8928021450653196913at_rat: $tType ).
thf(type_def_150,type,
set_Pr8263365689940771946t_char: $tType ).
thf(type_def_151,type,
set_Pr8146363407509552702ar_int: $tType ).
thf(type_def_152,type,
set_Pr1413074515586503650ar_nat: $tType ).
thf(type_def_153,type,
set_Pr4256460214963601898ar_rat: $tType ).
thf(type_def_154,type,
set_Pr3309569728657787619r_char: $tType ).
thf(type_def_155,type,
set_Sum_sum_nat_nat: $tType ).
thf(type_def_156,type,
produc3788275437394581276t_unit: $tType ).
thf(type_def_157,type,
product_prod_int_o: $tType ).
thf(type_def_158,type,
produc6865911496949736918t_unit: $tType ).
thf(type_def_159,type,
product_prod_int_rat: $tType ).
thf(type_def_160,type,
produc526117512892780850t_unit: $tType ).
thf(type_def_161,type,
product_prod_nat_rat: $tType ).
thf(type_def_162,type,
produc7822875418678951345atural: $tType ).
thf(type_def_163,type,
produc1219242969750017639nt_int: $tType ).
thf(type_def_164,type,
produc349518998152878311at_nat: $tType ).
thf(type_def_165,type,
produc1906917888121415911at_nat: $tType ).
thf(type_def_166,type,
produc7485711547916492274unit_o: $tType ).
thf(type_def_167,type,
produc600557818389255820it_nat: $tType ).
thf(type_def_168,type,
produc8459935480633519975t_unit: $tType ).
thf(type_def_169,type,
produc6315701296850634900it_rat: $tType ).
thf(type_def_170,type,
product_prod_rat_int: $tType ).
thf(type_def_171,type,
product_prod_rat_nat: $tType ).
thf(type_def_172,type,
product_prod_rat_rat: $tType ).
thf(type_def_173,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(type_def_174,type,
set_Pr903927857289325719_int_o: $tType ).
thf(type_def_175,type,
set_Pr5889264611543340172t_unit: $tType ).
thf(type_def_176,type,
set_Pr6292255179000445125nt_rat: $tType ).
thf(type_def_177,type,
set_Pr6123067485828015636nt_int: $tType ).
thf(type_def_178,type,
set_Pr7717912310451564380at_nat: $tType ).
thf(type_def_179,type,
set_Pr2543308735921124078nt_nat: $tType ).
thf(type_def_180,type,
set_Pr4155430604743465615at_nat: $tType ).
thf(type_def_181,type,
set_Pr6558897299634722526_nat_o: $tType ).
thf(type_def_182,type,
set_Pr2539167527615954998at_nat: $tType ).
thf(type_def_183,type,
set_Pr7098892610798258687nt_int: $tType ).
thf(type_def_184,type,
set_Pr4607231638325966922it_rat: $tType ).
thf(type_def_185,type,
produc3969062480670737046t_unit: $tType ).
thf(type_def_186,type,
produc8483956148555600810_a_int: $tType ).
thf(type_def_187,type,
produc5066145461314735602t_unit: $tType ).
thf(type_def_188,type,
produc3438435131210021710_a_nat: $tType ).
thf(type_def_189,type,
produc4146679068158859416_a_num: $tType ).
thf(type_def_190,type,
produc3629471303718939987t_unit: $tType ).
thf(type_def_191,type,
produc5561445381605014009at_nat: $tType ).
thf(type_def_192,type,
produc2296667697112141421t_unit: $tType ).
thf(type_def_193,type,
produc4041253808165279839at_nat: $tType ).
thf(type_def_194,type,
produc3922234789054302210ar_nat: $tType ).
thf(type_def_195,type,
produc414006230660905482ar_rat: $tType ).
thf(type_def_196,type,
produc143505574896075907r_char: $tType ).
thf(type_def_197,type,
produc8967755806399881310ar_int: $tType ).
thf(type_def_198,type,
produc3346328345660746739nteger: $tType ).
thf(type_def_199,type,
produc6945250483304103390nt_int: $tType ).
thf(type_def_200,type,
produc7248412053542808358at_nat: $tType ).
thf(type_def_201,type,
produc1709102135585200056nt_nat: $tType ).
thf(type_def_202,type,
produc1522404539988722607at_nat: $tType ).
thf(type_def_203,type,
produc8373899037510109440at_nat: $tType ).
thf(type_def_204,type,
produc556289286640904991nt_int: $tType ).
thf(type_def_205,type,
produc652263959640188542_nat_o: $tType ).
thf(type_def_206,type,
ref_ref_a: $tType ).
thf(type_def_207,type,
set_Pr553994874890374343at_nat: $tType ).
thf(type_def_208,type,
set_Pr5908833319024110760_num_o: $tType ).
thf(type_def_209,type,
set_Pr7669914128964046860_nat_o: $tType ).
thf(func_def_0,type,
set_se7592288975875140775at_nat: $tType ).
thf(func_def_1,type,
set_Pr7669914128964046860_nat_o: $tType ).
thf(func_def_2,type,
set_Pr7459493094073627847at_nat: $tType ).
thf(func_def_3,type,
set_se7255092946006855566_nat_o: $tType ).
thf(func_def_4,type,
produc1319942482725812455at_nat: $tType ).
thf(func_def_5,type,
produc101387210554329899nteger: $tType ).
thf(func_def_6,type,
set_Pr5564308138774400199at_nat: $tType ).
thf(func_def_7,type,
produc1906917888121415911at_nat: $tType ).
thf(func_def_8,type,
set_Pr553994874890374343at_nat: $tType ).
thf(func_def_9,type,
produc349518998152878311at_nat: $tType ).
thf(func_def_10,type,
produc2296667697112141421t_unit: $tType ).
thf(func_def_11,type,
produc4041253808165279839at_nat: $tType ).
thf(func_def_12,type,
set_se5479201105039950375at_nat: $tType ).
thf(func_def_13,type,
set_Pr7010166363911110284_nat_o: $tType ).
thf(func_def_14,type,
set_Pr4111642102156807771nteger: $tType ).
thf(func_def_15,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(func_def_16,type,
set_se9180647916752606350_nat_o: $tType ).
thf(func_def_17,type,
set_se6425085446898223655at_nat: $tType ).
thf(func_def_18,type,
produc3843707927480180839at_nat: $tType ).
thf(func_def_19,type,
produc4675096598859438275atural: $tType ).
thf(func_def_20,type,
produc723880050079548563nteger: $tType ).
thf(func_def_21,type,
produc3629471303718939987t_unit: $tType ).
thf(func_def_22,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(func_def_23,type,
set_Pr7098892610798258687nt_int: $tType ).
thf(func_def_24,type,
set_Pr4155430604743465615at_nat: $tType ).
thf(func_def_25,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(func_def_26,type,
produc3346328345660746739nteger: $tType ).
thf(func_def_27,type,
produc8126358835630522215t_unit: $tType ).
thf(func_def_28,type,
produc859450856879609959at_nat: $tType ).
thf(func_def_29,type,
produc556289286640904991nt_int: $tType ).
thf(func_def_30,type,
produc1522404539988722607at_nat: $tType ).
thf(func_def_31,type,
produc1219242969750017639nt_int: $tType ).
thf(func_def_32,type,
set_Pr3798168094891919931at_nat: $tType ).
thf(func_def_33,type,
set_Pr1133966238863718811t_unit: $tType ).
thf(func_def_34,type,
produc5561445381605014009at_nat: $tType ).
thf(func_def_35,type,
set_Co4375521073081744395nteger: $tType ).
thf(func_def_36,type,
set_Pr2539167527615954998at_nat: $tType ).
thf(func_def_37,type,
set_Pr49084382684228242at_int: $tType ).
thf(func_def_38,type,
set_Pr2543308735921124078nt_nat: $tType ).
thf(func_def_39,type,
set_Pr7717912310451564380at_nat: $tType ).
thf(func_def_40,type,
set_Pr6123067485828015636nt_int: $tType ).
thf(func_def_41,type,
set_li2168235667650531768at_nat: $tType ).
thf(func_def_42,type,
produc7812382424243267045t_unit: $tType ).
thf(func_def_43,type,
produc1799199577659733785_ref_a: $tType ).
thf(func_def_44,type,
set_Pr6558897299634722526_nat_o: $tType ).
thf(func_def_45,type,
set_Pr4811707699266497531nteger: $tType ).
thf(func_def_46,type,
produc5066145461314735602t_unit: $tType ).
thf(func_def_47,type,
produc3969062480670737046t_unit: $tType ).
thf(func_def_48,type,
produc8373899037510109440at_nat: $tType ).
thf(func_def_49,type,
produc4196048018000912732at_int: $tType ).
thf(func_def_50,type,
produc1709102135585200056nt_nat: $tType ).
thf(func_def_51,type,
produc7248412053542808358at_nat: $tType ).
thf(func_def_52,type,
produc6945250483304103390nt_int: $tType ).
thf(func_def_53,type,
set_Pr5094982260447487303t_unit: $tType ).
thf(func_def_54,type,
set_ch7978006088466058503at_nat: $tType ).
thf(func_def_55,type,
set_ch6383161263842509759nt_int: $tType ).
thf(func_def_56,type,
set_ra2113409117844698048at_nat: $tType ).
thf(func_def_57,type,
set_ra518564293221149304nt_int: $tType ).
thf(func_def_58,type,
set_na8845969913329135560at_nat: $tType ).
thf(func_def_59,type,
set_na7251125088705586816nt_int: $tType ).
thf(func_def_60,type,
set_in3169746454734514176um_num: $tType ).
thf(func_def_61,type,
set_in7748886932685137004at_nat: $tType ).
thf(func_def_62,type,
set_in6154042108061588260nt_int: $tType ).
thf(func_def_63,type,
set_se4612898379794543757t_unit: $tType ).
thf(func_def_64,type,
produc652263959640188542_nat_o: $tType ).
thf(func_def_65,type,
set_se4826145725398303499at_num: $tType ).
thf(func_def_66,type,
set_se7855581050983116737at_nat: $tType ).
thf(func_def_67,type,
set_se6260736226359567993nt_int: $tType ).
thf(func_def_68,type,
set_Pr8415741480598773322nteger: $tType ).
thf(func_def_69,type,
produc7822875418678951345atural: $tType ).
thf(func_def_70,type,
produc8923325533196201883nteger: $tType ).
thf(func_def_71,type,
set_Pr4607231638325966922it_rat: $tType ).
thf(func_def_72,type,
set_Pr1763845938948868674it_nat: $tType ).
thf(func_def_73,type,
set_Pr4334478416066269672t_unit: $tType ).
thf(func_def_74,type,
set_Pr5889264611543340172t_unit: $tType ).
thf(func_def_75,type,
set_Pr5908833319024110760_num_o: $tType ).
thf(func_def_76,type,
set_Pr5582243495563764594_nat_o: $tType ).
thf(func_def_77,type,
set_Pr8049984349381595834_int_o: $tType ).
thf(func_def_78,type,
set_Co726186806682698383nteger: $tType ).
thf(func_def_79,type,
produc8459935480633519975t_unit: $tType ).
thf(func_def_80,type,
set_Pr3309569728657787619r_char: $tType ).
thf(func_def_81,type,
set_Pr4256460214963601898ar_rat: $tType ).
thf(func_def_82,type,
set_Pr1413074515586503650ar_nat: $tType ).
thf(func_def_83,type,
set_Pr8146363407509552702ar_int: $tType ).
thf(func_def_84,type,
set_Pr8263365689940771946t_char: $tType ).
thf(func_def_85,type,
set_Pr5464989305201766866unit_o: $tType ).
thf(func_def_86,type,
set_Pr2926629348867340898t_char: $tType ).
thf(func_def_87,type,
set_Pr6671815714118170108t_unit: $tType ).
thf(func_def_88,type,
produc5288414631154139675_ref_a: $tType ).
thf(func_def_89,type,
set_he8644174446132254637t_unit: $tType ).
thf(func_def_90,type,
set_Pr8928021450653196913at_rat: $tType ).
thf(func_def_91,type,
set_Pr6084635751276098665at_nat: $tType ).
thf(func_def_92,type,
set_Pr3594552606344371909at_int: $tType ).
thf(func_def_93,type,
set_Pr8218934625190621173um_num: $tType ).
thf(func_def_94,type,
set_Pr3280342998896498603um_nat: $tType ).
thf(func_def_95,type,
set_Pr4105333604307423337at_rat: $tType ).
thf(func_def_96,type,
set_Pr6200539531224447659at_num: $tType ).
thf(func_def_97,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(func_def_98,type,
set_Pr7995236796853374141at_int: $tType ).
thf(func_def_99,type,
set_Pr6292255179000445125nt_rat: $tType ).
thf(func_def_100,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(func_def_101,type,
set_Pr958786334691620121nt_int: $tType ).
thf(func_def_102,type,
produc2963269191615333738nteger: $tType ).
thf(func_def_103,type,
produc6315701296850634900it_rat: $tType ).
thf(func_def_104,type,
produc600557818389255820it_nat: $tType ).
thf(func_def_105,type,
produc526117512892780850t_unit: $tType ).
thf(func_def_106,type,
produc6865911496949736918t_unit: $tType ).
thf(func_def_107,type,
set_ch7814610555394875923t_unit: $tType ).
thf(func_def_108,type,
set_Sum_sum_nat_nat: $tType ).
thf(func_def_109,type,
produc4146679068158859416_a_num: $tType ).
thf(func_def_110,type,
produc3438435131210021710_a_nat: $tType ).
thf(func_def_111,type,
produc8483956148555600810_a_int: $tType ).
thf(func_def_112,type,
set_rat_Product_unit: $tType ).
thf(func_def_113,type,
set_nat_num_o: $tType ).
thf(func_def_114,type,
set_nat_nat_o: $tType ).
thf(func_def_115,type,
set_int_int_o: $tType ).
thf(func_def_116,type,
produc143505574896075907r_char: $tType ).
thf(func_def_117,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(func_def_118,type,
set_Pr903927857289325719_int_o: $tType ).
thf(func_def_119,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(func_def_120,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(func_def_121,type,
produc6271795597528267376eger_o: $tType ).
thf(func_def_122,type,
produc414006230660905482ar_rat: $tType ).
thf(func_def_123,type,
produc3922234789054302210ar_nat: $tType ).
thf(func_def_124,type,
produc8967755806399881310ar_int: $tType ).
thf(func_def_125,type,
produc7485711547916492274unit_o: $tType ).
thf(func_def_126,type,
produc3788275437394581276t_unit: $tType ).
thf(func_def_127,type,
set_char_char: $tType ).
thf(func_def_128,type,
set_set_Product_unit: $tType ).
thf(func_def_129,type,
heap_e7401611519738050253t_unit: $tType ).
thf(func_def_130,type,
product_prod_rat_rat: $tType ).
thf(func_def_131,type,
product_prod_rat_nat: $tType ).
thf(func_def_132,type,
product_prod_rat_int: $tType ).
thf(func_def_133,type,
product_prod_num_num: $tType ).
thf(func_def_134,type,
product_prod_num_nat: $tType ).
thf(func_def_135,type,
product_prod_nat_rat: $tType ).
thf(func_def_136,type,
product_prod_nat_num: $tType ).
thf(func_def_137,type,
product_prod_nat_nat: $tType ).
thf(func_def_138,type,
product_prod_nat_int: $tType ).
thf(func_def_139,type,
product_prod_int_rat: $tType ).
thf(func_def_140,type,
product_prod_int_nat: $tType ).
thf(func_def_141,type,
product_prod_int_int: $tType ).
thf(func_def_142,type,
set_char_rat: $tType ).
thf(func_def_143,type,
set_char_nat: $tType ).
thf(func_def_144,type,
set_rat_char: $tType ).
thf(func_def_145,type,
set_nat_char: $tType ).
thf(func_def_146,type,
set_int_char: $tType ).
thf(func_def_147,type,
set_o_Product_unit: $tType ).
thf(func_def_148,type,
set_Product_prod_o_o: $tType ).
thf(func_def_149,type,
heap_H6156071679106078628t_unit: $tType ).
thf(func_def_150,type,
sum_sum_nat_nat: $tType ).
thf(func_def_151,type,
set_rat_rat: $tType ).
thf(func_def_152,type,
set_rat_nat: $tType ).
thf(func_def_153,type,
set_nat_rat: $tType ).
thf(func_def_154,type,
set_nat_nat: $tType ).
thf(func_def_155,type,
set_nat_int: $tType ).
thf(func_def_156,type,
set_int_rat: $tType ).
thf(func_def_157,type,
set_int_num: $tType ).
thf(func_def_158,type,
set_int_nat: $tType ).
thf(func_def_159,type,
set_int_int: $tType ).
thf(func_def_160,type,
heap_Heap_ref_a: $tType ).
thf(func_def_161,type,
set_set_char: $tType ).
thf(func_def_162,type,
pred_Product_unit: $tType ).
thf(func_def_163,type,
set_list_nat: $tType ).
thf(func_def_164,type,
product_prod_num_o: $tType ).
thf(func_def_165,type,
product_prod_nat_o: $tType ).
thf(func_def_166,type,
product_prod_int_o: $tType ).
thf(func_def_167,type,
product_prod_o_num: $tType ).
thf(func_def_168,type,
product_prod_o_nat: $tType ).
thf(func_def_169,type,
product_prod_o_int: $tType ).
thf(func_def_170,type,
set_char_o: $tType ).
thf(func_def_171,type,
set_set_rat: $tType ).
thf(func_def_172,type,
set_set_nat: $tType ).
thf(func_def_173,type,
set_set_int: $tType ).
thf(func_def_174,type,
set_Code_integer: $tType ).
thf(func_def_175,type,
set_Product_unit: $tType ).
thf(func_def_176,type,
set_rat_o: $tType ).
thf(func_def_177,type,
set_nat_o: $tType ).
thf(func_def_178,type,
set_int_o: $tType ).
thf(func_def_179,type,
set_o_nat: $tType ).
thf(func_def_180,type,
ref_ref_a: $tType ).
thf(func_def_181,type,
set_ref_a: $tType ).
thf(func_def_182,type,
product_prod_o_o: $tType ).
thf(func_def_183,type,
set_set_o: $tType ).
thf(func_def_184,type,
option_num: $tType ).
thf(func_def_185,type,
set_char: $tType ).
thf(func_def_186,type,
set_o_o: $tType ).
thf(func_def_187,type,
heap_Heap_a: $tType ).
thf(func_def_188,type,
list_nat: $tType ).
thf(func_def_189,type,
set_rat: $tType ).
thf(func_def_190,type,
set_num: $tType ).
thf(func_def_191,type,
set_nat: $tType ).
thf(func_def_192,type,
set_int: $tType ).
thf(func_def_193,type,
code_integer: $tType ).
thf(func_def_194,type,
product_unit: $tType ).
thf(func_def_195,type,
ref_a: $tType ).
thf(func_def_196,type,
literal: $tType ).
thf(func_def_197,type,
set_o: $tType ).
thf(func_def_198,type,
char: $tType ).
thf(func_def_199,type,
rat: $tType ).
thf(func_def_200,type,
num: $tType ).
thf(func_def_201,type,
nat: $tType ).
thf(func_def_202,type,
int: $tType ).
thf(func_def_203,type,
a: $tType ).
thf(func_def_204,type,
archim3151403230148437115or_rat: rat > int ).
thf(func_def_205,type,
bNF_Ca5157130669891357211al_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_206,type,
bNF_Ca5159621140400407487al_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_207,type,
bNF_Ca8448034394003515314at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_208,type,
bNF_Ca6037544080215331608at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_209,type,
bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
thf(func_def_210,type,
bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
thf(func_def_211,type,
bNF_Ca402612664642806191nteger: set_Pr958786334691620121nt_int > ( int > code_integer ) > $o ).
thf(func_def_212,type,
bNF_Ca1965613569405424510nt_int: set_Pr958786334691620121nt_int > ( int > int ) > $o ).
thf(func_def_213,type,
bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > ( int > nat ) > $o ).
thf(func_def_214,type,
bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > ( int > rat ) > $o ).
thf(func_def_215,type,
bNF_Ca30959104405961555nteger: set_Pr1261947904930325089at_nat > ( nat > code_integer ) > $o ).
thf(func_def_216,type,
bNF_Ca966259857504369954at_int: set_Pr1261947904930325089at_nat > ( nat > int ) > $o ).
thf(func_def_217,type,
bNF_Ca968750328013420230at_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > $o ).
thf(func_def_218,type,
bNF_Ca333620267926924494at_rat: set_Pr1261947904930325089at_nat > ( nat > rat ) > $o ).
thf(func_def_219,type,
bNF_Ca4946600973702282345at_int: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > int ) > $o ).
thf(func_def_220,type,
bNF_Ca4949091444211332621at_nat: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > nat ) > $o ).
thf(func_def_221,type,
bNF_Gr_o_o: set_o > ( $o > $o ) > set_Product_prod_o_o ).
thf(func_def_222,type,
bNF_Gr_int_int: set_int > ( int > int ) > set_Pr958786334691620121nt_int ).
thf(func_def_223,type,
bNF_Gr_int_nat: set_int > ( int > nat ) > set_Pr3448869479623346877nt_nat ).
thf(func_def_224,type,
bNF_Gr_nat_int: set_nat > ( nat > int ) > set_Pr7995236796853374141at_int ).
thf(func_def_225,type,
bNF_Gr_nat_nat: set_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_226,type,
bNF_Gr_nat_num: set_nat > ( nat > num ) > set_Pr6200539531224447659at_num ).
thf(func_def_227,type,
bNF_Gr_nat_rat: set_nat > ( nat > rat ) > set_Pr4105333604307423337at_rat ).
thf(func_def_228,type,
bNF_Gr_num_num: set_num > ( num > num ) > set_Pr8218934625190621173um_num ).
thf(func_def_229,type,
bNF_Gr1527221351080490466at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_230,type,
bNF_Gr7888059597227825506at_nat: set_se5479201105039950375at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr7459493094073627847at_nat ).
thf(func_def_231,type,
bNF_Gr1453458339979195462nteger: set_Co4375521073081744395nteger > ( ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_232,type,
bNF_Gr4092539093814444494nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_233,type,
bNF_Gr2243168462153404386nt_nat: set_int_int > ( ( int > int ) > int > nat ) > ( int > int ) > ( int > nat ) > $o ).
thf(func_def_234,type,
bNF_Gr6763702254253555408nt_num: set_int_nat > ( ( int > nat ) > int > num ) > ( int > nat ) > ( int > num ) > $o ).
thf(func_def_235,type,
bNF_Gr318824752125099290nt_num: set_int_num > ( ( int > num ) > int > num ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_236,type,
bNF_Gr952524912132828525nt_int: set_in6154042108061588260nt_int > ( ( int > product_prod_int_int ) > int > int ) > ( int > product_prod_int_int ) > ( int > int ) > $o ).
thf(func_def_237,type,
bNF_Gr1462982377596425817nt_nat: set_in7748886932685137004at_nat > ( ( int > product_prod_nat_nat ) > int > nat ) > ( int > product_prod_nat_nat ) > ( int > nat ) > $o ).
thf(func_def_238,type,
bNF_Gr5590197745039885111nt_num: set_in3169746454734514176um_num > ( ( int > product_prod_num_num ) > int > num ) > ( int > product_prod_num_num ) > ( int > num ) > $o ).
thf(func_def_239,type,
bNF_Gr1532745923208276441at_nat: set_li2168235667650531768at_nat > ( ( list_nat > product_prod_nat_nat ) > list_nat > nat ) > ( list_nat > product_prod_nat_nat ) > ( list_nat > nat ) > $o ).
thf(func_def_240,type,
bNF_Grp_nat_o_nat_o: set_nat_o > ( ( nat > $o ) > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_241,type,
bNF_Gr3847987472475283150at_nat: set_nat_nat > ( ( nat > nat ) > nat > nat ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_242,type,
bNF_Gr2878093617000900205at_int: set_na7251125088705586816nt_int > ( ( nat > product_prod_int_int ) > nat > int ) > ( nat > product_prod_int_int ) > ( nat > int ) > $o ).
thf(func_def_243,type,
bNF_Gr3388551082464497497at_nat: set_na8845969913329135560at_nat > ( ( nat > product_prod_nat_nat ) > nat > nat ) > ( nat > product_prod_nat_nat ) > ( nat > nat ) > $o ).
thf(func_def_244,type,
bNF_Gr6858100456814184557at_int: set_ra518564293221149304nt_int > ( ( rat > product_prod_int_int ) > rat > int ) > ( rat > product_prod_int_int ) > ( rat > int ) > $o ).
thf(func_def_245,type,
bNF_Gr7368557922277781849at_nat: set_ra2113409117844698048at_nat > ( ( rat > product_prod_nat_nat ) > rat > nat ) > ( rat > product_prod_nat_nat ) > ( rat > nat ) > $o ).
thf(func_def_246,type,
bNF_Gr6947267152677263533ar_int: set_ch6383161263842509759nt_int > ( ( char > product_prod_int_int ) > char > int ) > ( char > product_prod_int_int ) > ( char > int ) > $o ).
thf(func_def_247,type,
bNF_Gr1779741795384719769ar_nat: set_ch7978006088466058503at_nat > ( ( char > product_prod_nat_nat ) > char > nat ) > ( char > product_prod_nat_nat ) > ( char > nat ) > $o ).
thf(func_def_248,type,
bNF_Grp_o_o: set_o > ( $o > $o ) > $o > $o > $o ).
thf(func_def_249,type,
bNF_Gr395642070819736771t_unit: set_o > ( $o > product_unit ) > $o > product_unit > $o ).
thf(func_def_250,type,
bNF_Grp_o_rat: set_o > ( $o > rat ) > $o > rat > $o ).
thf(func_def_251,type,
bNF_Grp_o_char: set_o > ( $o > char ) > $o > char > $o ).
thf(func_def_252,type,
bNF_Gr6045950513751025625er_int: set_Code_integer > ( code_integer > int ) > code_integer > int > $o ).
thf(func_def_253,type,
bNF_Gr6510375311308651680t_unit: set_ref_a > ( ref_a > heap_e7401611519738050253t_unit ) > ref_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_254,type,
bNF_Gr6684649993275963353nteger: set_int > ( int > code_integer ) > int > code_integer > $o ).
thf(func_def_255,type,
bNF_Grp_int_int: set_int > ( int > int ) > int > int > $o ).
thf(func_def_256,type,
bNF_Grp_int_nat: set_int > ( int > nat ) > int > nat > $o ).
thf(func_def_257,type,
bNF_Grp_int_num: set_int > ( int > num ) > int > num > $o ).
thf(func_def_258,type,
bNF_Gr6591314147588017797at_nat: set_int > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat > $o ).
thf(func_def_259,type,
bNF_Grp_int_rat: set_int > ( int > rat ) > int > rat > $o ).
thf(func_def_260,type,
bNF_Grp_int_char: set_int > ( int > char ) > int > char > $o ).
thf(func_def_261,type,
bNF_Grp_list_nat_int: set_list_nat > ( list_nat > int ) > list_nat > int > $o ).
thf(func_def_262,type,
bNF_Gr600725020315365264st_nat: set_list_nat > ( list_nat > list_nat ) > list_nat > list_nat > $o ).
thf(func_def_263,type,
bNF_Gr4119388860389678161at_nat: set_list_nat > ( list_nat > product_prod_nat_nat ) > list_nat > product_prod_nat_nat > $o ).
thf(func_def_264,type,
bNF_Grp_nat_o: set_nat > ( nat > $o ) > nat > $o > $o ).
thf(func_def_265,type,
bNF_Grp_nat_int: set_nat > ( nat > int ) > nat > int > $o ).
thf(func_def_266,type,
bNF_Grp_nat_nat: set_nat > ( nat > nat ) > nat > nat > $o ).
thf(func_def_267,type,
bNF_Grp_nat_num: set_nat > ( nat > num ) > nat > num > $o ).
thf(func_def_268,type,
bNF_Gr3553472063123884001at_nat: set_nat > ( nat > product_prod_nat_nat ) > nat > product_prod_nat_nat > $o ).
thf(func_def_269,type,
bNF_Gr1993012052113314029t_unit: set_nat > ( nat > product_unit ) > nat > product_unit > $o ).
thf(func_def_270,type,
bNF_Grp_nat_rat: set_nat > ( nat > rat ) > nat > rat > $o ).
thf(func_def_271,type,
bNF_Grp_nat_char: set_nat > ( nat > char ) > nat > char > $o ).
thf(func_def_272,type,
bNF_Grp_num_num: set_num > ( num > num ) > num > num > $o ).
thf(func_def_273,type,
bNF_Gr5237703264515865432t_unit: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o ).
thf(func_def_274,type,
bNF_Gr5964920315653434322_ref_a: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > ref_a > $o ).
thf(func_def_275,type,
bNF_Gr2749509334501985047nt_int: set_Pr958786334691620121nt_int > ( product_prod_int_int > int ) > product_prod_int_int > int > $o ).
thf(func_def_276,type,
bNF_Gr8532703628021589765nt_num: set_Pr958786334691620121nt_int > ( product_prod_int_int > num ) > product_prod_int_int > num > $o ).
thf(func_def_277,type,
bNF_Gr8859634586176591525_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o > $o ).
thf(func_def_278,type,
bNF_Gr190934199572118623at_int: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > int ) > product_prod_nat_nat > int > $o ).
thf(func_def_279,type,
bNF_Gr193424670081168899at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat > $o ).
thf(func_def_280,type,
bNF_Gr5974128493091723341at_num: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > num ) > product_prod_nat_nat > num > $o ).
thf(func_def_281,type,
bNF_Gr7275288873855648526at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_282,type,
bNF_Grp_rat_int: set_rat > ( rat > int ) > rat > int > $o ).
thf(func_def_283,type,
bNF_Grp_rat_nat: set_rat > ( rat > nat ) > rat > nat > $o ).
thf(func_def_284,type,
bNF_Gr6883301533820405721at_nat: set_rat > ( rat > product_prod_nat_nat ) > rat > product_prod_nat_nat > $o ).
thf(func_def_285,type,
bNF_Grp_rat_rat: set_rat > ( rat > rat ) > rat > rat > $o ).
thf(func_def_286,type,
bNF_Grp_rat_char: set_rat > ( rat > char ) > rat > char > $o ).
thf(func_def_287,type,
bNF_Gr6677838525845560078at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_288,type,
bNF_Grp_char_int: set_char > ( char > int ) > char > int > $o ).
thf(func_def_289,type,
bNF_Grp_char_nat: set_char > ( char > nat ) > char > nat > $o ).
thf(func_def_290,type,
bNF_Gr8982933507515605408at_nat: set_char > ( char > product_prod_nat_nat ) > char > product_prod_nat_nat > $o ).
thf(func_def_291,type,
bNF_Grp_char_rat: set_char > ( char > rat ) > char > rat > $o ).
thf(func_def_292,type,
bNF_Grp_char_char: set_char > ( char > char ) > char > char > $o ).
thf(func_def_293,type,
bNF_co1764293801198077070nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > produc101387210554329899nteger ).
thf(func_def_294,type,
bNF_convol_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > product_prod_o_o ).
thf(func_def_295,type,
bNF_convol_o_o_nat: ( $o > $o ) > ( $o > nat ) > $o > product_prod_o_nat ).
thf(func_def_296,type,
bNF_convol_o_nat_o: ( $o > nat ) > ( $o > $o ) > $o > product_prod_nat_o ).
thf(func_def_297,type,
bNF_convol_o_nat_nat: ( $o > nat ) > ( $o > nat ) > $o > product_prod_nat_nat ).
thf(func_def_298,type,
bNF_convol_o_num_nat: ( $o > num ) > ( $o > nat ) > $o > product_prod_num_nat ).
thf(func_def_299,type,
bNF_co6169604788974073338nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > produc723880050079548563nteger ).
thf(func_def_300,type,
bNF_co3156833790671340178nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc101387210554329899nteger ).
thf(func_def_301,type,
bNF_co2174166945328636015nt_int: ( int > int ) > ( int > int ) > int > product_prod_int_int ).
thf(func_def_302,type,
bNF_co2176657415837686291nt_nat: ( int > int ) > ( int > nat ) > int > product_prod_int_nat ).
thf(func_def_303,type,
bNF_co1174813233427581459at_int: ( int > nat ) > ( int > int ) > int > product_prod_nat_int ).
thf(func_def_304,type,
bNF_co1177303703936631735at_nat: ( int > nat ) > ( int > nat ) > int > product_prod_nat_nat ).
thf(func_def_305,type,
bNF_co6958007526947186177at_num: ( int > nat ) > ( int > num ) > int > product_prod_nat_num ).
thf(func_def_306,type,
bNF_co8531006144098876929um_nat: ( int > num ) > ( int > nat ) > int > product_prod_num_nat ).
thf(func_def_307,type,
bNF_co5088337930254655563um_num: ( int > num ) > ( int > num ) > int > product_prod_num_num ).
thf(func_def_308,type,
bNF_convol_nat_o_o: ( nat > $o ) > ( nat > $o ) > nat > product_prod_o_o ).
thf(func_def_309,type,
bNF_convol_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > product_prod_o_nat ).
thf(func_def_310,type,
bNF_convol_nat_nat_o: ( nat > nat ) > ( nat > $o ) > nat > product_prod_nat_o ).
thf(func_def_311,type,
bNF_co805650143699787099at_nat: ( nat > nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).
thf(func_def_312,type,
bNF_convol_nat_num_o: ( nat > num ) > ( nat > $o ) > nat > product_prod_num_o ).
thf(func_def_313,type,
bNF_co8159352583862032293um_nat: ( nat > num ) > ( nat > nat ) > nat > product_prod_num_nat ).
thf(func_def_314,type,
bNF_co4716684370017810927um_num: ( nat > num ) > ( nat > num ) > nat > product_prod_num_num ).
thf(func_def_315,type,
bNF_convol_num_o_nat: ( num > $o ) > ( num > nat ) > num > product_prod_o_nat ).
thf(func_def_316,type,
bNF_co7969830008525221797at_nat: ( num > nat ) > ( num > nat ) > num > product_prod_nat_nat ).
thf(func_def_317,type,
bNF_co6100160411832691183um_nat: ( num > num ) > ( num > nat ) > num > product_prod_num_nat ).
thf(func_def_318,type,
bNF_co6607689160745551784nt_int: ( produc7812382424243267045t_unit > int ) > ( produc7812382424243267045t_unit > int ) > produc7812382424243267045t_unit > product_prod_int_int ).
thf(func_def_319,type,
bNF_co5610825919353547504at_nat: ( produc7812382424243267045t_unit > nat ) > ( produc7812382424243267045t_unit > nat ) > produc7812382424243267045t_unit > product_prod_nat_nat ).
thf(func_def_320,type,
bNF_co3748779267718262122nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_321,type,
bNF_co2751916026326257842at_nat: ( product_prod_int_int > nat ) > ( product_prod_int_int > nat ) > product_prod_int_int > product_prod_nat_nat ).
thf(func_def_322,type,
bNF_co49787548815638194nt_int: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > product_prod_int_int ).
thf(func_def_323,type,
bNF_co8276296344278409722at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_324,type,
bNF_co147202357524637304at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
thf(func_def_325,type,
bNF_cs4943907971211754724nteger: set_Pr8415741480598773322nteger > ( product_prod_int_int > int ) > ( produc2963269191615333738nteger > int ) > ( produc2963269191615333738nteger > product_prod_int_int ) > ( produc2963269191615333738nteger > produc2963269191615333738nteger ) > $o ).
thf(func_def_326,type,
bNF_cs7194553038297458973at_int: set_Pr49084382684228242at_int > ( produc859450856879609959at_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > ( produc4196048018000912732at_int > produc859450856879609959at_nat ) > ( produc4196048018000912732at_int > produc4196048018000912732at_int ) > $o ).
thf(func_def_327,type,
bNF_fs409234558581511823t_unit: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
thf(func_def_328,type,
bNF_fs4543836202474805097nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > product_prod_int_int ).
thf(func_def_329,type,
bNF_fs8167890477030535480nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_330,type,
bNF_fs6799373675401686564at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_331,type,
bNF_fs6342258632037972510at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc859450856879609959at_nat ).
thf(func_def_332,type,
bNF_fs1946732770515719151at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_333,type,
bNF_pi4515785505327359899nteger: ( int > int > $o ) > ( int > code_integer > $o ) > int > code_integer > int ).
thf(func_def_334,type,
bNF_pi770922605693484880at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > product_prod_nat_nat ).
thf(func_def_335,type,
bNF_re6580757339198446453_nat_o: ( ( $o > $o ) > ( $o > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_336,type,
bNF_re7413876800493218871nt_nat: ( ( $o > $o ) > ( int > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
thf(func_def_337,type,
bNF_re1515921786380824775at_nat: ( ( $o > $o ) > ( nat > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_338,type,
bNF_re7387973359137000979nt_num: ( ( $o > $o ) > ( nat > num ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_339,type,
bNF_re2961086658867094474nt_num: ( ( int > int ) > ( int > code_integer ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ).
thf(func_def_340,type,
bNF_re2034674868506727813nt_nat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ).
thf(func_def_341,type,
bNF_re7492190849051111027nt_num: ( ( int > int ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > num ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_342,type,
bNF_re5502197115626545091er_num: ( ( int > nat ) > ( code_integer > nat ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ).
thf(func_def_343,type,
bNF_re3642433447925381491nt_nat: ( ( int > nat ) > ( int > int ) > $o ) > ( ( int > num ) > ( int > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ).
thf(func_def_344,type,
bNF_re6307232852808291833nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
thf(func_def_345,type,
bNF_re4099335476084980305nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
thf(func_def_346,type,
bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_347,type,
bNF_re7435575058205011731_nat_o: ( ( int > nat ) > ( nat > $o ) > $o ) > ( ( int > num ) > ( nat > $o ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_348,type,
bNF_re717418264989850719at_nat: ( ( int > nat ) > ( nat > nat ) > $o ) > ( ( int > num ) > ( nat > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_349,type,
bNF_re4310571189260822741nt_num: ( ( int > nat ) > ( nat > num ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_350,type,
bNF_re7839584876883444355nt_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ) > ( ( int > num ) > ( int > int ) > int > num ) > ( ( code_integer > num ) > ( int > code_integer ) > int > num ) > $o ).
thf(func_def_351,type,
bNF_re6292805115969292119er_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ).
thf(func_def_352,type,
bNF_re4768042542643474933nt_num: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ).
thf(func_def_353,type,
bNF_re1982657550219213441nt_nat: ( ( nat > $o ) > ( int > int ) > $o ) > ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ).
thf(func_def_354,type,
bNF_re4102725726183926567nt_num: ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > ( int > num ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_355,type,
bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_356,type,
bNF_re2144779315220482269at_nat: ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_357,type,
bNF_re3930744952143938759_nat_o: ( ( nat > nat ) > ( $o > $o ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_358,type,
bNF_re8622501330148003679nt_num: ( ( nat > nat ) > ( int > nat ) > $o ) > ( ( nat > nat ) > ( int > num ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_359,type,
bNF_re7744223787735169245_nat_o: ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_360,type,
bNF_re3262823321055862553at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_361,type,
bNF_re1160762158786734233nt_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ) > ( ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( nat > nat ) > ( int > nat ) > int > nat ) > $o ).
thf(func_def_362,type,
bNF_re239970166668089693at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_363,type,
bNF_re584878643992547173nt_num: ( ( nat > nat ) > ( nat > num ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_364,type,
bNF_re3931674169038344211_nat_o: ( ( nat > num ) > ( $o > $o ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
thf(func_def_365,type,
bNF_re5843449549409830101nt_nat: ( ( nat > num ) > ( int > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
thf(func_def_366,type,
bNF_re6524732562925676389at_nat: ( ( nat > num ) > ( nat > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
thf(func_def_367,type,
bNF_re2655444144887082515er_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( code_integer > nat ) > code_integer > num ) > $o ).
thf(func_def_368,type,
bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_369,type,
bNF_re2742285375668209089nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
thf(func_def_370,type,
bNF_re4105200416192800571er_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( code_integer > num ) > code_integer > num ) > $o ).
thf(func_def_371,type,
bNF_re5446066262214944985nt_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( int > num ) > int > num ) > $o ).
thf(func_def_372,type,
bNF_re3284331099615978085nt_nat: ( ( product_prod_nat_nat > int ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ).
thf(func_def_373,type,
bNF_re8419181437172746013nt_nat: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ).
thf(func_def_374,type,
bNF_re2682547871993127601nt_num: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > num ) > ( int > num ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ).
thf(func_def_375,type,
bNF_rel_fun_o_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_376,type,
bNF_re4895681925607069953_o_nat: ( $o > int > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( int > nat ) > $o ).
thf(func_def_377,type,
bNF_re4209105892566519389_o_nat: ( $o > nat > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( nat > nat ) > $o ).
thf(func_def_378,type,
bNF_re766437678722298023_o_num: ( $o > nat > $o ) > ( $o > num > $o ) > ( $o > $o ) > ( nat > num ) > $o ).
thf(func_def_379,type,
bNF_re1181178334029315097nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_380,type,
bNF_re40212662316476751um_num: ( code_integer > code_integer > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( code_integer > num ) > $o ).
thf(func_def_381,type,
bNF_re8313794964846168862um_num: ( code_integer > int > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( int > num ) > $o ).
thf(func_def_382,type,
bNF_re1366391616432607057unit_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( ref_a > ref_a > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > $o ).
thf(func_def_383,type,
bNF_re5775369113877777_int_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ref_a > int > $o ) > ( heap_e7401611519738050253t_unit > int > $o ) > $o ).
thf(func_def_384,type,
bNF_re9202112420002600977_nat_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ref_a > nat > $o ) > ( heap_e7401611519738050253t_unit > nat > $o ) > $o ).
thf(func_def_385,type,
bNF_re1850668159662942673it_o_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( $o > $o > $o ) > ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ).
thf(func_def_386,type,
bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
thf(func_def_387,type,
bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
thf(func_def_388,type,
bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
thf(func_def_389,type,
bNF_re2828929484557863493at_int: ( int > code_integer > $o ) > ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ).
thf(func_def_390,type,
bNF_re5404797796594736747unit_o: ( int > int > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( int > ref_a > $o ) > ( int > heap_e7401611519738050253t_unit > $o ) > $o ).
thf(func_def_391,type,
bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(func_def_392,type,
bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
thf(func_def_393,type,
bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_394,type,
bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
thf(func_def_395,type,
bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
thf(func_def_396,type,
bNF_re4715010359784256181nt_nat: ( int > int > $o ) > ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ).
thf(func_def_397,type,
bNF_re3713166177374151349at_int: ( int > int > $o ) > ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ).
thf(func_def_398,type,
bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
thf(func_def_399,type,
bNF_re272988434038980259at_num: ( int > int > $o ) > ( nat > num > $o ) > ( int > nat ) > ( int > num ) > $o ).
thf(func_def_400,type,
bNF_re1845987051190671011um_nat: ( int > int > $o ) > ( num > nat > $o ) > ( int > num ) > ( int > nat ) > $o ).
thf(func_def_401,type,
bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_402,type,
bNF_re8766404587435608311at_nat: ( int > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > $o ).
thf(func_def_403,type,
bNF_re4914077030771115051_nat_o: ( int > nat > $o ) > ( nat > $o > $o ) > ( int > nat ) > ( nat > $o ) > $o ).
thf(func_def_404,type,
bNF_re3344003087646356989at_nat: ( int > nat > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( nat > nat ) > $o ).
thf(func_def_405,type,
bNF_re9124706910656911431at_num: ( int > nat > $o ) > ( nat > num > $o ) > ( int > nat ) > ( nat > num ) > $o ).
thf(func_def_406,type,
bNF_re3760060065607074657_num_o: ( int > nat > $o ) > ( num > $o > $o ) > ( int > num ) > ( nat > $o ) > $o ).
thf(func_def_407,type,
bNF_re1474333490953826375um_nat: ( int > nat > $o ) > ( num > nat > $o ) > ( int > num ) > ( nat > nat ) > $o ).
thf(func_def_408,type,
bNF_re4629543205785817921at_nat: ( list_nat > list_nat > $o ) > ( nat > nat > $o ) > ( list_nat > nat ) > ( list_nat > nat ) > $o ).
thf(func_def_409,type,
bNF_re439150893885221597_nat_o: ( nat > $o > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( $o > $o ) > $o ).
thf(func_def_410,type,
bNF_re8508505965575957011_num_o: ( nat > $o > $o ) > ( num > $o > $o ) > ( nat > num ) > ( $o > $o ) > $o ).
thf(func_def_411,type,
bNF_re8207659476513966505_o_int: ( nat > int > $o ) > ( $o > int > $o ) > ( nat > $o ) > ( int > int ) > $o ).
thf(func_def_412,type,
bNF_re8210149947023016781_o_nat: ( nat > int > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( int > nat ) > $o ).
thf(func_def_413,type,
bNF_re4767481733178795415_o_num: ( nat > int > $o ) > ( $o > num > $o ) > ( nat > $o ) > ( int > num ) > $o ).
thf(func_def_414,type,
bNF_re6025474579976152573at_nat: ( nat > int > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( int > nat ) > $o ).
thf(func_def_415,type,
bNF_re2582806366131931207at_num: ( nat > int > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( int > num ) > $o ).
thf(func_def_416,type,
bNF_re4155804983283621959um_nat: ( nat > int > $o ) > ( num > nat > $o ) > ( nat > num ) > ( int > nat ) > $o ).
thf(func_def_417,type,
bNF_re5655699643857186083unit_o: ( nat > nat > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( nat > ref_a > $o ) > ( nat > heap_e7401611519738050253t_unit > $o ) > $o ).
thf(func_def_418,type,
bNF_re605504016728627135_int_o: ( nat > nat > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( nat > int > $o ) > ( nat > int > $o ) > $o ).
thf(func_def_419,type,
bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_420,type,
bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_421,type,
bNF_re7523573913982466217_o_nat: ( nat > nat > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( nat > nat ) > $o ).
thf(func_def_422,type,
bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
thf(func_def_423,type,
bNF_re1402873238235875719_nat_o: ( nat > nat > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( nat > $o ) > $o ).
thf(func_def_424,type,
bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_425,type,
bNF_re2211152805895086571at_num: ( nat > nat > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( nat > num ) > $o ).
thf(func_def_426,type,
bNF_re3784151423046777323um_nat: ( nat > nat > $o ) > ( num > nat > $o ) > ( nat > num ) > ( nat > nat ) > $o ).
thf(func_def_427,type,
bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
thf(func_def_428,type,
bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
thf(func_def_429,type,
bNF_re4736500879113541833um_num: ( num > num > $o ) > ( num > num > $o ) > ( num > num ) > ( num > num ) > $o ).
thf(func_def_430,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_431,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_432,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_433,type,
bNF_re6202762543029211035nteger: ( product_prod_nat_nat > int > $o ) > ( int > code_integer > $o ) > ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ).
thf(func_def_434,type,
bNF_re5552630237950767466nt_int: ( product_prod_nat_nat > int > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( int > int ) > $o ).
thf(func_def_435,type,
bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
thf(func_def_436,type,
bNF_re8466801222876787014um_num: ( product_prod_nat_nat > int > $o ) > ( num > num > $o ) > ( product_prod_nat_nat > num ) > ( int > num ) > $o ).
thf(func_def_437,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_438,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_439,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_440,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_441,type,
bNF_re20414067882207223nt_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > $o ).
thf(func_def_442,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_443,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_444,type,
bNF_re1865807574169326223at_o_o: ( rat > rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).
thf(func_def_445,type,
bNF_re7554818335971813481nt_int: ( rat > rat > $o ) > ( int > int > $o ) > ( rat > int ) > ( rat > int ) > $o ).
thf(func_def_446,type,
bNF_re6557955094579809201at_nat: ( rat > rat > $o ) > ( nat > nat > $o ) > ( rat > nat ) > ( rat > nat ) > $o ).
thf(func_def_447,type,
bNF_re1692451286490762625ar_o_o: ( char > char > $o ) > ( $o > $o > $o ) > ( char > $o ) > ( char > $o ) > $o ).
thf(func_def_448,type,
bNF_re4780507660726531203_o_int: ( char > char > $o ) > ( $o > int > $o ) > ( char > $o ) > ( char > int ) > $o ).
thf(func_def_449,type,
bNF_re4782998131235581479_o_nat: ( char > char > $o ) > ( $o > nat > $o ) > ( char > $o ) > ( char > nat ) > $o ).
thf(func_def_450,type,
bNF_re6064627146911078825_int_o: ( char > char > $o ) > ( int > $o > $o ) > ( char > int ) > ( char > $o ) > $o ).
thf(func_def_451,type,
bNF_re4731199128827642459nt_int: ( char > char > $o ) > ( int > int > $o ) > ( char > int ) > ( char > int ) > $o ).
thf(func_def_452,type,
bNF_re4733689599336692735nt_nat: ( char > char > $o ) > ( int > nat > $o ) > ( char > int ) > ( char > nat ) > $o ).
thf(func_def_453,type,
bNF_re7885669492343766789_nat_o: ( char > char > $o ) > ( nat > $o > $o ) > ( char > nat ) > ( char > $o ) > $o ).
thf(func_def_454,type,
bNF_re3731845416926587903at_int: ( char > char > $o ) > ( nat > int > $o ) > ( char > nat ) > ( char > int ) > $o ).
thf(func_def_455,type,
bNF_re3734335887435638179at_nat: ( char > char > $o ) > ( nat > nat > $o ) > ( char > nat ) > ( char > nat ) > $o ).
thf(func_def_456,type,
bNF_sn8323453914685745821t_unit: ( ref_a > ref_a > $o ) > ( ref_a > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
thf(func_def_457,type,
bNF_sn8000174127721201323nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > produc2963269191615333738nteger ).
thf(func_def_458,type,
bNF_sn1062102010912252026nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_459,type,
bNF_sn8916957246138178918at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_460,type,
bNF_sn649997494946348640at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc4196048018000912732at_int ).
thf(func_def_461,type,
bNF_sn1857951156667551021at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_462,type,
bNF_vi7828673959370436579_int_o: ( ref_a > int ) > ( heap_e7401611519738050253t_unit > int ) > ( int > int > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_463,type,
bNF_vi4623496019404053219_nat_o: ( ref_a > nat ) > ( heap_e7401611519738050253t_unit > nat ) > ( nat > nat > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_464,type,
bNF_vi699694178825965831eger_o: ( int > int ) > ( code_integer > code_integer ) > ( int > code_integer > $o ) > int > code_integer > $o ).
thf(func_def_465,type,
bNF_vi2125572119366604152_int_o: ( int > int ) > ( code_integer > int ) > ( int > int > $o ) > int > code_integer > $o ).
thf(func_def_466,type,
bNF_vi3884084463199473129_int_o: ( int > int ) > ( int > int ) > ( int > int > $o ) > int > int > $o ).
thf(func_def_467,type,
bNF_vi3197508430158922565_int_o: ( int > int ) > ( nat > int ) > ( int > int > $o ) > int > nat > $o ).
thf(func_def_468,type,
bNF_vi5018550775591610529_nat_o: ( int > int ) > ( nat > nat ) > ( int > nat > $o ) > int > nat > $o ).
thf(func_def_469,type,
bNF_vi1281217848275042457_rat_o: ( int > int ) > ( nat > rat ) > ( int > rat > $o ) > int > nat > $o ).
thf(func_def_470,type,
bNF_vi9149698133064535136char_o: ( int > int ) > ( nat > char ) > ( int > char > $o ) > int > nat > $o ).
thf(func_def_471,type,
bNF_vi2193923016096921761_nat_o: ( int > nat ) > ( int > nat ) > ( nat > nat > $o ) > int > int > $o ).
thf(func_def_472,type,
bNF_vi7769575839906753835_rat_o: ( int > nat ) > ( num > rat ) > ( nat > rat > $o ) > int > num > $o ).
thf(func_def_473,type,
bNF_vi1300075849944819442char_o: ( int > nat ) > ( num > char ) > ( nat > char > $o ) > int > num > $o ).
thf(func_def_474,type,
bNF_vi2326032003723069084_num_o: ( int > num ) > ( code_integer > num ) > ( num > num > $o ) > int > code_integer > $o ).
thf(func_def_475,type,
bNF_vi2107963681178519309_num_o: ( int > num ) > ( int > num ) > ( num > num > $o ) > int > int > $o ).
thf(func_def_476,type,
bNF_vi2881549544236934259_int_o: ( int > product_prod_nat_nat ) > ( code_integer > int ) > ( product_prod_nat_nat > int > $o ) > int > code_integer > $o ).
thf(func_def_477,type,
bNF_vi1204582724742824157_nat_o: ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
thf(func_def_478,type,
bNF_vi467646977814820164_int_o: ( list_nat > int ) > ( code_integer > int ) > ( int > int > $o ) > list_nat > code_integer > $o ).
thf(func_def_479,type,
bNF_vi5202502398764838569_nat_o: ( list_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > list_nat > int > $o ).
thf(func_def_480,type,
bNF_vi5856767400800367702unit_o: ( nat > $o ) > ( $o > product_unit ) > ( $o > product_unit > $o ) > nat > $o > $o ).
thf(func_def_481,type,
bNF_vi3868162310295888627_rat_o: ( nat > $o ) > ( $o > rat ) > ( $o > rat > $o ) > nat > $o > $o ).
thf(func_def_482,type,
bNF_vi8816436626763797690char_o: ( nat > $o ) > ( $o > char ) > ( $o > char > $o ) > nat > $o > $o ).
thf(func_def_483,type,
bNF_vi7331807916455492308_int_o: ( nat > int ) > ( code_integer > int ) > ( int > int > $o ) > nat > code_integer > $o ).
thf(func_def_484,type,
bNF_vi8357618154448083105_int_o: ( nat > int ) > ( nat > int ) > ( int > int > $o ) > nat > nat > $o ).
thf(func_def_485,type,
bNF_vi1731478210338170163_nat_o: ( nat > int ) > ( num > nat ) > ( int > nat > $o ) > nat > num > $o ).
thf(func_def_486,type,
bNF_vi6818137723729380987_o_o_o: ( nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > nat > $o > $o ).
thf(func_def_487,type,
bNF_vi1443435967014148806unit_o: ( nat > nat ) > ( $o > product_unit ) > ( nat > product_unit > $o ) > nat > $o > $o ).
thf(func_def_488,type,
bNF_vi6667456707345531737_nat_o: ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_489,type,
bNF_vi2930123780028963665_rat_o: ( nat > nat ) > ( nat > rat ) > ( nat > rat > $o ) > nat > nat > $o ).
thf(func_def_490,type,
bNF_vi8943400373106913048char_o: ( nat > nat ) > ( nat > char ) > ( nat > char > $o ) > nat > nat > $o ).
thf(func_def_491,type,
bNF_vi190728152058600505_nat_o: ( nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat > int > $o ).
thf(func_def_492,type,
bNF_vi1633389952966819264_nat_o: ( product_prod_int_int > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_int_int > num > $o ).
thf(func_def_493,type,
bNF_vi5082502771524357669nt_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_494,type,
bNF_vi8966365312794588230_int_o: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_495,type,
bNF_vi33923956287962137eger_o: ( product_prod_nat_nat > int ) > ( int > code_integer ) > ( int > code_integer > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_496,type,
bNF_vi9094538908245281400_nat_o: ( product_prod_nat_nat > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_nat_nat > num > $o ).
thf(func_def_497,type,
bNF_vi2682369418337388893_int_o: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > ( int > int > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_498,type,
bNF_vi9025507403824386624_o_o_o: ( product_prod_nat_nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > product_prod_nat_nat > $o > $o ).
thf(func_def_499,type,
bNF_vi5493721401438417730_nat_o: ( product_prod_nat_nat > nat ) > ( int > nat ) > ( nat > nat > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_500,type,
bNF_vi5426221348228882691_int_o: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_501,type,
bNF_vi763171854521451549_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 ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_502,type,
bNF_vi508398028314858188_int_o: ( rat > int ) > ( code_integer > int ) > ( int > int > $o ) > rat > code_integer > $o ).
thf(func_def_503,type,
bNF_vi2997284877290766385_nat_o: ( rat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > rat > int > $o ).
thf(func_def_504,type,
bNF_vi7262943168399475603_int_o: ( char > int ) > ( code_integer > int ) > ( int > int > $o ) > char > code_integer > $o ).
thf(func_def_505,type,
bNF_vi728936465572800120_nat_o: ( char > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > char > int > $o ).
thf(func_def_506,type,
bNF_Gr2943678036615987864nt_int: set_o > ( $o > int ) > ( $o > int ) > set_Pr958786334691620121nt_int ).
thf(func_def_507,type,
bNF_Gr1946814795223983584at_nat: set_o > ( $o > nat ) > ( $o > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_508,type,
bNF_Gr7727518618234538026at_num: set_o > ( $o > nat ) > ( $o > num ) > set_Pr6200539531224447659at_num ).
thf(func_def_509,type,
bNF_Gr8686673574714534880nt_int: set_int > ( int > int ) > ( int > int ) > set_Pr958786334691620121nt_int ).
thf(func_def_510,type,
bNF_Gr7689810333322530600at_nat: set_int > ( int > nat ) > ( int > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_511,type,
bNF_Gr4247142119478309234at_num: set_int > ( int > nat ) > ( int > num ) > set_Pr6200539531224447659at_num ).
thf(func_def_512,type,
bNF_Gr8315020014477690244nt_int: set_nat > ( nat > int ) > ( nat > int ) > set_Pr958786334691620121nt_int ).
thf(func_def_513,type,
bNF_Gr7318156773085685964at_nat: set_nat > ( nat > nat ) > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_514,type,
bNF_Gr3875488559241464598at_num: set_nat > ( nat > nat ) > ( nat > num ) > set_Pr6200539531224447659at_num ).
thf(func_def_515,type,
bNF_Gr5511461681843259283at_num: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > num ) > set_Pr6200539531224447659at_num ).
thf(func_def_516,type,
bNF_Gr166583433173494904er_num: ( int > num ) > ( code_integer > num ) > ( int > code_integer > $o ) > num > num > $o ).
thf(func_def_517,type,
bNF_Gr7020624548710275655nt_num: ( int > num ) > ( int > num ) > ( int > int > $o ) > num > num > $o ).
thf(func_def_518,type,
bNF_Gr364077372107685167_int_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
thf(func_def_519,type,
bNF_Gr1354378531936274772nt_int: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
thf(func_def_520,type,
bNF_Gr6955563364113978072nt_nat: ( product_prod_nat_nat > nat ) > ( int > nat ) > ( product_prod_nat_nat > int > $o ) > nat > nat > $o ).
thf(func_def_521,type,
bNF_We7690717809131995284nc_o_o: set_o > set_o > set_o_o ).
thf(func_def_522,type,
bNF_We6830391624356636116_o_nat: set_o > set_nat > set_o_nat ).
thf(func_def_523,type,
bNF_We8730861560085513481t_unit: set_o > set_Product_unit > set_o_Product_unit ).
thf(func_def_524,type,
bNF_We8537379975951060974nt_int: set_int > set_int > set_int_int ).
thf(func_def_525,type,
bNF_We8539870446460111250nt_nat: set_int > set_nat > set_int_nat ).
thf(func_def_526,type,
bNF_We7904740386373615514nt_rat: set_int > set_rat > set_int_rat ).
thf(func_def_527,type,
bNF_We7538026264050006418at_int: set_nat > set_int > set_nat_int ).
thf(func_def_528,type,
bNF_We7540516734559056694at_nat: set_nat > set_nat > set_nat_nat ).
thf(func_def_529,type,
bNF_We6195730058148253354_rat_o: set_rat > set_o > set_rat_o ).
thf(func_def_530,type,
bNF_We7223962090624190782at_nat: set_rat > set_nat > set_rat_nat ).
thf(func_def_531,type,
bNF_We8564238559827753503t_unit: set_rat > set_Product_unit > set_rat_Product_unit ).
thf(func_def_532,type,
bNF_We6174688282833725809char_o: set_char > set_o > set_char_o ).
thf(func_def_533,type,
bNF_We935846424581991991ar_nat: set_char > set_nat > set_char_nat ).
thf(func_def_534,type,
bNF_We7396736742984212070t_unit: set_char > set_Product_unit > set_ch7814610555394875923t_unit ).
thf(func_def_535,type,
bNF_We2264329196211740764nt_int: set_int > ( int > int ) > ( int > int ) > ( int > int ) > int > int ).
thf(func_def_536,type,
bNF_We2266819666720791040nt_nat: set_int > ( int > int ) > ( int > nat ) > ( nat > int ) > int > int ).
thf(func_def_537,type,
bNF_We1264975484310686208at_int: set_int > ( int > nat ) > ( int > int ) > ( int > int ) > int > nat ).
thf(func_def_538,type,
bNF_We1267465954819736484at_nat: set_int > ( int > nat ) > ( int > nat ) > ( nat > int ) > int > nat ).
thf(func_def_539,type,
bNF_We1892675635974896128nt_int: set_int > ( nat > int ) > ( int > int ) > ( int > nat ) > int > int ).
thf(func_def_540,type,
bNF_We1895166106483946404nt_nat: set_int > ( nat > int ) > ( int > nat ) > ( nat > nat ) > int > int ).
thf(func_def_541,type,
bNF_We893321924073841572at_int: set_int > ( nat > nat ) > ( int > int ) > ( int > nat ) > int > nat ).
thf(func_def_542,type,
bNF_We895812394582891848at_nat: set_int > ( nat > nat ) > ( int > nat ) > ( nat > nat ) > int > nat ).
thf(func_def_543,type,
bNF_We576767280138975660at_int: set_int > ( nat > rat ) > ( int > int ) > ( int > nat ) > int > rat ).
thf(func_def_544,type,
bNF_We579257750648025936at_nat: set_int > ( nat > rat ) > ( int > nat ) > ( nat > nat ) > int > rat ).
thf(func_def_545,type,
bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_546,type,
basic_1872990034501187214nt_int: ( int > nat ) > ( int > nat ) > product_prod_int_int > nat ).
thf(func_def_547,type,
basic_1875480505010237490nt_nat: ( int > nat ) > ( nat > nat ) > product_prod_int_nat > nat ).
thf(func_def_548,type,
basic_873636322600132658at_int: ( nat > nat ) > ( int > nat ) > product_prod_nat_int > nat ).
thf(func_def_549,type,
basic_876126793109182934at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_550,type,
basic_685971451221398055t_unit: produc7812382424243267045t_unit > set_ref_a ).
thf(func_def_551,type,
basic_fsts_int_int: product_prod_int_int > set_int ).
thf(func_def_552,type,
basic_fsts_nat_nat: product_prod_nat_nat > set_nat ).
thf(func_def_553,type,
basic_fsts_nat_num: product_prod_nat_num > set_nat ).
thf(func_def_554,type,
basic_3661821009137050567at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat ).
thf(func_def_555,type,
basic_1274512288150691911at_nat: produc1319942482725812455at_nat > set_se5479201105039950375at_nat ).
thf(func_def_556,type,
basic_5328504652464829177at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_557,type,
basic_1496934909540232809t_unit: produc7812382424243267045t_unit > set_he8644174446132254637t_unit ).
thf(func_def_558,type,
basic_snds_int_int: product_prod_int_int > set_int ).
thf(func_def_559,type,
basic_snds_nat_nat: product_prod_nat_nat > set_nat ).
thf(func_def_560,type,
basic_snds_nat_num: product_prod_nat_num > set_num ).
thf(func_def_561,type,
basic_484852565060450053at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat ).
thf(func_def_562,type,
basic_5713354656523905413at_nat: produc1319942482725812455at_nat > set_se5479201105039950375at_nat ).
thf(func_def_563,type,
bit_take_bit_num: nat > num > option_num ).
thf(func_def_564,type,
code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
thf(func_def_565,type,
code_cr_integer: int > code_integer > $o ).
thf(func_def_566,type,
code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_567,type,
code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_568,type,
code_int_of_integer: code_integer > int ).
thf(func_def_569,type,
code_nat_of_integer: code_integer > nat ).
thf(func_def_570,type,
code_negative: num > code_integer ).
thf(func_def_571,type,
code_num_of_integer: code_integer > num ).
thf(func_def_572,type,
code_pcr_integer: int > code_integer > $o ).
thf(func_def_573,type,
complete_Inf_Inf_o_o: set_o_o > $o > $o ).
thf(func_def_574,type,
comple5770381748412298549_int_o: set_int_int_o > int > int > $o ).
thf(func_def_575,type,
comple4393433247856107946_int_o: set_int_o > int > $o ).
thf(func_def_576,type,
comple1675732732025788397_nat_o: set_nat_nat_o > nat > nat > $o ).
thf(func_def_577,type,
comple2433913294995299363_num_o: set_nat_num_o > nat > num > $o ).
thf(func_def_578,type,
comple6214475593288795910_nat_o: set_nat_o > nat > $o ).
thf(func_def_579,type,
comple4707286699709038525_int_o: set_Pr8049984349381595834_int_o > product_prod_int_int > $o ).
thf(func_def_580,type,
comple6265855634338933877_nat_o: set_Pr5582243495563764594_nat_o > product_prod_nat_nat > $o ).
thf(func_def_581,type,
comple8183010123678664591_nat_o: set_Pr7010166363911110284_nat_o > produc3843707927480180839at_nat > $o ).
thf(func_def_582,type,
comple8322679762649017525_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_583,type,
comple5307621999477653941_nat_o: set_se7255092946006855566_nat_o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_584,type,
complete_Inf_Inf_o: set_o > $o ).
thf(func_def_585,type,
complete_Inf_Inf_int: set_int > int ).
thf(func_def_586,type,
complete_Inf_Inf_nat: set_nat > nat ).
thf(func_def_587,type,
comple2584293577114468500t_unit: set_Product_unit > product_unit ).
thf(func_def_588,type,
comple3063163877087187839_set_o: set_set_o > set_o ).
thf(func_def_589,type,
comple3628384868704368283et_int: set_set_int > set_int ).
thf(func_def_590,type,
comple7806235888213564991et_nat: set_set_nat > set_nat ).
thf(func_def_591,type,
comple1626965760690514720nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_592,type,
comple1930127330929219688at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_593,type,
comple6868718957223342258at_num: set_se4826145725398303499at_num > set_Pr6200539531224447659at_num ).
thf(func_def_594,type,
comple6332534001959699150at_nat: set_se6425085446898223655at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_595,type,
comple6751905152567503566at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_596,type,
comple4403251139954110286at_nat: set_se7592288975875140775at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_597,type,
comple7216939928495492468t_unit: set_set_Product_unit > set_Product_unit ).
thf(func_def_598,type,
comple4298007329820168263et_rat: set_set_rat > set_rat ).
thf(func_def_599,type,
comple7965528767983648192t_char: set_set_char > set_char ).
thf(func_def_600,type,
complete_Sup_Sup_o_o: set_o_o > $o > $o ).
thf(func_def_601,type,
comple7687260386943045147_int_o: set_int_int_o > int > int > $o ).
thf(func_def_602,type,
comple6496622788309502864_int_o: set_int_o > int > $o ).
thf(func_def_603,type,
comple3592611370556534995_nat_o: set_nat_nat_o > nat > nat > $o ).
thf(func_def_604,type,
comple4350791933526045961_num_o: set_nat_num_o > nat > num > $o ).
thf(func_def_605,type,
comple8317665133742190828_nat_o: set_nat_o > nat > $o ).
thf(func_def_606,type,
comple342879659800731223_int_o: set_Pr8049984349381595834_int_o > product_prod_int_int > $o ).
thf(func_def_607,type,
comple1901448594430626575_nat_o: set_Pr5582243495563764594_nat_o > product_prod_nat_nat > $o ).
thf(func_def_608,type,
comple1177764198577243945_nat_o: set_Pr7010166363911110284_nat_o > produc3843707927480180839at_nat > $o ).
thf(func_def_609,type,
comple493620192902636699_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_610,type,
comple4502628867940267931_nat_o: set_se7255092946006855566_nat_o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_611,type,
complete_Sup_Sup_o: set_o > $o ).
thf(func_def_612,type,
complete_Sup_Sup_int: set_int > int ).
thf(func_def_613,type,
complete_Sup_Sup_nat: set_nat > nat ).
thf(func_def_614,type,
comple4687483117567863418t_unit: set_Product_unit > product_unit ).
thf(func_def_615,type,
comple90263536869209701_set_o: set_set_o > set_o ).
thf(func_def_616,type,
comple6989579708249578522t_unit: set_se4612898379794543757t_unit > set_he8644174446132254637t_unit ).
thf(func_def_617,type,
comple3221217463730067765et_int: set_set_int > set_int ).
thf(func_def_618,type,
comple7399068483239264473et_nat: set_set_nat > set_nat ).
thf(func_def_619,type,
comple5382143125604098054nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_620,type,
comple5685304695842803022at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_621,type,
comple1400524285282149784at_num: set_se4826145725398303499at_num > set_Pr6200539531224447659at_num ).
thf(func_def_622,type,
comple2748534634209756852at_nat: set_se6425085446898223655at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_623,type,
comple4364388969068068532at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_624,type,
comple7342073961973170484at_nat: set_se7592288975875140775at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_625,type,
comple3349607820504768346t_unit: set_set_Product_unit > set_Product_unit ).
thf(func_def_626,type,
comple3890839924845867745et_rat: set_set_rat > set_rat ).
thf(func_def_627,type,
comple4338141846124676698t_char: set_set_char > set_char ).
thf(func_def_628,type,
condit5488710616941104124bove_o: set_o > $o ).
thf(func_def_629,type,
condit1118808407379112185nteger: set_Code_integer > $o ).
thf(func_def_630,type,
condit2212336002400062152ve_int: set_int > $o ).
thf(func_def_631,type,
condit2214826472909112428ve_nat: set_nat > $o ).
thf(func_def_632,type,
condit2080475194861589617t_unit: set_Product_unit > $o ).
thf(func_def_633,type,
condit1579696412822616692ve_rat: set_rat > $o ).
thf(func_def_634,type,
condit5477540289124974626et_nat: set_set_nat > $o ).
thf(func_def_635,type,
condit5413489452508810728elow_o: set_o > $o ).
thf(func_def_636,type,
condit4933233095834890765nteger: set_Code_integer > $o ).
thf(func_def_637,type,
condit1735850657277959132ow_int: set_int > $o ).
thf(func_def_638,type,
condit1738341127787009408ow_nat: set_nat > $o ).
thf(func_def_639,type,
condit9161856309968323677t_unit: set_Product_unit > $o ).
thf(func_def_640,type,
condit1103211067700513672ow_rat: set_rat > $o ).
thf(func_def_641,type,
condit68592940725977398et_nat: set_set_nat > $o ).
thf(func_def_642,type,
nat_to_rat_surj: nat > rat ).
thf(func_def_643,type,
adjust_div: product_prod_int_int > int ).
thf(func_def_644,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_645,type,
unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_646,type,
unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
thf(func_def_647,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_648,type,
euclid4774559944035922753ze_int: int > nat ).
thf(func_def_649,type,
inverse_inverse_rat: rat > rat ).
thf(func_def_650,type,
finite_Fpow_int: set_int > set_set_int ).
thf(func_def_651,type,
finite_Fpow_nat: set_nat > set_set_nat ).
thf(func_def_652,type,
finite_Fpow_rat: set_rat > set_set_rat ).
thf(func_def_653,type,
finite_card_int: set_int > nat ).
thf(func_def_654,type,
finite_card_nat: set_nat > nat ).
thf(func_def_655,type,
finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat ).
thf(func_def_656,type,
finite_card_rat: set_rat > nat ).
thf(func_def_657,type,
finite6756937295472016048nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_658,type,
finite7905178416053733328on_o_o: set_o > ( $o > $o > $o ) > $o ).
thf(func_def_659,type,
finite4703585013658510744_o_nat: set_o > ( $o > nat > nat ) > $o ).
thf(func_def_660,type,
finite366418920864469932nteger: set_Code_integer > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_661,type,
finite5985214029334008090_int_o: set_int > ( int > $o > $o ) > $o ).
thf(func_def_662,type,
finite4582259249640653518nt_nat: set_int > ( int > nat > nat ) > $o ).
thf(func_def_663,type,
finite7806256374766696054_nat_o: set_nat > ( nat > $o > $o ) > $o ).
thf(func_def_664,type,
finite3582905537739598962at_nat: set_nat > ( nat > nat > nat ) > $o ).
thf(func_def_665,type,
finite1496024664758132007_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o > $o ) > $o ).
thf(func_def_666,type,
finite2110315540964234241at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > $o ).
thf(func_def_667,type,
finite2818816984019561153_nat_o: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > $o > $o ) > $o ).
thf(func_def_668,type,
finite8619596206551965927at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > nat > nat ) > $o ).
thf(func_def_669,type,
finite954763878425697269nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_670,type,
finite2426395113773319005_o_nat: set_o > ( $o > nat > nat ) > $o ).
thf(func_def_671,type,
finite917065715488314481nteger: set_Code_integer > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_672,type,
finite8981753823465611337nt_nat: set_int > ( int > nat > nat ) > $o ).
thf(func_def_673,type,
finite7982400111564556781at_nat: set_nat > ( nat > nat > nat ) > $o ).
thf(func_def_674,type,
finite5150387867909132486at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > $o ).
thf(func_def_675,type,
finite352855791390415404at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > nat > nat ) > $o ).
thf(func_def_676,type,
finite_finite_o: set_o > $o ).
thf(func_def_677,type,
finite_finite_int: set_int > $o ).
thf(func_def_678,type,
finite8100373058378681591st_nat: set_list_nat > $o ).
thf(func_def_679,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_680,type,
finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
thf(func_def_681,type,
finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_682,type,
finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).
thf(func_def_683,type,
finite4290736615968046902t_unit: set_Product_unit > $o ).
thf(func_def_684,type,
finite_finite_rat: set_rat > $o ).
thf(func_def_685,type,
finite_finite_char: set_char > $o ).
thf(func_def_686,type,
bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
thf(func_def_687,type,
comp_C2822359487432382964nteger: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_688,type,
comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_689,type,
comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_690,type,
comp_C7826480081638475456nteger: ( ( code_integer > code_integer ) > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ).
thf(func_def_691,type,
comp_C6484513282182537548nteger: ( ( code_integer > code_integer ) > produc101387210554329899nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc101387210554329899nteger ).
thf(func_def_692,type,
comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_693,type,
comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
thf(func_def_694,type,
comp_o_o_int: ( $o > $o ) > ( int > $o ) > int > $o ).
thf(func_def_695,type,
comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_696,type,
comp_o_o_num: ( $o > $o ) > ( num > $o ) > num > $o ).
thf(func_def_697,type,
comp_o_int_nat: ( $o > int ) > ( nat > $o ) > nat > int ).
thf(func_def_698,type,
comp_o_nat_o: ( $o > nat ) > ( $o > $o ) > $o > nat ).
thf(func_def_699,type,
comp_o_nat_int: ( $o > nat ) > ( int > $o ) > int > nat ).
thf(func_def_700,type,
comp_o_nat_nat: ( $o > nat ) > ( nat > $o ) > nat > nat ).
thf(func_def_701,type,
comp_o_num_o: ( $o > num ) > ( $o > $o ) > $o > num ).
thf(func_def_702,type,
comp_o_num_int: ( $o > num ) > ( int > $o ) > int > num ).
thf(func_def_703,type,
comp_o_num_nat: ( $o > num ) > ( nat > $o ) > nat > num ).
thf(func_def_704,type,
comp_o_num_num: ( $o > num ) > ( num > $o ) > num > num ).
thf(func_def_705,type,
comp_o7658611401268416066_o_nat: ( $o > product_prod_o_o ) > ( nat > $o ) > nat > product_prod_o_o ).
thf(func_def_706,type,
comp_o6895741221744486154t_unit: ( $o > set_o ) > ( product_unit > $o ) > product_unit > set_o ).
thf(func_def_707,type,
comp_o_set_int_nat: ( $o > set_int ) > ( nat > $o ) > nat > set_int ).
thf(func_def_708,type,
comp_o1521574261646630388t_unit: ( $o > set_int ) > ( product_unit > $o ) > product_unit > set_int ).
thf(func_def_709,type,
comp_o_set_nat_nat: ( $o > set_nat ) > ( nat > $o ) > nat > set_nat ).
thf(func_def_710,type,
comp_o9190160103024335696t_unit: ( $o > set_nat ) > ( product_unit > $o ) > product_unit > set_nat ).
thf(func_def_711,type,
comp_o2254869825208929t_unit: ( $o > set_Pr1261947904930325089at_nat ) > ( product_unit > $o ) > product_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_712,type,
comp_o4913564575355137019t_unit: ( $o > set_Pr4329608150637261639at_nat ) > ( product_unit > $o ) > product_unit > set_Pr4329608150637261639at_nat ).
thf(func_def_713,type,
comp_o_set_rat_nat: ( $o > set_rat ) > ( nat > $o ) > nat > set_rat ).
thf(func_def_714,type,
comp_o_char_o: ( $o > char ) > ( $o > $o ) > $o > char ).
thf(func_def_715,type,
comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_716,type,
comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_717,type,
comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
thf(func_def_718,type,
comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
thf(func_def_719,type,
comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
thf(func_def_720,type,
comp_C2177396528461469320um_int: ( code_integer > num ) > ( int > code_integer ) > int > num ).
thf(func_def_721,type,
comp_C8580465762518603278nteger: ( code_integer > num ) > ( produc2963269191615333738nteger > code_integer ) > produc2963269191615333738nteger > num ).
thf(func_def_722,type,
comp_h4837689053573563144t_unit: ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_723,type,
comp_h7449592329096033597t_unit: ( heap_e7401611519738050253t_unit > int ) > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > int ).
thf(func_def_724,type,
comp_h8354993580257045729t_unit: ( heap_e7401611519738050253t_unit > nat ) > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > nat ).
thf(func_def_725,type,
comp_h5940001671827863714t_unit: ( heap_e7401611519738050253t_unit > produc8126358835630522215t_unit ) > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > produc8126358835630522215t_unit ).
thf(func_def_726,type,
comp_r3604920825623061426t_unit: ( ref_a > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_727,type,
comp_r2143332150499412868t_unit: ( ref_a > ref_a ) > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > ref_a ).
thf(func_def_728,type,
comp_r7249815618783853587t_unit: ( ref_a > int ) > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > int ).
thf(func_def_729,type,
comp_r8155216869944865719t_unit: ( ref_a > nat ) > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > nat ).
thf(func_def_730,type,
comp_r6154141770783548544t_unit: ( ref_a > produc5288414631154139675_ref_a ) > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > produc5288414631154139675_ref_a ).
thf(func_def_731,type,
comp_i653165354545908656at_int: ( int > int > $o ) > ( produc4196048018000912732at_int > int ) > produc4196048018000912732at_int > int > $o ).
thf(func_def_732,type,
comp_i4519014998770822500at_int: ( int > int > int ) > ( produc4196048018000912732at_int > int ) > produc4196048018000912732at_int > int > int ).
thf(func_def_733,type,
comp_int_o_o: ( int > $o ) > ( $o > int ) > $o > $o ).
thf(func_def_734,type,
comp_int_o_int: ( int > $o ) > ( int > int ) > int > $o ).
thf(func_def_735,type,
comp_int_o_nat: ( int > $o ) > ( nat > int ) > nat > $o ).
thf(func_def_736,type,
comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
thf(func_def_737,type,
comp_int_int_o: ( int > int ) > ( $o > int ) > $o > int ).
thf(func_def_738,type,
comp_i2224564030725804698nteger: ( int > int ) > ( code_integer > int ) > code_integer > int ).
thf(func_def_739,type,
comp_int_int_int: ( int > int ) > ( int > int ) > int > int ).
thf(func_def_740,type,
comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
thf(func_def_741,type,
comp_i4330622015127193916nt_int: ( int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > int ).
thf(func_def_742,type,
comp_int_int_rat: ( int > int ) > ( rat > int ) > rat > int ).
thf(func_def_743,type,
comp_int_int_char: ( int > int ) > ( char > int ) > char > int ).
thf(func_def_744,type,
comp_int_nat_o: ( int > nat ) > ( $o > int ) > $o > nat ).
thf(func_def_745,type,
comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
thf(func_def_746,type,
comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
thf(func_def_747,type,
comp_i1292779930663060120nt_int: ( int > nat ) > ( product_prod_int_int > int ) > product_prod_int_int > nat ).
thf(func_def_748,type,
comp_i4471277238271202272at_nat: ( int > nat ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ).
thf(func_def_749,type,
comp_i5627883460353289149at_int: ( int > nat ) > ( produc4196048018000912732at_int > int ) > produc4196048018000912732at_int > nat ).
thf(func_def_750,type,
comp_int_nat_rat: ( int > nat ) > ( rat > int ) > rat > nat ).
thf(func_def_751,type,
comp_int_nat_char: ( int > nat ) > ( char > int ) > char > nat ).
thf(func_def_752,type,
comp_int_num_int: ( int > num ) > ( int > int ) > int > num ).
thf(func_def_753,type,
comp_int_num_nat: ( int > num ) > ( nat > int ) > nat > num ).
thf(func_def_754,type,
comp_int_num_num: ( int > num ) > ( num > int ) > num > num ).
thf(func_def_755,type,
comp_i3846818780818535807nteger: ( int > num ) > ( produc2963269191615333738nteger > int ) > produc2963269191615333738nteger > num ).
thf(func_def_756,type,
comp_i7231038107349025742nt_int: ( int > num ) > ( product_prod_int_int > int ) > product_prod_int_int > num ).
thf(func_def_757,type,
comp_i1186163378102392086at_nat: ( int > num ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > num ).
thf(func_def_758,type,
comp_i1108739374719436894at_int: ( int > product_prod_nat_nat ) > ( int > int ) > int > product_prod_nat_nat ).
thf(func_def_759,type,
comp_int_rat_nat: ( int > rat ) > ( nat > int ) > nat > rat ).
thf(func_def_760,type,
comp_int_set_nat_int: ( int > set_nat ) > ( int > int ) > int > set_nat ).
thf(func_def_761,type,
comp_nat_o_o: ( nat > $o ) > ( $o > nat ) > $o > $o ).
thf(func_def_762,type,
comp_nat_o_int: ( nat > $o ) > ( int > nat ) > int > $o ).
thf(func_def_763,type,
comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
thf(func_def_764,type,
comp_n1662990198670838940at_nat: ( nat > $o ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > $o ).
thf(func_def_765,type,
comp_nat_int_o: ( nat > int ) > ( $o > nat ) > $o > int ).
thf(func_def_766,type,
comp_nat_int_int: ( nat > int ) > ( int > nat ) > int > int ).
thf(func_def_767,type,
comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
thf(func_def_768,type,
comp_nat_int_num: ( nat > int ) > ( num > nat ) > num > int ).
thf(func_def_769,type,
comp_n5749082658982224864at_nat: ( nat > int ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > int ).
thf(func_def_770,type,
comp_nat_int_rat: ( nat > int ) > ( rat > nat ) > rat > int ).
thf(func_def_771,type,
comp_nat_int_char: ( nat > int ) > ( char > nat ) > char > int ).
thf(func_def_772,type,
comp_nat_nat_o: ( nat > nat ) > ( $o > nat ) > $o > nat ).
thf(func_def_773,type,
comp_nat_nat_int: ( nat > nat ) > ( int > nat ) > int > nat ).
thf(func_def_774,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_775,type,
comp_nat_nat_num: ( nat > nat ) > ( num > nat ) > num > nat ).
thf(func_def_776,type,
comp_n2711240574518091068at_nat: ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_777,type,
comp_nat_nat_rat: ( nat > nat ) > ( rat > nat ) > rat > nat ).
thf(func_def_778,type,
comp_nat_nat_char: ( nat > nat ) > ( char > nat ) > char > nat ).
thf(func_def_779,type,
comp_n2103536230552569900nteger: ( nat > num ) > ( code_integer > nat ) > code_integer > num ).
thf(func_def_780,type,
comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
thf(func_def_781,type,
comp_nat_num_nat: ( nat > num ) > ( nat > nat ) > nat > num ).
thf(func_def_782,type,
comp_nat_num_num: ( nat > num ) > ( num > nat ) > num > num ).
thf(func_def_783,type,
comp_n8649498751204056690at_nat: ( nat > num ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ).
thf(func_def_784,type,
comp_n8574565218330151774at_nat: ( nat > product_prod_nat_nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).
thf(func_def_785,type,
comp_n8531277669757933902um_int: ( nat > product_prod_num_num ) > ( int > nat ) > int > product_prod_num_num ).
thf(func_def_786,type,
comp_nat_rat_int: ( nat > rat ) > ( int > nat ) > int > rat ).
thf(func_def_787,type,
comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
thf(func_def_788,type,
comp_nat_rat_rat: ( nat > rat ) > ( rat > nat ) > rat > rat ).
thf(func_def_789,type,
comp_nat_rat_char: ( nat > rat ) > ( char > nat ) > char > rat ).
thf(func_def_790,type,
comp_nat_set_nat_int: ( nat > set_nat ) > ( int > nat ) > int > set_nat ).
thf(func_def_791,type,
comp_nat_set_nat_nat: ( nat > set_nat ) > ( nat > nat ) > nat > set_nat ).
thf(func_def_792,type,
comp_nat_set_rat_int: ( nat > set_rat ) > ( int > nat ) > int > set_rat ).
thf(func_def_793,type,
comp_nat_set_rat_nat: ( nat > set_rat ) > ( nat > nat ) > nat > set_rat ).
thf(func_def_794,type,
comp_nat_char_char: ( nat > char ) > ( char > nat ) > char > char ).
thf(func_def_795,type,
comp_num_o_o: ( num > $o ) > ( $o > num ) > $o > $o ).
thf(func_def_796,type,
comp_num_o_int: ( num > $o ) > ( int > num ) > int > $o ).
thf(func_def_797,type,
comp_num_o_nat: ( num > $o ) > ( nat > num ) > nat > $o ).
thf(func_def_798,type,
comp_num_o_num: ( num > $o ) > ( num > num ) > num > $o ).
thf(func_def_799,type,
comp_num_nat_int: ( num > nat ) > ( int > num ) > int > nat ).
thf(func_def_800,type,
comp_num_nat_nat: ( num > nat ) > ( nat > num ) > nat > nat ).
thf(func_def_801,type,
comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
thf(func_def_802,type,
comp_num_num_o: ( num > num ) > ( $o > num ) > $o > num ).
thf(func_def_803,type,
comp_n8557746072492896886nteger: ( num > num ) > ( code_integer > num ) > code_integer > num ).
thf(func_def_804,type,
comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
thf(func_def_805,type,
comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
thf(func_def_806,type,
comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
thf(func_def_807,type,
comp_num_set_int_int: ( num > set_int ) > ( int > num ) > int > set_int ).
thf(func_def_808,type,
comp_num_set_nat_int: ( num > set_nat ) > ( int > num ) > int > set_nat ).
thf(func_def_809,type,
comp_num_set_rat_int: ( num > set_rat ) > ( int > num ) > int > set_rat ).
thf(func_def_810,type,
comp_P8564252314792299288nteger: ( produc723880050079548563nteger > produc101387210554329899nteger ) > ( code_integer > produc723880050079548563nteger ) > code_integer > produc101387210554329899nteger ).
thf(func_def_811,type,
comp_P2137996956111167876_o_o_o: ( product_prod_o_o > $o ) > ( $o > product_prod_o_o ) > $o > $o ).
thf(func_def_812,type,
comp_P551574746845053877_o_o_o: ( product_prod_o_o > product_prod_o_o ) > ( $o > product_prod_o_o ) > $o > product_prod_o_o ).
thf(func_def_813,type,
comp_P7034811116587396339_o_nat: ( product_prod_o_o > product_prod_o_o ) > ( nat > product_prod_o_o ) > nat > product_prod_o_o ).
thf(func_def_814,type,
comp_P4785046977597218846at_nat: ( product_prod_o_o > product_prod_o_o ) > ( product_prod_nat_nat > product_prod_o_o ) > product_prod_nat_nat > product_prod_o_o ).
thf(func_def_815,type,
comp_P1471321874221585045at_o_o: ( product_prod_o_o > product_prod_nat_o ) > ( $o > product_prod_o_o ) > $o > product_prod_nat_o ).
thf(func_def_816,type,
comp_P465755969289462830at_int: ( product_prod_o_int > product_prod_o_nat ) > ( product_prod_nat_int > product_prod_o_int ) > product_prod_nat_int > product_prod_o_nat ).
thf(func_def_817,type,
comp_P1422407636550552773_nat_o: ( product_prod_o_nat > product_prod_o_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_o_nat ).
thf(func_def_818,type,
comp_P1391661485614827491at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( nat > product_prod_o_nat ) > nat > product_prod_o_nat ).
thf(func_def_819,type,
comp_P4962864564169660718at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( product_prod_nat_nat > product_prod_o_nat ) > product_prod_nat_nat > product_prod_o_nat ).
thf(func_def_820,type,
comp_P9057111047297513408at_int: ( product_prod_o_nat > product_prod_o_num ) > ( product_prod_nat_int > product_prod_o_nat ) > product_prod_nat_int > product_prod_o_num ).
thf(func_def_821,type,
comp_P196761593691424337_nat_o: ( product_prod_o_nat > product_prod_nat_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_nat_nat ).
thf(func_def_822,type,
comp_P972951341003599239_nat_o: ( product_prod_o_nat > product_prod_num_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_num_nat ).
thf(func_def_823,type,
comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
thf(func_def_824,type,
comp_P8237986404257982958t_unit: ( produc8126358835630522215t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc8126358835630522215t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_825,type,
comp_P3239167524078694454t_unit: ( produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_826,type,
comp_P1287623958910499840t_unit: ( produc1799199577659733785_ref_a > ref_a ) > ( produc7812382424243267045t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > ref_a ).
thf(func_def_827,type,
comp_P2006160480335490974_ref_a: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( produc1799199577659733785_ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ).
thf(func_def_828,type,
comp_P8019343326919024234t_unit: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc7812382424243267045t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_829,type,
comp_P6390991081591698364at_nat: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( product_prod_nat_nat > produc7812382424243267045t_unit ) > product_prod_nat_nat > heap_e7401611519738050253t_unit ).
thf(func_def_830,type,
comp_P7254561687666694144_ref_a: ( produc7812382424243267045t_unit > ref_a ) > ( produc1799199577659733785_ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > ref_a ).
thf(func_def_831,type,
comp_P4044372497395451596t_unit: ( produc7812382424243267045t_unit > ref_a ) > ( produc7812382424243267045t_unit > produc7812382424243267045t_unit ) > produc7812382424243267045t_unit > ref_a ).
thf(func_def_832,type,
comp_P7986581389989349338at_nat: ( produc7812382424243267045t_unit > ref_a ) > ( product_prod_nat_nat > produc7812382424243267045t_unit ) > product_prod_nat_nat > ref_a ).
thf(func_def_833,type,
comp_P9134237804721252988t_unit: ( produc5288414631154139675_ref_a > ref_a ) > ( produc7812382424243267045t_unit > produc5288414631154139675_ref_a ) > produc7812382424243267045t_unit > ref_a ).
thf(func_def_834,type,
comp_P9034173210191959223nt_int: ( product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > $o ).
thf(func_def_835,type,
comp_P6651465171681656048nt_int: ( product_prod_int_int > int ) > ( int > product_prod_int_int ) > int > int ).
thf(func_def_836,type,
comp_P6653955642190706324nt_nat: ( product_prod_int_int > int ) > ( nat > product_prod_int_int ) > nat > int ).
thf(func_def_837,type,
comp_P5356232565778667509nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > int ).
thf(func_def_838,type,
comp_P6018825582104210588nt_rat: ( product_prod_int_int > int ) > ( rat > product_prod_int_int ) > rat > int ).
thf(func_def_839,type,
comp_P4161745170962941589t_char: ( product_prod_int_int > int ) > ( char > product_prod_int_int ) > char > int ).
thf(func_def_840,type,
comp_P2318390481314533713nt_int: ( product_prod_int_int > nat ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > nat ).
thf(func_def_841,type,
comp_P2788356708182965334nt_int: ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_842,type,
comp_P2134349925370910487at_int: ( product_prod_int_int > product_prod_nat_nat ) > ( int > product_prod_int_int ) > int > product_prod_nat_nat ).
thf(func_def_843,type,
comp_P3488689526429045841nt_nat: ( product_prod_int_nat > nat ) > ( product_prod_int_nat > product_prod_int_nat ) > product_prod_int_nat > nat ).
thf(func_def_844,type,
comp_P1145193044942399421um_int: ( product_prod_int_nat > product_prod_nat_num ) > ( int > product_prod_int_nat ) > int > product_prod_nat_num ).
thf(func_def_845,type,
comp_P5799945282029801519_o_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_nat_o ).
thf(func_def_846,type,
comp_P8901546994122883554at_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( product_prod_nat_nat > product_prod_nat_o ) > product_prod_nat_nat > product_prod_nat_o ).
thf(func_def_847,type,
comp_P6576135029341976421_o_nat: ( product_prod_nat_o > product_prod_num_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_num_o ).
thf(func_def_848,type,
comp_P5807473265676440968nt_nat: ( product_prod_nat_o > product_prod_num_o ) > ( product_prod_int_nat > product_prod_nat_o ) > product_prod_int_nat > product_prod_num_o ).
thf(func_def_849,type,
comp_P397146161216181329at_int: ( product_prod_nat_int > nat ) > ( product_prod_nat_int > product_prod_nat_int ) > product_prod_nat_int > nat ).
thf(func_def_850,type,
comp_P8376639181999047357at_int: ( product_prod_nat_int > product_prod_num_nat ) > ( int > product_prod_nat_int ) > int > product_prod_num_nat ).
thf(func_def_851,type,
comp_P3772045228931366376nt_int: ( product_prod_nat_int > product_prod_num_nat ) > ( product_prod_int_int > product_prod_nat_int ) > product_prod_int_int > product_prod_num_nat ).
thf(func_def_852,type,
comp_P2002127591014248037at_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 ).
thf(func_def_853,type,
comp_P7900071416159368952at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > $o ).
thf(func_def_854,type,
comp_P3913276677246710332at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_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_855,type,
comp_P4524073163769703009at_int: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_856,type,
comp_P4605287290794827253at_nat: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int ).
thf(func_def_857,type,
comp_P1953119740877977564at_int: ( product_prod_nat_nat > nat ) > ( int > product_prod_nat_nat ) > int > nat ).
thf(func_def_858,type,
comp_P5292260908303971472st_nat: ( product_prod_nat_nat > nat ) > ( list_nat > product_prod_nat_nat ) > list_nat > nat ).
thf(func_def_859,type,
comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).
thf(func_def_860,type,
comp_P1567445206330693457at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > nat ).
thf(func_def_861,type,
comp_P8635049891247748876at_int: ( product_prod_nat_nat > nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > nat ).
thf(func_def_862,type,
comp_P1320480151300532104at_rat: ( product_prod_nat_nat > nat ) > ( rat > product_prod_nat_nat ) > rat > nat ).
thf(func_def_863,type,
comp_P1491501995297412481t_char: ( product_prod_nat_nat > nat ) > ( char > product_prod_nat_nat ) > char > nat ).
thf(func_def_864,type,
comp_P7428279379633703887at_int: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat ).
thf(func_def_865,type,
comp_P7430769850142754163at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > ( nat > product_prod_nat_nat ) > nat > product_prod_nat_nat ).
thf(func_def_866,type,
comp_P6334688330072917552at_int: ( product_prod_nat_nat > product_prod_nat_num ) > ( product_prod_nat_int > product_prod_nat_nat ) > product_prod_nat_int > product_prod_nat_num ).
thf(func_def_867,type,
comp_P5371577678113413053at_nat: ( product_prod_nat_nat > product_prod_num_nat ) > ( nat > product_prod_nat_nat ) > nat > product_prod_num_nat ).
thf(func_def_868,type,
comp_P5124699952429557552nt_nat: ( product_prod_nat_nat > product_prod_num_nat ) > ( product_prod_int_nat > product_prod_nat_nat ) > product_prod_int_nat > product_prod_num_nat ).
thf(func_def_869,type,
comp_P7387482301570536291um_int: ( product_prod_nat_nat > product_prod_num_num ) > ( int > product_prod_nat_nat ) > int > product_prod_num_num ).
thf(func_def_870,type,
comp_P9218946435557410242nt_int: ( product_prod_nat_nat > product_prod_num_num ) > ( product_prod_int_int > product_prod_nat_nat ) > product_prod_int_int > product_prod_num_num ).
thf(func_def_871,type,
comp_P8336958949797789649um_nat: ( product_prod_nat_num > nat ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > nat ).
thf(func_def_872,type,
comp_P5051845089628979463um_nat: ( product_prod_nat_num > num ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > num ).
thf(func_def_873,type,
comp_P3192427084145116251at_num: ( product_prod_num_nat > product_prod_o_nat ) > ( num > product_prod_num_nat ) > num > product_prod_o_nat ).
thf(func_def_874,type,
comp_P2539519431309506803at_num: ( product_prod_num_nat > product_prod_nat_nat ) > ( num > product_prod_num_nat ) > num > product_prod_nat_nat ).
thf(func_def_875,type,
comp_P480327259280165693at_num: ( product_prod_num_nat > product_prod_num_nat ) > ( num > product_prod_num_nat ) > num > product_prod_num_nat ).
thf(func_def_876,type,
comp_P4305060815297604026um_int: ( product_prod_num_num > num ) > ( int > product_prod_num_num ) > int > num ).
thf(func_def_877,type,
comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
thf(func_def_878,type,
comp_P4974406650942564362at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_879,type,
comp_P4528037747288561284at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_880,type,
comp_P3728553842126764068at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( produc1319942482725812455at_nat > produc1319942482725812455at_nat ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_881,type,
comp_P8235817900121468292at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_882,type,
comp_P5156358013004227690it_o_o: ( product_unit > $o ) > ( $o > product_unit ) > $o > $o ).
thf(func_def_883,type,
comp_P4985893458130756478_o_nat: ( product_unit > $o ) > ( nat > product_unit ) > nat > $o ).
thf(func_def_884,type,
comp_rat_o_o: ( rat > $o ) > ( $o > rat ) > $o > $o ).
thf(func_def_885,type,
comp_rat_o_nat: ( rat > $o ) > ( nat > rat ) > nat > $o ).
thf(func_def_886,type,
comp_rat_int_int: ( rat > int ) > ( int > rat ) > int > int ).
thf(func_def_887,type,
comp_rat_int_nat: ( rat > int ) > ( nat > rat ) > nat > int ).
thf(func_def_888,type,
comp_rat_int_char: ( rat > int ) > ( char > rat ) > char > int ).
thf(func_def_889,type,
comp_rat_nat_o: ( rat > nat ) > ( $o > rat ) > $o > nat ).
thf(func_def_890,type,
comp_rat_nat_int: ( rat > nat ) > ( int > rat ) > int > nat ).
thf(func_def_891,type,
comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
thf(func_def_892,type,
comp_rat_nat_rat: ( rat > nat ) > ( rat > rat ) > rat > nat ).
thf(func_def_893,type,
comp_rat_nat_char: ( rat > nat ) > ( char > rat ) > char > nat ).
thf(func_def_894,type,
comp_rat_num_nat: ( rat > num ) > ( nat > rat ) > nat > num ).
thf(func_def_895,type,
comp_rat_num_num: ( rat > num ) > ( num > rat ) > num > num ).
thf(func_def_896,type,
comp_rat_rat_nat: ( rat > rat ) > ( nat > rat ) > nat > rat ).
thf(func_def_897,type,
comp_rat_rat_char: ( rat > rat ) > ( char > rat ) > char > rat ).
thf(func_def_898,type,
comp_rat_char_char: ( rat > char ) > ( char > rat ) > char > char ).
thf(func_def_899,type,
comp_s4786119426940707554nteger: ( set_Co726186806682698383nteger > set_Code_integer ) > ( set_Pr4111642102156807771nteger > set_Co726186806682698383nteger ) > set_Pr4111642102156807771nteger > set_Code_integer ).
thf(func_def_900,type,
comp_s9189197539837705563_set_o: ( set_o > set_nat ) > ( set_o > set_o ) > set_o > set_nat ).
thf(func_def_901,type,
comp_s7717450105097109807et_nat: ( set_int > set_int ) > ( set_nat > set_int ) > set_nat > set_int ).
thf(func_def_902,type,
comp_s2487324123861929025et_int: ( set_int > set_int ) > ( set_set_int > set_int ) > set_set_int > set_int ).
thf(func_def_903,type,
comp_s5712175470073906149et_int: ( set_int > set_nat ) > ( set_set_int > set_int ) > set_set_int > set_nat ).
thf(func_def_904,type,
comp_s7011316712748663051_int_o: ( set_nat > set_int ) > ( $o > set_nat ) > $o > set_int ).
thf(func_def_905,type,
comp_s5617672292595496825nt_int: ( set_nat > set_int ) > ( int > set_nat ) > int > set_int ).
thf(func_def_906,type,
comp_s5620162763104547101nt_nat: ( set_nat > set_int ) > ( nat > set_nat ) > nat > set_int ).
thf(func_def_907,type,
comp_s6458263553158497821et_num: ( set_nat > set_int ) > ( set_num > set_nat ) > set_num > set_int ).
thf(func_def_908,type,
comp_s3768223441818958217et_nat: ( set_nat > set_int ) > ( set_set_nat > set_nat ) > set_set_nat > set_int ).
thf(func_def_909,type,
comp_s33089643564333159_nat_o: ( set_nat > set_nat ) > ( $o > set_nat ) > $o > set_nat ).
thf(func_def_910,type,
comp_s3430750717902475037at_int: ( set_nat > set_nat ) > ( int > set_nat ) > int > set_nat ).
thf(func_def_911,type,
comp_s3433241188411525313at_nat: ( set_nat > set_nat ) > ( nat > set_nat ) > nat > set_nat ).
thf(func_def_912,type,
comp_s8964582002068861047et_nat: ( set_nat > set_nat ) > ( set_nat > set_nat ) > set_nat > set_nat ).
thf(func_def_913,type,
comp_s6993074788030935341et_nat: ( set_nat > set_nat ) > ( set_set_nat > set_nat ) > set_set_nat > set_nat ).
thf(func_def_914,type,
comp_s8507027185284273247_rat_o: ( set_nat > set_rat ) > ( $o > set_nat ) > $o > set_rat ).
thf(func_def_915,type,
comp_s8253438564248248613at_int: ( set_nat > set_rat ) > ( int > set_nat ) > int > set_rat ).
thf(func_def_916,type,
comp_s8255929034757298889at_nat: ( set_nat > set_rat ) > ( nat > set_nat ) > nat > set_rat ).
thf(func_def_917,type,
comp_s6435139744279249717et_nat: ( set_nat > set_rat ) > ( set_set_nat > set_nat ) > set_set_nat > set_rat ).
thf(func_def_918,type,
comp_s7355055891894327172at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_919,type,
comp_s8709038167382007543et_int: ( set_set_int > set_int ) > ( set_set_int > set_set_int ) > set_set_int > set_int ).
thf(func_def_920,type,
comp_s1975749275458958491et_nat: ( set_set_int > set_int ) > ( set_set_nat > set_set_int ) > set_set_nat > set_int ).
thf(func_def_921,type,
comp_s6907669228194913343et_int: ( set_set_nat > set_nat ) > ( set_set_int > set_set_nat ) > set_set_int > set_nat ).
thf(func_def_922,type,
comp_s174380336271864291et_nat: ( set_set_nat > set_nat ) > ( set_set_nat > set_set_nat ) > set_set_nat > set_nat ).
thf(func_def_923,type,
comp_s703482200030188019et_nat: ( set_set_rat > set_rat ) > ( set_set_nat > set_set_rat ) > set_set_nat > set_rat ).
thf(func_def_924,type,
comp_char_o_o: ( char > $o ) > ( $o > char ) > $o > $o ).
thf(func_def_925,type,
comp_char_o_char: ( char > $o ) > ( char > char ) > char > $o ).
thf(func_def_926,type,
comp_char_int_char: ( char > int ) > ( char > char ) > char > int ).
thf(func_def_927,type,
comp_char_nat_int: ( char > nat ) > ( int > char ) > int > nat ).
thf(func_def_928,type,
comp_char_nat_nat: ( char > nat ) > ( nat > char ) > nat > nat ).
thf(func_def_929,type,
comp_char_nat_char: ( char > nat ) > ( char > char ) > char > nat ).
thf(func_def_930,type,
comp_char_num_nat: ( char > num ) > ( nat > char ) > nat > num ).
thf(func_def_931,type,
comp_char_num_num: ( char > num ) > ( num > char ) > num > num ).
thf(func_def_932,type,
comp_char_num_char: ( char > num ) > ( char > char ) > char > num ).
thf(func_def_933,type,
comp_char_rat_char: ( char > rat ) > ( char > char ) > char > rat ).
thf(func_def_934,type,
comp_char_set_int_o: ( char > set_int ) > ( $o > char ) > $o > set_int ).
thf(func_def_935,type,
comp_c3102392033783471720nt_nat: ( char > set_int ) > ( nat > char ) > nat > set_int ).
thf(func_def_936,type,
comp_c8883095856794026162nt_num: ( char > set_int ) > ( num > char ) > num > set_int ).
thf(func_def_937,type,
comp_char_set_nat_o: ( char > set_nat ) > ( $o > char ) > $o > set_nat ).
thf(func_def_938,type,
comp_c912979988581399656at_int: ( char > set_nat ) > ( int > char ) > int > set_nat ).
thf(func_def_939,type,
comp_c915470459090449932at_nat: ( char > set_nat ) > ( nat > char ) > nat > set_nat ).
thf(func_def_940,type,
comp_c6696174282101004374at_num: ( char > set_nat ) > ( num > char ) > num > set_nat ).
thf(func_def_941,type,
comp_char_set_rat_o: ( char > set_rat ) > ( $o > char ) > $o > set_rat ).
thf(func_def_942,type,
comp_c5735667834927173232at_int: ( char > set_rat ) > ( int > char ) > int > set_rat ).
thf(func_def_943,type,
comp_c5738158305436223508at_nat: ( char > set_rat ) > ( nat > char ) > nat > set_rat ).
thf(func_def_944,type,
comp_c2295490091592002142at_num: ( char > set_rat ) > ( num > char ) > num > set_rat ).
thf(func_def_945,type,
comp_char_char_char: ( char > char ) > ( char > char ) > char > char ).
thf(func_def_946,type,
fun_upd_o_o: ( $o > $o ) > $o > $o > $o > $o ).
thf(func_def_947,type,
fun_upd_o_nat: ( $o > nat ) > $o > nat > $o > nat ).
thf(func_def_948,type,
fun_up846054379331416818t_unit: ( $o > product_unit ) > $o > product_unit > $o > product_unit ).
thf(func_def_949,type,
fun_upd_o_set_o: ( $o > set_o ) > $o > set_o > $o > set_o ).
thf(func_def_950,type,
fun_up4718931970374059986t_unit: ( $o > set_Product_unit ) > $o > set_Product_unit > $o > set_Product_unit ).
thf(func_def_951,type,
fun_up8056716234270145717nteger: ( code_integer > code_integer > code_integer ) > code_integer > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
thf(func_def_952,type,
fun_up8139772397987072257nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_953,type,
fun_upd_int_o: ( int > $o ) > int > $o > int > $o ).
thf(func_def_954,type,
fun_upd_int_int: ( int > int ) > int > int > int > int ).
thf(func_def_955,type,
fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).
thf(func_def_956,type,
fun_upd_int_num: ( int > num ) > int > num > int > num ).
thf(func_def_957,type,
fun_up2220634978854545698t_unit: ( int > product_unit ) > int > product_unit > int > product_unit ).
thf(func_def_958,type,
fun_upd_int_set_o: ( int > set_o ) > int > set_o > int > set_o ).
thf(func_def_959,type,
fun_upd_int_set_nat: ( int > set_nat ) > int > set_nat > int > set_nat ).
thf(func_def_960,type,
fun_up5054257004045450754t_unit: ( int > set_Product_unit ) > int > set_Product_unit > int > set_Product_unit ).
thf(func_def_961,type,
fun_upd_nat_o: ( nat > $o ) > nat > $o > nat > $o ).
thf(func_def_962,type,
fun_upd_nat_int: ( nat > int ) > nat > int > nat > int ).
thf(func_def_963,type,
fun_upd_nat_nat: ( nat > nat ) > nat > nat > nat > nat ).
thf(func_def_964,type,
fun_upd_nat_rat: ( nat > rat ) > nat > rat > nat > rat ).
thf(func_def_965,type,
fun_upd_nat_set_o: ( nat > set_o ) > nat > set_o > nat > set_o ).
thf(func_def_966,type,
fun_up1220017903161424222t_unit: ( nat > set_Product_unit ) > nat > set_Product_unit > nat > set_Product_unit ).
thf(func_def_967,type,
fun_up5432024876597553480unit_o: ( product_unit > $o ) > product_unit > $o > product_unit > $o ).
thf(func_def_968,type,
fun_up6473050886840373792it_nat: ( product_unit > nat ) > product_unit > nat > product_unit > nat ).
thf(func_def_969,type,
fun_up6875000483049295805t_unit: ( product_unit > product_unit ) > product_unit > product_unit > product_unit > product_unit ).
thf(func_def_970,type,
fun_up1762901246852280360_set_o: ( product_unit > set_o ) > product_unit > set_o > product_unit > set_o ).
thf(func_def_971,type,
fun_up4569834200710200790et_nat: ( product_unit > set_nat ) > product_unit > set_nat > product_unit > set_nat ).
thf(func_def_972,type,
fun_up488859312337516701t_unit: ( product_unit > set_Product_unit ) > product_unit > set_Product_unit > product_unit > set_Product_unit ).
thf(func_def_973,type,
id_nat_o: ( nat > $o ) > nat > $o ).
thf(func_def_974,type,
id_nat_nat: ( nat > nat ) > nat > nat ).
thf(func_def_975,type,
id_Pro496765588584934260nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_976,type,
id_o: $o > $o ).
thf(func_def_977,type,
id_Code_integer: code_integer > code_integer ).
thf(func_def_978,type,
id_int: int > int ).
thf(func_def_979,type,
id_list_nat: list_nat > list_nat ).
thf(func_def_980,type,
id_nat: nat > nat ).
thf(func_def_981,type,
id_num: num > num ).
thf(func_def_982,type,
id_Pro2309048762231606924nteger: produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_983,type,
id_Pro4381231610383771306nt_int: product_prod_int_int > product_prod_int_int ).
thf(func_def_984,type,
id_Pro7559728917991913458at_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_985,type,
id_Pro8267972854940751164at_num: product_prod_nat_num > product_prod_nat_num ).
thf(func_def_986,type,
id_Pro8722402698821300696at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_987,type,
id_Pro6043886709289754456at_nat: produc1319942482725812455at_nat > produc1319942482725812455at_nat ).
thf(func_def_988,type,
id_Product_unit: product_unit > product_unit ).
thf(func_def_989,type,
id_rat: rat > rat ).
thf(func_def_990,type,
id_set_o: set_o > set_o ).
thf(func_def_991,type,
id_set_int: set_int > set_int ).
thf(func_def_992,type,
id_set_nat: set_nat > set_nat ).
thf(func_def_993,type,
id_set_num: set_num > set_num ).
thf(func_def_994,type,
id_set2334057505560298834at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_995,type,
id_set7849613212452405432at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_996,type,
id_char: char > char ).
thf(func_def_997,type,
inj_on5500977043710295017nteger: ( ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Co4375521073081744395nteger > $o ).
thf(func_def_998,type,
inj_on3998011822705705585nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Co726186806682698383nteger > $o ).
thf(func_def_999,type,
inj_on856898432580761861nt_nat: ( ( int > int ) > int > nat ) > set_int_int > $o ).
thf(func_def_1000,type,
inj_on7039184780174133295nt_int: ( ( int > int ) > set_Pr958786334691620121nt_int ) > set_int_int > $o ).
thf(func_def_1001,type,
inj_on5377432224680912883nt_num: ( ( int > nat ) > int > num ) > set_int_nat > $o ).
thf(func_def_1002,type,
inj_on_nat_o_nat_o: ( ( nat > $o ) > nat > $o ) > set_nat_o > $o ).
thf(func_def_1003,type,
inj_on2461717442902640625at_nat: ( ( nat > nat ) > nat > nat ) > set_nat_nat > $o ).
thf(func_def_1004,type,
inj_on3412903767820855855at_nat: ( ( nat > nat ) > set_Pr1261947904930325089at_nat ) > set_nat_nat > $o ).
thf(func_def_1005,type,
inj_on_o_o: ( $o > $o ) > set_o > $o ).
thf(func_def_1006,type,
inj_on_o_int: ( $o > int ) > set_o > $o ).
thf(func_def_1007,type,
inj_on_o_nat: ( $o > nat ) > set_o > $o ).
thf(func_def_1008,type,
inj_on4268752236855399398t_unit: ( $o > product_unit ) > set_o > $o ).
thf(func_def_1009,type,
inj_on_o_rat: ( $o > rat ) > set_o > $o ).
thf(func_def_1010,type,
inj_on_o_char: ( $o > char ) > set_o > $o ).
thf(func_def_1011,type,
inj_on108595395805848489nteger: ( code_integer > code_integer > code_integer ) > set_Code_integer > $o ).
thf(func_def_1012,type,
inj_on7031512951821619701nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer > $o ).
thf(func_def_1013,type,
inj_on1158064722259180589nteger: ( code_integer > code_integer ) > set_Code_integer > $o ).
thf(func_def_1014,type,
inj_on_int_o: ( int > $o ) > set_int > $o ).
thf(func_def_1015,type,
inj_on_int_int: ( int > int ) > set_int > $o ).
thf(func_def_1016,type,
inj_on_int_nat: ( int > nat ) > set_int > $o ).
thf(func_def_1017,type,
inj_on_int_num: ( int > num ) > set_int > $o ).
thf(func_def_1018,type,
inj_on5397397550511676250nt_int: ( int > product_prod_int_int ) > set_int > $o ).
thf(func_def_1019,type,
inj_on8575894858119818402at_nat: ( int > product_prod_nat_nat ) > set_int > $o ).
thf(func_def_1020,type,
inj_on4178023183795006766t_unit: ( int > product_unit ) > set_int > $o ).
thf(func_def_1021,type,
inj_on3049792774292151987st_nat: ( list_nat > list_nat ) > set_list_nat > $o ).
thf(func_def_1022,type,
inj_on7574789179980466158at_nat: ( list_nat > product_prod_nat_nat ) > set_list_nat > $o ).
thf(func_def_1023,type,
inj_on_nat_o: ( nat > $o ) > set_nat > $o ).
thf(func_def_1024,type,
inj_on_nat_int: ( nat > int ) > set_nat > $o ).
thf(func_def_1025,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_1026,type,
inj_on_nat_num: ( nat > num ) > set_nat > $o ).
thf(func_def_1027,type,
inj_on5538052773655684606at_nat: ( nat > product_prod_nat_nat ) > set_nat > $o ).
thf(func_def_1028,type,
inj_on6246296710604522312at_num: ( nat > product_prod_nat_num ) > set_nat > $o ).
thf(func_def_1029,type,
inj_on7061601236592826506t_unit: ( nat > product_unit ) > set_nat > $o ).
thf(func_def_1030,type,
inj_on_nat_rat: ( nat > rat ) > set_nat > $o ).
thf(func_def_1031,type,
inj_on_nat_char: ( nat > char ) > set_nat > $o ).
thf(func_def_1032,type,
inj_on_num_o: ( num > $o ) > set_num > $o ).
thf(func_def_1033,type,
inj_on_num_int: ( num > int ) > set_num > $o ).
thf(func_def_1034,type,
inj_on_num_nat: ( num > nat ) > set_num > $o ).
thf(func_def_1035,type,
inj_on20428373856169009nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Pr4811707699266497531nteger > $o ).
thf(func_def_1036,type,
inj_on6454360653267994289nt_int: ( product_prod_int_int > product_prod_int_int ) > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1037,type,
inj_on2178005380612969504at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1038,type,
inj_on8969904277767023793at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1039,type,
inj_on2339680571444523825at_num: ( product_prod_num_nat > product_prod_nat_num ) > set_Pr3280342998896498603um_nat > $o ).
thf(func_def_1040,type,
inj_on991952103320416098_nat_o: ( produc859450856879609959at_nat > $o ) > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1041,type,
inj_on490725545064285830at_nat: ( produc859450856879609959at_nat > nat ) > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1042,type,
inj_on229527429751349963at_nat: ( produc859450856879609959at_nat > product_prod_nat_nat ) > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1043,type,
inj_on1041401102088758999t_unit: ( produc859450856879609959at_nat > product_unit ) > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1044,type,
inj_on8430303779476321073at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1045,type,
inj_on3108384905993948887t_unit: ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1046,type,
inj_on3942866938762682161at_nat: ( produc1319942482725812455at_nat > produc1319942482725812455at_nat ) > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_1047,type,
inj_on8854722734121536060unit_o: ( product_unit > $o ) > set_Product_unit > $o ).
thf(func_def_1048,type,
inj_on8427948621271784584it_int: ( product_unit > int ) > set_Product_unit > $o ).
thf(func_def_1049,type,
inj_on8430439091780834860it_nat: ( product_unit > nat ) > set_Product_unit > $o ).
thf(func_def_1050,type,
inj_on8151373323710067377t_unit: ( product_unit > product_unit ) > set_Product_unit > $o ).
thf(func_def_1051,type,
inj_on7795309031694339124it_rat: ( product_unit > rat ) > set_Product_unit > $o ).
thf(func_def_1052,type,
inj_on1959294024837303853t_char: ( product_unit > char ) > set_Product_unit > $o ).
thf(func_def_1053,type,
inj_on_rat_o: ( rat > $o ) > set_rat > $o ).
thf(func_def_1054,type,
inj_on_rat_int: ( rat > int ) > set_rat > $o ).
thf(func_def_1055,type,
inj_on_rat_nat: ( rat > nat ) > set_rat > $o ).
thf(func_def_1056,type,
inj_on8867882244352206326at_nat: ( rat > product_prod_nat_nat ) > set_rat > $o ).
thf(func_def_1057,type,
inj_on_rat_rat: ( rat > rat ) > set_rat > $o ).
thf(func_def_1058,type,
inj_on6435365835345961783et_int: ( set_int > set_int ) > set_set_int > $o ).
thf(func_def_1059,type,
inj_on1389844818000382683et_nat: ( set_int > set_nat ) > set_set_int > $o ).
thf(func_def_1060,type,
inj_on426556184350386907et_int: ( set_nat > set_int ) > set_set_nat > $o ).
thf(func_def_1061,type,
inj_on4604407203859583615et_nat: ( set_nat > set_nat ) > set_set_nat > $o ).
thf(func_def_1062,type,
inj_on1096178645466186887et_rat: ( set_nat > set_rat ) > set_set_nat > $o ).
thf(func_def_1063,type,
inj_on699426629415580343at_nat: ( set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ) > set_se7855581050983116737at_nat > $o ).
thf(func_def_1064,type,
inj_on1468925692805905105at_nat: ( set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ) > set_se5479201105039950375at_nat > $o ).
thf(func_def_1065,type,
inj_on_char_o: ( char > $o ) > set_char > $o ).
thf(func_def_1066,type,
inj_on_char_int: ( char > int ) > set_char > $o ).
thf(func_def_1067,type,
inj_on_char_nat: ( char > nat ) > set_char > $o ).
thf(func_def_1068,type,
inj_on1021528964648911549at_nat: ( char > product_prod_nat_nat ) > set_char > $o ).
thf(func_def_1069,type,
inj_on_char_char: ( char > char ) > set_char > $o ).
thf(func_def_1070,type,
map_fu1227494855608507351um_num: ( code_integer > int ) > ( num > num ) > ( int > num ) > code_integer > num ).
thf(func_def_1071,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_1072,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_1073,type,
map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(func_def_1074,type,
map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
thf(func_def_1075,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_1076,type,
the_inv_into_o_o: set_o > ( $o > $o ) > $o > $o ).
thf(func_def_1077,type,
the_inv_into_o_int: set_o > ( $o > int ) > int > $o ).
thf(func_def_1078,type,
the_inv_into_o_nat: set_o > ( $o > nat ) > nat > $o ).
thf(func_def_1079,type,
the_inv_into_o_rat: set_o > ( $o > rat ) > rat > $o ).
thf(func_def_1080,type,
the_inv_into_o_char: set_o > ( $o > char ) > char > $o ).
thf(func_def_1081,type,
the_inv_into_int_o: set_int > ( int > $o ) > $o > int ).
thf(func_def_1082,type,
the_inv_into_int_int: set_int > ( int > int ) > int > int ).
thf(func_def_1083,type,
the_inv_into_int_nat: set_int > ( int > nat ) > nat > int ).
thf(func_def_1084,type,
the_inv_into_int_num: set_int > ( int > num ) > num > int ).
thf(func_def_1085,type,
the_inv_into_int_rat: set_int > ( int > rat ) > rat > int ).
thf(func_def_1086,type,
the_inv_into_nat_o: set_nat > ( nat > $o ) > $o > nat ).
thf(func_def_1087,type,
the_inv_into_nat_int: set_nat > ( nat > int ) > int > nat ).
thf(func_def_1088,type,
the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
thf(func_def_1089,type,
the_inv_into_nat_num: set_nat > ( nat > num ) > num > nat ).
thf(func_def_1090,type,
the_inv_into_nat_rat: set_nat > ( nat > rat ) > rat > nat ).
thf(func_def_1091,type,
the_in9023905271258939222t_char: set_nat > ( nat > char ) > char > nat ).
thf(func_def_1092,type,
the_inv_into_num_o: set_num > ( num > $o ) > $o > num ).
thf(func_def_1093,type,
the_inv_into_num_int: set_num > ( num > int ) > int > num ).
thf(func_def_1094,type,
the_inv_into_num_nat: set_num > ( num > nat ) > nat > num ).
thf(func_def_1095,type,
the_in43325605794470270unit_o: set_Product_unit > ( product_unit > $o ) > $o > product_unit ).
thf(func_def_1096,type,
the_in3915408195775746418it_rat: set_Product_unit > ( product_unit > rat ) > rat > product_unit ).
thf(func_def_1097,type,
the_in3194898024646563179t_char: set_Product_unit > ( product_unit > char ) > char > product_unit ).
thf(func_def_1098,type,
the_inv_into_rat_o: set_rat > ( rat > $o ) > $o > rat ).
thf(func_def_1099,type,
the_inv_into_rat_nat: set_rat > ( rat > nat ) > nat > rat ).
thf(func_def_1100,type,
fun_in_rel_int_int: set_Pr958786334691620121nt_int > int > int > $o ).
thf(func_def_1101,type,
fun_in_rel_nat_nat: set_Pr1261947904930325089at_nat > nat > nat > $o ).
thf(func_def_1102,type,
fun_in_rel_nat_num: set_Pr6200539531224447659at_num > nat > num > $o ).
thf(func_def_1103,type,
fun_in8056734985859589634at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1104,type,
fun_in6812141508599261570at_nat: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1105,type,
fun_is_measure_int: ( int > nat ) > $o ).
thf(func_def_1106,type,
fun_max_strict: set_Pr4329608150637261639at_nat ).
thf(func_def_1107,type,
fun_max_weak: set_Pr4329608150637261639at_nat ).
thf(func_def_1108,type,
fun_min_strict: set_Pr4329608150637261639at_nat ).
thf(func_def_1109,type,
fun_min_weak: set_Pr4329608150637261639at_nat ).
thf(func_def_1110,type,
fun_pair_leq: set_Pr8693737435421807431at_nat ).
thf(func_def_1111,type,
fun_pair_less: set_Pr8693737435421807431at_nat ).
thf(func_def_1112,type,
fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).
thf(func_def_1113,type,
fun_rp8445993449185644698at_nat: produc1319942482725812455at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > produc1319942482725812455at_nat ).
thf(func_def_1114,type,
gcd_Gcd_int: set_int > int ).
thf(func_def_1115,type,
gcd_Gcd_nat: set_nat > nat ).
thf(func_def_1116,type,
gcd_Lcm_int: set_int > int ).
thf(func_def_1117,type,
gcd_Lcm_nat: set_nat > nat ).
thf(func_def_1118,type,
abs_abs_Code_integer: code_integer > code_integer ).
thf(func_def_1119,type,
abs_abs_int: int > int ).
thf(func_def_1120,type,
abs_abs_rat: rat > rat ).
thf(func_def_1121,type,
minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
thf(func_def_1122,type,
minus_minus_int: int > int > int ).
thf(func_def_1123,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_1124,type,
minus_minus_rat: rat > rat > rat ).
thf(func_def_1125,type,
minus_minus_set_o: set_o > set_o > set_o ).
thf(func_def_1126,type,
minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_1127,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(func_def_1128,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1129,type,
minus_7052513330764642158od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_1130,type,
minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1131,type,
minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1132,type,
minus_8321449233255521966at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1133,type,
minus_8235382265540049710at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_1134,type,
minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1135,type,
minus_8674369445256047406at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_1136,type,
minus_6452836326544984404t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1137,type,
minus_minus_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_1138,type,
minus_minus_set_char: set_char > set_char > set_char ).
thf(func_def_1139,type,
one_one_Code_integer: code_integer ).
thf(func_def_1140,type,
one_one_int: int ).
thf(func_def_1141,type,
one_one_nat: nat ).
thf(func_def_1142,type,
plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
thf(func_def_1143,type,
plus_plus_int: int > int > int ).
thf(func_def_1144,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_1145,type,
plus_plus_num: num > num > num ).
thf(func_def_1146,type,
plus_plus_rat: rat > rat > rat ).
thf(func_def_1147,type,
sgn_sgn_Code_integer: code_integer > code_integer ).
thf(func_def_1148,type,
sgn_sgn_int: int > int ).
thf(func_def_1149,type,
times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
thf(func_def_1150,type,
times_times_int: int > int > int ).
thf(func_def_1151,type,
times_times_nat: nat > nat > nat ).
thf(func_def_1152,type,
times_times_rat: rat > rat > rat ).
thf(func_def_1153,type,
uminus1351360451143612070nteger: code_integer > code_integer ).
thf(func_def_1154,type,
uminus_uminus_int: int > int ).
thf(func_def_1155,type,
uminus2952777764628376836t_unit: product_unit > product_unit ).
thf(func_def_1156,type,
uminus_uminus_rat: rat > rat ).
thf(func_def_1157,type,
zero_z3403309356797280102nteger: code_integer ).
thf(func_def_1158,type,
zero_zero_int: int ).
thf(func_def_1159,type,
zero_zero_nat: nat ).
thf(func_def_1160,type,
the_Pr5012129486825234846t_unit: ( produc7812382424243267045t_unit > $o ) > produc7812382424243267045t_unit ).
thf(func_def_1161,type,
the_Pr4378521158711661632nt_int: ( product_prod_int_int > $o ) > product_prod_int_int ).
thf(func_def_1162,type,
the_Pr7557018466319803784at_nat: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_1163,type,
the_Pr8265262403268641490at_num: ( product_prod_nat_num > $o ) > product_prod_nat_num ).
thf(func_def_1164,type,
the_Pr4604535484834969198at_nat: ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat ).
thf(func_def_1165,type,
the_Pr4877703158196064750at_nat: ( produc1319942482725812455at_nat > $o ) > produc1319942482725812455at_nat ).
thf(func_def_1166,type,
defaul566961228789861419t_unit: product_unit ).
thf(func_def_1167,type,
lim_Product_unit: heap_e7401611519738050253t_unit > nat ).
thf(func_def_1168,type,
heap_b146640354529102224_ref_a: heap_Heap_ref_a > ( ref_a > heap_Heap_ref_a ) > heap_Heap_ref_a ).
thf(func_def_1169,type,
heap_effect_ref_a: heap_Heap_ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > $o ).
thf(func_def_1170,type,
heap_e2830298082929533060t_unit: heap_H6156071679106078628t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > product_unit > $o ).
thf(func_def_1171,type,
heap_effect_a: heap_Heap_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > a > $o ).
thf(func_def_1172,type,
heap_guard_ref_a: ( heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > produc7812382424243267045t_unit ) > heap_Heap_ref_a ).
thf(func_def_1173,type,
heap_heap_ref_a: ( heap_e7401611519738050253t_unit > produc7812382424243267045t_unit ) > heap_Heap_ref_a ).
thf(func_def_1174,type,
heap_raise_ref_a: literal > heap_Heap_ref_a ).
thf(func_def_1175,type,
heap_return_ref_a: ref_a > heap_Heap_ref_a ).
thf(func_def_1176,type,
heap_success_ref_a: heap_Heap_ref_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_1177,type,
heap_tap_ref_a: ( heap_e7401611519738050253t_unit > ref_a ) > heap_Heap_ref_a ).
thf(func_def_1178,type,
heap_tap_a: ( heap_e7401611519738050253t_unit > a ) > heap_Heap_a ).
thf(func_def_1179,type,
if_Code_integer: $o > code_integer > code_integer > code_integer ).
thf(func_def_1180,type,
if_Heap_Heap_ref_a: $o > heap_Heap_ref_a > heap_Heap_ref_a > heap_Heap_ref_a ).
thf(func_def_1181,type,
if_int: $o > int > int > int ).
thf(func_def_1182,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_1183,type,
if_num: $o > num > num > num ).
thf(func_def_1184,type,
if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
thf(func_def_1185,type,
if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1186,type,
if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
thf(func_def_1187,type,
if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1188,type,
if_Pro3444522238938527101atural: $o > produc4675096598859438275atural > produc4675096598859438275atural > produc4675096598859438275atural ).
thf(func_def_1189,type,
if_Pro4507677147265585453at_nat: $o > produc859450856879609959at_nat > produc859450856879609959at_nat > produc859450856879609959at_nat ).
thf(func_def_1190,type,
if_Pro3594990065127090477at_nat: $o > produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_1191,type,
if_Product_unit: $o > product_unit > product_unit > product_unit ).
thf(func_def_1192,type,
if_rat: $o > rat > rat > rat ).
thf(func_def_1193,type,
if_set_o: $o > set_o > set_o > set_o ).
thf(func_def_1194,type,
if_set_nat: $o > set_nat > set_nat > set_nat ).
thf(func_def_1195,type,
if_set1508868558775481357at_nat: $o > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1196,type,
if_set3208018901896979469at_nat: $o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1197,type,
if_set_Product_unit: $o > set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1198,type,
abs_Integ: product_prod_nat_nat > int ).
thf(func_def_1199,type,
rep_Integ: int > product_prod_nat_nat ).
thf(func_def_1200,type,
cr_int: product_prod_nat_nat > int > $o ).
thf(func_def_1201,type,
int_ge_less_than: int > set_Pr958786334691620121nt_int ).
thf(func_def_1202,type,
int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
thf(func_def_1203,type,
intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1204,type,
nat2: int > nat ).
thf(func_def_1205,type,
pcr_int: product_prod_nat_nat > int > $o ).
thf(func_def_1206,type,
inf_inf_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
thf(func_def_1207,type,
inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_1208,type,
inf_inf_nat_num_o: ( nat > num > $o ) > ( nat > num > $o ) > nat > num > $o ).
thf(func_def_1209,type,
inf_in6124848772414083356_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_1210,type,
inf_in6969519006101653788_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1211,type,
inf_inf_int: int > int > int ).
thf(func_def_1212,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_1213,type,
inf_inf_Product_unit: product_unit > product_unit > product_unit ).
thf(func_def_1214,type,
inf_inf_rat: rat > rat > rat ).
thf(func_def_1215,type,
inf_inf_set_o: set_o > set_o > set_o ).
thf(func_def_1216,type,
inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_1217,type,
inf_inf_set_int: set_int > set_int > set_int ).
thf(func_def_1218,type,
inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_1219,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1220,type,
inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1221,type,
inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1222,type,
inf_in7510916698018314649at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
thf(func_def_1223,type,
inf_in4302113700860409141at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1224,type,
inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1225,type,
inf_in2456762090751560885at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_1226,type,
inf_in4660618365625256667t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1227,type,
inf_inf_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_1228,type,
inf_inf_set_char: set_char > set_char > set_char ).
thf(func_def_1229,type,
sup_su1544571744061072657eger_o: ( int > code_integer > $o ) > ( int > code_integer > $o ) > int > code_integer > $o ).
thf(func_def_1230,type,
sup_sup_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
thf(func_def_1231,type,
sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_1232,type,
sup_sup_nat_num_o: ( nat > num > $o ) > ( nat > num > $o ) > nat > num > $o ).
thf(func_def_1233,type,
sup_su5231854730092680051_int_o: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_1234,type,
sup_su362511073950362882_nat_o: ( 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 > $o ).
thf(func_def_1235,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_1236,type,
sup_su6164525874564267778_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1237,type,
sup_sup_int: int > int > int ).
thf(func_def_1238,type,
sup_sup_nat: nat > nat > nat ).
thf(func_def_1239,type,
sup_sup_Product_unit: product_unit > product_unit > product_unit ).
thf(func_def_1240,type,
sup_sup_rat: rat > rat > rat ).
thf(func_def_1241,type,
sup_sup_set_o: set_o > set_o > set_o ).
thf(func_def_1242,type,
sup_sup_set_int: set_int > set_int > set_int ).
thf(func_def_1243,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1244,type,
sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_1245,type,
sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
thf(func_def_1246,type,
sup_su4058753791541417424t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit ).
thf(func_def_1247,type,
sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1248,type,
sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
thf(func_def_1249,type,
sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1250,type,
sup_su2042722026077122175at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
thf(func_def_1251,type,
sup_su4209953369189666580t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit ).
thf(func_def_1252,type,
sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1253,type,
sup_su2851927382625014182unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o ).
thf(func_def_1254,type,
sup_su1639320892072265582it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat ).
thf(func_def_1255,type,
sup_su6481247232241170203t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit ).
thf(func_def_1256,type,
sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1257,type,
sup_su5395584912770621083at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_1258,type,
sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_1259,type,
sup_sup_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_1260,type,
sup_sup_set_set_o: set_set_o > set_set_o > set_set_o ).
thf(func_def_1261,type,
sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
thf(func_def_1262,type,
sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
thf(func_def_1263,type,
sup_su474284620922681339at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat ).
thf(func_def_1264,type,
sup_su5975557051335651745t_unit: set_set_Product_unit > set_set_Product_unit > set_set_Product_unit ).
thf(func_def_1265,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
thf(func_def_1266,type,
quotie9062115205763428814nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > code_integer > $o ) > $o ).
thf(func_def_1267,type,
quotie8207154290130328982nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > $o ).
thf(func_def_1268,type,
quotie8803226531959296410nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > $o ).
thf(func_def_1269,type,
quotient_o_o: ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_1270,type,
quotient_o_nat: ( $o > $o > $o ) > ( $o > nat ) > ( nat > $o ) > ( $o > nat > $o ) > $o ).
thf(func_def_1271,type,
quotie2291698863146621601nteger: ( int > int > $o ) > ( int > code_integer ) > ( code_integer > int ) > ( int > code_integer > $o ) > $o ).
thf(func_def_1272,type,
quotient_int_int: ( int > int > $o ) > ( int > int ) > ( int > int ) > ( int > int > $o ) > $o ).
thf(func_def_1273,type,
quotient_int_nat: ( int > int > $o ) > ( int > nat ) > ( nat > int ) > ( int > nat > $o ) > $o ).
thf(func_def_1274,type,
quotient_int_num: ( int > int > $o ) > ( int > num ) > ( num > int ) > ( int > num > $o ) > $o ).
thf(func_def_1275,type,
quotient_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( $o > nat ) > ( nat > $o > $o ) > $o ).
thf(func_def_1276,type,
quotient_nat_int: ( nat > nat > $o ) > ( nat > int ) > ( int > nat ) > ( nat > int > $o ) > $o ).
thf(func_def_1277,type,
quotient_nat_nat: ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > $o ).
thf(func_def_1278,type,
quotient_nat_num: ( nat > nat > $o ) > ( nat > num ) > ( num > nat ) > ( nat > num > $o ) > $o ).
thf(func_def_1279,type,
quotient_nat_rat: ( nat > nat > $o ) > ( nat > rat ) > ( rat > nat ) > ( nat > rat > $o ) > $o ).
thf(func_def_1280,type,
quotient_nat_char: ( nat > nat > $o ) > ( nat > char ) > ( char > nat ) > ( nat > char > $o ) > $o ).
thf(func_def_1281,type,
quotient_num_int: ( num > num > $o ) > ( num > int ) > ( int > num ) > ( num > int > $o ) > $o ).
thf(func_def_1282,type,
quotient_num_nat: ( num > num > $o ) > ( num > nat ) > ( nat > num ) > ( num > nat > $o ) > $o ).
thf(func_def_1283,type,
quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_1284,type,
quotie4166942682936818134at_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 ) > $o ).
thf(func_def_1285,type,
quotient_rat_int: ( rat > rat > $o ) > ( rat > int ) > ( int > rat ) > ( rat > int > $o ) > $o ).
thf(func_def_1286,type,
quotient_rat_nat: ( rat > rat > $o ) > ( rat > nat ) > ( nat > rat ) > ( rat > nat > $o ) > $o ).
thf(func_def_1287,type,
quotient_rat_rat: ( rat > rat > $o ) > ( rat > rat ) > ( rat > rat ) > ( rat > rat > $o ) > $o ).
thf(func_def_1288,type,
quotient_rat_char: ( rat > rat > $o ) > ( rat > char ) > ( char > rat ) > ( rat > char > $o ) > $o ).
thf(func_def_1289,type,
quotient_char_int: ( char > char > $o ) > ( char > int ) > ( int > char ) > ( char > int > $o ) > $o ).
thf(func_def_1290,type,
quotient_char_nat: ( char > char > $o ) > ( char > nat ) > ( nat > char ) > ( char > nat > $o ) > $o ).
thf(func_def_1291,type,
quotient_char_rat: ( char > char > $o ) > ( char > rat ) > ( rat > char ) > ( char > rat > $o ) > $o ).
thf(func_def_1292,type,
quotient_char_char: ( char > char > $o ) > ( char > char ) > ( char > char ) > ( char > char > $o ) > $o ).
thf(func_def_1293,type,
all_interval_nat: ( nat > $o ) > nat > nat > $o ).
thf(func_def_1294,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_1295,type,
nil_nat: list_nat ).
thf(func_def_1296,type,
list_ex_nat: ( nat > $o ) > list_nat > $o ).
thf(func_def_1297,type,
upt: nat > nat > list_nat ).
thf(func_def_1298,type,
suc: nat > nat ).
thf(func_def_1299,type,
case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
thf(func_def_1300,type,
semiring_1_Nats_int: set_int ).
thf(func_def_1301,type,
semiri1314217659103216013at_int: nat > int ).
thf(func_def_1302,type,
nat_int_decode: nat > int ).
thf(func_def_1303,type,
nat_int_encode: int > nat ).
thf(func_def_1304,type,
nat_list_decode: nat > list_nat ).
thf(func_def_1305,type,
nat_list_decode_rel: nat > nat > $o ).
thf(func_def_1306,type,
nat_list_encode: list_nat > nat ).
thf(func_def_1307,type,
nat_prod_decode: nat > product_prod_nat_nat ).
thf(func_def_1308,type,
nat_prod_encode: product_prod_nat_nat > nat ).
thf(func_def_1309,type,
nat_sum_decode: nat > sum_sum_nat_nat ).
thf(func_def_1310,type,
nat_sum_encode: sum_sum_nat_nat > nat ).
thf(func_def_1311,type,
nat_triangle: nat > nat ).
thf(func_def_1312,type,
bit0: num > num ).
thf(func_def_1313,type,
bit1: num > num ).
thf(func_def_1314,type,
one: num ).
thf(func_def_1315,type,
case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
thf(func_def_1316,type,
num_of_nat: nat > num ).
thf(func_def_1317,type,
numera6620942414471956472nteger: num > code_integer ).
thf(func_def_1318,type,
numeral_numeral_int: num > int ).
thf(func_def_1319,type,
numeral_numeral_nat: num > nat ).
thf(func_def_1320,type,
none_num: option_num ).
thf(func_def_1321,type,
some_num: num > option_num ).
thf(func_def_1322,type,
case_option_num_num: num > ( num > num ) > option_num > num ).
thf(func_def_1323,type,
case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
thf(func_def_1324,type,
order_aboveS_int: set_Pr958786334691620121nt_int > int > set_int ).
thf(func_def_1325,type,
order_aboveS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
thf(func_def_1326,type,
order_1761765819289301284nt_int: set_Pr2560585780119916871nt_int > product_prod_int_int > set_Pr958786334691620121nt_int ).
thf(func_def_1327,type,
order_4940263126897443436at_nat: set_Pr8693737435421807431at_nat > product_prod_nat_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1328,type,
order_4440095836999870412at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_1329,type,
order_2442354982230848562at_nat: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_1330,type,
order_6238756238976269133r_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_1331,type,
order_4471489696718655927on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1332,type,
order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1333,type,
order_7480980593162297270at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1334,type,
order_2711500226769404828at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_1335,type,
order_888282469287196226t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_1336,type,
order_5942792088423767318at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1337,type,
order_1878278401035043452at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_1338,type,
order_1960202971199294558of_int: ( int > int > $o ) > set_int > set_Pr958786334691620121nt_int ).
thf(func_def_1339,type,
order_1962693441708344834of_nat: ( nat > nat > $o ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1340,type,
order_8809246210994205103at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1341,type,
order_8308734813930759573at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_1342,type,
order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
thf(func_def_1343,type,
order_2615775362358406454r_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_1344,type,
order_2886507596567047182on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1345,type,
order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1346,type,
order_8331247224601271455at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1347,type,
order_2339240034117818117at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_1348,type,
order_3164716736300062379t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_1349,type,
order_1968183844437341695at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1350,type,
order_423636163458052581at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_1351,type,
bot_bo341146761387662761eger_o: int > code_integer > $o ).
thf(func_def_1352,type,
bot_bot_int_int_o: int > int > $o ).
thf(func_def_1353,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(func_def_1354,type,
bot_bot_nat_num_o: nat > num > $o ).
thf(func_def_1355,type,
bot_bo5438875203632553179_int_o: product_prod_nat_nat > int > $o ).
thf(func_def_1356,type,
bot_bo4898103413517107610_nat_o: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1357,type,
bot_bo394778441745866138_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1358,type,
bot_bo3364206721330744218_nat_o: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1359,type,
bot_bo2717538794563056311t_unit: pred_Product_unit ).
thf(func_def_1360,type,
bot_bot_Product_unit: product_unit ).
thf(func_def_1361,type,
bot_bot_set_o: set_o ).
thf(func_def_1362,type,
bot_bo3686245532977126937t_unit: set_he8644174446132254637t_unit ).
thf(func_def_1363,type,
bot_bot_set_ref_a: set_ref_a ).
thf(func_def_1364,type,
bot_bot_set_int: set_int ).
thf(func_def_1365,type,
bot_bot_set_nat: set_nat ).
thf(func_def_1366,type,
bot_bot_set_num: set_num ).
thf(func_def_1367,type,
bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).
thf(func_def_1368,type,
bot_bo66526543525301729_o_nat: set_Pr2101469702781467981_o_nat ).
thf(func_def_1369,type,
bot_bo4402188677660116584t_unit: set_Pr6671815714118170108t_unit ).
thf(func_def_1370,type,
bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
thf(func_def_1371,type,
bot_bo1114129665703605383_nat_o: set_Pr3149072824959771635_nat_o ).
thf(func_def_1372,type,
bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1373,type,
bot_bo7038385379056416535at_num: set_Pr6200539531224447659at_num ).
thf(func_def_1374,type,
bot_bo5043309098482578556t_unit: set_Pr4334478416066269672t_unit ).
thf(func_def_1375,type,
bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat ).
thf(func_def_1376,type,
bot_bo7193250159860175667at_nat: set_Pr5564308138774400199at_nat ).
thf(func_def_1377,type,
bot_bo3195362268743713342unit_o: set_Pr5464989305201766866unit_o ).
thf(func_def_1378,type,
bot_bo2472676621365177558it_nat: set_Pr1763845938948868674it_nat ).
thf(func_def_1379,type,
bot_bo6659885642593197735at_nat: set_Pr3798168094891919931at_nat ).
thf(func_def_1380,type,
bot_bo1654022762305692595t_unit: set_Pr5094982260447487303t_unit ).
thf(func_def_1381,type,
bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_1382,type,
bot_bo4948859079157340979at_nat: set_Pr7459493094073627847at_nat ).
thf(func_def_1383,type,
bot_bo3957492148770167129t_unit: set_Product_unit ).
thf(func_def_1384,type,
bot_bot_set_rat: set_rat ).
thf(func_def_1385,type,
bot_bot_set_set_nat: set_set_nat ).
thf(func_def_1386,type,
bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat ).
thf(func_def_1387,type,
bot_bo1534825418459847827at_nat: set_se5479201105039950375at_nat ).
thf(func_def_1388,type,
bot_bot_set_char: set_char ).
thf(func_def_1389,type,
ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
thf(func_def_1390,type,
ord_less_int: int > int > $o ).
thf(func_def_1391,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_1392,type,
ord_less_rat: rat > rat > $o ).
thf(func_def_1393,type,
ord_le7522433683449569238eger_o: ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > $o ).
thf(func_def_1394,type,
ord_le6931201860925936491_num_o: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > $o ).
thf(func_def_1395,type,
ord_le4541714130423454556_num_o: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > $o ).
thf(func_def_1396,type,
ord_le8615040745438789472_int_o: ( ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ) > ( ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ) > $o ).
thf(func_def_1397,type,
ord_le2932013042137311317nt_o_o: ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > $o ).
thf(func_def_1398,type,
ord_le6141271677531915726eger_o: ( ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ) > ( ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ) > $o ).
thf(func_def_1399,type,
ord_le1714508135640884727_nat_o: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > $o ).
thf(func_def_1400,type,
ord_le2484784447047653514_int_o: ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > $o ).
thf(func_def_1401,type,
ord_le3602516367967493612eger_o: ( code_integer > code_integer > $o ) > ( code_integer > code_integer > $o ) > $o ).
thf(func_def_1402,type,
ord_le996066559646421213eger_o: ( int > code_integer > $o ) > ( int > code_integer > $o ) > $o ).
thf(func_def_1403,type,
ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(func_def_1404,type,
ord_le8236914709048111138_rat_o: ( int > rat > $o ) > ( int > rat > $o ) > $o ).
thf(func_def_1405,type,
ord_le7608100903186094441char_o: ( int > char > $o ) > ( int > char > $o ) > $o ).
thf(func_def_1406,type,
ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_1407,type,
ord_le3404735783095501756_num_o: ( nat > num > $o ) > ( nat > num > $o ) > $o ).
thf(func_def_1408,type,
ord_le1897120724991155070_rat_o: ( nat > rat > $o ) > ( nat > rat > $o ) > $o ).
thf(func_def_1409,type,
ord_le4878496333587278021char_o: ( nat > char > $o ) > ( nat > char > $o ) > $o ).
thf(func_def_1410,type,
ord_le6124364862034508274_num_o: ( num > num > $o ) > ( num > num > $o ) > $o ).
thf(func_def_1411,type,
ord_le129227817499904167_int_o: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_1412,type,
ord_le5604493270027003598_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_1413,type,
ord_le3222257882335906850_int_o: ( rat > int > $o ) > ( rat > int > $o ) > $o ).
thf(func_def_1414,type,
ord_le5467402850006352766_nat_o: ( rat > nat > $o ) > ( rat > nat > $o ) > $o ).
thf(func_def_1415,type,
ord_le4717968354871517046_rat_o: ( rat > rat > $o ) > ( rat > rat > $o ) > $o ).
thf(func_def_1416,type,
ord_le6546876390139131069char_o: ( rat > char > $o ) > ( rat > char > $o ) > $o ).
thf(func_def_1417,type,
ord_le3935385432712749774_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
thf(func_def_1418,type,
ord_le3072208448688395470_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).
thf(func_def_1419,type,
ord_le3396192186225775209_int_o: ( char > int > $o ) > ( char > int > $o ) > $o ).
thf(func_def_1420,type,
ord_le5641337153896221125_nat_o: ( char > nat > $o ) > ( char > nat > $o ) > $o ).
thf(func_def_1421,type,
ord_le4891902658761385405_rat_o: ( char > rat > $o ) > ( char > rat > $o ) > $o ).
thf(func_def_1422,type,
ord_le2540245887939449860char_o: ( char > char > $o ) > ( char > char > $o ) > $o ).
thf(func_def_1423,type,
ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
thf(func_def_1424,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_1425,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_1426,type,
ord_le3221252021190050221t_unit: product_unit > product_unit > $o ).
thf(func_def_1427,type,
ord_less_eq_rat: rat > rat > $o ).
thf(func_def_1428,type,
ord_le348599935723844335nteger: set_Co726186806682698383nteger > set_Co726186806682698383nteger > $o ).
thf(func_def_1429,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_1430,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(func_def_1431,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_1432,type,
ord_less_eq_set_num: set_num > set_num > $o ).
thf(func_def_1433,type,
ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_1434,type,
ord_le6472378536984071597_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(func_def_1435,type,
ord_le518195775913581980t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > $o ).
thf(func_def_1436,type,
ord_le5525191956872776187t_unit: set_Pr1133966238863718811t_unit > set_Pr1133966238863718811t_unit > $o ).
thf(func_def_1437,type,
ord_le2638047946463454698nteger: set_Pr8415741480598773322nteger > set_Pr8415741480598773322nteger > $o ).
thf(func_def_1438,type,
ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1439,type,
ord_le5333435103577920093nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_1440,type,
ord_le7519981659162375251_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > $o ).
thf(func_def_1441,type,
ord_le656430383953171549at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > $o ).
thf(func_def_1442,type,
ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1443,type,
ord_le8085105155179020875at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > $o ).
thf(func_def_1444,type,
ord_le1468274181084648008t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > $o ).
thf(func_def_1445,type,
ord_le5989899228261996553at_rat: set_Pr4105333604307423337at_rat > set_Pr4105333604307423337at_rat > $o ).
thf(func_def_1446,type,
ord_le5164908622851071819um_nat: set_Pr3280342998896498603um_nat > set_Pr3280342998896498603um_nat > $o ).
thf(func_def_1447,type,
ord_le880128212290418581um_num: set_Pr8218934625190621173um_num > set_Pr8218934625190621173um_num > $o ).
thf(func_def_1448,type,
ord_le4604737605482584818at_int: set_Pr49084382684228242at_int > set_Pr49084382684228242at_int > $o ).
thf(func_def_1449,type,
ord_le3000389064537975527at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1450,type,
ord_le3091953645718357095at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_1451,type,
ord_le8534741403851954546unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > $o ).
thf(func_def_1452,type,
ord_le8121013740822022818it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > $o ).
thf(func_def_1453,type,
ord_le8681960759543468507at_nat: set_Pr3798168094891919931at_nat > set_Pr3798168094891919931at_nat > $o ).
thf(func_def_1454,type,
ord_le930853871177014503t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_1455,type,
ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1456,type,
ord_le5997549366648089703at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_1457,type,
ord_le3507040750410214029t_unit: set_Product_unit > set_Product_unit > $o ).
thf(func_def_1458,type,
ord_less_eq_set_rat: set_rat > set_rat > $o ).
thf(func_def_1459,type,
ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
thf(func_def_1460,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1461,type,
ord_le2077887516847798113at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_1462,type,
ord_le7966958417815640519at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > $o ).
thf(func_def_1463,type,
ord_le513522071413781156et_rat: set_set_rat > set_set_rat > $o ).
thf(func_def_1464,type,
ord_less_eq_set_char: set_char > set_char > $o ).
thf(func_def_1465,type,
order_3677659787690696076nt_int: ( int > int ) > $o ).
thf(func_def_1466,type,
order_3680150258199746352nt_nat: ( int > nat ) > $o ).
thf(func_def_1467,type,
order_2678306075789641520at_int: ( nat > int ) > $o ).
thf(func_def_1468,type,
order_2680796546298691796at_nat: ( nat > nat ) > $o ).
thf(func_def_1469,type,
order_2045666486212196060at_rat: ( nat > rat ) > $o ).
thf(func_def_1470,type,
order_mono_o_int: ( $o > int ) > $o ).
thf(func_def_1471,type,
order_mono_o_nat: ( $o > nat ) > $o ).
thf(func_def_1472,type,
order_7782127260464396005t_unit: ( $o > product_unit ) > $o ).
thf(func_def_1473,type,
order_mono_int_int: ( int > int ) > $o ).
thf(func_def_1474,type,
order_mono_int_nat: ( int > nat ) > $o ).
thf(func_def_1475,type,
order_2843698775922903023t_unit: ( int > product_unit ) > $o ).
thf(func_def_1476,type,
order_mono_nat_int: ( nat > int ) > $o ).
thf(func_def_1477,type,
order_mono_nat_nat: ( nat > nat ) > $o ).
thf(func_def_1478,type,
order_5727276828720722763t_unit: ( nat > product_unit ) > $o ).
thf(func_def_1479,type,
order_mono_nat_rat: ( nat > rat ) > $o ).
thf(func_def_1480,type,
order_7093624213399680841it_int: ( product_unit > int ) > $o ).
thf(func_def_1481,type,
order_7096114683908731117it_nat: ( product_unit > nat ) > $o ).
thf(func_def_1482,type,
order_4454465170704313136t_unit: ( product_unit > product_unit ) > $o ).
thf(func_def_1483,type,
order_509894322932672675et_nat: ( product_unit > set_nat ) > $o ).
thf(func_def_1484,type,
order_7928700340835332885t_unit: ( set_nat > product_unit ) > $o ).
thf(func_def_1485,type,
order_1005506198798982270et_nat: ( set_nat > set_nat ) > $o ).
thf(func_def_1486,type,
order_6722886889984875411nt_int: ( int > int ) > $o ).
thf(func_def_1487,type,
order_6725377360493925687nt_nat: ( int > nat ) > $o ).
thf(func_def_1488,type,
order_6090247300407429951nt_rat: ( int > rat ) > $o ).
thf(func_def_1489,type,
order_5723533178083820855at_int: ( nat > int ) > $o ).
thf(func_def_1490,type,
order_5726023648592871131at_nat: ( nat > nat ) > $o ).
thf(func_def_1491,type,
order_5090893588506375395at_rat: ( nat > rat ) > $o ).
thf(func_def_1492,type,
order_5406978534148954943at_int: ( rat > int ) > $o ).
thf(func_def_1493,type,
order_5409469004658005219at_nat: ( rat > nat ) > $o ).
thf(func_def_1494,type,
order_4774338944571509483at_rat: ( rat > rat ) > $o ).
thf(func_def_1495,type,
top_top_int_int_o: int > int > $o ).
thf(func_def_1496,type,
top_top_nat_nat_o: nat > nat > $o ).
thf(func_def_1497,type,
top_top_nat_num_o: nat > num > $o ).
thf(func_def_1498,type,
top_to8903224817164384382_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1499,type,
top_to1326704617074743934_nat_o: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1500,type,
top_top_Product_unit: product_unit ).
thf(func_def_1501,type,
top_to3639204395728341691nteger: set_Co4375521073081744395nteger ).
thf(func_def_1502,type,
top_to3804862627464599871nteger: set_Co726186806682698383nteger ).
thf(func_def_1503,type,
top_top_set_int_int: set_int_int ).
thf(func_def_1504,type,
top_top_set_int_nat: set_int_nat ).
thf(func_def_1505,type,
top_top_set_int_rat: set_int_rat ).
thf(func_def_1506,type,
top_top_set_int_char: set_int_char ).
thf(func_def_1507,type,
top_top_set_nat_o: set_nat_o ).
thf(func_def_1508,type,
top_top_set_nat_nat: set_nat_nat ).
thf(func_def_1509,type,
top_top_set_nat_rat: set_nat_rat ).
thf(func_def_1510,type,
top_top_set_nat_char: set_nat_char ).
thf(func_def_1511,type,
top_top_set_rat_nat: set_rat_nat ).
thf(func_def_1512,type,
top_top_set_rat_rat: set_rat_rat ).
thf(func_def_1513,type,
top_top_set_rat_char: set_rat_char ).
thf(func_def_1514,type,
top_top_set_char_nat: set_char_nat ).
thf(func_def_1515,type,
top_top_set_char_rat: set_char_rat ).
thf(func_def_1516,type,
top_to8079350907815874599r_char: set_char_char ).
thf(func_def_1517,type,
top_top_set_o: set_o ).
thf(func_def_1518,type,
top_to4645266643341252675nteger: set_Code_integer ).
thf(func_def_1519,type,
top_to3956321331435058429t_unit: set_he8644174446132254637t_unit ).
thf(func_def_1520,type,
top_top_set_ref_a: set_ref_a ).
thf(func_def_1521,type,
top_top_set_int: set_int ).
thf(func_def_1522,type,
top_top_set_list_nat: set_list_nat ).
thf(func_def_1523,type,
top_top_set_nat: set_nat ).
thf(func_def_1524,type,
top_top_set_num: set_num ).
thf(func_def_1525,type,
top_to2363841527343591755nteger: set_Pr4811707699266497531nteger ).
thf(func_def_1526,type,
top_to2503719809363509323t_unit: set_Pr1133966238863718811t_unit ).
thf(func_def_1527,type,
top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int ).
thf(func_def_1528,type,
top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1529,type,
top_to385025497714130939at_num: set_Pr6200539531224447659at_num ).
thf(func_def_1530,type,
top_to7513191607651882425at_rat: set_Pr4105333604307423337at_rat ).
thf(func_def_1531,type,
top_to7107842681480589234t_char: set_Pr2926629348867340898t_char ).
thf(func_def_1532,type,
top_to7002410609688830997at_int: set_Pr3594552606344371909at_int ).
thf(func_def_1533,type,
top_to269121717765781945at_nat: set_Pr6084635751276098665at_nat ).
thf(func_def_1534,type,
top_to3112507417142880193at_rat: set_Pr8928021450653196913at_rat ).
thf(func_def_1535,type,
top_to3221206985699244474t_char: set_Pr8263365689940771946t_char ).
thf(func_def_1536,type,
top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_1537,type,
top_to5281548843312042519at_nat: set_Pr7459493094073627847at_nat ).
thf(func_def_1538,type,
top_to3104204703268025230ar_int: set_Pr8146363407509552702ar_int ).
thf(func_def_1539,type,
top_to5594287848199751986ar_nat: set_Pr1413074515586503650ar_nat ).
thf(func_def_1540,type,
top_to8437673547576850234ar_rat: set_Pr4256460214963601898ar_rat ).
thf(func_def_1541,type,
top_to1235241553633177651r_char: set_Pr3309569728657787619r_char ).
thf(func_def_1542,type,
top_to1996260823553986621t_unit: set_Product_unit ).
thf(func_def_1543,type,
top_top_set_rat: set_rat ).
thf(func_def_1544,type,
top_top_set_char: set_char ).
thf(func_def_1545,type,
top_to6661820994512907621at_nat: set_Sum_sum_nat_nat ).
thf(func_def_1546,type,
eval_Product_unit: pred_Product_unit > product_unit > $o ).
thf(func_def_1547,type,
single_Product_unit: product_unit > pred_Product_unit ).
thf(func_def_1548,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(func_def_1549,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(func_def_1550,type,
product_Pair_o_nat: $o > nat > product_prod_o_nat ).
thf(func_def_1551,type,
produc3901946521647900940t_unit: $o > product_unit > produc3788275437394581276t_unit ).
thf(func_def_1552,type,
produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
thf(func_def_1553,type,
produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_1554,type,
produc8256076736985659095t_unit: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > produc8126358835630522215t_unit ).
thf(func_def_1555,type,
produc2564672488694626579_ref_a: heap_e7401611519738050253t_unit > ref_a > produc1799199577659733785_ref_a ).
thf(func_def_1556,type,
produc6544324848051098391t_unit: ref_a > heap_e7401611519738050253t_unit > produc7812382424243267045t_unit ).
thf(func_def_1557,type,
produc1340070678782110931_ref_a: ref_a > ref_a > produc5288414631154139675_ref_a ).
thf(func_def_1558,type,
product_Pair_int_o: int > $o > product_prod_int_o ).
thf(func_def_1559,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(func_def_1560,type,
product_Pair_int_nat: int > nat > product_prod_int_nat ).
thf(func_def_1561,type,
produc550872421827702152t_unit: int > product_unit > produc6865911496949736918t_unit ).
thf(func_def_1562,type,
product_Pair_int_rat: int > rat > product_prod_int_rat ).
thf(func_def_1563,type,
product_Pair_nat_o: nat > $o > product_prod_nat_o ).
thf(func_def_1564,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(func_def_1565,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_1566,type,
product_Pair_nat_num: nat > num > product_prod_nat_num ).
thf(func_def_1567,type,
produc3434450474625521892t_unit: nat > product_unit > produc526117512892780850t_unit ).
thf(func_def_1568,type,
product_Pair_nat_rat: nat > rat > product_prod_nat_rat ).
thf(func_def_1569,type,
product_Pair_num_nat: num > nat > product_prod_num_nat ).
thf(func_def_1570,type,
product_Pair_num_num: num > num > product_prod_num_num ).
thf(func_def_1571,type,
produc5069803637994805237atural: pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural ).
thf(func_def_1572,type,
produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int ).
thf(func_def_1573,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(func_def_1574,type,
produc4662710985925991255at_nat: produc859450856879609959at_nat > produc859450856879609959at_nat > produc349518998152878311at_nat ).
thf(func_def_1575,type,
produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat ).
thf(func_def_1576,type,
produc8487917018914037602unit_o: product_unit > $o > produc7485711547916492274unit_o ).
thf(func_def_1577,type,
produc4803288329813530246it_nat: product_unit > nat > produc600557818389255820it_nat ).
thf(func_def_1578,type,
produc5692694829384537815t_unit: product_unit > product_unit > produc8459935480633519975t_unit ).
thf(func_def_1579,type,
produc4168158269727034510it_rat: product_unit > rat > produc6315701296850634900it_rat ).
thf(func_def_1580,type,
product_Pair_rat_int: rat > int > product_prod_rat_int ).
thf(func_def_1581,type,
product_Pair_rat_nat: rat > nat > product_prod_rat_nat ).
thf(func_def_1582,type,
product_Pair_rat_rat: rat > rat > product_prod_rat_rat ).
thf(func_def_1583,type,
produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
thf(func_def_1584,type,
produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).
thf(func_def_1585,type,
product_Sigma_o_o: set_o > ( $o > set_o ) > set_Product_prod_o_o ).
thf(func_def_1586,type,
product_Sigma_o_int: set_o > ( $o > set_int ) > set_Pr8834758594704517033_o_int ).
thf(func_def_1587,type,
product_Sigma_o_nat: set_o > ( $o > set_nat ) > set_Pr2101469702781467981_o_nat ).
thf(func_def_1588,type,
produc411009820408249917t_unit: set_o > ( $o > set_Product_unit ) > set_Pr6671815714118170108t_unit ).
thf(func_def_1589,type,
produc5882431272649516420nteger: set_Code_integer > ( code_integer > set_Code_integer ) > set_Pr4811707699266497531nteger ).
thf(func_def_1590,type,
produc3946373962484743846t_unit: set_ref_a > ( ref_a > set_he8644174446132254637t_unit ) > set_Pr1133966238863718811t_unit ).
thf(func_def_1591,type,
product_Sigma_int_o: set_int > ( int > set_o ) > set_Pr903927857289325719_int_o ).
thf(func_def_1592,type,
produc1453890548195736866nt_int: set_int > ( int > set_int ) > set_Pr958786334691620121nt_int ).
thf(func_def_1593,type,
produc1456381018704787142nt_nat: set_int > ( int > set_nat ) > set_Pr3448869479623346877nt_nat ).
thf(func_def_1594,type,
produc2622961094310184599t_unit: set_int > ( int > set_Product_unit ) > set_Pr5889264611543340172t_unit ).
thf(func_def_1595,type,
produc821250958618291406nt_rat: set_int > ( int > set_rat ) > set_Pr6292255179000445125nt_rat ).
thf(func_def_1596,type,
product_Sigma_nat_o: set_nat > ( nat > set_o ) > set_Pr3149072824959771635_nat_o ).
thf(func_def_1597,type,
produc454536836294682310at_int: set_nat > ( nat > set_int ) > set_Pr7995236796853374141at_int ).
thf(func_def_1598,type,
produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1599,type,
produc6237731129814287028at_num: set_nat > ( nat > set_num ) > set_Pr6200539531224447659at_num ).
thf(func_def_1600,type,
produc7854212285064481439nt_int: set_nat > ( nat > set_Pr958786334691620121nt_int ) > set_Pr6123067485828015636nt_int ).
thf(func_def_1601,type,
produc1809337555817847783at_nat: set_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr7717912310451564380at_nat ).
thf(func_def_1602,type,
produc5506539147108004339t_unit: set_nat > ( nat > set_Product_unit ) > set_Pr4334478416066269672t_unit ).
thf(func_def_1603,type,
produc9045269283572012658at_rat: set_nat > ( nat > set_rat ) > set_Pr4105333604307423337at_rat ).
thf(func_def_1604,type,
produc4754187946284079723t_char: set_nat > ( nat > set_char ) > set_Pr2926629348867340898t_char ).
thf(func_def_1605,type,
produc7810729746965977780um_nat: set_num > ( num > set_nat ) > set_Pr3280342998896498603um_nat ).
thf(func_def_1606,type,
produc1007865297704999105nt_nat: set_Pr958786334691620121nt_int > ( product_prod_int_int > set_nat ) > set_Pr2543308735921124078nt_nat ).
thf(func_def_1607,type,
produc245848125267896712nt_int: set_Pr958786334691620121nt_int > ( product_prod_int_int > set_Pr958786334691620121nt_int ) > set_Pr2560585780119916871nt_int ).
thf(func_def_1608,type,
produc3424345432876038864at_nat: set_Pr958786334691620121nt_int > ( product_prod_int_int > set_Pr1261947904930325089at_nat ) > set_Pr4155430604743465615at_nat ).
thf(func_def_1609,type,
produc203973861852599583_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_o ) > set_Pr6558897299634722526_nat_o ).
thf(func_def_1610,type,
produc7672662199629908489at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_Pr2539167527615954998at_nat ).
thf(func_def_1611,type,
produc8806266479013559872nt_int: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_Pr958786334691620121nt_int ) > set_Pr7098892610798258687nt_int ).
thf(func_def_1612,type,
produc2761391749766926216at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_Pr1261947904930325089at_nat ) > set_Pr8693737435421807431at_nat ).
thf(func_def_1613,type,
produc4441300235185154312at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat ) > set_Pr5564308138774400199at_nat ).
thf(func_def_1614,type,
produc4996980317674386579unit_o: set_Product_unit > ( product_unit > set_o ) > set_Pr5464989305201766866unit_o ).
thf(func_def_1615,type,
produc6875377002296012693it_nat: set_Product_unit > ( product_unit > set_nat ) > set_Pr1763845938948868674it_nat ).
thf(func_def_1616,type,
produc3904733337175673596at_nat: set_Product_unit > ( product_unit > set_Pr1261947904930325089at_nat ) > set_Pr3798168094891919931at_nat ).
thf(func_def_1617,type,
produc6121607364029222536t_unit: set_Product_unit > ( product_unit > set_Product_unit ) > set_Pr5094982260447487303t_unit ).
thf(func_def_1618,type,
produc6240246942209516957it_rat: set_Product_unit > ( product_unit > set_rat ) > set_Pr4607231638325966922it_rat ).
thf(func_def_1619,type,
produc137982192359816398at_int: set_rat > ( rat > set_int ) > set_Pr3594552606344371909at_int ).
thf(func_def_1620,type,
produc140472662868866674at_nat: set_rat > ( rat > set_nat ) > set_Pr6084635751276098665at_nat ).
thf(func_def_1621,type,
produc8728714639637146746at_rat: set_rat > ( rat > set_rat ) > set_Pr8928021450653196913at_rat ).
thf(func_def_1622,type,
produc1427039474575272051t_char: set_rat > ( rat > set_char ) > set_Pr8263365689940771946t_char ).
thf(func_def_1623,type,
produc7726050920695093128at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_1624,type,
produc6258361011560675592at_nat: set_se5479201105039950375at_nat > ( set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ) > set_Pr7459493094073627847at_nat ).
thf(func_def_1625,type,
produc1836876251250453959ar_int: set_char > ( char > set_int ) > set_Pr8146363407509552702ar_int ).
thf(func_def_1626,type,
produc1839366721759504235ar_nat: set_char > ( char > set_nat ) > set_Pr1413074515586503650ar_nat ).
thf(func_def_1627,type,
produc1204236661673008499ar_rat: set_char > ( char > set_rat ) > set_Pr4256460214963601898ar_rat ).
thf(func_def_1628,type,
produc2936396906406871148r_char: set_char > ( char > set_char ) > set_Pr3309569728657787619r_char ).
thf(func_def_1629,type,
product_Unity: product_unit ).
thf(func_def_1630,type,
produc3195571438000033749nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1631,type,
produc4508741384315284437t_unit: ( ref_a > ref_a ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
thf(func_def_1632,type,
produc5845103964736263686t_unit: ( ref_a > int ) > produc7812382424243267045t_unit > produc3969062480670737046t_unit ).
thf(func_def_1633,type,
produc6143945040009431475nt_int: ( ref_a > int ) > produc8483956148555600810_a_int > product_prod_int_int ).
thf(func_def_1634,type,
produc6942186945380262242t_unit: ( ref_a > nat ) > produc7812382424243267045t_unit > produc5066145461314735602t_unit ).
thf(func_def_1635,type,
produc5147081798617427195at_nat: ( ref_a > nat ) > produc3438435131210021710_a_nat > product_prod_nat_nat ).
thf(func_def_1636,type,
produc1704413584773205829at_num: ( ref_a > nat ) > produc4146679068158859416_a_num > product_prod_nat_num ).
thf(func_def_1637,type,
produc5323809043756447493t_unit: ( ref_a > set_Pr1261947904930325089at_nat ) > produc7812382424243267045t_unit > produc3629471303718939987t_unit ).
thf(func_def_1638,type,
produc4016808307611786905at_nat: ( ref_a > set_Pr1261947904930325089at_nat ) > produc5561445381605014009at_nat > produc3843707927480180839at_nat ).
thf(func_def_1639,type,
produc5988837738927868575t_unit: ( ref_a > set_Pr4329608150637261639at_nat ) > produc7812382424243267045t_unit > produc2296667697112141421t_unit ).
thf(func_def_1640,type,
produc2316621926130398489at_nat: ( ref_a > set_Pr4329608150637261639at_nat ) > produc4041253808165279839at_nat > produc1319942482725812455at_nat ).
thf(func_def_1641,type,
produc2355237562570658114nt_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1642,type,
produc986720760941809198at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1643,type,
produc6767424583952363640at_num: ( nat > nat ) > product_prod_nat_num > product_prod_nat_num ).
thf(func_def_1644,type,
produc5380969780118646373at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_1645,type,
produc6529295065807390923at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > produc1319942482725812455at_nat > produc1319942482725812455at_nat ).
thf(func_def_1646,type,
produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1647,type,
produc3038839249364385243_ref_a: ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
thf(func_def_1648,type,
produc3558794870892339738_ref_a: ( heap_e7401611519738050253t_unit > int ) > produc7812382424243267045t_unit > produc8483956148555600810_a_int ).
thf(func_def_1649,type,
produc6768910348387636265nt_int: ( heap_e7401611519738050253t_unit > int ) > produc3969062480670737046t_unit > product_prod_int_int ).
thf(func_def_1650,type,
produc8366372614399963582_ref_a: ( heap_e7401611519738050253t_unit > nat ) > produc7812382424243267045t_unit > produc3438435131210021710_a_nat ).
thf(func_def_1651,type,
produc5772047106995631985at_nat: ( heap_e7401611519738050253t_unit > nat ) > produc5066145461314735602t_unit > product_prod_nat_nat ).
thf(func_def_1652,type,
produc7633249859560231688_ref_a: ( heap_e7401611519738050253t_unit > num ) > produc7812382424243267045t_unit > produc4146679068158859416_a_num ).
thf(func_def_1653,type,
produc3902377510303101371um_nat: ( heap_e7401611519738050253t_unit > num ) > produc5066145461314735602t_unit > product_prod_nat_num ).
thf(func_def_1654,type,
produc2928627021203296111_ref_a: ( heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat ) > produc7812382424243267045t_unit > produc5561445381605014009at_nat ).
thf(func_def_1655,type,
produc8705118745468743695at_nat: ( heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat ) > produc3629471303718939987t_unit > produc3843707927480180839at_nat ).
thf(func_def_1656,type,
produc5080965012319039829_ref_a: ( heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat ) > produc7812382424243267045t_unit > produc4041253808165279839at_nat ).
thf(func_def_1657,type,
produc5990651871820846223at_nat: ( heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat ) > produc2296667697112141421t_unit > produc1319942482725812455at_nat ).
thf(func_def_1658,type,
produc4463282112584876420nt_int: ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1659,type,
produc3094765310956027504at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1660,type,
produc1225095714263496890um_nat: ( nat > num ) > product_prod_nat_nat > product_prod_nat_num ).
thf(func_def_1661,type,
produc1035573138926686394at_nat: ( num > nat ) > product_prod_nat_num > product_prod_nat_nat ).
thf(func_def_1662,type,
produc8389275579088931588um_nat: ( num > num ) > product_prod_nat_num > product_prod_nat_num ).
thf(func_def_1663,type,
produc6468969725218530979at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_1664,type,
produc8057050257526108681at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > produc1319942482725812455at_nat > produc1319942482725812455at_nat ).
thf(func_def_1665,type,
produc175634133007206835_int_o: ( product_prod_int_int > $o ) > int > int > $o ).
thf(func_def_1666,type,
produc1016772743285680337nt_int: ( product_prod_int_int > int ) > int > int > int ).
thf(func_def_1667,type,
produc8249235968001453780nt_int: ( product_prod_int_int > product_prod_int_int ) > int > int > product_prod_int_int ).
thf(func_def_1668,type,
produc3704529784387675049_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat > nat > product_prod_nat_nat > $o ).
thf(func_def_1669,type,
produc3610074571335452306at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > nat > nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1670,type,
produc1310100445399344235_nat_o: ( product_prod_nat_nat > $o ) > nat > nat > $o ).
thf(func_def_1671,type,
produc156083480235303841_num_o: ( product_prod_nat_num > $o ) > nat > num > $o ).
thf(func_def_1672,type,
produc7820828192191229133_nat_o: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1673,type,
produc447603880154497357_nat_o: ( produc1319942482725812455at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1674,type,
produc8005341501107743676_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(func_def_1675,type,
produc7926200574084438792nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_1676,type,
produc297006045350968285nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1677,type,
produc4780622933104268256_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1678,type,
produc1854806715440696265at_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_1679,type,
produc4724772261320961782nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc723880050079548563nteger > produc101387210554329899nteger ).
thf(func_def_1680,type,
produc1928436952130685430_o_o_o: ( $o > $o ) > ( $o > $o ) > product_prod_o_o > product_prod_o_o ).
thf(func_def_1681,type,
produc8070579729948654068nt_nat: ( $o > $o ) > ( int > nat ) > product_prod_o_int > product_prod_o_nat ).
thf(func_def_1682,type,
produc7071226018047599512at_nat: ( $o > $o ) > ( nat > nat ) > product_prod_o_nat > product_prod_o_nat ).
thf(func_def_1683,type,
produc3628557804203378146at_num: ( $o > $o ) > ( nat > num ) > product_prod_o_nat > product_prod_o_num ).
thf(func_def_1684,type,
produc9141321880750005618at_o_o: ( $o > nat ) > ( $o > $o ) > product_prod_o_o > product_prod_nat_o ).
thf(func_def_1685,type,
produc6587185857518356756at_nat: ( $o > nat ) > ( nat > nat ) > product_prod_o_nat > product_prod_nat_nat ).
thf(func_def_1686,type,
produc4527993685489015646at_nat: ( $o > num ) > ( nat > nat ) > product_prod_o_nat > product_prod_num_nat ).
thf(func_def_1687,type,
produc1802105962441033582nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1688,type,
produc3456481717235892722t_unit: ( ref_a > ref_a ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
thf(func_def_1689,type,
produc6036585564866528938nt_int: ( int > int ) > ( int > int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1690,type,
produc5039722323474524658at_nat: ( int > int ) > ( nat > nat ) > product_prod_int_nat > product_prod_int_nat ).
thf(func_def_1691,type,
produc4404592263388028922at_rat: ( int > int ) > ( nat > rat ) > product_prod_int_nat > product_prod_int_rat ).
thf(func_def_1692,type,
produc5664932004629684302nt_int: ( int > nat ) > ( int > int ) > product_prod_int_int > product_prod_nat_int ).
thf(func_def_1693,type,
produc5667422475138734578nt_nat: ( int > nat ) > ( int > nat ) > product_prod_int_int > product_prod_nat_nat ).
thf(func_def_1694,type,
produc2224754261294513212nt_num: ( int > nat ) > ( int > num ) > product_prod_int_int > product_prod_nat_num ).
thf(func_def_1695,type,
produc8298419091753553490_nat_o: ( int > nat ) > ( nat > $o ) > product_prod_int_nat > product_prod_nat_o ).
thf(func_def_1696,type,
produc4665578292728629746at_int: ( int > nat ) > ( nat > int ) > product_prod_int_nat > product_prod_nat_int ).
thf(func_def_1697,type,
produc4668068763237680022at_nat: ( int > nat ) > ( nat > nat ) > product_prod_int_nat > product_prod_nat_nat ).
thf(func_def_1698,type,
produc1225400549393458656at_num: ( int > nat ) > ( nat > num ) > product_prod_int_nat > product_prod_nat_num ).
thf(func_def_1699,type,
produc4032938703151184286at_rat: ( int > nat ) > ( nat > rat ) > product_prod_int_nat > product_prod_nat_rat ).
thf(func_def_1700,type,
produc3608230303109393468nt_nat: ( int > num ) > ( int > nat ) > product_prod_int_int > product_prod_num_nat ).
thf(func_def_1701,type,
produc165562089265172102nt_num: ( int > num ) > ( int > num ) > product_prod_int_int > product_prod_num_num ).
thf(func_def_1702,type,
produc9074608839065728392_nat_o: ( int > num ) > ( nat > $o ) > product_prod_int_nat > product_prod_num_o ).
thf(func_def_1703,type,
produc2608876591208338912at_nat: ( int > num ) > ( nat > nat ) > product_prod_int_nat > product_prod_num_nat ).
thf(func_def_1704,type,
produc8248099538878400170nt_int: ( nat > $o ) > ( int > int ) > product_prod_nat_int > product_prod_o_int ).
thf(func_def_1705,type,
produc8250590009387450446nt_nat: ( nat > $o ) > ( int > nat ) > product_prod_nat_int > product_prod_o_nat ).
thf(func_def_1706,type,
produc4807921795543229080nt_num: ( nat > $o ) > ( int > num ) > product_prod_nat_int > product_prod_o_num ).
thf(func_def_1707,type,
produc6957950696844810486_nat_o: ( nat > $o ) > ( nat > $o ) > product_prod_nat_nat > product_prod_o_o ).
thf(func_def_1708,type,
produc7251236297486395890at_nat: ( nat > $o ) > ( nat > nat ) > product_prod_nat_nat > product_prod_o_nat ).
thf(func_def_1709,type,
produc8346403496959479886nt_int: ( nat > int ) > ( int > int ) > product_prod_nat_int > product_prod_int_int ).
thf(func_def_1710,type,
produc8348893967468530162nt_nat: ( nat > int ) > ( int > nat ) > product_prod_nat_int > product_prod_int_nat ).
thf(func_def_1711,type,
produc7347049785058425330at_int: ( nat > int ) > ( nat > int ) > product_prod_nat_nat > product_prod_int_int ).
thf(func_def_1712,type,
produc5477380188365894716um_int: ( nat > int ) > ( num > int ) > product_prod_nat_num > product_prod_int_int ).
thf(func_def_1713,type,
produc2001155298098703512at_o_o: ( nat > nat ) > ( $o > $o ) > product_prod_nat_o > product_prod_nat_o ).
thf(func_def_1714,type,
produc7974749936722635250nt_int: ( nat > nat ) > ( int > int ) > product_prod_nat_int > product_prod_nat_int ).
thf(func_def_1715,type,
produc7977240407231685526nt_nat: ( nat > nat ) > ( int > nat ) > product_prod_nat_int > product_prod_nat_nat ).
thf(func_def_1716,type,
produc4534572193387464160nt_num: ( nat > nat ) > ( int > num ) > product_prod_nat_int > product_prod_nat_num ).
thf(func_def_1717,type,
produc4787215299218314158_nat_o: ( nat > nat ) > ( nat > $o ) > product_prod_nat_nat > product_prod_nat_o ).
thf(func_def_1718,type,
produc6977886695330630970at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1719,type,
produc3535218481486409604at_num: ( nat > nat ) > ( nat > num ) > product_prod_nat_nat > product_prod_nat_num ).
thf(func_def_1720,type,
produc5108217098638100356um_nat: ( nat > nat ) > ( num > nat ) > product_prod_nat_num > product_prod_nat_nat ).
thf(func_def_1721,type,
produc1665548884793878990um_num: ( nat > nat ) > ( num > num ) > product_prod_nat_num > product_prod_nat_num ).
thf(func_def_1722,type,
produc3264868786340801506um_o_o: ( nat > num ) > ( $o > $o ) > product_prod_nat_o > product_prod_num_o ).
thf(func_def_1723,type,
produc5918048235202344416nt_nat: ( nat > num ) > ( int > nat ) > product_prod_nat_int > product_prod_num_nat ).
thf(func_def_1724,type,
produc4918694523301289860at_nat: ( nat > num ) > ( nat > nat ) > product_prod_nat_nat > product_prod_num_nat ).
thf(func_def_1725,type,
produc1476026309457068494at_num: ( nat > num ) > ( nat > num ) > product_prod_nat_nat > product_prod_num_num ).
thf(func_def_1726,type,
produc8746822746284154874nt_int: ( nat > rat ) > ( int > int ) > product_prod_nat_int > product_prod_rat_int ).
thf(func_def_1727,type,
produc8749313216793205150nt_nat: ( nat > rat ) > ( int > nat ) > product_prod_nat_int > product_prod_rat_nat ).
thf(func_def_1728,type,
produc170006858110003436at_nat: ( nat > set_Pr1261947904930325089at_nat ) > ( num > set_Pr1261947904930325089at_nat ) > product_prod_nat_num > produc3843707927480180839at_nat ).
thf(func_def_1729,type,
produc8319293927732033832at_nat: ( num > $o ) > ( nat > nat ) > product_prod_num_nat > product_prod_o_nat ).
thf(func_def_1730,type,
produc4208724500416182148at_nat: ( num > nat ) > ( nat > nat ) > product_prod_num_nat > product_prod_nat_nat ).
thf(func_def_1731,type,
produc2149532328386841038at_nat: ( num > num ) > ( nat > nat ) > product_prod_num_nat > product_prod_num_nat ).
thf(func_def_1732,type,
produc3932168101365401472at_num: ( set_Pr1261947904930325089at_nat > nat ) > ( set_Pr1261947904930325089at_nat > num ) > produc3843707927480180839at_nat > product_prod_nat_num ).
thf(func_def_1733,type,
produc1547070076189439812at_rat: ( char > char ) > ( nat > rat ) > produc3922234789054302210ar_nat > produc414006230660905482ar_rat ).
thf(func_def_1734,type,
produc8759894717825771837t_char: ( char > char ) > ( nat > char ) > produc3922234789054302210ar_nat > produc143505574896075907r_char ).
thf(func_def_1735,type,
produc1863155021832019360at_int: ( char > char ) > ( rat > int ) > produc414006230660905482ar_rat > produc8967755806399881310ar_int ).
thf(func_def_1736,type,
produc1865645492341069636at_nat: ( char > char ) > ( rat > nat ) > produc414006230660905482ar_rat > produc3922234789054302210ar_nat ).
thf(func_def_1737,type,
produc1230515432254573900at_rat: ( char > char ) > ( rat > rat ) > produc414006230660905482ar_rat > produc414006230660905482ar_rat ).
thf(func_def_1738,type,
produc5432746246116964165t_char: ( char > char ) > ( rat > char ) > produc414006230660905482ar_rat > produc143505574896075907r_char ).
thf(func_def_1739,type,
produc5842583022792146073ar_int: ( char > char ) > ( char > int ) > produc143505574896075907r_char > produc8967755806399881310ar_int ).
thf(func_def_1740,type,
produc5845073493301196349ar_nat: ( char > char ) > ( char > nat ) > produc143505574896075907r_char > produc3922234789054302210ar_nat ).
thf(func_def_1741,type,
produc5209943433214700613ar_rat: ( char > char ) > ( char > rat ) > produc143505574896075907r_char > produc414006230660905482ar_rat ).
thf(func_def_1742,type,
produc7830753070125841726r_char: ( char > char ) > ( char > char ) > produc143505574896075907r_char > produc143505574896075907r_char ).
thf(func_def_1743,type,
produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
thf(func_def_1744,type,
produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
thf(func_def_1745,type,
produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
thf(func_def_1746,type,
produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
thf(func_def_1747,type,
produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1748,type,
produc4281629032016041417nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc3346328345660746739nteger > produc8923325533196201883nteger ).
thf(func_def_1749,type,
produc4426278547552487717t_unit: ( heap_e7401611519738050253t_unit > ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > produc7812382424243267045t_unit ).
thf(func_def_1750,type,
produc4924168586796184916unit_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > $o ).
thf(func_def_1751,type,
produc2552614499379209865t_unit: ( ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1752,type,
produc4846201513286513633_ref_a: ( ref_a > heap_e7401611519738050253t_unit > ref_a ) > produc7812382424243267045t_unit > ref_a ).
thf(func_def_1753,type,
produc2058451029528183389_ref_a: ( ref_a > heap_e7401611519738050253t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > produc1799199577659733785_ref_a ).
thf(func_def_1754,type,
produc540600059291021473eger_o: ( int > code_integer > $o ) > produc2963269191615333738nteger > $o ).
thf(func_def_1755,type,
produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(func_def_1756,type,
produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_1757,type,
produc8213879946458358998nt_nat: ( int > int > nat ) > product_prod_int_int > nat ).
thf(func_def_1758,type,
produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1759,type,
produc8423408460612925143nt_nat: ( int > int > product_prod_int_nat ) > product_prod_int_int > product_prod_int_nat ).
thf(func_def_1760,type,
produc3246203729202673879at_int: ( int > int > product_prod_nat_int ) > product_prod_int_int > product_prod_nat_int ).
thf(func_def_1761,type,
produc4257766111578684402_set_o: ( int > int > set_o ) > product_prod_int_int > set_o ).
thf(func_def_1762,type,
produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
thf(func_def_1763,type,
produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
thf(func_def_1764,type,
produc5385566376148791347nt_nat: ( int > nat > product_prod_int_nat ) > product_prod_int_nat > product_prod_int_nat ).
thf(func_def_1765,type,
produc1877337817755394619nt_rat: ( int > nat > product_prod_int_rat ) > product_prod_int_nat > product_prod_int_rat ).
thf(func_def_1766,type,
produc208361644738540083at_int: ( int > nat > product_prod_nat_int ) > product_prod_int_nat > product_prod_nat_int ).
thf(func_def_1767,type,
produc877984105854340063at_rat: ( int > nat > product_prod_nat_rat ) > product_prod_int_nat > product_prod_nat_rat ).
thf(func_def_1768,type,
produc6663371796859813939nt_nat: ( nat > int > product_prod_int_nat ) > product_prod_nat_int > product_prod_int_nat ).
thf(func_def_1769,type,
produc1486167065449562675at_int: ( nat > int > product_prod_nat_int ) > product_prod_nat_int > product_prod_nat_int ).
thf(func_def_1770,type,
produc1169612421514696763at_int: ( nat > int > product_prod_rat_int ) > product_prod_nat_int > product_prod_rat_int ).
thf(func_def_1771,type,
produc5347463441023893471at_nat: ( nat > int > product_prod_rat_nat ) > product_prod_nat_int > product_prod_rat_nat ).
thf(func_def_1772,type,
produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1773,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_1774,type,
produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1775,type,
produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
thf(func_def_1776,type,
produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
thf(func_def_1777,type,
produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_1778,type,
produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1779,type,
produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
thf(func_def_1780,type,
produc59986286002894506_set_o: ( nat > nat > set_o ) > product_prod_nat_nat > set_o ).
thf(func_def_1781,type,
produc2011625207790711856et_int: ( nat > nat > set_int ) > product_prod_nat_nat > set_int ).
thf(func_def_1782,type,
produc6189476227299908564et_nat: ( nat > nat > set_nat ) > product_prod_nat_nat > set_nat ).
thf(func_def_1783,type,
produc8197505143624133779at_nat: ( nat > nat > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1784,type,
produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
thf(func_def_1785,type,
produc4970712607118878916um_int: ( nat > num > int ) > product_prod_nat_num > int ).
thf(func_def_1786,type,
produc4973203077627929192um_nat: ( nat > num > nat ) > product_prod_nat_num > nat ).
thf(func_def_1787,type,
produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
thf(func_def_1788,type,
produc8564434177180591209at_nat: ( nat > num > product_prod_nat_nat ) > product_prod_nat_num > product_prod_nat_nat ).
thf(func_def_1789,type,
produc49306077274653107at_num: ( nat > num > product_prod_nat_num ) > product_prod_nat_num > product_prod_nat_num ).
thf(func_def_1790,type,
produc836176033315069408_set_o: ( nat > num > set_o ) > product_prod_nat_num > set_o ).
thf(func_def_1791,type,
produc9175805072616146554et_int: ( nat > num > set_int ) > product_prod_nat_num > set_int ).
thf(func_def_1792,type,
produc4130284055270567454et_nat: ( nat > num > set_nat ) > product_prod_nat_num > set_nat ).
thf(func_def_1793,type,
produc859037500352796105at_nat: ( nat > num > set_Pr1261947904930325089at_nat ) > product_prod_nat_num > set_Pr1261947904930325089at_nat ).
thf(func_def_1794,type,
produc4306188689235752475_int_o: ( nat > product_prod_int_int > $o ) > produc6945250483304103390nt_int > $o ).
thf(func_def_1795,type,
produc5864757623865647827_nat_o: ( nat > product_prod_nat_nat > $o ) > produc7248412053542808358at_nat > $o ).
thf(func_def_1796,type,
produc6857965554392702720_nat_o: ( num > nat > $o ) > product_prod_num_nat > $o ).
thf(func_def_1797,type,
produc5219324331026901427at_num: ( num > nat > product_prod_nat_num ) > product_prod_num_nat > product_prod_nat_num ).
thf(func_def_1798,type,
produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
thf(func_def_1799,type,
produc6665183775751917029atural: ( pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural ) > produc4675096598859438275atural > produc4675096598859438275atural ).
thf(func_def_1800,type,
produc5441891513209881465_nat_o: ( product_prod_int_int > nat > $o ) > produc1709102135585200056nt_nat > $o ).
thf(func_def_1801,type,
produc1676490119946744748_int_o: ( product_prod_int_int > product_prod_int_int > $o ) > produc1219242969750017639nt_int > $o ).
thf(func_def_1802,type,
produc3235059054576640100_nat_o: ( product_prod_int_int > product_prod_nat_nat > $o ) > produc1522404539988722607at_nat > $o ).
thf(func_def_1803,type,
produc6937227050501860053_int_o: ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > $o ).
thf(func_def_1804,type,
produc8758269395934548017_nat_o: ( product_prod_nat_nat > nat > $o ) > produc8373899037510109440at_nat > $o ).
thf(func_def_1805,type,
produc5031841752791441652_int_o: ( product_prod_nat_nat > product_prod_int_int > $o ) > produc556289286640904991nt_int > $o ).
thf(func_def_1806,type,
produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).
thf(func_def_1807,type,
produc410239310623530412_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > $o ).
thf(func_def_1808,type,
produc7548845685434208379at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_1809,type,
produc9020218426428501292_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > produc1319942482725812455at_nat > $o ).
thf(func_def_1810,type,
produc5456455677105495163at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ) > produc1319942482725812455at_nat > produc1319942482725812455at_nat ).
thf(func_def_1811,type,
product_fst_o_o: product_prod_o_o > $o ).
thf(func_def_1812,type,
product_fst_o_int: product_prod_o_int > $o ).
thf(func_def_1813,type,
product_fst_o_nat: product_prod_o_nat > $o ).
thf(func_def_1814,type,
produc5219655352205527288t_unit: produc3788275437394581276t_unit > $o ).
thf(func_def_1815,type,
produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_1816,type,
produc1861665112190112313nteger: produc3346328345660746739nteger > code_integer ).
thf(func_def_1817,type,
produc2762368996035445955t_unit: produc8126358835630522215t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1818,type,
produc5717040794327095847_ref_a: produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ).
thf(func_def_1819,type,
produc473321116828791851t_unit: produc7812382424243267045t_unit > ref_a ).
thf(func_def_1820,type,
produc6942380573175061695_ref_a: produc5288414631154139675_ref_a > ref_a ).
thf(func_def_1821,type,
product_fst_int_o: product_prod_int_o > int ).
thf(func_def_1822,type,
produc45500017171379470nteger: produc2963269191615333738nteger > int ).
thf(func_def_1823,type,
product_fst_int_int: product_prod_int_int > int ).
thf(func_def_1824,type,
product_fst_int_nat: product_prod_int_nat > int ).
thf(func_def_1825,type,
produc917050878549155996t_unit: produc6865911496949736918t_unit > int ).
thf(func_def_1826,type,
product_fst_nat_o: product_prod_nat_o > nat ).
thf(func_def_1827,type,
product_fst_nat_int: product_prod_nat_int > nat ).
thf(func_def_1828,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1829,type,
product_fst_nat_num: product_prod_nat_num > nat ).
thf(func_def_1830,type,
produc3800628931346975736t_unit: produc526117512892780850t_unit > nat ).
thf(func_def_1831,type,
product_fst_num_nat: product_prod_num_nat > num ).
thf(func_def_1832,type,
product_fst_num_num: product_prod_num_num > num ).
thf(func_def_1833,type,
produc6435950281062462810_nat_o: produc652263959640188542_nat_o > product_prod_nat_nat ).
thf(func_def_1834,type,
produc4619704898428564714at_int: produc4196048018000912732at_int > product_prod_nat_nat ).
thf(func_def_1835,type,
produc3213797794245857475at_nat: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_1836,type,
produc582253812616888142unit_o: produc7485711547916492274unit_o > product_unit ).
thf(func_def_1837,type,
produc5169466786534984090it_nat: produc600557818389255820it_nat > product_unit ).
thf(func_def_1838,type,
produc6963936691090040003t_unit: produc8459935480633519975t_unit > product_unit ).
thf(func_def_1839,type,
produc6011863565407846595at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1840,type,
produc4486455499028916547at_nat: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1841,type,
product_snd_o_o: product_prod_o_o > $o ).
thf(func_def_1842,type,
product_snd_o_int: product_prod_o_int > int ).
thf(func_def_1843,type,
product_snd_o_nat: product_prod_o_nat > nat ).
thf(func_def_1844,type,
produc2875488738488844090t_unit: produc3788275437394581276t_unit > product_unit ).
thf(func_def_1845,type,
produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_1846,type,
produc7955729907432593271nteger: produc3346328345660746739nteger > produc8923325533196201883nteger ).
thf(func_def_1847,type,
produc1692618790031806469t_unit: produc8126358835630522215t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1848,type,
produc6369869760173755749_ref_a: produc1799199577659733785_ref_a > ref_a ).
thf(func_def_1849,type,
produc1126150082675451753t_unit: produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1850,type,
produc8185483580310833921_ref_a: produc5288414631154139675_ref_a > ref_a ).
thf(func_def_1851,type,
product_snd_int_o: product_prod_int_o > $o ).
thf(func_def_1852,type,
produc2153544567185597776nteger: produc2963269191615333738nteger > code_integer ).
thf(func_def_1853,type,
product_snd_int_int: product_prod_int_int > int ).
thf(func_def_1854,type,
product_snd_int_nat: product_prod_int_nat > nat ).
thf(func_def_1855,type,
product_snd_nat_o: product_prod_nat_o > $o ).
thf(func_def_1856,type,
product_snd_nat_int: product_prod_nat_int > int ).
thf(func_def_1857,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1858,type,
product_snd_nat_num: product_prod_nat_num > num ).
thf(func_def_1859,type,
produc8850949007409916470t_unit: produc526117512892780850t_unit > product_unit ).
thf(func_def_1860,type,
product_snd_num_nat: product_prod_num_nat > nat ).
thf(func_def_1861,type,
product_snd_num_num: product_prod_num_num > num ).
thf(func_def_1862,type,
produc668916169454083228_nat_o: produc652263959640188542_nat_o > $o ).
thf(func_def_1863,type,
produc3064508320661873192at_int: produc4196048018000912732at_int > int ).
thf(func_def_1864,type,
produc6408287024330202629at_nat: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_1865,type,
produc7461459235754980752unit_o: produc7485711547916492274unit_o > $o ).
thf(func_def_1866,type,
produc996414825743149016it_nat: produc600557818389255820it_nat > nat ).
thf(func_def_1867,type,
produc6786084904866402309t_unit: produc8459935480633519975t_unit > product_unit ).
thf(func_def_1868,type,
produc2937545259423399429at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1869,type,
produc826222791318859909at_nat: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1870,type,
produc6214465446503547763_ref_a: produc1799199577659733785_ref_a > produc7812382424243267045t_unit ).
thf(func_def_1871,type,
produc970745769005243767t_unit: produc7812382424243267045t_unit > produc1799199577659733785_ref_a ).
thf(func_def_1872,type,
product_swap_int_int: product_prod_int_int > product_prod_int_int ).
thf(func_def_1873,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1874,type,
product_swap_nat_num: product_prod_nat_num > product_prod_num_nat ).
thf(func_def_1875,type,
product_swap_num_nat: product_prod_num_nat > product_prod_nat_num ).
thf(func_def_1876,type,
produc3946833401584108663at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
thf(func_def_1877,type,
produc5396952528824381687at_nat: produc1319942482725812455at_nat > produc1319942482725812455at_nat ).
thf(func_def_1878,type,
produc929334515565554804at_nat: set_nat > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1879,type,
produc3241716407206042770at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1880,type,
product_Abs_unit: $o > product_unit ).
thf(func_def_1881,type,
product_Rep_unit: product_unit > $o ).
thf(func_def_1882,type,
random6974930770145893639ompred: ( produc7822875418678951345atural > produc4675096598859438275atural ) > produc7822875418678951345atural > produc4675096598859438275atural ).
thf(func_def_1883,type,
fract: int > int > rat ).
thf(func_def_1884,type,
field_6020823756834552118ts_rat: set_rat ).
thf(func_def_1885,type,
normalize: product_prod_int_int > product_prod_int_int ).
thf(func_def_1886,type,
quotient_of: rat > product_prod_int_int ).
thf(func_def_1887,type,
alloc_a: a > heap_e7401611519738050253t_unit > produc7812382424243267045t_unit ).
thf(func_def_1888,type,
change_ref_a: ( ref_a > ref_a ) > ref_ref_a > heap_Heap_ref_a ).
thf(func_def_1889,type,
change_a: ( a > a ) > ref_a > heap_Heap_a ).
thf(func_def_1890,type,
get_ref_a: heap_e7401611519738050253t_unit > ref_ref_a > ref_a ).
thf(func_def_1891,type,
get_a: heap_e7401611519738050253t_unit > ref_a > a ).
thf(func_def_1892,type,
lookup_ref_a: ref_ref_a > heap_Heap_ref_a ).
thf(func_def_1893,type,
lookup_a: ref_a > heap_Heap_a ).
thf(func_def_1894,type,
noteq_a_a: ref_a > ref_a > $o ).
thf(func_def_1895,type,
present_a: heap_e7401611519738050253t_unit > ref_a > $o ).
thf(func_def_1896,type,
ref_a2: a > heap_Heap_ref_a ).
thf(func_def_1897,type,
ref_a3: a > heap_Heap_ref_a ).
thf(func_def_1898,type,
set_ref_a2: ref_ref_a > ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1899,type,
set_a: ref_a > a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_1900,type,
update_a: ref_a > a > heap_H6156071679106078628t_unit ).
thf(func_def_1901,type,
field_o: set_Product_prod_o_o > set_o ).
thf(func_def_1902,type,
field_int: set_Pr958786334691620121nt_int > set_int ).
thf(func_def_1903,type,
field_nat: set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_1904,type,
field_4706345496283612622at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1905,type,
field_3044959742847878580at_nat: set_Pr553994874890374343at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1906,type,
field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1907,type,
field_Product_unit: set_Pr5094982260447487303t_unit > set_Product_unit ).
thf(func_def_1908,type,
field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).
thf(func_def_1909,type,
field_1428494348145443988at_nat: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat ).
thf(func_def_1910,type,
id_o2: set_Product_prod_o_o ).
thf(func_def_1911,type,
id_int2: set_Pr958786334691620121nt_int ).
thf(func_def_1912,type,
id_nat2: set_Pr1261947904930325089at_nat ).
thf(func_def_1913,type,
id_Pro2258643101195443293at_nat: set_Pr8693737435421807431at_nat ).
thf(func_def_1914,type,
id_Pro5428700290092274115at_nat: set_Pr5564308138774400199at_nat ).
thf(func_def_1915,type,
id_set1796276052702428605at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_1916,type,
id_set4888139568991089827at_nat: set_Pr7459493094073627847at_nat ).
thf(func_def_1917,type,
id_on_o: set_o > set_Product_prod_o_o ).
thf(func_def_1918,type,
id_on_int: set_int > set_Pr958786334691620121nt_int ).
thf(func_def_1919,type,
id_on_nat: set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1920,type,
id_on_num: set_num > set_Pr8218934625190621173um_num ).
thf(func_def_1921,type,
id_on_8598933527810153430nt_int: set_Pr958786334691620121nt_int > set_Pr2560585780119916871nt_int ).
thf(func_def_1922,type,
id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1923,type,
id_on_7869290023980668164at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_1924,type,
id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_1925,type,
id_on_3275838214495744996at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_1926,type,
conver1062113817206378758nt_int: ( ( int > product_prod_int_int ) > ( int > int ) > $o ) > ( int > int ) > ( int > product_prod_int_int ) > $o ).
thf(func_def_1927,type,
conver1572571282669976050nt_nat: ( ( int > product_prod_nat_nat ) > ( int > nat ) > $o ) > ( int > nat ) > ( int > product_prod_nat_nat ) > $o ).
thf(func_def_1928,type,
conver5699786650113435344nt_num: ( ( int > product_prod_num_num ) > ( int > num ) > $o ) > ( int > num ) > ( int > product_prod_num_num ) > $o ).
thf(func_def_1929,type,
conver6066198818478722162at_nat: ( ( list_nat > product_prod_nat_nat ) > ( list_nat > nat ) > $o ) > ( list_nat > nat ) > ( list_nat > product_prod_nat_nat ) > $o ).
thf(func_def_1930,type,
conver2987682522074450438at_int: ( ( nat > product_prod_int_int ) > ( nat > int ) > $o ) > ( nat > int ) > ( nat > product_prod_int_int ) > $o ).
thf(func_def_1931,type,
conver3498139987538047730at_nat: ( ( nat > product_prod_nat_nat ) > ( nat > nat ) > $o ) > ( nat > nat ) > ( nat > product_prod_nat_nat ) > $o ).
thf(func_def_1932,type,
conver3229387634306789365nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_1933,type,
conver6967689361887734790at_int: ( ( rat > product_prod_int_int ) > ( rat > int ) > $o ) > ( rat > int ) > ( rat > product_prod_int_int ) > $o ).
thf(func_def_1934,type,
conver7478146827351332082at_nat: ( ( rat > product_prod_nat_nat ) > ( rat > nat ) > $o ) > ( rat > nat ) > ( rat > product_prod_nat_nat ) > $o ).
thf(func_def_1935,type,
conver1155128050257070662ar_int: ( ( char > product_prod_int_int ) > ( char > int ) > $o ) > ( char > int ) > ( char > product_prod_int_int ) > $o ).
thf(func_def_1936,type,
conver5210974729819302706ar_nat: ( ( char > product_prod_nat_nat ) > ( char > nat ) > $o ) > ( char > nat ) > ( char > product_prod_nat_nat ) > $o ).
thf(func_def_1937,type,
conversep_o_o: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_1938,type,
conver1462408618118490240er_int: ( code_integer > int > $o ) > int > code_integer > $o ).
thf(func_def_1939,type,
conver2101108097643427968nteger: ( int > code_integer > $o ) > code_integer > int > $o ).
thf(func_def_1940,type,
conversep_int_int: ( int > int > $o ) > int > int > $o ).
thf(func_def_1941,type,
conversep_int_nat: ( int > nat > $o ) > nat > int > $o ).
thf(func_def_1942,type,
conver1866313717161370910at_nat: ( int > product_prod_nat_nat > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_1943,type,
conver909888920752868663st_nat: ( list_nat > list_nat > $o ) > list_nat > list_nat > $o ).
thf(func_def_1944,type,
conversep_nat_o: ( nat > $o > $o ) > $o > nat > $o ).
thf(func_def_1945,type,
conversep_nat_int: ( nat > int > $o ) > int > nat > $o ).
thf(func_def_1946,type,
conversep_nat_nat: ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_1947,type,
conversep_nat_num: ( nat > num > $o ) > num > nat > $o ).
thf(func_def_1948,type,
conversep_nat_rat: ( nat > rat > $o ) > rat > nat > $o ).
thf(func_def_1949,type,
conversep_nat_char: ( nat > char > $o ) > char > nat > $o ).
thf(func_def_1950,type,
conversep_num_nat: ( num > nat > $o ) > nat > num > $o ).
thf(func_def_1951,type,
conversep_num_num: ( num > num > $o ) > num > num > $o ).
thf(func_def_1952,type,
conver4368408235330554745_ref_a: ( produc7812382424243267045t_unit > ref_a > $o ) > ref_a > produc7812382424243267045t_unit > $o ).
thf(func_def_1953,type,
conver7247880940930113968nt_int: ( product_prod_int_int > int > $o ) > int > product_prod_int_int > $o ).
thf(func_def_1954,type,
conver4689305806000247544at_int: ( product_prod_nat_nat > int > $o ) > int > product_prod_nat_nat > $o ).
thf(func_def_1955,type,
conver4691796276509297820at_nat: ( product_prod_nat_nat > nat > $o ) > nat > product_prod_nat_nat > $o ).
thf(func_def_1956,type,
conver6965824823119931701at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1957,type,
conversep_rat_int: ( rat > int > $o ) > int > rat > $o ).
thf(func_def_1958,type,
conversep_rat_nat: ( rat > nat > $o ) > nat > rat > $o ).
thf(func_def_1959,type,
conversep_rat_rat: ( rat > rat > $o ) > rat > rat > $o ).
thf(func_def_1960,type,
conversep_rat_char: ( rat > char > $o ) > char > rat > $o ).
thf(func_def_1961,type,
conver5243090411617913141at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1962,type,
conver9095369822871743413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1963,type,
conversep_char_int: ( char > int > $o ) > int > char > $o ).
thf(func_def_1964,type,
conversep_char_nat: ( char > nat > $o ) > nat > char > $o ).
thf(func_def_1965,type,
conversep_char_rat: ( char > rat > $o ) > rat > char > $o ).
thf(func_def_1966,type,
conversep_char_char: ( char > char > $o ) > char > char > $o ).
thf(func_def_1967,type,
inv_image_int_int: set_Pr958786334691620121nt_int > ( int > int ) > set_Pr958786334691620121nt_int ).
thf(func_def_1968,type,
inv_image_int_nat: set_Pr958786334691620121nt_int > ( nat > int ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1969,type,
inv_im8510909985083594081at_nat: set_Pr958786334691620121nt_int > ( set_Pr1261947904930325089at_nat > int ) > set_Pr4329608150637261639at_nat ).
thf(func_def_1970,type,
inv_image_nat_int: set_Pr1261947904930325089at_nat > ( int > nat ) > set_Pr958786334691620121nt_int ).
thf(func_def_1971,type,
inv_image_nat_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1972,type,
inv_im6750873321330482877at_nat: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_1973,type,
inv_im2354225701593503139at_nat: set_Pr1261947904930325089at_nat > ( set_Pr4329608150637261639at_nat > nat ) > set_Pr7459493094073627847at_nat ).
thf(func_def_1974,type,
inv_im4434751243573137211at_int: set_Pr4329608150637261639at_nat > ( int > set_Pr1261947904930325089at_nat ) > set_Pr958786334691620121nt_int ).
thf(func_def_1975,type,
inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1976,type,
inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
thf(func_def_1977,type,
inv_im2900519150384625825at_int: set_Pr7459493094073627847at_nat > ( int > set_Pr4329608150637261639at_nat ) > set_Pr958786334691620121nt_int ).
thf(func_def_1978,type,
inv_im2903009620893676101at_nat: set_Pr7459493094073627847at_nat > ( nat > set_Pr4329608150637261639at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1979,type,
refl_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_1980,type,
refl_on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1981,type,
refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1982,type,
refl_o7122697186039111552at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1983,type,
refl_o7446464703481863270at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_1984,type,
refl_on_Product_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_1985,type,
refl_o6955724340487615712at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1986,type,
refl_o6272981002401706822at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_1987,type,
relcom1820845089908643850nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_1988,type,
relcom7212586982944386682nteger: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
thf(func_def_1989,type,
relcom6733878598652036755nt_int: ( ( int > int ) > ( int > product_prod_int_int ) > $o ) > ( ( int > product_prod_int_int ) > ( int > int ) > $o ) > ( int > int ) > ( int > int ) > $o ).
thf(func_def_1990,type,
relcom2406850561174050523nt_nat: ( ( int > nat ) > ( int > product_prod_nat_nat ) > $o ) > ( ( int > product_prod_nat_nat ) > ( int > nat ) > $o ) > ( int > nat ) > ( int > nat ) > $o ).
thf(func_def_1991,type,
relcom1848932251921554756er_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( code_integer > num ) > ( code_integer > num ) > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
thf(func_def_1992,type,
relcom7779292856395800339nt_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( code_integer > num ) > ( int > num ) > $o ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_1993,type,
relcom1533066287727470739er_num: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
thf(func_def_1994,type,
relcom9025577121137075810nt_num: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_1995,type,
relcom1697847500783689711nt_num: ( ( int > num ) > ( int > product_prod_num_num ) > $o ) > ( ( int > product_prod_num_num ) > ( int > num ) > $o ) > ( int > num ) > ( int > num ) > $o ).
thf(func_def_1996,type,
relcom2127790875031262553er_int: ( ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > $o ) > ( ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ) > ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ).
thf(func_def_1997,type,
relcom5920149085449455271at_nat: ( ( list_nat > nat ) > ( list_nat > product_prod_nat_nat ) > $o ) > ( ( list_nat > product_prod_nat_nat ) > ( list_nat > nat ) > $o ) > ( list_nat > nat ) > ( list_nat > nat ) > $o ).
thf(func_def_1998,type,
relcom3290293904592725231at_int: ( ( nat > int ) > ( nat > product_prod_int_int ) > $o ) > ( ( nat > product_prod_int_int ) > ( nat > int ) > $o ) > ( nat > int ) > ( nat > int ) > $o ).
thf(func_def_1999,type,
relcom8186637903969514807at_nat: ( ( nat > nat ) > ( nat > product_prod_nat_nat ) > $o ) > ( ( nat > product_prod_nat_nat ) > ( nat > nat ) > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_2000,type,
relcom458776940982682326nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
thf(func_def_2001,type,
relcom4829277440228594702nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer > $o ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ).
thf(func_def_2002,type,
relcom4574826104943343961nteger: ( ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > $o ) > ( ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ) > ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ).
thf(func_def_2003,type,
relcom4272412204205018633nt_nat: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
thf(func_def_2004,type,
relcom531901107642208332nt_nat: ( ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
thf(func_def_2005,type,
relcom4982215633375716084nt_int: ( ( 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 ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
thf(func_def_2006,type,
relcom2810802720173317863at_int: ( ( rat > int ) > ( rat > product_prod_int_int ) > $o ) > ( ( rat > product_prod_int_int ) > ( rat > int ) > $o ) > ( rat > int ) > ( rat > int ) > $o ).
thf(func_def_2007,type,
relcom7707146719550107439at_nat: ( ( rat > nat ) > ( rat > product_prod_nat_nat ) > $o ) > ( ( rat > product_prod_nat_nat ) > ( rat > nat ) > $o ) > ( rat > nat ) > ( rat > nat ) > $o ).
thf(func_def_2008,type,
relcom4417706183330134766ar_int: ( ( char > int ) > ( char > product_prod_int_int ) > $o ) > ( ( char > product_prod_int_int ) > ( char > int ) > $o ) > ( char > int ) > ( char > int ) > $o ).
thf(func_def_2009,type,
relcom8141925468094106422ar_nat: ( ( char > nat ) > ( char > product_prod_nat_nat ) > $o ) > ( ( char > product_prod_nat_nat ) > ( char > nat ) > $o ) > ( char > nat ) > ( char > nat ) > $o ).
thf(func_def_2010,type,
relcompp_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_2011,type,
relcompp_o_o_nat: ( $o > $o > $o ) > ( $o > nat > $o ) > $o > nat > $o ).
thf(func_def_2012,type,
relcom692387321444912665nteger: ( code_integer > int > $o ) > ( int > code_integer > $o ) > code_integer > code_integer > $o ).
thf(func_def_2013,type,
relcom3789353511612409832nt_int: ( code_integer > int > $o ) > ( int > int > $o ) > code_integer > int > $o ).
thf(func_def_2014,type,
relcom3136146828236442456t_unit: ( ref_a > produc7812382424243267045t_unit > $o ) > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
thf(func_def_2015,type,
relcom8320293257703906841nteger: ( int > code_integer > $o ) > ( code_integer > code_integer > $o ) > int > code_integer > $o ).
thf(func_def_2016,type,
relcom328798225758222312er_int: ( int > code_integer > $o ) > ( code_integer > int > $o ) > int > int > $o ).
thf(func_def_2017,type,
relcom967497705283160040nteger: ( int > int > $o ) > ( int > code_integer > $o ) > int > code_integer > $o ).
thf(func_def_2018,type,
relcompp_int_int_int: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
thf(func_def_2019,type,
relcompp_int_int_nat: ( int > int > $o ) > ( int > nat > $o ) > int > nat > $o ).
thf(func_def_2020,type,
relcompp_int_nat_int: ( int > nat > $o ) > ( nat > int > $o ) > int > int > $o ).
thf(func_def_2021,type,
relcompp_int_nat_num: ( int > nat > $o ) > ( nat > num > $o ) > int > num > $o ).
thf(func_def_2022,type,
relcom3664783465810776136nt_int: ( int > product_prod_int_int > $o ) > ( product_prod_int_int > int > $o ) > int > int > $o ).
thf(func_def_2023,type,
relcom1106208330880909712at_int: ( int > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > int > int > $o ).
thf(func_def_2024,type,
relcom716700242784427165at_nat: ( int > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > product_prod_nat_nat > $o ).
thf(func_def_2025,type,
relcom7887202796854296604nteger: ( list_nat > int > $o ) > ( int > code_integer > $o ) > list_nat > code_integer > $o ).
thf(func_def_2026,type,
relcom8030397737370142931st_nat: ( list_nat > list_nat > $o ) > ( list_nat > list_nat > $o ) > list_nat > list_nat > $o ).
thf(func_def_2027,type,
relcom170568170053003356at_int: ( list_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > list_nat > int > $o ).
thf(func_def_2028,type,
relcompp_nat_o_o: ( nat > $o > $o ) > ( $o > $o > $o ) > nat > $o > $o ).
thf(func_def_2029,type,
relcompp_nat_o_nat: ( nat > $o > $o ) > ( $o > nat > $o ) > nat > nat > $o ).
thf(func_def_2030,type,
relcom3277315637376110988nteger: ( nat > int > $o ) > ( int > code_integer > $o ) > nat > code_integer > $o ).
thf(func_def_2031,type,
relcompp_nat_int_int: ( nat > int > $o ) > ( int > int > $o ) > nat > int > $o ).
thf(func_def_2032,type,
relcompp_nat_int_nat: ( nat > int > $o ) > ( int > nat > $o ) > nat > nat > $o ).
thf(func_def_2033,type,
relcompp_nat_nat_int: ( nat > nat > $o ) > ( nat > int > $o ) > nat > int > $o ).
thf(func_def_2034,type,
relcompp_nat_nat_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_2035,type,
relcompp_nat_nat_num: ( nat > nat > $o ) > ( nat > num > $o ) > nat > num > $o ).
thf(func_def_2036,type,
relcom8569543703982574316at_int: ( nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > nat > int > $o ).
thf(func_def_2037,type,
relcom8572034174491624592at_nat: ( nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > nat > $o ) > nat > nat > $o ).
thf(func_def_2038,type,
relcompp_nat_rat_nat: ( nat > rat > $o ) > ( rat > nat > $o ) > nat > nat > $o ).
thf(func_def_2039,type,
relcom8112501251453913252ar_nat: ( nat > char > $o ) > ( char > nat > $o ) > nat > nat > $o ).
thf(func_def_2040,type,
relcompp_num_nat_int: ( num > nat > $o ) > ( nat > int > $o ) > num > int > $o ).
thf(func_def_2041,type,
relcompp_num_nat_num: ( num > nat > $o ) > ( nat > num > $o ) > num > num > $o ).
thf(func_def_2042,type,
relcompp_num_num_num: ( num > num > $o ) > ( num > num > $o ) > num > num > $o ).
thf(func_def_2043,type,
relcom2949942408940504938nt_int: ( product_prod_nat_nat > int > $o ) > ( int > int > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_2044,type,
relcom8911704206367525917at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
thf(func_def_2045,type,
relcom282571730187242960at_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 > $o ).
thf(func_def_2046,type,
relcom3409376902655092628nteger: ( rat > int > $o ) > ( int > code_integer > $o ) > rat > code_integer > $o ).
thf(func_def_2047,type,
relcompp_rat_int_rat: ( rat > int > $o ) > ( int > rat > $o ) > rat > rat > $o ).
thf(func_def_2048,type,
relcompp_rat_nat_rat: ( rat > nat > $o ) > ( nat > rat > $o ) > rat > rat > $o ).
thf(func_def_2049,type,
relcom1211213461163567844at_int: ( rat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > rat > int > $o ).
thf(func_def_2050,type,
relcompp_rat_rat_rat: ( rat > rat > $o ) > ( rat > rat > $o ) > rat > rat > $o ).
thf(func_def_2051,type,
relcom1505247221262953652ar_rat: ( rat > char > $o ) > ( char > rat > $o ) > rat > rat > $o ).
thf(func_def_2052,type,
relcom8363394528208558896at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2053,type,
relcom5819909836510906509nteger: ( char > int > $o ) > ( int > code_integer > $o ) > char > code_integer > $o ).
thf(func_def_2054,type,
relcom750623199913152513t_char: ( char > int > $o ) > ( int > char > $o ) > char > char > $o ).
thf(func_def_2055,type,
relcom6755291642603558309t_char: ( char > nat > $o ) > ( nat > char > $o ) > char > char > $o ).
thf(func_def_2056,type,
relcom7879471502873553579at_int: ( char > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > char > int > $o ).
thf(func_def_2057,type,
relcom3428143170894750637t_char: ( char > rat > $o ) > ( rat > char > $o ) > char > char > $o ).
thf(func_def_2058,type,
relcom5872928454965100966r_char: ( char > char > $o ) > ( char > char > $o ) > char > char > $o ).
thf(func_def_2059,type,
total_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_2060,type,
total_on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_2061,type,
total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2062,type,
total_3592101749530773125at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2063,type,
total_1513685709984341995at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_2064,type,
total_5665700600833547665t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_2065,type,
total_7212417256332265445at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_2066,type,
total_5117575981256876747at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_2067,type,
trans_4347625901269045472at_nat: set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2068,type,
divide_divide_int: int > int > int ).
thf(func_def_2069,type,
divide_divide_rat: rat > rat > rat ).
thf(func_def_2070,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_2071,type,
modulo_modulo_nat: nat > nat > nat ).
thf(func_def_2072,type,
zero_n2684676970156552555ol_int: $o > int ).
thf(func_def_2073,type,
collec5651646645946169514nteger: ( ( code_integer > code_integer > code_integer ) > $o ) > set_Co4375521073081744395nteger ).
thf(func_def_2074,type,
collect_int_int: ( ( int > int ) > $o ) > set_int_int ).
thf(func_def_2075,type,
collect_int_nat: ( ( int > nat ) > $o ) > set_int_nat ).
thf(func_def_2076,type,
collect_int_num: ( ( int > num ) > $o ) > set_int_num ).
thf(func_def_2077,type,
collec2229320974926845999nt_int: ( ( int > product_prod_int_int ) > $o ) > set_in6154042108061588260nt_int ).
thf(func_def_2078,type,
collec2532482545165550967at_nat: ( ( int > product_prod_nat_nat ) > $o ) > set_in7748886932685137004at_nat ).
thf(func_def_2079,type,
collec266097228571071243um_num: ( ( int > product_prod_num_num ) > $o ) > set_in3169746454734514176um_num ).
thf(func_def_2080,type,
collec3092956710985254339at_nat: ( ( list_nat > product_prod_nat_nat ) > $o ) > set_li2168235667650531768at_nat ).
thf(func_def_2081,type,
collect_nat_o: ( ( nat > $o ) > $o ) > set_nat_o ).
thf(func_def_2082,type,
collect_nat_nat: ( ( nat > nat ) > $o ) > set_nat_nat ).
thf(func_def_2083,type,
collec8414850927317488011nt_int: ( ( nat > product_prod_int_int ) > $o ) > set_na7251125088705586816nt_int ).
thf(func_def_2084,type,
collec8718012497556192979at_nat: ( ( nat > product_prod_nat_nat ) > $o ) > set_na8845969913329135560at_nat ).
thf(func_def_2085,type,
collec2521308361159233923nt_int: ( ( rat > product_prod_int_int ) > $o ) > set_ra518564293221149304nt_int ).
thf(func_def_2086,type,
collec2824469931397938891at_nat: ( ( rat > product_prod_nat_nat ) > $o ) > set_ra2113409117844698048at_nat ).
thf(func_def_2087,type,
collec1380656525566158922nt_int: ( ( char > product_prod_int_int ) > $o ) > set_ch6383161263842509759nt_int ).
thf(func_def_2088,type,
collec1683818095804863890at_nat: ( ( char > product_prod_nat_nat ) > $o ) > set_ch7978006088466058503at_nat ).
thf(func_def_2089,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_2090,type,
collect_ref_a: ( ref_a > $o ) > set_ref_a ).
thf(func_def_2091,type,
collect_int: ( int > $o ) > set_int ).
thf(func_def_2092,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_2093,type,
collec3252306575900995386t_unit: ( produc7812382424243267045t_unit > $o ) > set_Pr1133966238863718811t_unit ).
thf(func_def_2094,type,
collec7215431352809750357nteger: ( produc2963269191615333738nteger > $o ) > set_Pr8415741480598773322nteger ).
thf(func_def_2095,type,
collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
thf(func_def_2096,type,
collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2097,type,
collec4100598399430923318at_num: ( product_prod_nat_num > $o ) > set_Pr6200539531224447659at_num ).
thf(func_def_2098,type,
collec5600542410287506995nt_int: ( produc6945250483304103390nt_int > $o ) > set_Pr6123067485828015636nt_int ).
thf(func_def_2099,type,
collec5903703980526211963at_nat: ( produc7248412053542808358at_nat > $o ) > set_Pr7717912310451564380at_nat ).
thf(func_def_2100,type,
collec1522684865789554998um_nat: ( product_prod_num_nat > $o ) > set_Pr3280342998896498603um_nat ).
thf(func_def_2101,type,
collec2230928802738392704um_num: ( product_prod_num_num > $o ) > set_Pr8218934625190621173um_num ).
thf(func_def_2102,type,
collec364394062568603661nt_nat: ( produc1709102135585200056nt_nat > $o ) > set_Pr2543308735921124078nt_nat ).
thf(func_def_2103,type,
collec7447955092554649554nt_int: ( produc1219242969750017639nt_int > $o ) > set_Pr2560585780119916871nt_int ).
thf(func_def_2104,type,
collec7751116662793354522at_nat: ( produc1522404539988722607at_nat > $o ) > set_Pr4155430604743465615at_nat ).
thf(func_def_2105,type,
collec2851339944984316337at_int: ( produc4196048018000912732at_int > $o ) > set_Pr49084382684228242at_int ).
thf(func_def_2106,type,
collec7029190964493513045at_nat: ( produc8373899037510109440at_nat > $o ) > set_Pr2539167527615954998at_nat ).
thf(func_def_2107,type,
collec6785001409445536906nt_int: ( produc556289286640904991nt_int > $o ) > set_Pr7098892610798258687nt_int ).
thf(func_def_2108,type,
collec7088162979684241874at_nat: ( produc859450856879609959at_nat > $o ) > set_Pr8693737435421807431at_nat ).
thf(func_def_2109,type,
collec6321179662152712658at_nat: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2110,type,
collec7872792499061297490at_nat: ( produc1319942482725812455at_nat > $o ) > set_Pr7459493094073627847at_nat ).
thf(func_def_2111,type,
collect_rat: ( rat > $o ) > set_rat ).
thf(func_def_2112,type,
collec5514110066124741708at_nat: ( set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat ).
thf(func_def_2113,type,
collec4573900263915890866at_nat: ( set_Pr4329608150637261639at_nat > $o ) > set_se5479201105039950375at_nat ).
thf(func_def_2114,type,
pow_o: set_o > set_set_o ).
thf(func_def_2115,type,
pow_int: set_int > set_set_int ).
thf(func_def_2116,type,
pow_nat: set_nat > set_set_nat ).
thf(func_def_2117,type,
pow_Pr3466873192417945886at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2118,type,
pow_Pr1023649790151954692at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2119,type,
pow_Product_unit: set_Product_unit > set_set_Product_unit ).
thf(func_def_2120,type,
pow_rat: set_rat > set_set_rat ).
thf(func_def_2121,type,
image_o_o_set_o: ( ( $o > $o ) > set_o ) > set_o_o > set_set_o ).
thf(func_def_2122,type,
image_1365644804893650413_int_o: ( ( int > int > $o ) > product_prod_int_int > $o ) > set_int_int_o > set_Pr8049984349381595834_int_o ).
thf(func_def_2123,type,
image_int_o_set_int: ( ( int > $o ) > set_int ) > set_int_o > set_set_int ).
thf(func_def_2124,type,
image_6646056845087809525nt_int: ( ( int > int ) > int > int ) > set_int_int > set_int_int ).
thf(func_def_2125,type,
image_1600535827742230425nt_nat: ( ( int > int ) > int > nat ) > set_int_int > set_int_nat ).
thf(func_def_2126,type,
image_1234974663384347033nt_int: ( ( int > nat ) > int > int ) > set_int_nat > set_int_int ).
thf(func_def_2127,type,
image_5412825682893543741nt_nat: ( ( int > nat ) > int > nat ) > set_int_nat > set_int_nat ).
thf(func_def_2128,type,
image_1904597124500147013nt_rat: ( ( int > nat ) > int > rat ) > set_int_nat > set_int_rat ).
thf(func_def_2129,type,
image_4174709274675160035t_unit: ( ( int > rat ) > product_unit ) > set_int_rat > set_Product_unit ).
thf(func_def_2130,type,
image_4409302170498516394t_unit: ( ( int > char ) > product_unit ) > set_int_char > set_Product_unit ).
thf(func_def_2131,type,
image_7429393840292777309_nat_o: ( ( nat > nat > $o ) > product_prod_nat_nat > $o ) > set_nat_nat_o > set_Pr5582243495563764594_nat_o ).
thf(func_def_2132,type,
image_8484515203959327177_num_o: ( ( nat > num > $o ) > product_prod_nat_num > $o ) > set_nat_num_o > set_Pr5908833319024110760_num_o ).
thf(func_def_2133,type,
image_nat_o_set_nat: ( ( nat > $o ) > set_nat ) > set_nat_o > set_set_nat ).
thf(func_def_2134,type,
image_5437939712159429529nt_int: ( ( nat > int ) > int > int ) > set_nat_int > set_int_int ).
thf(func_def_2135,type,
image_392418694813850429nt_nat: ( ( nat > int ) > int > nat ) > set_nat_int > set_int_nat ).
thf(func_def_2136,type,
image_26857530455967037nt_int: ( ( nat > nat ) > int > int ) > set_nat_nat > set_int_int ).
thf(func_def_2137,type,
image_4204708549965163745nt_nat: ( ( nat > nat ) > int > nat ) > set_nat_nat > set_int_nat ).
thf(func_def_2138,type,
image_696479991571767017nt_rat: ( ( nat > nat ) > int > rat ) > set_nat_nat > set_int_rat ).
thf(func_def_2139,type,
image_340470173791133503t_unit: ( ( nat > rat ) > product_unit ) > set_nat_rat > set_Product_unit ).
thf(func_def_2140,type,
image_4600008085730780422t_unit: ( ( nat > char ) > product_unit ) > set_nat_char > set_Product_unit ).
thf(func_def_2141,type,
image_4447441447610994254nt_int: ( ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ) > set_Pr8049984349381595834_int_o > set_se6260736226359567993nt_int ).
thf(func_def_2142,type,
image_7124889717316225246at_nat: ( ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ) > set_Pr5582243495563764594_nat_o > set_se7855581050983116737at_nat ).
thf(func_def_2143,type,
image_6580737572886966642at_num: ( ( product_prod_nat_num > $o ) > set_Pr6200539531224447659at_num ) > set_Pr5908833319024110760_num_o > set_se4826145725398303499at_num ).
thf(func_def_2144,type,
image_4902389024228248874at_nat: ( ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ) > set_Pr7010166363911110284_nat_o > set_se5479201105039950375at_nat ).
thf(func_def_2145,type,
image_5694205205332509994at_nat: ( ( produc1319942482725812455at_nat > $o ) > set_Pr7459493094073627847at_nat ) > set_Pr7669914128964046860_nat_o > set_se7592288975875140775at_nat ).
thf(func_def_2146,type,
image_2910438736038083391t_unit: ( ( rat > nat ) > product_unit ) > set_rat_nat > set_Product_unit ).
thf(func_def_2147,type,
image_1193274288206594871t_unit: ( ( rat > rat ) > product_unit ) > set_rat_rat > set_Product_unit ).
thf(func_def_2148,type,
image_6940606515012899070t_unit: ( ( rat > char ) > product_unit ) > set_rat_char > set_Product_unit ).
thf(func_def_2149,type,
image_6226802281960588479_nat_o: ( ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > $o ) > set_se9180647916752606350_nat_o > set_Pr7010166363911110284_nat_o ).
thf(func_def_2150,type,
image_5235725667318448191_nat_o: ( ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > produc1319942482725812455at_nat > $o ) > set_se7255092946006855566_nat_o > set_Pr7669914128964046860_nat_o ).
thf(func_def_2151,type,
image_108929247839792006t_unit: ( ( char > nat ) > product_unit ) > set_char_nat > set_Product_unit ).
thf(func_def_2152,type,
image_7615136836863079294t_unit: ( ( char > rat ) > product_unit ) > set_char_rat > set_Product_unit ).
thf(func_def_2153,type,
image_8077363282794994245t_unit: ( ( char > char ) > product_unit ) > set_char_char > set_Product_unit ).
thf(func_def_2154,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_2155,type,
image_o_Code_integer: ( $o > code_integer ) > set_o > set_Code_integer ).
thf(func_def_2156,type,
image_o_int: ( $o > int ) > set_o > set_int ).
thf(func_def_2157,type,
image_o_nat: ( $o > nat ) > set_o > set_nat ).
thf(func_def_2158,type,
image_3855930084881510382at_nat: ( $o > product_prod_nat_nat ) > set_o > set_Pr1261947904930325089at_nat ).
thf(func_def_2159,type,
image_o_Product_unit: ( $o > product_unit ) > set_o > set_Product_unit ).
thf(func_def_2160,type,
image_o_rat: ( $o > rat ) > set_o > set_rat ).
thf(func_def_2161,type,
image_o_set_o: ( $o > set_o ) > set_o > set_set_o ).
thf(func_def_2162,type,
image_o_set_int: ( $o > set_int ) > set_o > set_set_int ).
thf(func_def_2163,type,
image_o_set_nat: ( $o > set_nat ) > set_o > set_set_nat ).
thf(func_def_2164,type,
image_7077428525161401678at_nat: ( $o > set_Pr1261947904930325089at_nat ) > set_o > set_se7855581050983116737at_nat ).
thf(func_def_2165,type,
image_8493167801588156084at_nat: ( $o > set_Pr8693737435421807431at_nat ) > set_o > set_se6425085446898223655at_nat ).
thf(func_def_2166,type,
image_2496312346330513076at_nat: ( $o > set_Pr4329608150637261639at_nat ) > set_o > set_se5479201105039950375at_nat ).
thf(func_def_2167,type,
image_663195431845683034t_unit: ( $o > set_Product_unit ) > set_o > set_set_Product_unit ).
thf(func_def_2168,type,
image_o_set_rat: ( $o > set_rat ) > set_o > set_set_rat ).
thf(func_def_2169,type,
image_o_set_char: ( $o > set_char ) > set_o > set_set_char ).
thf(func_def_2170,type,
image_o_char: ( $o > char ) > set_o > set_char ).
thf(func_def_2171,type,
image_2177946750938214461nteger: ( code_integer > code_integer > code_integer ) > set_Code_integer > set_Co726186806682698383nteger ).
thf(func_def_2172,type,
image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).
thf(func_def_2173,type,
image_5570573867351727369t_unit: ( ref_a > set_he8644174446132254637t_unit ) > set_ref_a > set_se4612898379794543757t_unit ).
thf(func_def_2174,type,
image_int_o: ( int > $o ) > set_int > set_o ).
thf(func_def_2175,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_2176,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(func_def_2177,type,
image_int_num: ( int > num ) > set_int > set_num ).
thf(func_def_2178,type,
image_5705468584675977158nt_int: ( int > product_prod_int_int ) > set_int > set_Pr958786334691620121nt_int ).
thf(func_def_2179,type,
image_659947567330398058nt_nat: ( int > product_prod_int_nat ) > set_int > set_Pr3448869479623346877nt_nat ).
thf(func_def_2180,type,
image_8883965892284119310at_nat: ( int > product_prod_nat_nat ) > set_int > set_Pr1261947904930325089at_nat ).
thf(func_def_2181,type,
image_7722540232540426402um_num: ( int > product_prod_num_num ) > set_int > set_Pr8218934625190621173um_num ).
thf(func_def_2182,type,
image_5846526143423701914t_unit: ( int > product_unit ) > set_int > set_Product_unit ).
thf(func_def_2183,type,
image_int_rat: ( int > rat ) > set_int > set_rat ).
thf(func_def_2184,type,
image_int_set_o: ( int > set_o ) > set_int > set_set_o ).
thf(func_def_2185,type,
image_int_set_int: ( int > set_int ) > set_int > set_set_int ).
thf(func_def_2186,type,
image_int_set_nat: ( int > set_nat ) > set_int > set_set_nat ).
thf(func_def_2187,type,
image_8635204845542730022nt_int: ( int > set_Pr958786334691620121nt_int ) > set_int > set_se6260736226359567993nt_int ).
thf(func_def_2188,type,
image_8938366415781434990at_nat: ( int > set_Pr1261947904930325089at_nat ) > set_int > set_se7855581050983116737at_nat ).
thf(func_def_2189,type,
image_525487068563185620at_nat: ( int > set_Pr8693737435421807431at_nat ) > set_int > set_se6425085446898223655at_nat ).
thf(func_def_2190,type,
image_8658272795163236474t_unit: ( int > set_Product_unit ) > set_int > set_set_Product_unit ).
thf(func_def_2191,type,
image_7976474329151083847st_nat: ( list_nat > list_nat ) > set_list_nat > set_list_nat ).
thf(func_def_2192,type,
image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
thf(func_def_2193,type,
image_2795870212791037530at_nat: ( list_nat > product_prod_nat_nat ) > set_list_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2194,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(func_def_2195,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(func_def_2196,type,
image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).
thf(func_def_2197,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_2198,type,
image_nat_num: ( nat > num ) > set_nat > set_num ).
thf(func_def_2199,type,
image_2667626500211843362nt_int: ( nat > product_prod_int_int ) > set_nat > set_Pr958786334691620121nt_int ).
thf(func_def_2200,type,
image_6845477519721040070nt_nat: ( nat > product_prod_int_nat ) > set_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_2201,type,
image_3337248961327643342nt_rat: ( nat > product_prod_int_rat ) > set_nat > set_Pr6292255179000445125nt_rat ).
thf(func_def_2202,type,
image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2203,type,
image_3276603626957510736at_nat: ( nat > produc859450856879609959at_nat ) > set_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2204,type,
image_3978134465758882403it_nat: ( nat > produc600557818389255820it_nat ) > set_nat > set_Pr1763845938948868674it_nat ).
thf(func_def_2205,type,
image_469905907365485675it_rat: ( nat > produc6315701296850634900it_rat ) > set_nat > set_Pr4607231638325966922it_rat ).
thf(func_def_2206,type,
image_1351718144375922894at_int: ( nat > product_prod_rat_int ) > set_nat > set_Pr3594552606344371909at_int ).
thf(func_def_2207,type,
image_5529569163885119602at_nat: ( nat > product_prod_rat_nat ) > set_nat > set_Pr6084635751276098665at_nat ).
thf(func_def_2208,type,
image_2021340605491722874at_rat: ( nat > product_prod_rat_rat ) > set_nat > set_Pr8928021450653196913at_rat ).
thf(func_def_2209,type,
image_2499013659892586576at_nat: ( nat > produc3843707927480180839at_nat ) > set_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2210,type,
image_8730104196221521654t_unit: ( nat > product_unit ) > set_nat > set_Product_unit ).
thf(func_def_2211,type,
image_nat_rat: ( nat > rat ) > set_nat > set_rat ).
thf(func_def_2212,type,
image_nat_set_o: ( nat > set_o ) > set_nat > set_set_o ).
thf(func_def_2213,type,
image_nat_set_int: ( nat > set_int ) > set_nat > set_set_int ).
thf(func_def_2214,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(func_def_2215,type,
image_7178329752028323786at_nat: ( nat > set_Pr1261947904930325089at_nat ) > set_nat > set_se7855581050983116737at_nat ).
thf(func_def_2216,type,
image_2893549341467670548at_num: ( nat > set_Pr6200539531224447659at_num ) > set_nat > set_se4826145725398303499at_num ).
thf(func_def_2217,type,
image_4592875511192039216at_nat: ( nat > set_Pr8693737435421807431at_nat ) > set_nat > set_se6425085446898223655at_nat ).
thf(func_def_2218,type,
image_1087905878993176368at_nat: ( nat > set_Pr4329608150637261639at_nat ) > set_nat > set_se5479201105039950375at_nat ).
thf(func_def_2219,type,
image_4824033694279209942t_unit: ( nat > set_Product_unit ) > set_nat > set_set_Product_unit ).
thf(func_def_2220,type,
image_nat_set_rat: ( nat > set_rat ) > set_nat > set_set_rat ).
thf(func_def_2221,type,
image_nat_set_char: ( nat > set_char ) > set_nat > set_set_char ).
thf(func_def_2222,type,
image_nat_char: ( nat > char ) > set_nat > set_char ).
thf(func_def_2223,type,
image_678696785212003926at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat ).
thf(func_def_2224,type,
image_num_o: ( num > $o ) > set_num > set_o ).
thf(func_def_2225,type,
image_num_int: ( num > int ) > set_num > set_int ).
thf(func_def_2226,type,
image_num_nat: ( num > nat ) > set_num > set_nat ).
thf(func_def_2227,type,
image_num_num: ( num > num ) > set_num > set_num ).
thf(func_def_2228,type,
image_4778453735051108682at_num: ( num > set_Pr6200539531224447659at_num ) > set_num > set_se4826145725398303499at_num ).
thf(func_def_2229,type,
image_7896445794123959606_o_o_o: ( product_prod_o_o > $o ) > set_Product_prod_o_o > set_o ).
thf(func_def_2230,type,
image_8105710389281276538_nat_o: ( product_prod_o_nat > $o ) > set_Pr2101469702781467981_o_nat > set_o ).
thf(func_def_2231,type,
image_4888532181312399726at_nat: ( product_prod_o_nat > nat ) > set_Pr2101469702781467981_o_nat > set_nat ).
thf(func_def_2232,type,
image_8742399529945250561unit_o: ( produc3788275437394581276t_unit > $o ) > set_Pr6671815714118170108t_unit > set_o ).
thf(func_def_2233,type,
image_4419268941131634678t_unit: ( produc3788275437394581276t_unit > product_unit ) > set_Pr6671815714118170108t_unit > set_Product_unit ).
thf(func_def_2234,type,
image_17660834435998945t_unit: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > set_Pr1133966238863718811t_unit > set_he8644174446132254637t_unit ).
thf(func_def_2235,type,
image_7136766188234240905_ref_a: ( produc7812382424243267045t_unit > ref_a ) > set_Pr1133966238863718811t_unit > set_ref_a ).
thf(func_def_2236,type,
image_1531683682067511245nt_int: ( produc7812382424243267045t_unit > product_prod_int_int ) > set_Pr1133966238863718811t_unit > set_Pr958786334691620121nt_int ).
thf(func_def_2237,type,
image_4710180989675653397at_nat: ( produc7812382424243267045t_unit > product_prod_nat_nat ) > set_Pr1133966238863718811t_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_2238,type,
image_90517134139374612_o_int: ( product_prod_int_o > int ) > set_Pr903927857289325719_int_o > set_int ).
thf(func_def_2239,type,
image_2135063354759101220_int_o: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int > set_o ).
thf(func_def_2240,type,
image_5042161079198086560nt_int: ( product_prod_int_int > int ) > set_Pr958786334691620121nt_int > set_int ).
thf(func_def_2241,type,
image_5044651549707136836nt_nat: ( product_prod_int_int > nat ) > set_Pr958786334691620121nt_int > set_nat ).
thf(func_def_2242,type,
image_2653370878348428101nt_int: ( product_prod_int_int > product_prod_int_int ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2243,type,
image_6831221897857624809nt_nat: ( product_prod_int_int > product_prod_int_nat ) > set_Pr958786334691620121nt_int > set_Pr3448869479623346877nt_nat ).
thf(func_def_2244,type,
image_1654017166447373545at_int: ( product_prod_int_int > product_prod_nat_int ) > set_Pr958786334691620121nt_int > set_Pr7995236796853374141at_int ).
thf(func_def_2245,type,
image_5831868185956570253at_nat: ( product_prod_int_int > product_prod_nat_nat ) > set_Pr958786334691620121nt_int > set_Pr1261947904930325089at_nat ).
thf(func_def_2246,type,
image_6540112122905407959at_num: ( product_prod_int_int > product_prod_nat_num ) > set_Pr958786334691620121nt_int > set_Pr6200539531224447659at_num ).
thf(func_def_2247,type,
image_8858061497167895027at_nat: ( product_prod_int_int > produc859450856879609959at_nat ) > set_Pr958786334691620121nt_int > set_Pr8693737435421807431at_nat ).
thf(func_def_2248,type,
image_6029125644611338739at_nat: ( product_prod_int_int > produc3843707927480180839at_nat ) > set_Pr958786334691620121nt_int > set_Pr4329608150637261639at_nat ).
thf(func_def_2249,type,
image_2855239504505064772at_int: ( product_prod_int_nat > int ) > set_Pr3448869479623346877nt_nat > set_int ).
thf(func_def_2250,type,
image_7928304878501623365nt_nat: ( product_prod_int_nat > product_prod_int_nat ) > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_2251,type,
image_4420076320108226637nt_rat: ( product_prod_int_nat > product_prod_int_rat ) > set_Pr3448869479623346877nt_nat > set_Pr6292255179000445125nt_rat ).
thf(func_def_2252,type,
image_2751100147091372101at_int: ( product_prod_int_nat > product_prod_nat_int ) > set_Pr3448869479623346877nt_nat > set_Pr7995236796853374141at_int ).
thf(func_def_2253,type,
image_3420722608207172081at_rat: ( product_prod_int_nat > product_prod_nat_rat ) > set_Pr3448869479623346877nt_nat > set_Pr4105333604307423337at_rat ).
thf(func_def_2254,type,
image_7716461468295075337it_int: ( produc6865911496949736918t_unit > int ) > set_Pr5889264611543340172t_unit > set_int ).
thf(func_def_2255,type,
image_7478392465989118804at_o_o: ( product_prod_nat_o > $o ) > set_Pr3149072824959771635_nat_o > set_o ).
thf(func_def_2256,type,
image_8629803608462650132_o_nat: ( product_prod_nat_o > nat ) > set_Pr3149072824959771635_nat_o > set_nat ).
thf(func_def_2257,type,
image_893334214595316897nt_int: ( product_prod_nat_int > product_prod_int_int ) > set_Pr7995236796853374141at_int > set_Pr958786334691620121nt_int ).
thf(func_def_2258,type,
image_5071185234104513605nt_nat: ( product_prod_nat_int > product_prod_int_nat ) > set_Pr7995236796853374141at_int > set_Pr3448869479623346877nt_nat ).
thf(func_def_2259,type,
image_9117352539549038149at_int: ( product_prod_nat_int > product_prod_nat_int ) > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int ).
thf(func_def_2260,type,
image_8800797895614172237at_int: ( product_prod_nat_int > product_prod_rat_int ) > set_Pr7995236796853374141at_int > set_Pr3594552606344371909at_int ).
thf(func_def_2261,type,
image_3755276878268593137at_nat: ( product_prod_nat_int > product_prod_rat_nat ) > set_Pr7995236796853374141at_int > set_Pr6084635751276098665at_nat ).
thf(func_def_2262,type,
image_3693632289388996572_nat_o: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > set_o ).
thf(func_def_2263,type,
image_2483585944268220136at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > set_int ).
thf(func_def_2264,type,
image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_2265,type,
image_1990417195239315453nt_int: ( product_prod_nat_nat > product_prod_int_int ) > set_Pr1261947904930325089at_nat > set_Pr958786334691620121nt_int ).
thf(func_def_2266,type,
image_5168914502847457605at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2267,type,
image_5877158439796295311at_num: ( product_prod_nat_nat > product_prod_nat_num ) > set_Pr1261947904930325089at_nat > set_Pr6200539531224447659at_num ).
thf(func_def_2268,type,
image_1119892238107900587at_nat: ( product_prod_nat_nat > produc859450856879609959at_nat ) > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2269,type,
image_6169909464789311569t_unit: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > set_Product_unit ).
thf(func_def_2270,type,
image_501298686397505212_set_o: ( product_prod_nat_nat > set_o ) > set_Pr1261947904930325089at_nat > set_set_o ).
thf(func_def_2271,type,
image_15824709712370754et_nat: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > set_set_nat ).
thf(func_def_2272,type,
image_5423882813909314213at_nat: ( product_prod_nat_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2273,type,
image_5803077947706746251at_nat: ( product_prod_nat_nat > set_Pr8693737435421807431at_nat ) > set_Pr1261947904930325089at_nat > set_se6425085446898223655at_nat ).
thf(func_def_2274,type,
image_121980125215734065t_unit: ( product_prod_nat_nat > set_Product_unit ) > set_Pr1261947904930325089at_nat > set_set_Product_unit ).
thf(func_def_2275,type,
image_4451812852358507538_num_o: ( product_prod_nat_num > $o ) > set_Pr6200539531224447659at_num > set_o ).
thf(func_def_2276,type,
image_4501981038234393650um_int: ( product_prod_nat_num > int ) > set_Pr6200539531224447659at_num > set_int ).
thf(func_def_2277,type,
image_4504471508743443926um_nat: ( product_prod_nat_num > nat ) > set_Pr6200539531224447659at_num > set_nat ).
thf(func_def_2278,type,
image_1039142661021589043nt_int: ( product_prod_nat_num > product_prod_int_int ) > set_Pr6200539531224447659at_num > set_Pr958786334691620121nt_int ).
thf(func_def_2279,type,
image_4217639968629731195at_nat: ( product_prod_nat_num > product_prod_nat_nat ) > set_Pr6200539531224447659at_num > set_Pr1261947904930325089at_nat ).
thf(func_def_2280,type,
image_4925883905578568901at_num: ( product_prod_nat_num > product_prod_nat_num ) > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
thf(func_def_2281,type,
image_2347970371937200581um_nat: ( product_prod_nat_num > product_prod_num_nat ) > set_Pr6200539531224447659at_num > set_Pr3280342998896498603um_nat ).
thf(func_def_2282,type,
image_2708129733610033121at_nat: ( product_prod_nat_num > produc3843707927480180839at_nat ) > set_Pr6200539531224447659at_num > set_Pr4329608150637261639at_nat ).
thf(func_def_2283,type,
image_3884712837920099081it_nat: ( produc526117512892780850t_unit > nat ) > set_Pr4334478416066269672t_unit > set_nat ).
thf(func_def_2284,type,
image_5511522805742971924t_unit: ( produc526117512892780850t_unit > product_unit ) > set_Pr4334478416066269672t_unit > set_Product_unit ).
thf(func_def_2285,type,
image_7762062833379733445at_num: ( product_prod_num_nat > product_prod_nat_num ) > set_Pr3280342998896498603um_nat > set_Pr6200539531224447659at_num ).
thf(func_def_2286,type,
image_3275415580317762038_nat_o: ( produc859450856879609959at_nat > $o ) > set_Pr8693737435421807431at_nat > set_o ).
thf(func_def_2287,type,
image_6160980552072806642at_nat: ( produc859450856879609959at_nat > nat ) > set_Pr8693737435421807431at_nat > set_nat ).
thf(func_def_2288,type,
image_6706873702294942047at_nat: ( produc859450856879609959at_nat > product_prod_nat_nat ) > set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2289,type,
image_6321802852832981957at_nat: ( produc859450856879609959at_nat > produc859450856879609959at_nat ) > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2290,type,
image_7637461350386011077at_nat: ( produc859450856879609959at_nat > produc3843707927480180839at_nat ) > set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2291,type,
image_8487516615895632747t_unit: ( produc859450856879609959at_nat > product_unit ) > set_Pr8693737435421807431at_nat > set_Product_unit ).
thf(func_def_2292,type,
image_2819269535336293544et_nat: ( produc859450856879609959at_nat > set_nat ) > set_Pr8693737435421807431at_nat > set_set_nat ).
thf(func_def_2293,type,
image_1384942819424619199at_nat: ( produc859450856879609959at_nat > set_Pr1261947904930325089at_nat ) > set_Pr8693737435421807431at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2294,type,
image_6654316230217496229at_nat: ( produc859450856879609959at_nat > set_Pr8693737435421807431at_nat ) > set_Pr8693737435421807431at_nat > set_se6425085446898223655at_nat ).
thf(func_def_2295,type,
image_3876558564303283877at_nat: ( produc859450856879609959at_nat > set_Pr4329608150637261639at_nat ) > set_Pr8693737435421807431at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2296,type,
image_1801747192096393899it_o_o: ( produc7485711547916492274unit_o > $o ) > set_Pr5464989305201766866unit_o > set_o ).
thf(func_def_2297,type,
image_4246157487713968288t_unit: ( produc7485711547916492274unit_o > product_unit ) > set_Pr5464989305201766866unit_o > set_Product_unit ).
thf(func_def_2298,type,
image_6725568594985674851at_nat: ( produc600557818389255820it_nat > nat ) > set_Pr1763845938948868674it_nat > set_nat ).
thf(func_def_2299,type,
image_7474191388529947450t_unit: ( produc600557818389255820it_nat > product_unit ) > set_Pr1763845938948868674it_nat > set_Product_unit ).
thf(func_def_2300,type,
image_262127665112854123t_unit: ( produc8459935480633519975t_unit > product_unit ) > set_Pr5094982260447487303t_unit > set_Product_unit ).
thf(func_def_2301,type,
image_8033574621161215657at_num: ( produc3843707927480180839at_nat > product_prod_nat_num ) > set_Pr4329608150637261639at_nat > set_Pr6200539531224447659at_num ).
thf(func_def_2302,type,
image_5653576389946358725at_nat: ( produc3843707927480180839at_nat > produc859450856879609959at_nat ) > set_Pr4329608150637261639at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2303,type,
image_960689587819713477at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2304,type,
image_7082456443403096939t_unit: ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > set_Product_unit ).
thf(func_def_2305,type,
image_3160451284896210088et_nat: ( produc3843707927480180839at_nat > set_nat ) > set_Pr4329608150637261639at_nat > set_set_nat ).
thf(func_def_2306,type,
image_7979982168039674559at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2307,type,
image_7260680879217540773at_nat: ( produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat ) > set_Pr4329608150637261639at_nat > set_se6425085446898223655at_nat ).
thf(func_def_2308,type,
image_7364710425340685989at_nat: ( produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2309,type,
image_3313167189156628421at_nat: ( produc1319942482725812455at_nat > produc1319942482725812455at_nat ) > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_2310,type,
image_2699825501378146573ar_rat: ( produc3922234789054302210ar_nat > produc414006230660905482ar_rat ) > set_Pr1413074515586503650ar_nat > set_Pr4256460214963601898ar_rat ).
thf(func_def_2311,type,
image_5973708714899544198r_char: ( produc3922234789054302210ar_nat > produc143505574896075907r_char ) > set_Pr1413074515586503650ar_nat > set_Pr3309569728657787619r_char ).
thf(func_def_2312,type,
image_4975014655635759961ar_int: ( produc414006230660905482ar_rat > produc8967755806399881310ar_int ) > set_Pr4256460214963601898ar_rat > set_Pr8146363407509552702ar_int ).
thf(func_def_2313,type,
image_9152865675144956669ar_nat: ( produc414006230660905482ar_rat > produc3922234789054302210ar_nat ) > set_Pr4256460214963601898ar_rat > set_Pr1413074515586503650ar_nat ).
thf(func_def_2314,type,
image_5644637116751559941ar_rat: ( produc414006230660905482ar_rat > produc414006230660905482ar_rat ) > set_Pr4256460214963601898ar_rat > set_Pr4256460214963601898ar_rat ).
thf(func_def_2315,type,
image_8036680598759533694r_char: ( produc414006230660905482ar_rat > produc143505574896075907r_char ) > set_Pr4256460214963601898ar_rat > set_Pr3309569728657787619r_char ).
thf(func_def_2316,type,
image_6605449789044937888ar_int: ( produc143505574896075907r_char > produc8967755806399881310ar_int ) > set_Pr3309569728657787619r_char > set_Pr8146363407509552702ar_int ).
thf(func_def_2317,type,
image_1559928771699358788ar_nat: ( produc143505574896075907r_char > produc3922234789054302210ar_nat ) > set_Pr3309569728657787619r_char > set_Pr1413074515586503650ar_nat ).
thf(func_def_2318,type,
image_7275072250160737868ar_rat: ( produc143505574896075907r_char > produc414006230660905482ar_rat ) > set_Pr3309569728657787619r_char > set_Pr4256460214963601898ar_rat ).
thf(func_def_2319,type,
image_7676512070627423941r_char: ( produc143505574896075907r_char > produc143505574896075907r_char ) > set_Pr3309569728657787619r_char > set_Pr3309569728657787619r_char ).
thf(func_def_2320,type,
image_Product_unit_o: ( product_unit > $o ) > set_Product_unit > set_o ).
thf(func_def_2321,type,
image_873079544045703924it_int: ( product_unit > int ) > set_Product_unit > set_int ).
thf(func_def_2322,type,
image_875570014554754200it_nat: ( product_unit > nat ) > set_Product_unit > set_nat ).
thf(func_def_2323,type,
image_405062704495631173t_unit: ( product_unit > product_unit ) > set_Product_unit > set_Product_unit ).
thf(func_def_2324,type,
image_240439954468258464it_rat: ( product_unit > rat ) > set_Product_unit > set_rat ).
thf(func_def_2325,type,
image_6930536745178679216_set_o: ( product_unit > set_o ) > set_Product_unit > set_set_o ).
thf(func_def_2326,type,
image_3995998972318789802et_int: ( product_unit > set_int ) > set_Product_unit > set_set_int ).
thf(func_def_2327,type,
image_8173849991827986510et_nat: ( product_unit > set_nat ) > set_Product_unit > set_set_nat ).
thf(func_def_2328,type,
image_3617315916088684441at_nat: ( product_unit > set_Pr1261947904930325089at_nat ) > set_Product_unit > set_se7855581050983116737at_nat ).
thf(func_def_2329,type,
image_7288820656315755647at_nat: ( product_unit > set_Pr8693737435421807431at_nat ) > set_Product_unit > set_se6425085446898223655at_nat ).
thf(func_def_2330,type,
image_5172358348707908735at_nat: ( product_unit > set_Pr4329608150637261639at_nat ) > set_Product_unit > set_se5479201105039950375at_nat ).
thf(func_def_2331,type,
image_7778121751606633509t_unit: ( product_unit > set_Product_unit ) > set_Product_unit > set_set_Product_unit ).
thf(func_def_2332,type,
image_4665621433434589782et_rat: ( product_unit > set_rat ) > set_Product_unit > set_set_rat ).
thf(func_def_2333,type,
image_5325685772115642575t_char: ( product_unit > set_char ) > set_Product_unit > set_set_char ).
thf(func_def_2334,type,
image_7248553556944771225t_char: ( product_unit > char ) > set_Product_unit > set_char ).
thf(func_def_2335,type,
image_rat_o: ( rat > $o ) > set_rat > set_o ).
thf(func_def_2336,type,
image_rat_int: ( rat > int ) > set_rat > set_int ).
thf(func_def_2337,type,
image_rat_nat: ( rat > nat ) > set_rat > set_nat ).
thf(func_def_2338,type,
image_5997455970908365082nt_int: ( rat > product_prod_int_int ) > set_rat > set_Pr958786334691620121nt_int ).
thf(func_def_2339,type,
image_9175953278516507234at_nat: ( rat > product_prod_nat_nat ) > set_rat > set_Pr1261947904930325089at_nat ).
thf(func_def_2340,type,
image_2327579789247107822t_unit: ( rat > product_unit ) > set_rat > set_Product_unit ).
thf(func_def_2341,type,
image_rat_rat: ( rat > rat ) > set_rat > set_rat ).
thf(func_def_2342,type,
image_rat_set_nat: ( rat > set_nat ) > set_rat > set_set_nat ).
thf(func_def_2343,type,
image_rat_char: ( rat > char ) > set_rat > set_char ).
thf(func_def_2344,type,
image_set_o_o_o: ( set_o > $o > $o ) > set_set_o > set_o_o ).
thf(func_def_2345,type,
image_set_o_o: ( set_o > $o ) > set_set_o > set_o ).
thf(func_def_2346,type,
image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
thf(func_def_2347,type,
image_set_int_int_o: ( set_int > int > $o ) > set_set_int > set_int_o ).
thf(func_def_2348,type,
image_set_int_o: ( set_int > $o ) > set_set_int > set_o ).
thf(func_def_2349,type,
image_524474410958335435et_int: ( set_int > set_int ) > set_set_int > set_set_int ).
thf(func_def_2350,type,
image_4702325430467532143et_nat: ( set_int > set_nat ) > set_set_int > set_set_nat ).
thf(func_def_2351,type,
image_set_nat_nat_o: ( set_nat > nat > $o ) > set_set_nat > set_nat_o ).
thf(func_def_2352,type,
image_set_nat_o: ( set_nat > $o ) > set_set_nat > set_o ).
thf(func_def_2353,type,
image_6369283972875870912t_unit: ( set_nat > product_unit ) > set_set_nat > set_Product_unit ).
thf(func_def_2354,type,
image_3739036796817536367et_int: ( set_nat > set_int ) > set_set_nat > set_set_int ).
thf(func_def_2355,type,
image_7916887816326733075et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).
thf(func_def_2356,type,
image_6521575952113991828at_nat: ( set_nat > set_Pr1261947904930325089at_nat ) > set_set_nat > set_se7855581050983116737at_nat ).
thf(func_def_2357,type,
image_4408659257933336347et_rat: ( set_nat > set_rat ) > set_set_nat > set_set_rat ).
thf(func_def_2358,type,
image_4446226961036766042_int_o: ( set_Pr958786334691620121nt_int > int > int > $o ) > set_se6260736226359567993nt_int > set_int_int_o ).
thf(func_def_2359,type,
image_701744273176368580_int_o: ( set_Pr958786334691620121nt_int > $o ) > set_se6260736226359567993nt_int > set_o ).
thf(func_def_2360,type,
image_6923511907955291850_nat_o: ( set_Pr1261947904930325089at_nat > nat > nat > $o ) > set_se7855581050983116737at_nat > set_nat_nat_o ).
thf(func_def_2361,type,
image_5253903537071781336_nat_o: ( set_Pr1261947904930325089at_nat > product_prod_nat_nat > $o ) > set_se7855581050983116737at_nat > set_Pr5582243495563764594_nat_o ).
thf(func_def_2362,type,
image_7457375456213313148_nat_o: ( set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat > set_o ).
thf(func_def_2363,type,
image_5853224409075402146et_nat: ( set_Pr1261947904930325089at_nat > set_nat ) > set_se7855581050983116737at_nat > set_set_nat ).
thf(func_def_2364,type,
image_3684629450409544005at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2365,type,
image_6898982319499645995at_nat: ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat ) > set_se7855581050983116737at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2366,type,
image_2055017250723459638_num_o: ( set_Pr6200539531224447659at_num > nat > num > $o ) > set_se4826145725398303499at_num > set_nat_num_o ).
thf(func_def_2367,type,
image_1013614488123988933at_nat: ( set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ) > set_se6425085446898223655at_nat > set_se6425085446898223655at_nat ).
thf(func_def_2368,type,
image_4859512832475012440_nat_o: ( set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat > $o ) > set_se5479201105039950375at_nat > set_Pr7010166363911110284_nat_o ).
thf(func_def_2369,type,
image_6595146019508340652_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_se5479201105039950375at_nat > set_se9180647916752606350_nat_o ).
thf(func_def_2370,type,
image_3568060456209098518_nat_o: ( set_Pr4329608150637261639at_nat > $o ) > set_se5479201105039950375at_nat > set_o ).
thf(func_def_2371,type,
image_4303274092540115909at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2372,type,
image_1124969593608450885at_nat: ( set_Pr4329608150637261639at_nat > set_Pr7459493094073627847at_nat ) > set_se5479201105039950375at_nat > set_se7592288975875140775at_nat ).
thf(func_def_2373,type,
image_5337237954834410540_nat_o: ( set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_se7592288975875140775at_nat > set_se7255092946006855566_nat_o ).
thf(func_def_2374,type,
image_4019945301284682565t_unit: ( set_Product_unit > set_Product_unit ) > set_set_Product_unit > set_set_Product_unit ).
thf(func_def_2375,type,
image_char_o: ( char > $o ) > set_char > set_o ).
thf(func_def_2376,type,
image_char_int: ( char > int ) > set_char > set_int ).
thf(func_def_2377,type,
image_char_nat: ( char > nat ) > set_char > set_nat ).
thf(func_def_2378,type,
image_5204326662208377313nt_int: ( char > product_prod_int_int ) > set_char > set_Pr958786334691620121nt_int ).
thf(func_def_2379,type,
image_8382823969816519465at_nat: ( char > product_prod_nat_nat ) > set_char > set_Pr1261947904930325089at_nat ).
thf(func_def_2380,type,
image_4337914935673063477t_unit: ( char > product_unit ) > set_char > set_Product_unit ).
thf(func_def_2381,type,
image_char_rat: ( char > rat ) > set_char > set_rat ).
thf(func_def_2382,type,
image_char_char: ( char > char ) > set_char > set_char ).
thf(func_def_2383,type,
image_1320371278474632150at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat ).
thf(func_def_2384,type,
insert_o: $o > set_o > set_o ).
thf(func_def_2385,type,
insert8563697753282147485t_unit: heap_e7401611519738050253t_unit > set_he8644174446132254637t_unit > set_he8644174446132254637t_unit ).
thf(func_def_2386,type,
insert_ref_a: ref_a > set_ref_a > set_ref_a ).
thf(func_def_2387,type,
insert_int: int > set_int > set_int ).
thf(func_def_2388,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_2389,type,
insert_num: num > set_num > set_num ).
thf(func_def_2390,type,
insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_2391,type,
insert7948214739558299847_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
thf(func_def_2392,type,
insert9112848208840649964t_unit: produc3788275437394581276t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit ).
thf(func_def_2393,type,
insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_2394,type,
insert2233377226759017069_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
thf(func_def_2395,type,
insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2396,type,
insert8920054152555992091at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
thf(func_def_2397,type,
insert6804906068341198690t_unit: produc526117512892780850t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit ).
thf(func_def_2398,type,
insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2399,type,
insert5475735164933346999at_nat: produc349518998152878311at_nat > set_Pr553994874890374343at_nat > set_Pr553994874890374343at_nat ).
thf(func_def_2400,type,
insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
thf(func_def_2401,type,
insert3586912282507785154unit_o: produc7485711547916492274unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o ).
thf(func_def_2402,type,
insert6879346373837673660it_nat: produc600557818389255820it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat ).
thf(func_def_2403,type,
insert4616891024742550839t_unit: produc8459935480633519975t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit ).
thf(func_def_2404,type,
insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2405,type,
insert291458823148189367at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
thf(func_def_2406,type,
insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_2407,type,
insert_rat: rat > set_rat > set_rat ).
thf(func_def_2408,type,
insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2409,type,
insert2290795007606087959at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat ).
thf(func_def_2410,type,
the_elem_int: set_int > int ).
thf(func_def_2411,type,
the_elem_nat: set_nat > nat ).
thf(func_def_2412,type,
the_elem_rat: set_rat > rat ).
thf(func_def_2413,type,
vimage4289680085338140859nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Pr4111642102156807771nteger > set_Co726186806682698383nteger ).
thf(func_def_2414,type,
vimage_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_2415,type,
vimage_o_nat: ( $o > nat ) > set_nat > set_o ).
thf(func_def_2416,type,
vimage8945963521958007626od_o_o: ( $o > product_prod_o_o ) > set_Product_prod_o_o > set_o ).
thf(func_def_2417,type,
vimage4304346610107161470_int_o: ( $o > product_prod_int_o ) > set_Pr903927857289325719_int_o > set_o ).
thf(func_def_2418,type,
vimage6125388955539849434_nat_o: ( $o > product_prod_nat_o ) > set_Pr3149072824959771635_nat_o > set_o ).
thf(func_def_2419,type,
vimage4222377557387472176t_unit: ( $o > product_unit ) > set_Product_unit > set_o ).
thf(func_def_2420,type,
vimage_o_rat: ( $o > rat ) > set_rat > set_o ).
thf(func_def_2421,type,
vimage_o_char: ( $o > char ) > set_char > set_o ).
thf(func_def_2422,type,
vimage6029918387083761651nteger: ( code_integer > code_integer > code_integer ) > set_Co726186806682698383nteger > set_Code_integer ).
thf(func_def_2423,type,
vimage6839621282666897215nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Pr4111642102156807771nteger > set_Code_integer ).
thf(func_def_2424,type,
vimage_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_2425,type,
vimage_int_nat: ( int > nat ) > set_nat > set_int ).
thf(func_def_2426,type,
vimage_int_num: ( int > num ) > set_num > set_int ).
thf(func_def_2427,type,
vimage7872673496510460816nt_int: ( int > product_prod_int_int ) > set_Pr958786334691620121nt_int > set_int ).
thf(func_def_2428,type,
vimage1827798767263827160at_nat: ( int > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_int ).
thf(func_def_2429,type,
vimage8527374361057053988at_nat: ( list_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_list_nat ).
thf(func_def_2430,type,
vimage_nat_o: ( nat > $o ) > set_o > set_nat ).
thf(func_def_2431,type,
vimage_nat_int: ( nat > int ) > set_int > set_nat ).
thf(func_def_2432,type,
vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_2433,type,
vimage_nat_num: ( nat > num ) > set_num > set_nat ).
thf(func_def_2434,type,
vimage5656379182745576100_o_nat: ( nat > product_prod_o_nat ) > set_Pr2101469702781467981_o_nat > set_nat ).
thf(func_def_2435,type,
vimage9012682431555523728nt_nat: ( nat > product_prod_int_nat ) > set_Pr3448869479623346877nt_nat > set_nat ).
thf(func_def_2436,type,
vimage8013328719654469172at_nat: ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_2437,type,
vimage6435164912253009178at_nat: ( nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_nat ).
thf(func_def_2438,type,
vimage4884490618288580032t_unit: ( nat > product_unit ) > set_Product_unit > set_nat ).
thf(func_def_2439,type,
vimage_nat_rat: ( nat > rat ) > set_rat > set_nat ).
thf(func_def_2440,type,
vimage_nat_char: ( nat > char ) > set_char > set_nat ).
thf(func_def_2441,type,
vimage5436458796434496692at_num: ( num > product_prod_nat_num ) > set_Pr6200539531224447659at_num > set_num ).
thf(func_def_2442,type,
vimage6116673589273818795t_unit: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > set_he8644174446132254637t_unit > set_Pr1133966238863718811t_unit ).
thf(func_def_2443,type,
vimage2910454108108208703_ref_a: ( produc7812382424243267045t_unit > ref_a ) > set_ref_a > set_Pr1133966238863718811t_unit ).
thf(func_def_2444,type,
vimage2444243245536687506_nat_o: ( product_prod_nat_nat > $o ) > set_o > set_Pr1261947904930325089at_nat ).
thf(func_def_2445,type,
vimage1024995831485383111t_unit: ( product_prod_nat_nat > heap_e7401611519738050253t_unit ) > set_he8644174446132254637t_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_2446,type,
vimage7322659125625010723_ref_a: ( product_prod_nat_nat > ref_a ) > set_ref_a > set_Pr1261947904930325089at_nat ).
thf(func_def_2447,type,
vimage4650790856102703794at_int: ( product_prod_nat_nat > int ) > set_int > set_Pr1261947904930325089at_nat ).
thf(func_def_2448,type,
vimage4653281326611754070at_nat: ( product_prod_nat_nat > nat ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2449,type,
vimage4308919176130087787t_unit: ( product_prod_nat_nat > produc7812382424243267045t_unit ) > set_Pr1133966238863718811t_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_2450,type,
vimage2449269961533847803at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2451,type,
vimage3104651464403166471t_unit: ( product_prod_nat_nat > product_unit ) > set_Product_unit > set_Pr1261947904930325089at_nat ).
thf(func_def_2452,type,
vimage8808348054653608838unit_o: ( product_unit > $o ) > set_o > set_Product_unit ).
thf(func_def_2453,type,
vimage6253328473476588386it_nat: ( product_unit > nat ) > set_nat > set_Product_unit ).
thf(func_def_2454,type,
vimage508909887551888138t_unit: ( product_unit > produc3788275437394581276t_unit ) > set_Pr6671815714118170108t_unit > set_Product_unit ).
thf(func_def_2455,type,
vimage4422279681566046568t_unit: ( product_unit > produc6865911496949736918t_unit ) > set_Pr5889264611543340172t_unit > set_Product_unit ).
thf(func_def_2456,type,
vimage7305857734363866308t_unit: ( product_unit > produc526117512892780850t_unit ) > set_Pr4334478416066269672t_unit > set_Product_unit ).
thf(func_def_2457,type,
vimage7995052115951654139t_unit: ( product_unit > product_unit ) > set_Product_unit > set_Product_unit ).
thf(func_def_2458,type,
vimage5618198413390092650it_rat: ( product_unit > rat ) > set_rat > set_Product_unit ).
thf(func_def_2459,type,
vimage2648087219933717859t_char: ( product_unit > char ) > set_char > set_Product_unit ).
thf(func_def_2460,type,
vimage_rat_int: ( rat > int ) > set_int > set_rat ).
thf(func_def_2461,type,
vimage_rat_nat: ( rat > nat ) > set_nat > set_rat ).
thf(func_def_2462,type,
vimage2119786153496215084at_nat: ( rat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_rat ).
thf(func_def_2463,type,
vimage_rat_rat: ( rat > rat ) > set_rat > set_rat ).
thf(func_def_2464,type,
vimage_rat_char: ( rat > char ) > set_char > set_rat ).
thf(func_def_2465,type,
vimage_char_int: ( char > int ) > set_int > set_char ).
thf(func_def_2466,type,
vimage_char_nat: ( char > nat ) > set_nat > set_char ).
thf(func_def_2467,type,
vimage8942442433166402803at_nat: ( char > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_char ).
thf(func_def_2468,type,
vimage_char_rat: ( char > rat ) > set_rat > set_char ).
thf(func_def_2469,type,
vimage_char_char: ( char > char ) > set_char > set_char ).
thf(func_def_2470,type,
set_or1266510415728281911st_int: int > int > set_int ).
thf(func_def_2471,type,
set_or1269000886237332187st_nat: nat > nat > set_nat ).
thf(func_def_2472,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(func_def_2473,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(func_def_2474,type,
set_ord_atLeast_nat: nat > set_nat ).
thf(func_def_2475,type,
set_ord_atMost_nat: nat > set_nat ).
thf(func_def_2476,type,
set_or1210151606488870762an_nat: nat > set_nat ).
thf(func_def_2477,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(func_def_2478,type,
comm_s629917340098488124ar_nat: char > nat ).
thf(func_def_2479,type,
unique3096191561947761185of_nat: nat > char ).
thf(func_def_2480,type,
left_t2884206969071330nteger: ( code_integer > code_integer > $o ) > $o ).
thf(func_def_2481,type,
left_t1735413524555719857er_int: ( code_integer > int > $o ) > $o ).
thf(func_def_2482,type,
left_t2374113004080657585nteger: ( int > code_integer > $o ) > $o ).
thf(func_def_2483,type,
left_total_int_int: ( int > int > $o ) > $o ).
thf(func_def_2484,type,
left_t8261381459436684205at_nat: ( int > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2485,type,
left_t1861001511420785031at_int: ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_2486,type,
left_t5646938096895998950at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2487,type,
left_u6156896403773009178er_int: ( code_integer > int > $o ) > $o ).
thf(func_def_2488,type,
left_u6795595883297946906nteger: ( int > code_integer > $o ) > $o ).
thf(func_def_2489,type,
left_unique_int_int: ( int > int > $o ) > $o ).
thf(func_def_2490,type,
left_u1182257597767569412at_nat: ( int > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2491,type,
left_unique_nat_nat: ( nat > nat > $o ) > $o ).
thf(func_def_2492,type,
left_unique_num_num: ( num > num > $o ) > $o ).
thf(func_def_2493,type,
left_u4005249686606446046at_int: ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_2494,type,
left_u7296345956935681743at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2495,type,
right_7281159819619925802nteger: ( int > code_integer > $o ) > $o ).
thf(func_def_2496,type,
right_total_int_int: ( int > int > $o ) > $o ).
thf(func_def_2497,type,
right_total_nat_nat: ( nat > nat > $o ) > $o ).
thf(func_def_2498,type,
right_total_num_num: ( num > num > $o ) > $o ).
thf(func_def_2499,type,
right_1157779049177982926at_int: ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_2500,type,
right_4094035864313884895at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2501,type,
right_5866438497372881682nteger: ( code_integer > code_integer > $o ) > $o ).
thf(func_def_2502,type,
right_7836862732553076961er_int: ( code_integer > int > $o ) > $o ).
thf(func_def_2503,type,
right_8475562212078014689nteger: ( int > code_integer > $o ) > $o ).
thf(func_def_2504,type,
right_unique_int_int: ( int > int > $o ) > $o ).
thf(func_def_2505,type,
right_8621877368619751767at_int: ( product_prod_nat_nat > int > $o ) > $o ).
thf(func_def_2506,type,
right_1383565826979811350at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_2507,type,
type_definition_o_o: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_2508,type,
type_d7121381646445849148_o_nat: ( $o > nat ) > ( nat > $o ) > set_nat > $o ).
thf(func_def_2509,type,
type_d3678713432601627782_o_num: ( $o > num ) > ( num > $o ) > set_num > $o ).
thf(func_def_2510,type,
type_d6486251586359353412_o_rat: ( $o > rat ) > ( rat > $o ) > set_rat > $o ).
thf(func_def_2511,type,
type_d9076672964931703357o_char: ( $o > char ) > ( char > $o ) > set_char > $o ).
thf(func_def_2512,type,
type_d8403010662121346494_int_o: ( int > $o ) > ( $o > int ) > set_o > $o ).
thf(func_def_2513,type,
type_d7247357190169752966nt_int: ( int > int ) > ( int > int ) > set_int > $o ).
thf(func_def_2514,type,
type_d7249847660678803242nt_nat: ( int > nat ) > ( nat > int ) > set_nat > $o ).
thf(func_def_2515,type,
type_d7732240953928457511at_nat: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2516,type,
type_d1000680970699258650_nat_o: ( nat > $o ) > ( $o > nat ) > set_o > $o ).
thf(func_def_2517,type,
type_d6248003478268698410at_int: ( nat > int ) > ( int > nat ) > set_int > $o ).
thf(func_def_2518,type,
type_d6250493948777748686at_nat: ( nat > nat ) > ( nat > nat ) > set_nat > $o ).
thf(func_def_2519,type,
type_d2807825734933527320at_num: ( nat > num ) > ( num > nat ) > set_num > $o ).
thf(func_def_2520,type,
type_d5615363888691252950at_rat: ( nat > rat ) > ( rat > nat ) > set_rat > $o ).
thf(func_def_2521,type,
type_d5945782884131516111t_char: ( nat > char ) > ( char > nat ) > set_char > $o ).
thf(func_def_2522,type,
type_d9070036042389994064_num_o: ( num > $o ) > ( $o > num ) > set_o > $o ).
thf(func_def_2523,type,
type_d4380824352085218072um_nat: ( num > nat ) > ( nat > num ) > set_nat > $o ).
thf(func_def_2524,type,
type_d938156138240996706um_num: ( num > num ) > ( num > num ) > set_num > $o ).
thf(func_def_2525,type,
type_d3745694291998722336um_rat: ( num > rat ) > ( rat > num ) > set_rat > $o ).
thf(func_def_2526,type,
type_d4396077731765706521m_char: ( num > char ) > ( char > num ) > set_char > $o ).
thf(func_def_2527,type,
type_d1331861005912558337at_int: ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > set_int > $o ).
thf(func_def_2528,type,
type_d281131942595027436at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2529,type,
type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).
thf(func_def_2530,type,
type_d5933939304842882774at_nat: ( rat > nat ) > ( nat > rat ) > set_nat > $o ).
thf(func_def_2531,type,
accp_nat: ( nat > nat > $o ) > nat > $o ).
thf(func_def_2532,type,
less_than: set_Pr1261947904930325089at_nat ).
thf(func_def_2533,type,
lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_2534,type,
max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2535,type,
min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2536,type,
pred_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_2537,type,
wf_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2538,type,
wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2539,type,
member_o_o: ( $o > $o ) > set_o_o > $o ).
thf(func_def_2540,type,
member_o_nat: ( $o > nat ) > set_o_nat > $o ).
thf(func_def_2541,type,
member2370919827131729009t_unit: ( $o > product_unit ) > set_o_Product_unit > $o ).
thf(func_def_2542,type,
member2790140394383616496nteger: ( code_integer > code_integer ) > set_Co726186806682698383nteger > $o ).
thf(func_def_2543,type,
member254662033361028077nt_int: ( int > product_prod_int_int ) > set_in6154042108061588260nt_int > $o ).
thf(func_def_2544,type,
member557823603599733045at_nat: ( int > product_prod_nat_nat ) > set_in7748886932685137004at_nat > $o ).
thf(func_def_2545,type,
member7514810323860029129um_num: ( int > product_prod_num_num ) > set_in3169746454734514176um_num > $o ).
thf(func_def_2546,type,
member3963856813518191233at_nat: ( list_nat > product_prod_nat_nat ) > set_li2168235667650531768at_nat > $o ).
thf(func_def_2547,type,
member_nat_int: ( nat > int ) > set_nat_int > $o ).
thf(func_def_2548,type,
member6440191985751670089nt_int: ( nat > product_prod_int_int ) > set_na7251125088705586816nt_int > $o ).
thf(func_def_2549,type,
member6743353555990375057at_nat: ( nat > product_prod_nat_nat ) > set_na8845969913329135560at_nat > $o ).
thf(func_def_2550,type,
member_rat_o: ( rat > $o ) > set_rat_o > $o ).
thf(func_def_2551,type,
member_rat_nat: ( rat > nat ) > set_rat_nat > $o ).
thf(func_def_2552,type,
member546649419593416001nt_int: ( rat > product_prod_int_int ) > set_ra518564293221149304nt_int > $o ).
thf(func_def_2553,type,
member849810989832120969at_nat: ( rat > product_prod_nat_nat ) > set_ra2113409117844698048at_nat > $o ).
thf(func_def_2554,type,
member7011034171605722901t_unit: ( rat > product_unit ) > set_rat_Product_unit > $o ).
thf(func_def_2555,type,
member_char_o: ( char > $o ) > set_char_o > $o ).
thf(func_def_2556,type,
member_char_nat: ( char > nat ) > set_char_nat > $o ).
thf(func_def_2557,type,
member2992454361780672008nt_int: ( char > product_prod_int_int ) > set_ch6383161263842509759nt_int > $o ).
thf(func_def_2558,type,
member3295615932019376976at_nat: ( char > product_prod_nat_nat ) > set_ch7978006088466058503at_nat > $o ).
thf(func_def_2559,type,
member379592906918970460t_unit: ( char > product_unit ) > set_ch7814610555394875923t_unit > $o ).
thf(func_def_2560,type,
member_o: $o > set_o > $o ).
thf(func_def_2561,type,
member_Code_integer: code_integer > set_Code_integer > $o ).
thf(func_def_2562,type,
member242389114213480694t_unit: heap_e7401611519738050253t_unit > set_he8644174446132254637t_unit > $o ).
thf(func_def_2563,type,
member_ref_a: ref_a > set_ref_a > $o ).
thf(func_def_2564,type,
member_int: int > set_int > $o ).
thf(func_def_2565,type,
member_nat: nat > set_nat > $o ).
thf(func_def_2566,type,
member_num: num > set_num > $o ).
thf(func_def_2567,type,
member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_2568,type,
member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o ).
thf(func_def_2569,type,
member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(func_def_2570,type,
member7849944260330398460t_unit: produc7812382424243267045t_unit > set_Pr1133966238863718811t_unit > $o ).
thf(func_def_2571,type,
member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o ).
thf(func_def_2572,type,
member4345257455949424659nteger: produc2963269191615333738nteger > set_Pr8415741480598773322nteger > $o ).
thf(func_def_2573,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_2574,type,
member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_2575,type,
member6310962623043647828_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > $o ).
thf(func_def_2576,type,
member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o ).
thf(func_def_2577,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2578,type,
member9148766508732265716at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > $o ).
thf(func_def_2579,type,
member6570852975090897396um_nat: product_prod_num_nat > set_Pr3280342998896498603um_nat > $o ).
thf(func_def_2580,type,
member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o ).
thf(func_def_2581,type,
member2200362271989506215_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > $o ).
thf(func_def_2582,type,
member8394280151737582451at_int: produc4196048018000912732at_int > set_Pr49084382684228242at_int > $o ).
thf(func_def_2583,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_2584,type,
member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o ).
thf(func_def_2585,type,
member7821138191923116944t_unit: produc8459935480633519975t_unit > set_Pr5094982260447487303t_unit > $o ).
thf(func_def_2586,type,
member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_2587,type,
member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o ).
thf(func_def_2588,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(func_def_2589,type,
member_rat: rat > set_rat > $o ).
thf(func_def_2590,type,
member_set_o: set_o > set_set_o > $o ).
thf(func_def_2591,type,
member_set_int: set_int > set_set_int > $o ).
thf(func_def_2592,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_2593,type,
member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_2594,type,
member6273874620674182256at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat > $o ).
thf(func_def_2595,type,
member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o ).
thf(func_def_2596,type,
member_char: char > set_char > $o ).
thf(func_def_2597,type,
h: heap_e7401611519738050253t_unit ).
thf(func_def_2598,type,
h2: heap_e7401611519738050253t_unit ).
thf(func_def_2599,type,
r: ref_a ).
thf(func_def_2601,type,
x: a ).
thf(func_def_2620,type,
sP0: set_Product_unit > set_Product_unit > set_nat > set_nat > $o ).
thf(func_def_2621,type,
sP1: nat > list_nat > $o ).
thf(func_def_2622,type,
sP2: set_o > set_nat > set_o > set_nat > $o ).
thf(func_def_2623,type,
sP3: set_Product_unit > set_Product_unit > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2624,type,
sP4: set_o > set_Product_unit > set_Product_unit > set_o > $o ).
thf(func_def_2625,type,
sP5: set_Product_unit > set_Product_unit > set_Product_unit > set_Product_unit > $o ).
thf(func_def_2626,type,
sP6: set_o > set_Product_unit > set_o > set_Product_unit > $o ).
thf(func_def_2627,type,
sP7: set_o > set_o > set_o > set_o > $o ).
thf(func_def_2628,type,
sP8: set_Product_unit > set_Product_unit > set_nat > set_nat > $o ).
thf(func_def_2629,type,
sP9: set_nat > set_nat > set_nat > set_nat > $o ).
thf(func_def_2630,type,
sP10: set_o > set_nat > set_o > set_nat > $o ).
thf(func_def_2631,type,
sK11: set_int > ( nat > int ) > set_nat > set_nat ).
thf(func_def_2632,type,
sK12: ( nat > product_unit ) > ( $o > product_unit ) > set_nat > set_o > $o ).
thf(func_def_2633,type,
sK13: ( nat > product_unit ) > ( $o > product_unit ) > set_nat > set_o > nat ).
thf(func_def_2634,type,
sK14: int > ( int > int ) > set_int > int ).
thf(func_def_2635,type,
sK15: set_nat > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_2636,type,
sK16: product_prod_nat_num > ( nat > nat ) > ( nat > num ) > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_2637,type,
sK17: product_prod_nat_num > ( nat > nat ) > ( nat > num ) > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_2638,type,
sK18: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > int ) > int ).
thf(func_def_2639,type,
sK19: ( rat > int ) > ( int > int > $o ) > int ).
thf(func_def_2640,type,
sK20: int > set_o > ( $o > set_int ) > $o ).
thf(func_def_2641,type,
sK21: produc3843707927480180839at_nat > produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2642,type,
sK22: produc3843707927480180839at_nat > produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2643,type,
sK23: product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_2644,type,
sK24: product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_2645,type,
sK25: set_int > int ).
thf(func_def_2646,type,
sK26: ( nat > int ) > set_int > set_nat > nat ).
thf(func_def_2647,type,
sK27: ( nat > int ) > set_int > ( nat > $o ) > nat ).
thf(func_def_2648,type,
sK28: ( int > code_integer > $o ) > ( int > code_integer > $o ) > int ).
thf(func_def_2649,type,
sK29: ( int > code_integer > $o ) > ( int > code_integer > $o ) > code_integer ).
thf(func_def_2650,type,
sK30: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_2651,type,
sK31: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_2652,type,
sK32: produc1319942482725812455at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2653,type,
sK33: produc1319942482725812455at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2654,type,
sK34: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int > ( product_prod_int_int > $o ) > product_prod_int_int ).
thf(func_def_2655,type,
sK35: ( nat > nat ) > set_nat > set_nat > set_nat ).
thf(func_def_2656,type,
sK36: int > ( nat > set_int ) > set_nat > nat ).
thf(func_def_2657,type,
sK37: ( $o > $o > $o ) > ( char > $o ) > ( char > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_2658,type,
sK38: ( $o > $o > $o ) > ( char > $o ) > ( char > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_2659,type,
sK39: ( num > set_Pr1261947904930325089at_nat ) > ( nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > set_Pr6200539531224447659at_num > nat ).
thf(func_def_2660,type,
sK40: ( num > set_Pr1261947904930325089at_nat ) > ( nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > set_Pr6200539531224447659at_num > num ).
thf(func_def_2661,type,
sK41: set_nat > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_2662,type,
sK42: set_nat > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_2663,type,
sK43: product_prod_nat_nat > ( num > nat ) > set_Pr6200539531224447659at_num > ( nat > nat ) > num ).
thf(func_def_2664,type,
sK44: product_prod_nat_nat > ( num > nat ) > set_Pr6200539531224447659at_num > ( nat > nat ) > nat ).
thf(func_def_2665,type,
sK45: product_unit > ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_2666,type,
sK46: product_unit > ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > product_unit ).
thf(func_def_2667,type,
sK47: ( int > nat ) > set_nat > set_int > ( nat > nat ) > int ).
thf(func_def_2668,type,
sK48: set_int > nat > ( int > nat ) > int ).
thf(func_def_2669,type,
sK49: set_o > ( $o > set_int ) > $o ).
thf(func_def_2670,type,
sK50: ( char > nat ) > ( $o > nat > $o ) > ( char > $o ) > ( $o > nat > $o ) > $o ).
thf(func_def_2671,type,
sK51: ( char > nat ) > ( $o > nat > $o ) > ( char > $o ) > ( $o > nat > $o ) > nat ).
thf(func_def_2672,type,
sK52: int > ( nat > int ) > nat ).
thf(func_def_2673,type,
sK53: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2674,type,
sK54: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2675,type,
sK55: ( nat > product_unit ) > set_nat > product_unit ).
thf(func_def_2676,type,
sK56: ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > int > int ).
thf(func_def_2677,type,
sK57: ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2678,type,
sK58: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_2679,type,
sK59: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_2680,type,
sK60: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2681,type,
sK61: ( rat > rat ) > rat ).
thf(func_def_2682,type,
sK62: rat > ( rat > rat ) > rat ).
thf(func_def_2683,type,
sK63: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_2684,type,
sK64: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_2685,type,
sK65: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > nat ).
thf(func_def_2686,type,
sK66: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > nat ).
thf(func_def_2687,type,
sK67: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > ( set_nat > $o ) > set_nat ).
thf(func_def_2688,type,
sK68: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > ( set_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2689,type,
sK69: ( $o > product_unit ) > set_o > product_unit > $o ).
thf(func_def_2690,type,
sK70: ( rat > char ) > char > rat ).
thf(func_def_2691,type,
sK71: product_prod_nat_num > nat ).
thf(func_def_2692,type,
sK72: product_prod_nat_num > num ).
thf(func_def_2693,type,
sK73: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > $o ) > set_int > product_prod_nat_nat ).
thf(func_def_2694,type,
sK74: set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2695,type,
sK75: int > product_prod_int_int > ( int > int > set_int ) > int ).
thf(func_def_2696,type,
sK76: int > product_prod_int_int > ( int > int > set_int ) > int ).
thf(func_def_2697,type,
sK77: set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_2698,type,
sK78: set_Pr4329608150637261639at_nat > produc1906917888121415911at_nat > produc3843707927480180839at_nat ).
thf(func_def_2699,type,
sK79: ( nat > nat > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > $o ) > nat ).
thf(func_def_2700,type,
sK80: ( nat > nat > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > $o ) > nat ).
thf(func_def_2701,type,
sK81: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2702,type,
sK82: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2703,type,
sK83: set_int > set_nat > ( int > nat ) > set_int ).
thf(func_def_2704,type,
sK84: ( int > int > $o ) > ( int > int > int ) > ( int > $o ) > int ).
thf(func_def_2705,type,
sK85: ( int > int > $o ) > ( int > int > int ) > ( int > $o ) > int ).
thf(func_def_2706,type,
sK86: ( int > product_unit ) > ( int > product_unit ) > set_int > int ).
thf(func_def_2707,type,
sK87: ( nat > num ) > ( int > nat ) > ( nat > num ) > ( int > nat ) > nat ).
thf(func_def_2708,type,
sK88: ( nat > num ) > ( int > nat ) > ( nat > num ) > ( int > nat ) > nat ).
thf(func_def_2709,type,
sK89: set_nat > ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_2710,type,
sK90: set_int > ( int > nat ) > ( int > nat ) > int ).
thf(func_def_2711,type,
sK91: ( nat > nat ) > ( product_unit > nat ) > set_Product_unit > set_nat > product_unit ).
thf(func_def_2712,type,
sK92: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_2713,type,
sK93: set_Product_unit > ( product_unit > int ) > ( product_unit > int ) > product_unit ).
thf(func_def_2714,type,
sK94: ( produc3843707927480180839at_nat > product_unit ) > ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_2715,type,
sK95: product_prod_nat_nat > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > product_prod_nat_nat ).
thf(func_def_2716,type,
sK96: set_Pr1261947904930325089at_nat > product_unit > ( product_prod_nat_nat > product_unit ) > product_prod_nat_nat ).
thf(func_def_2717,type,
sK97: set_Pr1261947904930325089at_nat > product_unit > ( product_prod_nat_nat > product_unit ) > product_unit ).
thf(func_def_2718,type,
sK98: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_2719,type,
sK99: set_Product_unit > ( product_unit > nat ) > nat > product_unit ).
thf(func_def_2720,type,
sK100: set_nat > nat > nat ).
thf(func_def_2721,type,
sK101: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > ( product_prod_nat_nat > product_unit ) > product_prod_nat_nat ).
thf(func_def_2722,type,
sK102: ( set_rat > $o ) > set_nat > ( nat > rat ) > set_rat ).
thf(func_def_2723,type,
sK103: ( set_rat > $o ) > set_nat > ( nat > rat ) > set_nat ).
thf(func_def_2724,type,
sK104: ( $o > set_nat ) > set_o > set_nat > $o ).
thf(func_def_2725,type,
sK105: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_2726,type,
sK106: ( nat > int ) > set_nat > ( set_int > $o ) > set_nat ).
thf(func_def_2727,type,
sK107: ( nat > int ) > set_nat > ( set_int > $o ) > set_int ).
thf(func_def_2728,type,
sK108: set_o > set_nat > ( $o > set_nat ) > $o ).
thf(func_def_2729,type,
sK109: ( rat > int ) > int > rat ).
thf(func_def_2730,type,
sK110: ( $o > int ) > set_o > ( $o > int ) > $o ).
thf(func_def_2731,type,
sK111: set_o > set_nat > ( $o > nat ) > ( nat > nat ) > $o ).
thf(func_def_2732,type,
sK112: set_o > ( $o > int ) > int > $o ).
thf(func_def_2733,type,
sK113: ( int > int ) > set_int > set_int > set_int ).
thf(func_def_2734,type,
sK114: nat > ( $o > nat ) > set_o > $o ).
thf(func_def_2735,type,
sK115: set_o > ( $o > nat ) > $o ).
thf(func_def_2736,type,
sK116: ( nat > int ) > int > set_nat > nat ).
thf(func_def_2737,type,
sK117: ( $o > int ) > set_o > set_int > $o ).
thf(func_def_2738,type,
sK118: set_nat > $o > ( nat > $o ) > set_o > set_nat ).
thf(func_def_2739,type,
sK119: set_nat > $o > ( nat > $o ) > set_o > nat ).
thf(func_def_2740,type,
sK120: ( nat > nat ) > ( int > nat ) > set_int > set_nat > int ).
thf(func_def_2741,type,
sK121: ( produc1319942482725812455at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2742,type,
sK122: ( produc1319942482725812455at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2743,type,
sK123: ( int > int ) > set_int > set_int > set_int ).
thf(func_def_2744,type,
sK124: set_rat > nat > rat ).
thf(func_def_2745,type,
sK125: set_int > ( int > int ) > ( int > int ) > int ).
thf(func_def_2746,type,
sK126: set_int > ( int > set_int ) > set_int > int ).
thf(func_def_2747,type,
sK127: set_nat > ( nat > set_nat ) > nat ).
thf(func_def_2748,type,
sK128: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2749,type,
sK129: ( int > int ) > ( int > int ) > set_int > int ).
thf(func_def_2750,type,
sK130: ( int > int ) > set_int > int ).
thf(func_def_2751,type,
sK131: ( int > set_nat ) > set_int > set_nat > int ).
thf(func_def_2752,type,
sK132: set_int > set_Pr958786334691620121nt_int > int ).
thf(func_def_2753,type,
sK133: set_nat > ( nat > product_unit ) > ( nat > product_unit ) > nat ).
thf(func_def_2754,type,
sK134: set_int > ( int > nat ) > set_nat > set_int ).
thf(func_def_2755,type,
sK135: ( int > nat ) > nat > set_int > int ).
thf(func_def_2756,type,
sK136: ( int > nat ) > ( set_nat > $o ) > set_int > set_int ).
thf(func_def_2757,type,
sK137: ( int > nat ) > ( set_nat > $o ) > set_int > set_nat ).
thf(func_def_2758,type,
sK138: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2759,type,
sK139: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).
thf(func_def_2760,type,
sK140: set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2761,type,
sK141: ( product_unit > set_nat ) > set_Product_unit > set_nat > product_unit ).
thf(func_def_2762,type,
sK142: ( product_unit > set_nat ) > set_Product_unit > set_nat > product_unit ).
thf(func_def_2763,type,
sK143: set_Pr1261947904930325089at_nat > set_nat > nat > product_prod_nat_nat ).
thf(func_def_2764,type,
sK144: ( nat > rat ) > set_nat > ( rat > $o ) > nat ).
thf(func_def_2765,type,
sK145: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_2766,type,
sK146: set_rat > set_nat > ( nat > rat ) > set_nat ).
thf(func_def_2767,type,
sK147: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2768,type,
sK148: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2769,type,
sK149: ( int > $o ) > set_int > ( int > $o ) > int ).
thf(func_def_2770,type,
sK150: set_o > set_o > ( $o > set_nat ) > ( $o > set_nat ) > $o ).
thf(func_def_2771,type,
sK151: set_o > set_o > ( $o > set_nat ) > ( $o > set_nat ) > $o ).
thf(func_def_2772,type,
sK152: set_nat > ( nat > set_nat ) > ( nat > set_nat ) > nat ).
thf(func_def_2773,type,
sK153: set_nat > int > ( nat > int ) > nat ).
thf(func_def_2774,type,
sK154: set_o > product_unit > ( $o > product_unit ) > $o ).
thf(func_def_2775,type,
sK155: set_o > product_unit > ( $o > product_unit ) > product_unit ).
thf(func_def_2776,type,
sK156: ( int > rat ) > set_int > rat > int ).
thf(func_def_2777,type,
sK157: ( nat > rat ) > ( nat > rat ) > set_nat > nat ).
thf(func_def_2778,type,
sK158: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2779,type,
sK159: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_2780,type,
sK160: ( char > int ) > ( int > $o > $o ) > ( char > $o ) > ( int > $o > $o ) > $o ).
thf(func_def_2781,type,
sK161: ( char > int ) > ( int > $o > $o ) > ( char > $o ) > ( int > $o > $o ) > int ).
thf(func_def_2782,type,
sK162: ( rat > nat ) > ( rat > nat ) > ( nat > nat > $o ) > rat > product_prod_nat_nat ).
thf(func_def_2783,type,
sK163: ( int > int > product_prod_int_int ) > product_prod_int_int > ( int > int > product_prod_int_int ) > int ).
thf(func_def_2784,type,
sK164: ( int > int > product_prod_int_int ) > product_prod_int_int > ( int > int > product_prod_int_int ) > int ).
thf(func_def_2785,type,
sK165: product_unit > ( nat > product_unit ) > set_nat > nat ).
thf(func_def_2786,type,
sK166: product_unit > ( nat > product_unit ) > set_nat > product_unit ).
thf(func_def_2787,type,
sK167: ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2788,type,
sK168: ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > int > int ).
thf(func_def_2789,type,
sK169: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_2790,type,
sK170: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_2791,type,
sK171: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2792,type,
sK172: ( nat > product_unit ) > set_nat > product_unit > product_unit ).
thf(func_def_2793,type,
sK173: set_int > ( int > nat ) > ( int > nat ) > set_int > int ).
thf(func_def_2794,type,
sK174: ( nat > nat ) > nat > set_nat > nat ).
thf(func_def_2795,type,
sK175: product_prod_nat_num > int > ( nat > num > set_int ) > nat ).
thf(func_def_2796,type,
sK176: product_prod_nat_num > int > ( nat > num > set_int ) > num ).
thf(func_def_2797,type,
sK177: heap_Heap_ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2798,type,
sK178: heap_Heap_ref_a > heap_e7401611519738050253t_unit > ref_a ).
thf(func_def_2799,type,
sK179: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_2800,type,
sK180: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_2801,type,
sK181: ( product_prod_int_int > $o ) > ( int > int > product_prod_int_int ) > product_prod_int_int > int ).
thf(func_def_2802,type,
sK182: ( product_prod_int_int > $o ) > ( int > int > product_prod_int_int ) > product_prod_int_int > int ).
thf(func_def_2803,type,
sK183: ( nat > nat ) > set_nat > ( set_nat > $o ) > set_nat ).
thf(func_def_2804,type,
sK184: ( nat > nat ) > set_nat > ( set_nat > $o ) > set_nat ).
thf(func_def_2805,type,
sK185: ( int > nat ) > set_int > set_nat > set_int ).
thf(func_def_2806,type,
sK186: ( $o > int ) > ( $o > int ) > set_o > $o ).
thf(func_def_2807,type,
sK187: ( int > $o ) > set_nat > ( nat > int ) > int ).
thf(func_def_2808,type,
sK188: set_int > int > ( int > int ) > int ).
thf(func_def_2809,type,
sK189: set_nat > set_rat > ( nat > rat ) > nat ).
thf(func_def_2810,type,
sK190: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_2811,type,
sK191: set_Product_unit > set_o > $o > ( product_unit > $o ) > product_unit ).
thf(func_def_2812,type,
sK192: set_Product_unit > set_o > $o > ( product_unit > $o ) > set_Product_unit ).
thf(func_def_2813,type,
sK193: ( int > product_unit ) > set_int > ( int > product_unit ) > int ).
thf(func_def_2814,type,
sK194: ( $o > product_prod_nat_nat ) > set_o > $o ).
thf(func_def_2815,type,
sK195: ( nat > $o ) > $o > nat ).
thf(func_def_2816,type,
sK196: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2817,type,
sK197: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_2818,type,
sK198: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2819,type,
sK199: product_prod_nat_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_2820,type,
sK200: product_unit > $o ).
thf(func_def_2821,type,
sK201: $o > product_unit ).
thf(func_def_2822,type,
sK202: product_prod_nat_num > ( int > nat ) > ( int > num ) > set_Pr958786334691620121nt_int > int ).
thf(func_def_2823,type,
sK203: product_prod_nat_num > ( int > nat ) > ( int > num ) > set_Pr958786334691620121nt_int > int ).
thf(func_def_2824,type,
sK204: set_nat > ( nat > rat ) > rat ).
thf(func_def_2825,type,
sK205: ( rat > nat ) > ( nat > rat ) > rat ).
thf(func_def_2826,type,
sK206: ( int > int ) > set_int > int ).
thf(func_def_2827,type,
sK207: set_nat > ( $o > set_nat ) > set_o > $o ).
thf(func_def_2828,type,
sK208: int > ( $o > int ) > set_o > $o ).
thf(func_def_2829,type,
sK209: int > set_int > ( int > set_int ) > int ).
thf(func_def_2830,type,
sK210: ( int > int ) > int > set_int > int ).
thf(func_def_2831,type,
sK211: ( nat > nat > $o ) > ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_2832,type,
sK212: ( nat > nat > $o ) > ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_2833,type,
sK213: set_Pr1261947904930325089at_nat > nat ).
thf(func_def_2834,type,
sK214: set_nat > ( nat > product_unit ) > ( nat > product_unit ) > nat ).
thf(func_def_2835,type,
sK215: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2836,type,
sK216: set_Pr1261947904930325089at_nat > set_nat > ( product_prod_nat_nat > set_nat ) > set_nat ).
thf(func_def_2837,type,
sK217: set_Pr1261947904930325089at_nat > set_nat > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_2838,type,
sK218: ( product_unit > int ) > set_Product_unit > int > product_unit ).
thf(func_def_2839,type,
sK219: set_int > ( int > int ) > ( int > int ) > int ).
thf(func_def_2840,type,
sK220: int > product_prod_int_int > int ).
thf(func_def_2841,type,
sK221: ( int > int > $o ) > ( char > int ) > ( char > int ) > ( int > int > $o ) > int ).
thf(func_def_2842,type,
sK222: ( int > int > $o ) > ( char > int ) > ( char > int ) > ( int > int > $o ) > int ).
thf(func_def_2843,type,
sK223: product_unit > ( product_unit > product_unit ) > set_Product_unit > product_unit ).
thf(func_def_2844,type,
sK224: ( $o > int ) > int > set_o > $o ).
thf(func_def_2845,type,
sK225: ( rat > rat ) > ( rat > rat ) > rat ).
thf(func_def_2846,type,
sK226: ( int > int > $o ) > ( nat > int ) > ( nat > int ) > nat > product_prod_int_int ).
thf(func_def_2847,type,
sK227: set_o > $o ).
thf(func_def_2848,type,
sK228: ( nat > int ) > set_nat > nat > nat ).
thf(func_def_2849,type,
sK229: ( nat > nat > set_nat ) > nat > product_prod_nat_nat > nat ).
thf(func_def_2850,type,
sK230: ( nat > nat > set_nat ) > nat > product_prod_nat_nat > nat ).
thf(func_def_2851,type,
sK231: ( int > int ) > set_int > ( set_int > $o ) > set_int ).
thf(func_def_2852,type,
sK232: ( int > int ) > set_int > ( set_int > $o ) > set_int ).
thf(func_def_2853,type,
sK233: set_Product_unit > ( int > product_unit ) > set_int > product_unit > int ).
thf(func_def_2854,type,
sK234: set_Product_unit > ( int > product_unit ) > set_int > product_unit > set_int ).
thf(func_def_2855,type,
sK235: ( $o > code_integer ) > set_o > code_integer > $o ).
thf(func_def_2856,type,
sK236: product_prod_nat_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat > ( nat > nat ) > nat ).
thf(func_def_2857,type,
sK237: product_prod_nat_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat > ( nat > nat ) > nat ).
thf(func_def_2858,type,
sK238: set_o > set_int > ( int > product_unit ) > ( $o > product_unit ) > int ).
thf(func_def_2859,type,
sK239: set_o > set_int > ( int > product_unit ) > ( $o > product_unit ) > $o ).
thf(func_def_2860,type,
sK240: $o > ( product_prod_nat_nat > set_o ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_2861,type,
sK241: ( int > char ) > ( char > int ) > int ).
thf(func_def_2862,type,
sK242: ( nat > set_o ) > $o > set_nat > nat ).
thf(func_def_2863,type,
sK243: ( nat > nat ) > set_nat > set_nat > nat ).
thf(func_def_2864,type,
sK244: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_2865,type,
sK245: ( nat > rat ) > rat > nat ).
thf(func_def_2866,type,
sK246: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_2867,type,
sK247: product_prod_nat_num > nat > ( nat > num > set_nat ) > num ).
thf(func_def_2868,type,
sK248: product_prod_nat_num > nat > ( nat > num > set_nat ) > nat ).
thf(func_def_2869,type,
sK249: product_unit > ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit ).
thf(func_def_2870,type,
sK250: product_unit > ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_2871,type,
sK251: nat > ( rat > nat ) > rat ).
thf(func_def_2872,type,
sK252: rat > nat > ( rat > nat ) > rat ).
thf(func_def_2873,type,
sK253: set_nat > set_rat > nat > rat ).
thf(func_def_2874,type,
sK254: set_nat > set_rat > rat > nat ).
thf(func_def_2875,type,
sK255: ( ( product_prod_nat_nat > $o ) > $o ) > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_2876,type,
sK256: ( ( product_prod_nat_nat > $o ) > $o ) > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_2877,type,
sK257: product_prod_nat_nat > $o > ( nat > nat > set_o ) > nat ).
thf(func_def_2878,type,
sK258: product_prod_nat_nat > $o > ( nat > nat > set_o ) > nat ).
thf(func_def_2879,type,
sK259: produc1319942482725812455at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2880,type,
sK260: produc1319942482725812455at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat ).
thf(func_def_2881,type,
sK261: set_nat > ( nat > $o ) > $o ).
thf(func_def_2882,type,
sK262: ( $o > set_nat ) > set_o > ( $o > set_nat ) > $o ).
thf(func_def_2883,type,
sK263: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat ).
thf(func_def_2884,type,
sK264: set_o > ( $o > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > $o ).
thf(func_def_2885,type,
sK265: set_rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_2886,type,
sK266: $o > ( rat > $o ) > rat ).
thf(func_def_2887,type,
sK267: rat > $o > ( rat > $o ) > rat ).
thf(func_def_2888,type,
sK268: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat ).
thf(func_def_2889,type,
sK269: ( int > product_unit ) > set_int > product_unit > product_unit ).
thf(func_def_2890,type,
sK270: ( int > product_unit ) > set_int > product_unit > int ).
thf(func_def_2891,type,
sK271: set_nat > set_nat > nat > nat ).
thf(func_def_2892,type,
sK272: ( int > num ) > ( num > num > $o ) > ( code_integer > num ) > ( int > code_integer > $o ) > code_integer ).
thf(func_def_2893,type,
sK273: ( int > num ) > ( num > num > $o ) > ( code_integer > num ) > ( int > code_integer > $o ) > int ).
thf(func_def_2894,type,
sK274: ( char > int ) > ( $o > int > $o ) > ( char > $o ) > ( $o > int > $o ) > $o ).
thf(func_def_2895,type,
sK275: ( char > int ) > ( $o > int > $o ) > ( char > $o ) > ( $o > int > $o ) > int ).
thf(func_def_2896,type,
sK276: set_int > set_nat > ( nat > int ) > set_nat ).
thf(func_def_2897,type,
sK277: nat > ( rat > nat ) > rat ).
thf(func_def_2898,type,
sK278: ( rat > nat ) > nat ).
thf(func_def_2899,type,
sK279: set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat > nat ).
thf(func_def_2900,type,
sK280: set_o > ( $o > set_nat ) > ( $o > set_nat ) > $o ).
thf(func_def_2901,type,
sK281: set_o > ( $o > product_unit ) > ( $o > product_unit ) > $o ).
thf(func_def_2902,type,
sK282: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_2903,type,
sK283: ( $o > product_unit ) > ( nat > product_unit ) > set_nat > set_o > nat ).
thf(func_def_2904,type,
sK284: ( $o > product_unit ) > ( nat > product_unit ) > set_nat > set_o > $o ).
thf(func_def_2905,type,
sK285: int > set_nat > ( nat > int ) > nat ).
thf(func_def_2906,type,
sK286: set_nat > ( nat > set_nat ) > ( nat > set_nat ) > nat ).
thf(func_def_2907,type,
sK287: ( nat > rat ) > rat > nat ).
thf(func_def_2908,type,
sK288: ( product_prod_int_int > $o ) > ( int > int > $o ) > ( int > int > product_prod_int_int ) > int ).
thf(func_def_2909,type,
sK289: ( product_prod_int_int > $o ) > ( int > int > $o ) > ( int > int > product_prod_int_int ) > int ).
thf(func_def_2910,type,
sK290: set_o > set_nat > ( nat > $o ) > nat ).
thf(func_def_2911,type,
sK291: ( $o > $o > $o ) > ( nat > $o ) > $o ).
thf(func_def_2912,type,
sK292: set_int > ( int > set_Pr1261947904930325089at_nat ) > int ).
thf(func_def_2913,type,
sK293: set_Product_unit > set_nat > ( nat > nat ) > ( product_unit > nat ) > product_unit ).
thf(func_def_2914,type,
sK294: ( ref_a > heap_e7401611519738050253t_unit > $o ) > set_ref_a > ( ref_a > heap_e7401611519738050253t_unit > $o ) > set_he8644174446132254637t_unit > ref_a ).
thf(func_def_2915,type,
sK295: ( ref_a > heap_e7401611519738050253t_unit > $o ) > set_ref_a > ( ref_a > heap_e7401611519738050253t_unit > $o ) > set_he8644174446132254637t_unit > heap_e7401611519738050253t_unit ).
thf(func_def_2916,type,
sK296: ( nat > int ) > set_nat > set_int > nat ).
thf(func_def_2917,type,
sK297: set_o > rat > ( $o > rat ) > $o ).
thf(func_def_2918,type,
sK298: nat > list_nat > nat ).
thf(func_def_2919,type,
sK299: set_int > set_o > ( $o > product_unit ) > ( int > product_unit ) > $o ).
thf(func_def_2920,type,
sK300: set_int > set_o > ( $o > product_unit ) > ( int > product_unit ) > int ).
thf(func_def_2921,type,
sK301: set_nat > ( nat > product_unit ) > product_unit ).
thf(func_def_2922,type,
sK302: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > int ).
thf(func_def_2923,type,
sK303: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > int ).
thf(func_def_2924,type,
sK304: set_int > ( nat > int ) > set_nat > set_nat ).
thf(func_def_2925,type,
sK305: set_o > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_2926,type,
sK306: nat > ( nat > nat ) > nat ).
thf(func_def_2927,type,
sK307: ( product_unit > product_unit ) > set_Product_unit > ( product_unit > product_unit ) > product_unit ).
thf(func_def_2928,type,
sK308: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_2929,type,
sK309: ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_2930,type,
sK310: ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_2931,type,
sK311: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_2932,type,
sK312: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_2933,type,
sK313: product_prod_nat_nat > ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_2934,type,
sK314: product_prod_nat_nat > ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_2935,type,
sK315: ( $o > $o ) > ( $o > $o ) > ( nat > $o ) > $o ).
thf(func_def_2936,type,
sK316: ( int > int ) > int > set_int > int ).
thf(func_def_2937,type,
sK317: set_int > set_nat > ( nat > set_int ) > nat ).
thf(func_def_2938,type,
sK318: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_2939,type,
sK319: ( product_unit > nat ) > ( product_unit > nat ) > set_Product_unit > product_unit ).
thf(func_def_2940,type,
sK320: int > set_Product_unit > ( product_unit > int ) > product_unit ).
thf(func_def_2941,type,
sK321: ( rat > $o ) > set_nat > ( nat > rat ) > rat ).
thf(func_def_2942,type,
sK322: ( char > int ) > int > char ).
thf(func_def_2943,type,
sK323: ( int > int ) > set_Pr958786334691620121nt_int > product_prod_int_int > ( int > int ) > int ).
thf(func_def_2944,type,
sK324: ( int > int ) > set_Pr958786334691620121nt_int > product_prod_int_int > ( int > int ) > int ).
thf(func_def_2945,type,
sK325: ( nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_2946,type,
sK326: ( $o > product_unit ) > ( $o > product_unit ) > set_o > $o ).
thf(func_def_2947,type,
sK327: set_Product_unit > product_unit > ( product_unit > product_unit ) > product_unit ).
thf(func_def_2948,type,
sK328: ( produc3843707927480180839at_nat > set_nat ) > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_2949,type,
sK329: ( nat > num > set_nat ) > product_prod_nat_num > nat > nat ).
thf(func_def_2950,type,
sK330: ( nat > num > set_nat ) > product_prod_nat_num > nat > num ).
thf(func_def_2951,type,
sK331: set_int > ( int > set_nat ) > nat > int ).
thf(func_def_2952,type,
sK332: ( nat > rat ) > set_nat > ( set_rat > $o ) > set_rat ).
thf(func_def_2953,type,
sK333: ( nat > rat ) > set_nat > ( set_rat > $o ) > set_nat ).
thf(func_def_2954,type,
sK334: set_o > ( $o > rat ) > rat > $o ).
thf(func_def_2955,type,
sK335: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > nat ).
thf(func_def_2956,type,
sK336: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > num ).
thf(func_def_2957,type,
sK337: set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > nat ).
thf(func_def_2958,type,
sK338: nat > ( nat > nat ) > nat > nat ).
thf(func_def_2959,type,
sK339: ( nat > nat ) > nat > nat ).
thf(func_def_2960,type,
sK340: ( $o > set_o ) > set_o > $o ).
thf(func_def_2961,type,
sK341: set_int > ( int > set_nat ) > set_nat > int ).
thf(func_def_2962,type,
sK342: set_int > ( int > set_nat ) > set_nat > set_nat ).
thf(func_def_2963,type,
sK343: set_nat > nat > ( nat > set_nat ) > nat ).
thf(func_def_2964,type,
sK344: set_o > set_o > $o > ( $o > $o ) > $o ).
thf(func_def_2965,type,
sK345: set_o > set_o > $o > ( $o > $o ) > set_o ).
thf(func_def_2966,type,
sK346: ( nat > nat > set_nat ) > nat > product_prod_nat_nat > nat ).
thf(func_def_2967,type,
sK347: ( nat > nat > set_nat ) > nat > product_prod_nat_nat > nat ).
thf(func_def_2968,type,
sK348: set_int > ( int > int ) > ( int > $o ) > int ).
thf(func_def_2969,type,
sK349: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat ).
thf(func_def_2970,type,
sK350: set_Product_unit > nat > ( product_unit > nat ) > product_unit ).
thf(func_def_2971,type,
sK351: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2972,type,
sK352: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2973,type,
sK353: ( nat > rat ) > set_nat > nat ).
thf(func_def_2974,type,
sK354: set_nat > nat ).
thf(func_def_2975,type,
sK355: ( nat > product_unit ) > set_nat > product_unit > nat ).
thf(func_def_2976,type,
sK356: ( int > int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > int ).
thf(func_def_2977,type,
sK357: ( int > int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > int ).
thf(func_def_2978,type,
sK358: product_prod_int_int > int ).
thf(func_def_2979,type,
sK359: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat ).
thf(func_def_2980,type,
sK360: set_int > ( int > set_o ) > $o > int ).
thf(func_def_2981,type,
sK361: ( nat > produc3843707927480180839at_nat ) > set_nat > produc3843707927480180839at_nat ).
thf(func_def_2982,type,
sK362: ( rat > int ) > int > rat ).
thf(func_def_2983,type,
sK363: rat > ( rat > int ) > int > rat ).
thf(func_def_2984,type,
sK364: ( product_prod_nat_nat > nat ) > set_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2985,type,
sK365: set_int > nat > ( int > nat ) > int ).
thf(func_def_2986,type,
sK366: set_o > product_unit > ( $o > product_unit ) > $o ).
thf(func_def_2987,type,
sK367: ( nat > set_nat ) > product_prod_nat_nat > set_nat > nat ).
thf(func_def_2988,type,
sK368: ( nat > set_nat ) > product_prod_nat_nat > set_nat > nat ).
thf(func_def_2989,type,
sK369: ( $o > set_nat ) > set_nat > set_o > $o ).
thf(func_def_2990,type,
sK370: set_Product_unit > ( product_unit > set_o ) > product_unit ).
thf(func_def_2991,type,
sK371: ( nat > int ) > set_nat > int ).
thf(func_def_2992,type,
sK372: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_2993,type,
sK373: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_2994,type,
sK374: ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_2995,type,
sK375: ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_2996,type,
sK376: ( nat > nat ) > set_nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_2997,type,
sK377: set_nat > ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_2998,type,
sK378: ( nat > nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_2999,type,
sK379: ( nat > nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_3000,type,
sK380: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3001,type,
sK381: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3002,type,
sK382: set_int > ( int > set_nat ) > ( int > set_nat ) > int ).
thf(func_def_3003,type,
sK383: set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_3004,type,
sK384: nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3005,type,
sK385: set_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3006,type,
sK386: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3007,type,
sK387: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3008,type,
sK388: ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3009,type,
sK389: ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3010,type,
sK390: product_unit > set_int > ( int > product_unit ) > int ).
thf(func_def_3011,type,
sK391: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_3012,type,
sK392: nat > ( $o > nat ) > set_o > $o ).
thf(func_def_3013,type,
sK393: set_int > product_unit > ( int > product_unit ) > int ).
thf(func_def_3014,type,
sK394: ( rat > rat ) > rat > rat ).
thf(func_def_3015,type,
sK395: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat ).
thf(func_def_3016,type,
sK396: set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3017,type,
sK397: ( int > nat ) > set_int > set_nat > set_int ).
thf(func_def_3018,type,
sK398: ( product_unit > nat ) > ( product_unit > nat ) > set_Product_unit > product_unit ).
thf(func_def_3019,type,
sK399: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3020,type,
sK400: ( char > char ) > ( char > char ) > char ).
thf(func_def_3021,type,
sK401: product_prod_nat_num > ( nat > num > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > num ).
thf(func_def_3022,type,
sK402: product_prod_nat_num > ( nat > num > set_Pr1261947904930325089at_nat ) > product_prod_nat_nat > nat ).
thf(func_def_3023,type,
sK403: int > ( nat > int ) > set_nat > nat ).
thf(func_def_3024,type,
sK404: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3025,type,
sK405: int > ( rat > int ) > rat ).
thf(func_def_3026,type,
sK406: ( int > nat ) > set_o > set_int > ( $o > nat ) > $o ).
thf(func_def_3027,type,
sK407: rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_3028,type,
sK408: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_3029,type,
sK409: ( int > int ) > set_int > ( int > int ) > int ).
thf(func_def_3030,type,
sK410: ( $o > set_nat ) > set_nat > set_o > $o ).
thf(func_def_3031,type,
sK411: ( nat > set_int ) > set_nat > nat ).
thf(func_def_3032,type,
sK412: ( int > int ) > ( int > int ) > int ).
thf(func_def_3033,type,
sK413: set_Product_unit > set_nat > ( nat > product_unit ) > product_unit > set_nat ).
thf(func_def_3034,type,
sK414: set_Product_unit > set_nat > ( nat > product_unit ) > product_unit > nat ).
thf(func_def_3035,type,
sK415: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > product_prod_nat_nat ).
thf(func_def_3036,type,
sK416: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > int ).
thf(func_def_3037,type,
sK417: int > product_prod_int_int > int ).
thf(func_def_3038,type,
sK418: ( int > set_nat ) > set_int > ( int > set_nat ) > int ).
thf(func_def_3039,type,
sK419: product_prod_nat_nat > ( int > nat ) > ( int > nat ) > set_Pr958786334691620121nt_int > int ).
thf(func_def_3040,type,
sK420: product_prod_nat_nat > ( int > nat ) > ( int > nat ) > set_Pr958786334691620121nt_int > int ).
thf(func_def_3041,type,
sK421: ( int > nat ) > set_int > ( set_nat > $o ) > set_nat ).
thf(func_def_3042,type,
sK422: ( int > nat ) > set_int > ( set_nat > $o ) > set_int ).
thf(func_def_3043,type,
sK423: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3044,type,
sK424: set_Product_unit > ( product_unit > product_unit ) > product_unit > product_unit ).
thf(func_def_3045,type,
sK425: set_nat > ( produc3843707927480180839at_nat > set_nat ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3046,type,
sK426: rat > ( int > rat ) > set_int > int ).
thf(func_def_3047,type,
sK427: ( rat > int ) > int ).
thf(func_def_3048,type,
sK428: int > ( rat > int ) > rat ).
thf(func_def_3049,type,
sK429: set_rat > set_nat > ( nat > rat ) > set_nat ).
thf(func_def_3050,type,
sK430: ( char > rat ) > rat ).
thf(func_def_3051,type,
sK431: rat > ( char > rat ) > char ).
thf(func_def_3052,type,
sK432: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > product_prod_nat_nat ).
thf(func_def_3053,type,
sK433: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3054,type,
sK434: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3055,type,
sK435: nat > ( $o > nat ) > set_o > $o ).
thf(func_def_3056,type,
sK436: ( $o > nat > $o ) > ( char > $o ) > ( char > nat ) > ( $o > nat > $o ) > nat ).
thf(func_def_3057,type,
sK437: ( $o > nat > $o ) > ( char > $o ) > ( char > nat ) > ( $o > nat > $o ) > $o ).
thf(func_def_3058,type,
sK438: ( rat > rat ) > ( rat > rat ) > rat ).
thf(func_def_3059,type,
sK439: product_prod_int_int > ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3060,type,
sK440: product_prod_int_int > ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3061,type,
sK441: ( nat > product_unit ) > ( nat > product_unit ) > set_nat > set_nat > nat ).
thf(func_def_3062,type,
sK442: ( nat > product_unit ) > ( nat > product_unit ) > set_nat > set_nat > nat ).
thf(func_def_3063,type,
sK443: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3064,type,
sK444: product_prod_int_int > ( int > set_int ) > set_int > int ).
thf(func_def_3065,type,
sK445: product_prod_int_int > ( int > set_int ) > set_int > int ).
thf(func_def_3066,type,
sK446: product_prod_nat_nat > nat ).
thf(func_def_3067,type,
sK447: product_prod_nat_nat > nat ).
thf(func_def_3068,type,
sK448: int > set_nat > ( nat > int ) > nat ).
thf(func_def_3069,type,
sK449: ( char > char ) > char > char ).
thf(func_def_3070,type,
sK450: ( int > int > set_int ) > int > product_prod_int_int > int ).
thf(func_def_3071,type,
sK451: ( int > int > set_int ) > int > product_prod_int_int > int ).
thf(func_def_3072,type,
sK452: set_nat > ( int > nat ) > ( int > $o ) > int ).
thf(func_def_3073,type,
sK453: ( nat > nat ) > set_nat > nat > nat ).
thf(func_def_3074,type,
sK454: set_nat > ( $o > $o ) > ( nat > $o ) > ( $o > $o ) > nat ).
thf(func_def_3075,type,
sK455: set_Product_unit > ( product_unit > int ) > ( product_unit > int ) > product_unit ).
thf(func_def_3076,type,
sK456: set_int > set_nat > ( int > nat ) > int ).
thf(func_def_3077,type,
sK457: ( char > nat ) > nat > char ).
thf(func_def_3078,type,
sK458: nat > ( rat > nat ) > rat ).
thf(func_def_3079,type,
sK459: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > product_prod_nat_nat ).
thf(func_def_3080,type,
sK460: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > product_prod_nat_nat ).
thf(func_def_3081,type,
sK461: product_unit > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > product_unit ) > produc3843707927480180839at_nat ).
thf(func_def_3082,type,
sK462: product_unit > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > product_unit ) > product_unit ).
thf(func_def_3083,type,
sK463: ( product_prod_int_int > $o ) > int ).
thf(func_def_3084,type,
sK464: ( product_prod_int_int > $o ) > int ).
thf(func_def_3085,type,
sK465: ( char > rat ) > rat > char ).
thf(func_def_3086,type,
sK466: ( int > int > $o ) > ( char > int ) > ( char > int ) > char > product_prod_int_int ).
thf(func_def_3087,type,
sK467: ( char > char ) > char > char ).
thf(func_def_3088,type,
sK468: set_nat > ( nat > set_int ) > nat ).
thf(func_def_3089,type,
sK469: product_prod_nat_nat > nat ).
thf(func_def_3090,type,
sK470: product_prod_nat_nat > nat ).
thf(func_def_3091,type,
sK471: int > set_int > ( int > int ) > int ).
thf(func_def_3092,type,
sK472: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ).
thf(func_def_3093,type,
sK473: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ).
thf(func_def_3094,type,
sK474: set_o > product_prod_o_o > $o ).
thf(func_def_3095,type,
sK475: ( int > nat ) > set_int > nat > int ).
thf(func_def_3096,type,
sK476: set_int > product_unit > ( int > product_unit ) > int ).
thf(func_def_3097,type,
sK477: set_int > product_unit > ( int > product_unit ) > int ).
thf(func_def_3098,type,
sK478: set_nat > ( nat > set_nat ) > ( nat > set_nat ) > nat ).
thf(func_def_3099,type,
sK479: rat > ( rat > rat ) > rat ).
thf(func_def_3100,type,
sK480: set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3101,type,
sK481: ( $o > set_o ) > $o > set_o > $o ).
thf(func_def_3102,type,
sK482: ( int > int ) > ( set_int > $o ) > set_int > set_int ).
thf(func_def_3103,type,
sK483: ( int > int ) > ( set_int > $o ) > set_int > set_int ).
thf(func_def_3104,type,
sK484: set_nat > product_unit > ( nat > product_unit ) > nat ).
thf(func_def_3105,type,
sK485: ( rat > int ) > ( int > rat ) > int ).
thf(func_def_3106,type,
sK486: rat > ( nat > rat ) > set_nat > nat ).
thf(func_def_3107,type,
sK487: int > code_integer > ( int > int > $o ) > ( int > code_integer > $o ) > int ).
thf(func_def_3108,type,
sK488: product_prod_int_int > ( int > int > int ) > ( int > int > int ) > int ).
thf(func_def_3109,type,
sK489: product_prod_int_int > ( int > int > int ) > ( int > int > int ) > int ).
thf(func_def_3110,type,
sK490: ( $o > int > $o ) > ( char > $o ) > ( $o > int > $o ) > ( char > int ) > int ).
thf(func_def_3111,type,
sK491: ( $o > int > $o ) > ( char > $o ) > ( $o > int > $o ) > ( char > int ) > $o ).
thf(func_def_3112,type,
sK492: set_int > set_int > int > int ).
thf(func_def_3113,type,
sK493: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_3114,type,
sK494: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_3115,type,
sK495: ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > product_prod_nat_nat > $o ).
thf(func_def_3116,type,
sK496: ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > int > $o ).
thf(func_def_3117,type,
sK497: nat > rat > ( nat > rat ) > nat ).
thf(func_def_3118,type,
sK498: rat > ( nat > rat ) > nat ).
thf(func_def_3119,type,
sK499: set_Product_unit > ( product_unit > product_unit ) > product_unit > set_Product_unit > product_unit ).
thf(func_def_3120,type,
sK500: set_Product_unit > ( product_unit > product_unit ) > product_unit > set_Product_unit > set_Product_unit ).
thf(func_def_3121,type,
sK501: set_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( nat > product_prod_nat_nat ) > set_nat ).
thf(func_def_3122,type,
sK502: set_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3123,type,
sK503: set_int > set_int > int > int ).
thf(func_def_3124,type,
sK504: set_int > set_int > int > int ).
thf(func_def_3125,type,
sK505: nat > rat ).
thf(func_def_3126,type,
sK506: set_o > ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_3127,type,
sK507: set_Product_unit > set_Pr5094982260447487303t_unit > product_unit ).
thf(func_def_3128,type,
sK508: set_Pr5094982260447487303t_unit > set_Product_unit ).
thf(func_def_3129,type,
sK509: product_unit > set_Pr5094982260447487303t_unit > product_unit ).
thf(func_def_3130,type,
sK510: rat > ( char > rat ) > char ).
thf(func_def_3131,type,
sK511: set_rat > set_nat > rat > nat ).
thf(func_def_3132,type,
sK512: set_rat > set_nat > nat > rat ).
thf(func_def_3133,type,
sK513: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat ).
thf(func_def_3134,type,
sK514: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3135,type,
sK515: produc3843707927480180839at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat ).
thf(func_def_3136,type,
sK516: ( nat > num > $o ) > product_prod_nat_num > num ).
thf(func_def_3137,type,
sK517: ( nat > num > $o ) > product_prod_nat_num > nat ).
thf(func_def_3138,type,
sK518: set_nat > ( nat > set_nat ) > ( nat > set_nat ) > nat ).
thf(func_def_3139,type,
sK519: ( nat > nat ) > set_nat > set_nat > set_nat ).
thf(func_def_3140,type,
sK520: set_int > ( nat > set_int ) > set_nat > nat ).
thf(func_def_3141,type,
sK521: ( rat > nat ) > ( nat > rat ) > rat ).
thf(func_def_3142,type,
sK522: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_3143,type,
sK523: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_3144,type,
sK524: ( nat > char ) > char > nat ).
thf(func_def_3145,type,
sK525: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3146,type,
sK526: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3147,type,
sK527: set_Pr1261947904930325089at_nat > set_nat > nat ).
thf(func_def_3148,type,
sK528: set_Pr1261947904930325089at_nat > set_nat > nat ).
thf(func_def_3149,type,
sK529: ( int > product_unit ) > set_int > ( int > product_unit ) > int ).
thf(func_def_3150,type,
sK530: set_Product_unit > ( product_unit > int ) > int > product_unit ).
thf(func_def_3151,type,
sK531: set_o > product_unit > ( $o > product_unit ) > $o ).
thf(func_def_3152,type,
sK532: nat > ( int > nat ) > set_int > int ).
thf(func_def_3153,type,
sK533: ( nat > $o ) > ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_3154,type,
sK534: set_int > ( int > int ) > ( int > int ) > int ).
thf(func_def_3155,type,
sK535: set_Pr1261947904930325089at_nat > ( nat > $o ) > ( nat > product_prod_nat_nat ) > nat ).
thf(func_def_3156,type,
sK536: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int > product_prod_int_int ).
thf(func_def_3157,type,
sK537: ( produc3843707927480180839at_nat > nat > nat ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3158,type,
sK538: ( produc3843707927480180839at_nat > nat > nat ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3159,type,
sK539: ( char > rat ) > ( rat > char ) > char ).
thf(func_def_3160,type,
sK540: int > ( nat > int ) > set_nat > nat ).
thf(func_def_3161,type,
sK541: ( int > nat ) > ( int > int ) > ( int > nat ) > int ).
thf(func_def_3162,type,
sK542: product_unit > set_o > ( $o > product_unit ) > $o ).
thf(func_def_3163,type,
sK543: product_unit > set_o > ( $o > product_unit ) > $o ).
thf(func_def_3164,type,
sK544: product_unit > ( $o > product_unit ) > set_o > $o ).
thf(func_def_3165,type,
sK545: product_unit > ( $o > product_unit ) > set_o > product_unit ).
thf(func_def_3166,type,
sK546: ( rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_3167,type,
sK547: ( rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_3168,type,
sK548: set_int > ( int > product_prod_nat_nat ) > int ).
thf(func_def_3169,type,
sK549: set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat ).
thf(func_def_3170,type,
sK550: set_int > nat > ( int > set_nat ) > int ).
thf(func_def_3171,type,
sK551: ( int > product_unit ) > set_int > set_int > ( int > product_unit ) > int ).
thf(func_def_3172,type,
sK552: ( int > product_unit ) > set_int > set_int > ( int > product_unit ) > int ).
thf(func_def_3173,type,
sK553: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit ).
thf(func_def_3174,type,
sK554: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3175,type,
sK555: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3176,type,
sK556: ( int > nat ) > ( int > int ) > ( int > nat ) > ( int > int ) > int ).
thf(func_def_3177,type,
sK557: ( int > nat ) > ( int > int ) > ( int > nat ) > ( int > int ) > int ).
thf(func_def_3178,type,
sK558: set_nat > set_o > ( $o > set_nat ) > $o ).
thf(func_def_3179,type,
sK559: set_nat > set_o > ( $o > set_nat ) > $o ).
thf(func_def_3180,type,
sK560: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_3181,type,
sK561: product_unit > ( product_unit > product_unit ) > set_Product_unit > product_unit ).
thf(func_def_3182,type,
sK562: product_unit > ( product_unit > product_unit ) > set_Product_unit > product_unit ).
thf(func_def_3183,type,
sK563: ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3184,type,
sK564: ( char > int ) > int ).
thf(func_def_3185,type,
sK565: int > ( char > int ) > char ).
thf(func_def_3186,type,
sK566: ( product_prod_nat_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3187,type,
sK567: ( rat > nat ) > nat > rat ).
thf(func_def_3188,type,
sK568: set_int > set_Pr958786334691620121nt_int > int ).
thf(func_def_3189,type,
sK569: set_Pr958786334691620121nt_int > set_int ).
thf(func_def_3190,type,
sK570: int > set_Pr958786334691620121nt_int > int ).
thf(func_def_3191,type,
sK571: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > product_unit ).
thf(func_def_3192,type,
sK572: ( $o > $o ) > product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_3193,type,
sK573: ( $o > $o ) > product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_3194,type,
sK574: product_unit > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > product_prod_nat_nat ).
thf(func_def_3195,type,
sK575: product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_3196,type,
sK576: product_prod_int_int > ( int > int > $o ) > int ).
thf(func_def_3197,type,
sK577: list_nat > nat > nat ).
thf(func_def_3198,type,
sK578: ( $o > set_int ) > set_int > set_o > $o ).
thf(func_def_3199,type,
sK579: produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > ref_a ).
thf(func_def_3200,type,
sK580: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_3201,type,
sK581: set_int > set_nat > nat > int ).
thf(func_def_3202,type,
sK582: set_int > set_nat > int > nat ).
thf(func_def_3203,type,
sK583: ( nat > nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_3204,type,
sK584: int > ( char > int ) > char ).
thf(func_def_3205,type,
sK585: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3206,type,
sK586: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3207,type,
sK587: set_rat > set_nat > ( nat > rat ) > set_nat ).
thf(func_def_3208,type,
sK588: set_nat > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_3209,type,
sK589: ( $o > set_Pr1261947904930325089at_nat ) > set_o > $o ).
thf(func_def_3210,type,
sK590: set_o > ( nat > product_unit ) > ( $o > product_unit ) > set_nat > $o ).
thf(func_def_3211,type,
sK591: set_o > ( nat > product_unit ) > ( $o > product_unit ) > set_nat > nat ).
thf(func_def_3212,type,
sK592: ( $o > product_unit ) > ( $o > product_unit ) > set_o > set_o > $o ).
thf(func_def_3213,type,
sK593: ( $o > product_unit ) > ( $o > product_unit ) > set_o > set_o > $o ).
thf(func_def_3214,type,
sK594: set_nat > nat > ( nat > set_nat ) > nat ).
thf(func_def_3215,type,
sK595: set_nat > ( $o > set_nat ) > set_o > set_nat ).
thf(func_def_3216,type,
sK596: set_nat > ( $o > set_nat ) > set_o > $o ).
thf(func_def_3217,type,
sK597: ( int > set_o ) > $o > set_int > int ).
thf(func_def_3218,type,
sK598: ( nat > char ) > ( char > nat ) > nat ).
thf(func_def_3219,type,
sK599: ( nat > nat ) > set_nat > set_nat > set_nat ).
thf(func_def_3220,type,
sK600: set_int > ( int > nat ) > int ).
thf(func_def_3221,type,
sK601: ( int > num ) > ( num > num > $o ) > ( int > num ) > int > product_prod_num_num ).
thf(func_def_3222,type,
sK602: ( nat > int ) > set_nat > int > nat ).
thf(func_def_3223,type,
sK603: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3224,type,
sK604: ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > product_prod_nat_nat > $o ).
thf(func_def_3225,type,
sK605: ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > int > $o ).
thf(func_def_3226,type,
sK606: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > int ).
thf(func_def_3227,type,
sK607: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat ).
thf(func_def_3228,type,
sK608: ( $o > nat ) > set_o > ( int > nat ) > set_int > $o ).
thf(func_def_3229,type,
sK609: int > set_o > ( $o > int ) > $o ).
thf(func_def_3230,type,
sK610: ( nat > int ) > product_prod_int_int > set_Pr1261947904930325089at_nat > ( nat > int ) > nat ).
thf(func_def_3231,type,
sK611: ( nat > int ) > product_prod_int_int > set_Pr1261947904930325089at_nat > ( nat > int ) > nat ).
thf(func_def_3232,type,
sK612: ( produc3843707927480180839at_nat > product_unit ) > ( produc3843707927480180839at_nat > product_unit ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3233,type,
sK613: ( nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_3234,type,
sK614: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3235,type,
sK615: set_o > ( $o > set_nat ) > ( $o > set_nat ) > $o ).
thf(func_def_3236,type,
sK616: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_3237,type,
sK617: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_3238,type,
sK618: set_o > ( $o > nat ) > nat > $o ).
thf(func_def_3239,type,
sK619: nat > set_Product_unit > ( product_unit > nat ) > product_unit ).
thf(func_def_3240,type,
sK620: ( $o > set_nat ) > set_o > product_prod_o_nat > $o ).
thf(func_def_3241,type,
sK621: ( $o > set_nat ) > set_o > product_prod_o_nat > nat ).
thf(func_def_3242,type,
sK622: set_nat > ( nat > product_unit ) > set_nat > ( nat > product_unit ) > nat ).
thf(func_def_3243,type,
sK623: set_nat > ( nat > product_unit ) > set_nat > ( nat > product_unit ) > nat ).
thf(func_def_3244,type,
sK624: set_o > ( $o > nat ) > ( $o > nat ) > $o ).
thf(func_def_3245,type,
sK625: ( int > product_unit ) > set_int > ( nat > product_unit ) > set_nat > nat ).
thf(func_def_3246,type,
sK626: ( int > product_unit ) > set_int > ( nat > product_unit ) > set_nat > int ).
thf(func_def_3247,type,
sK627: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3248,type,
sK628: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3249,type,
sK629: int > set_Product_unit > ( product_unit > int ) > product_unit ).
thf(func_def_3250,type,
sK630: set_int > ( int > nat ) > set_nat > nat ).
thf(func_def_3251,type,
sK631: nat > set_int > ( int > nat ) > int ).
thf(func_def_3252,type,
sK632: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3253,type,
sK633: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3254,type,
sK634: ( product_prod_nat_nat > nat ) > set_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3255,type,
sK635: nat > ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3256,type,
sK636: ( nat > nat ) > set_nat > nat > nat ).
thf(func_def_3257,type,
sK637: ( int > code_integer > $o ) > code_integer > ( int > int > $o ) > int > int ).
thf(func_def_3258,type,
sK638: code_integer > set_o > ( $o > code_integer ) > $o ).
thf(func_def_3259,type,
sK639: set_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3260,type,
sK640: ( nat > int ) > ( nat > int ) > set_nat > nat ).
thf(func_def_3261,type,
sK641: set_se7855581050983116737at_nat > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3262,type,
sK642: ( nat > char ) > char > nat ).
thf(func_def_3263,type,
sK643: set_int > product_unit > ( int > product_unit ) > int ).
thf(func_def_3264,type,
sK644: ( int > product_unit ) > set_int > set_o > ( $o > product_unit ) > $o ).
thf(func_def_3265,type,
sK645: ( int > product_unit ) > set_int > set_o > ( $o > product_unit ) > int ).
thf(func_def_3266,type,
sK646: ( product_prod_int_int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3267,type,
sK647: ( product_prod_int_int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3268,type,
sK648: product_prod_nat_o > ( nat > set_o ) > set_nat > nat ).
thf(func_def_3269,type,
sK649: product_prod_nat_o > ( nat > set_o ) > set_nat > $o ).
thf(func_def_3270,type,
sK650: ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( nat > nat > $o ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_3271,type,
sK651: ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( nat > nat > $o ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).
thf(func_def_3272,type,
sK652: set_o > product_unit > ( $o > product_unit ) > $o ).
thf(func_def_3273,type,
sK653: ( int > int ) > set_int > set_int > set_int ).
thf(func_def_3274,type,
sK654: set_Pr958786334691620121nt_int > int ).
thf(func_def_3275,type,
sK655: ( nat > rat ) > set_rat > rat > set_nat > nat ).
thf(func_def_3276,type,
sK656: ( nat > rat ) > set_rat > rat > set_nat > set_nat ).
thf(func_def_3277,type,
sK657: ( product_unit > $o ) > $o ).
thf(func_def_3278,type,
sK658: product_prod_int_int > int ).
thf(func_def_3279,type,
sK659: product_prod_int_int > int ).
thf(func_def_3280,type,
sK660: set_o > set_o > ( $o > $o ) > $o ).
thf(func_def_3281,type,
sK661: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3282,type,
sK662: set_o > ( $o > set_nat ) > set_o > ( $o > set_nat ) > $o ).
thf(func_def_3283,type,
sK663: set_o > ( $o > set_nat ) > set_o > ( $o > set_nat ) > $o ).
thf(func_def_3284,type,
sK664: set_Product_unit > ( product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit ).
thf(func_def_3285,type,
sK665: nat > product_prod_nat_nat > nat ).
thf(func_def_3286,type,
sK666: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3287,type,
sK667: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3288,type,
sK668: ( int > nat ) > ( int > nat ) > ( nat > nat > $o ) > int > product_prod_nat_nat ).
thf(func_def_3289,type,
sK669: ( int > $o ) > set_int > set_o > int ).
thf(func_def_3290,type,
sK670: ( nat > int ) > ( set_int > $o ) > set_nat > set_nat ).
thf(func_def_3291,type,
sK671: ( nat > int ) > ( set_int > $o ) > set_nat > set_int ).
thf(func_def_3292,type,
sK672: $o > ( $o > $o ) > set_o > $o ).
thf(func_def_3293,type,
sK673: product_prod_int_nat > ( int > set_nat ) > set_int > int ).
thf(func_def_3294,type,
sK674: product_prod_int_nat > ( int > set_nat ) > set_int > nat ).
thf(func_def_3295,type,
sK675: set_int > set_int > ( int > int ) > int ).
thf(func_def_3296,type,
sK676: set_nat > ( nat > product_unit ) > ( nat > product_unit ) > nat ).
thf(func_def_3297,type,
sK677: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3298,type,
sK678: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3299,type,
sK679: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > heap_Heap_ref_a > ( ref_a > heap_Heap_ref_a ) > ref_a ).
thf(func_def_3300,type,
sK680: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > heap_Heap_ref_a > ( ref_a > heap_Heap_ref_a ) > heap_e7401611519738050253t_unit ).
thf(func_def_3301,type,
sK681: ( int > product_unit ) > product_unit > set_int > int ).
thf(func_def_3302,type,
sK682: ( nat > set_num ) > set_nat > product_prod_nat_num > nat ).
thf(func_def_3303,type,
sK683: ( nat > set_num ) > set_nat > product_prod_nat_num > num ).
thf(func_def_3304,type,
sK684: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_3305,type,
sK685: set_nat > $o > ( nat > set_o ) > nat ).
thf(func_def_3306,type,
sK686: set_int > ( set_int > $o ) > ( int > int ) > set_int ).
thf(func_def_3307,type,
sK687: set_int > ( set_int > $o ) > ( int > int ) > set_int ).
thf(func_def_3308,type,
sK688: char > ( char > int ) > int > char ).
thf(func_def_3309,type,
sK689: ( char > int ) > int > char ).
thf(func_def_3310,type,
sK690: ( char > $o ) > ( nat > $o > $o ) > ( char > nat ) > ( nat > $o > $o ) > nat ).
thf(func_def_3311,type,
sK691: ( char > $o ) > ( nat > $o > $o ) > ( char > nat ) > ( nat > $o > $o ) > $o ).
thf(func_def_3312,type,
sK692: ( int > int ) > ( int > int ) > set_int > int ).
thf(func_def_3313,type,
sK693: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3314,type,
sK694: set_o > ( $o > nat ) > nat > $o ).
thf(func_def_3315,type,
sK695: ( product_unit > set_int ) > set_Product_unit > product_unit ).
thf(func_def_3316,type,
sK696: nat > product_prod_nat_num > num ).
thf(func_def_3317,type,
sK697: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3318,type,
sK698: nat > set_nat > ( nat > rat ) > nat ).
thf(func_def_3319,type,
sK699: int > ( char > int ) > char ).
thf(func_def_3320,type,
sK700: set_nat > ( nat > nat ) > nat ).
thf(func_def_3321,type,
sK701: ( int > set_int ) > set_int > int ).
thf(func_def_3322,type,
sK702: set_int > nat > int ).
thf(func_def_3323,type,
sK703: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3324,type,
sK704: set_nat > set_int > ( int > set_nat ) > set_nat ).
thf(func_def_3325,type,
sK705: set_nat > set_int > ( int > set_nat ) > int ).
thf(func_def_3326,type,
sK706: set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3327,type,
sK707: produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3328,type,
sK708: produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3329,type,
sK709: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer > code_integer ).
thf(func_def_3330,type,
sK710: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3331,type,
sK711: ( rat > char ) > char > rat ).
thf(func_def_3332,type,
sK712: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit ).
thf(func_def_3333,type,
sK713: product_prod_nat_nat > nat ).
thf(func_def_3334,type,
sK714: ( nat > int ) > ( int > nat ) > int ).
thf(func_def_3335,type,
sK715: ( char > rat ) > ( rat > char ) > rat ).
thf(func_def_3336,type,
sK716: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3337,type,
sK717: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3338,type,
sK718: ( int > $o ) > ( int > int ) > set_int > int ).
thf(func_def_3339,type,
sK719: ( $o > $o > $o ) > ( char > $o ) > ( $o > $o > $o ) > ( char > $o ) > $o ).
thf(func_def_3340,type,
sK720: ( $o > $o > $o ) > ( char > $o ) > ( $o > $o > $o ) > ( char > $o ) > $o ).
thf(func_def_3341,type,
sK721: set_int > set_int > int > int ).
thf(func_def_3342,type,
sK722: product_prod_int_o > ( int > set_o ) > set_int > int ).
thf(func_def_3343,type,
sK723: product_prod_int_o > ( int > set_o ) > set_int > $o ).
thf(func_def_3344,type,
sK724: set_se7855581050983116737at_nat > product_prod_nat_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3345,type,
sK725: set_nat > set_o > ( $o > nat ) > ( nat > nat ) > $o ).
thf(func_def_3346,type,
sK726: set_nat > ( nat > nat ) > nat ).
thf(func_def_3347,type,
sK727: product_prod_int_int > int ).
thf(func_def_3348,type,
sK728: product_prod_int_int > int ).
thf(func_def_3349,type,
sK729: ( int > nat ) > nat > set_int > int ).
thf(func_def_3350,type,
sK730: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).
thf(func_def_3351,type,
sK731: int > ( $o > int ) > set_o > $o ).
thf(func_def_3352,type,
sK732: ( nat > int ) > ( int > int > $o ) > int ).
thf(func_def_3353,type,
sK733: int > ( int > int ) > set_int > int ).
thf(func_def_3354,type,
sK734: set_Product_unit > set_nat > ( product_unit > set_nat ) > product_unit ).
thf(func_def_3355,type,
sK735: ( product_unit > nat ) > set_Product_unit > set_int > ( int > nat ) > product_unit ).
thf(func_def_3356,type,
sK736: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3357,type,
sK737: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3358,type,
sK738: set_o > ( $o > set_nat ) > ( $o > set_nat ) > $o ).
thf(func_def_3359,type,
sK739: set_nat > ( nat > rat ) > ( set_rat > $o ) > set_rat ).
thf(func_def_3360,type,
sK740: set_nat > ( nat > rat ) > ( set_rat > $o ) > set_nat ).
thf(func_def_3361,type,
sK741: ( nat > nat > $o ) > ( list_nat > nat ) > ( list_nat > nat ) > list_nat > product_prod_nat_nat ).
thf(func_def_3362,type,
sK742: ( nat > nat > $o ) > ( rat > nat ) > nat ).
thf(func_def_3363,type,
sK743: set_nat > set_int > nat > int ).
thf(func_def_3364,type,
sK744: set_nat > set_int > int > nat ).
thf(func_def_3365,type,
sK745: set_int > ( int > int ) > ( int > $o ) > int ).
thf(func_def_3366,type,
sK746: set_o > product_unit > ( $o > product_unit ) > $o ).
thf(func_def_3367,type,
sK747: ( int > int ) > product_prod_int_int > product_prod_int_int > int ).
thf(func_def_3368,type,
sK748: ( int > int ) > product_prod_int_int > product_prod_int_int > int ).
thf(func_def_3369,type,
sK749: ( nat > nat ) > ( nat > nat > $o ) > ( nat > nat ) > nat > product_prod_nat_nat ).
thf(func_def_3370,type,
sK750: set_nat > set_rat > nat > rat ).
thf(func_def_3371,type,
sK751: ( char > nat ) > nat ).
thf(func_def_3372,type,
sK752: nat > ( char > nat ) > char ).
thf(func_def_3373,type,
sK753: set_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3374,type,
sK754: set_int > set_nat > ( int > set_nat ) > int ).
thf(func_def_3375,type,
sK755: set_int > set_nat > ( int > set_nat ) > int ).
thf(func_def_3376,type,
sK756: nat > set_o > ( $o > nat ) > $o ).
thf(func_def_3377,type,
sK757: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_3378,type,
sK758: set_int > set_int > ( int > set_int ) > int ).
thf(func_def_3379,type,
sK759: ( heap_e7401611519738050253t_unit > ref_a > $o ) > ref_a ).
thf(func_def_3380,type,
sK760: ( heap_e7401611519738050253t_unit > ref_a > $o ) > heap_e7401611519738050253t_unit ).
thf(func_def_3381,type,
sK761: ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_nat > set_nat ).
thf(func_def_3382,type,
sK762: set_int > set_nat > int > nat ).
thf(func_def_3383,type,
sK763: produc3843707927480180839at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3384,type,
sK764: product_prod_nat_num > product_prod_nat_num > ( nat > nat ) > num ).
thf(func_def_3385,type,
sK765: product_prod_nat_num > product_prod_nat_num > ( nat > nat ) > nat ).
thf(func_def_3386,type,
sK766: set_nat > ( nat > product_unit ) > product_unit > nat ).
thf(func_def_3387,type,
sK767: ( product_unit > set_nat ) > set_Product_unit > set_nat > product_unit ).
thf(func_def_3388,type,
sK768: ( rat > nat ) > ( nat > rat ) > nat ).
thf(func_def_3389,type,
sK769: ( $o > int ) > set_o > ( $o > int ) > $o ).
thf(func_def_3390,type,
sK770: ( nat > $o ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_3391,type,
sK771: ( char > char ) > char ).
thf(func_def_3392,type,
sK772: char > ( char > char ) > char ).
thf(func_def_3393,type,
sK773: ( int > nat > $o ) > ( int > nat > $o ) > ( char > nat ) > ( char > int ) > nat ).
thf(func_def_3394,type,
sK774: ( int > nat > $o ) > ( int > nat > $o ) > ( char > nat ) > ( char > int ) > int ).
thf(func_def_3395,type,
sK775: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_3396,type,
sK776: ( set_nat > $o ) > set_int > ( int > nat ) > set_nat ).
thf(func_def_3397,type,
sK777: ( set_nat > $o ) > set_int > ( int > nat ) > set_int ).
thf(func_def_3398,type,
sK778: set_Product_prod_o_o > set_o > $o ).
thf(func_def_3399,type,
sK779: set_Product_prod_o_o > set_o > $o ).
thf(func_def_3400,type,
sK780: set_o > ( $o > int ) > int > $o ).
thf(func_def_3401,type,
sK781: ( int > int ) > set_int > int > int ).
thf(func_def_3402,type,
sK782: set_nat > ( nat > int ) > int > nat ).
thf(func_def_3403,type,
sK783: ( nat > $o ) > ( nat > rat ) > set_rat > nat ).
thf(func_def_3404,type,
sK784: ( int > int > int ) > ( product_prod_int_int > int ) > int ).
thf(func_def_3405,type,
sK785: ( int > int > int ) > ( product_prod_int_int > int ) > int ).
thf(func_def_3406,type,
sK786: ( nat > nat ) > ( set_nat > $o ) > set_nat > set_nat ).
thf(func_def_3407,type,
sK787: ( nat > nat ) > ( set_nat > $o ) > set_nat > set_nat ).
thf(func_def_3408,type,
sK788: set_nat > ( nat > product_unit ) > product_unit ).
thf(func_def_3409,type,
sK789: set_Product_unit > ( product_unit > nat ) > nat > product_unit ).
thf(func_def_3410,type,
sK790: set_nat > nat > ( nat > nat ) > nat ).
thf(func_def_3411,type,
sK791: ( int > int > $o ) > ( int > int > $o ) > ( $o > $o ) > int ).
thf(func_def_3412,type,
sK792: ( int > int > $o ) > ( int > int > $o ) > ( $o > $o ) > int ).
thf(func_def_3413,type,
sK793: ( int > product_unit ) > set_nat > set_int > ( nat > product_unit ) > int ).
thf(func_def_3414,type,
sK794: ( int > product_unit ) > set_nat > set_int > ( nat > product_unit ) > nat ).
thf(func_def_3415,type,
sK795: $o > set_set_o > set_o ).
thf(func_def_3416,type,
sK796: ( int > int ) > set_int > set_int > int ).
thf(func_def_3417,type,
sK797: ( char > $o ) > $o > char ).
thf(func_def_3418,type,
sK798: char > ( char > $o ) > $o > char ).
thf(func_def_3419,type,
sK799: rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_3420,type,
sK800: ( nat > rat ) > ( rat > rat > $o ) > rat ).
thf(func_def_3421,type,
sK801: nat > ( $o > nat ) > set_o > $o ).
thf(func_def_3422,type,
sK802: set_nat > set_nat > nat > nat ).
thf(func_def_3423,type,
sK803: set_o > set_nat > ( $o > set_nat ) > $o ).
thf(func_def_3424,type,
sK804: set_Product_unit > ( product_unit > set_Product_unit ) > product_unit ).
thf(func_def_3425,type,
sK805: ( int > int > set_o ) > $o > product_prod_int_int > int ).
thf(func_def_3426,type,
sK806: ( int > int > set_o ) > $o > product_prod_int_int > int ).
thf(func_def_3427,type,
sK807: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > set_nat > produc3843707927480180839at_nat ).
thf(func_def_3428,type,
sK808: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > set_nat > produc3843707927480180839at_nat ).
thf(func_def_3429,type,
sK809: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > set_nat > set_nat ).
thf(func_def_3430,type,
sK810: set_nat > set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat ).
thf(func_def_3431,type,
sK811: set_Product_unit > ( product_unit > set_o ) > product_unit ).
thf(func_def_3432,type,
sK812: set_nat > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3433,type,
sK813: set_o > ( $o > $o ) > $o ).
thf(func_def_3434,type,
sK814: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3435,type,
sK815: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3436,type,
sK816: ( nat > int ) > set_Pr6200539531224447659at_num > product_prod_int_int > ( num > int ) > nat ).
thf(func_def_3437,type,
sK817: ( nat > int ) > set_Pr6200539531224447659at_num > product_prod_int_int > ( num > int ) > num ).
thf(func_def_3438,type,
sK818: product_prod_int_int > ( int > int > int ) > ( int > $o ) > int ).
thf(func_def_3439,type,
sK819: product_prod_int_int > ( int > int > int ) > ( int > $o ) > int ).
thf(func_def_3440,type,
sK820: ( product_unit > product_unit ) > product_unit > set_Product_unit > product_unit ).
thf(func_def_3441,type,
sK821: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3442,type,
sK822: ( int > int > set_o ) > $o > product_prod_int_int > int ).
thf(func_def_3443,type,
sK823: ( int > int > set_o ) > $o > product_prod_int_int > int ).
thf(func_def_3444,type,
sK824: set_int > ( int > set_Product_unit ) > int ).
thf(func_def_3445,type,
sK825: ( nat > nat > $o ) > ( char > nat ) > ( char > nat ) > ( nat > nat > $o ) > nat ).
thf(func_def_3446,type,
sK826: ( nat > nat > $o ) > ( char > nat ) > ( char > nat ) > ( nat > nat > $o ) > nat ).
thf(func_def_3447,type,
sK827: product_prod_nat_num > num > nat ).
thf(func_def_3448,type,
sK828: set_nat > ( nat > product_prod_nat_nat ) > product_prod_nat_nat ).
thf(func_def_3449,type,
sK829: set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3450,type,
sK830: ( $o > set_nat ) > set_nat > set_o > $o ).
thf(func_def_3451,type,
sK831: ( $o > set_nat ) > set_nat > set_o > $o ).
thf(func_def_3452,type,
sK832: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3453,type,
sK833: ( product_prod_nat_nat > set_nat ) > set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3454,type,
sK834: ( product_prod_nat_nat > set_nat ) > set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3455,type,
sK835: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3456,type,
sK836: set_int > ( int > set_nat ) > ( int > set_nat ) > int ).
thf(func_def_3457,type,
sK837: set_Product_unit > ( product_unit > product_unit ) > product_unit > product_unit ).
thf(func_def_3458,type,
sK838: set_Product_unit > ( product_unit > product_unit ) > product_unit > product_unit ).
thf(func_def_3459,type,
sK839: ( nat > product_unit ) > set_nat > ( nat > product_unit ) > nat ).
thf(func_def_3460,type,
sK840: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_3461,type,
sK841: set_nat > ( int > set_nat ) > set_int > int ).
thf(func_def_3462,type,
sK842: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_3463,type,
sK843: set_int > ( int > product_unit ) > ( int > product_unit ) > int ).
thf(func_def_3464,type,
sK844: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat ).
thf(func_def_3465,type,
sK845: set_Pr4329608150637261639at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3466,type,
sK846: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3467,type,
sK847: set_int > ( int > product_unit ) > ( int > product_unit ) > set_int > int ).
thf(func_def_3468,type,
sK848: set_int > ( int > product_unit ) > ( int > product_unit ) > set_int > int ).
thf(func_def_3469,type,
sK849: ( produc3843707927480180839at_nat > product_unit ) > product_unit > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3470,type,
sK850: set_nat > ( $o > set_nat ) > set_o > $o ).
thf(func_def_3471,type,
sK851: set_nat > ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3472,type,
sK852: ( int > nat ) > ( nat > num ) > ( nat > num ) > nat ).
thf(func_def_3473,type,
sK853: ( nat > nat ) > set_nat > nat > nat ).
thf(func_def_3474,type,
sK854: ( nat > $o ) > set_nat > nat ).
thf(func_def_3475,type,
sK855: ( $o > set_int ) > product_prod_o_int > set_o > $o ).
thf(func_def_3476,type,
sK856: ( $o > set_int ) > product_prod_o_int > set_o > int ).
thf(func_def_3477,type,
sK857: set_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3478,type,
sK858: set_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_nat ).
thf(func_def_3479,type,
sK859: set_nat > ( nat > nat > nat ) > nat ).
thf(func_def_3480,type,
sK860: set_nat > ( nat > nat > nat ) > nat ).
thf(func_def_3481,type,
sK861: set_int > set_nat > ( int > set_nat ) > int ).
thf(func_def_3482,type,
sK862: nat > product_prod_nat_nat > nat ).
thf(func_def_3483,type,
sK863: ( int > int ) > ( nat > int ) > set_int > set_nat > int ).
thf(func_def_3484,type,
sK864: ( char > nat ) > nat > char ).
thf(func_def_3485,type,
sK865: char > ( char > nat ) > nat > char ).
thf(func_def_3486,type,
sK866: nat > ( nat > $o ) > nat ).
thf(func_def_3487,type,
sK867: nat > ( nat > $o ) > nat ).
thf(func_def_3488,type,
sK868: set_Product_prod_o_o > set_o > $o ).
thf(func_def_3489,type,
sK869: product_unit > set_int > ( int > product_unit ) > int ).
thf(func_def_3490,type,
sK870: product_unit > set_int > ( int > product_unit ) > int ).
thf(func_def_3491,type,
sK871: ( int > nat ) > set_int > set_nat > int ).
thf(func_def_3492,type,
sK872: set_o > set_nat > ( $o > set_nat ) > $o ).
thf(func_def_3493,type,
sK873: set_o > set_nat > ( $o > set_nat ) > set_nat ).
thf(func_def_3494,type,
sK874: set_nat > ( nat > nat ) > nat ).
thf(func_def_3495,type,
sK875: set_int > $o > ( int > $o ) > int ).
thf(func_def_3496,type,
sK876: set_int > set_int > ( int > int ) > ( int > int ) > int ).
thf(func_def_3497,type,
sK877: ( int > int > $o ) > set_int > ( int > int > $o ) > set_int > int ).
thf(func_def_3498,type,
sK878: ( int > int > $o ) > set_int > ( int > int > $o ) > set_int > int ).
thf(func_def_3499,type,
sK879: ( int > int ) > set_int > ( int > int ) > set_int > int ).
thf(func_def_3500,type,
sK880: set_nat > ( nat > int ) > int ).
thf(func_def_3501,type,
sK881: ( nat > set_Pr1261947904930325089at_nat ) > set_nat > nat ).
thf(func_def_3502,type,
sK882: ( nat > set_nat ) > set_nat > nat > product_prod_nat_nat ).
thf(func_def_3503,type,
sK883: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_3504,type,
sK884: ( char > int ) > ( int > $o > $o ) > ( char > $o ) > ( int > $o > $o ) > $o ).
thf(func_def_3505,type,
sK885: ( char > int ) > ( int > $o > $o ) > ( char > $o ) > ( int > $o > $o ) > int ).
thf(func_def_3506,type,
sK886: ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3507,type,
sK887: set_nat > ( nat > int ) > ( set_int > $o ) > set_int ).
thf(func_def_3508,type,
sK888: set_nat > ( nat > int ) > ( set_int > $o ) > set_nat ).
thf(func_def_3509,type,
sK889: ( $o > product_unit ) > set_o > ( nat > product_unit ) > set_nat > $o ).
thf(func_def_3510,type,
sK890: ( $o > product_unit ) > set_o > ( nat > product_unit ) > set_nat > nat ).
thf(func_def_3511,type,
sK891: ( int > int ) > ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_3512,type,
sK892: ( nat > nat ) > set_nat > ( int > nat ) > set_int > nat ).
thf(func_def_3513,type,
sK893: ( char > nat ) > nat > char ).
thf(func_def_3514,type,
sK894: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3515,type,
sK895: ( int > set_nat ) > set_int > set_nat > int ).
thf(func_def_3516,type,
sK896: ( int > set_nat ) > set_int > set_nat > int ).
thf(func_def_3517,type,
sK897: set_int > ( int > set_o ) > int ).
thf(func_def_3518,type,
sK898: nat > ( rat > nat ) > rat ).
thf(func_def_3519,type,
sK899: product_prod_o_o > ( $o > set_o ) > set_o > $o ).
thf(func_def_3520,type,
sK900: product_prod_o_o > ( $o > set_o ) > set_o > $o ).
thf(func_def_3521,type,
sK901: set_nat > rat > ( nat > rat ) > nat ).
thf(func_def_3522,type,
sK902: ( nat > product_prod_nat_nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_3523,type,
sK903: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3524,type,
sK904: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3525,type,
sK905: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3526,type,
sK906: ( int > code_integer > $o ) > ( int > code_integer > $o ) > code_integer ).
thf(func_def_3527,type,
sK907: ( int > code_integer > $o ) > ( int > code_integer > $o ) > int ).
thf(func_def_3528,type,
sK908: ( nat > set_Pr1261947904930325089at_nat ) > set_nat > nat ).
thf(func_def_3529,type,
sK909: int > ( int > set_int ) > set_int > int ).
thf(func_def_3530,type,
sK910: product_prod_nat_num > ( nat > num > set_o ) > $o > nat ).
thf(func_def_3531,type,
sK911: product_prod_nat_num > ( nat > num > set_o ) > $o > num ).
thf(func_def_3532,type,
sK912: product_prod_nat_nat > ( nat > nat > set_int ) > int > nat ).
thf(func_def_3533,type,
sK913: product_prod_nat_nat > ( nat > nat > set_int ) > int > nat ).
thf(func_def_3534,type,
sK914: set_int > ( int > set_o ) > int ).
thf(func_def_3535,type,
sK915: set_int > ( int > product_unit ) > product_unit > int ).
thf(func_def_3536,type,
sK916: ( $o > set_nat ) > set_o > $o ).
thf(func_def_3537,type,
sK917: nat > ( $o > nat ) > set_o > $o ).
thf(func_def_3538,type,
sK918: char > ( rat > char ) > rat ).
thf(func_def_3539,type,
sK919: ( rat > char ) > char ).
thf(func_def_3540,type,
sK920: $o > ( nat > num > set_o ) > product_prod_nat_num > nat ).
thf(func_def_3541,type,
sK921: $o > ( nat > num > set_o ) > product_prod_nat_num > num ).
thf(func_def_3542,type,
sK922: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_3543,type,
sK923: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_3544,type,
sK924: ( nat > num ) > ( int > nat ) > ( nat > num ) > set_int > int ).
thf(func_def_3545,type,
sK925: ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ).
thf(func_def_3546,type,
sK926: ( produc3843707927480180839at_nat > set_nat ) > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3547,type,
sK927: ( nat > num ) > ( nat > num ) > ( int > nat ) > nat ).
thf(func_def_3548,type,
sK928: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3549,type,
sK929: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3550,type,
sK930: int > ( int > int ) > set_int > int ).
thf(func_def_3551,type,
sK931: set_nat > nat > nat ).
thf(func_def_3552,type,
sK932: set_o > nat > ( $o > set_nat ) > $o ).
thf(func_def_3553,type,
sK933: set_o > ( $o > set_int ) > set_int > $o ).
thf(func_def_3554,type,
sK934: ( nat > $o ) > $o > set_nat > nat ).
thf(func_def_3555,type,
sK935: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3556,type,
sK936: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_3557,type,
sK937: set_nat > ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3558,type,
sK938: set_nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_3559,type,
sK939: ( $o > nat ) > set_o > ( $o > nat ) > $o ).
thf(func_def_3560,type,
sK940: set_int > int > ( int > int ) > int ).
thf(func_def_3561,type,
sK941: set_nat > ( set_nat > $o ) > ( nat > nat ) > set_nat ).
thf(func_def_3562,type,
sK942: set_nat > ( set_nat > $o ) > ( nat > nat ) > set_nat ).
thf(func_def_3563,type,
sK943: ( int > int ) > set_int > int > int ).
thf(func_def_3564,type,
sK944: ( product_prod_nat_num > $o ) > nat ).
thf(func_def_3565,type,
sK945: ( product_prod_nat_num > $o ) > num ).
thf(func_def_3566,type,
sK946: ( int > int > $o ) > ( char > int ) > int ).
thf(func_def_3567,type,
sK947: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3568,type,
sK948: set_set_nat > nat > set_nat ).
thf(func_def_3569,type,
sK949: set_nat > ( int > product_unit ) > ( nat > product_unit ) > set_int > int ).
thf(func_def_3570,type,
sK950: set_nat > ( int > product_unit ) > ( nat > product_unit ) > set_int > nat ).
thf(func_def_3571,type,
sK951: ( char > nat ) > ( char > int ) > ( nat > int > $o ) > ( nat > int > $o ) > nat ).
thf(func_def_3572,type,
sK952: ( char > nat ) > ( char > int ) > ( nat > int > $o ) > ( nat > int > $o ) > int ).
thf(func_def_3573,type,
sK953: produc7812382424243267045t_unit > ref_a > heap_e7401611519738050253t_unit ).
thf(func_def_3574,type,
sK954: set_Pr958786334691620121nt_int > ( product_prod_int_int > nat ) > product_prod_int_int ).
thf(func_def_3575,type,
sK955: set_int > product_prod_int_int > int ).
thf(func_def_3576,type,
sK956: set_nat > ( $o > nat ) > set_o > $o ).
thf(func_def_3577,type,
sK957: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int ).
thf(func_def_3578,type,
sK958: ( nat > int ) > set_nat > nat ).
thf(func_def_3579,type,
sK959: ( 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 ) > int ).
thf(func_def_3580,type,
sK960: ( 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 ) > product_prod_nat_nat ).
thf(func_def_3581,type,
sK961: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3582,type,
sK962: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3583,type,
sK963: product_prod_nat_nat > set_nat > nat ).
thf(func_def_3584,type,
sK964: int > ( int > nat ) > set_int > int ).
thf(func_def_3585,type,
sK965: ( nat > nat ) > set_nat > set_int > ( int > nat ) > nat ).
thf(func_def_3586,type,
sK966: set_Pr1261947904930325089at_nat > ( set_nat > $o ) > ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3587,type,
sK967: set_Pr1261947904930325089at_nat > ( set_nat > $o ) > ( product_prod_nat_nat > nat ) > set_nat ).
thf(func_def_3588,type,
sK968: rat > ( int > rat ) > set_int > int ).
thf(func_def_3589,type,
sK969: ( int > product_unit ) > ( int > product_unit ) > set_int > int ).
thf(func_def_3590,type,
sK970: set_rat > nat > rat ).
thf(func_def_3591,type,
sK971: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3592,type,
sK972: set_nat > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3593,type,
sK973: set_nat > set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > set_nat ).
thf(func_def_3594,type,
sK974: ( nat > rat ) > ( rat > nat ) > nat ).
thf(func_def_3595,type,
sK975: ( nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_3596,type,
sK976: ( nat > set_nat ) > set_nat > set_nat > set_nat ).
thf(func_def_3597,type,
sK977: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_3598,type,
sK978: set_Product_unit > ( int > nat ) > ( product_unit > nat ) > set_int > product_unit ).
thf(func_def_3599,type,
sK979: set_Pr958786334691620121nt_int > set_int > int ).
thf(func_def_3600,type,
sK980: set_Pr958786334691620121nt_int > set_int > int ).
thf(func_def_3601,type,
sK981: set_Product_unit > set_nat > ( product_unit > set_nat ) > product_unit ).
thf(func_def_3602,type,
sK982: set_Product_unit > set_nat > ( product_unit > set_nat ) > product_unit ).
thf(func_def_3603,type,
sK983: ( int > nat ) > ( int > nat ) > set_int > set_int > int ).
thf(func_def_3604,type,
sK984: ( $o > product_unit ) > product_unit > set_o > $o ).
thf(func_def_3605,type,
sK985: product_prod_nat_num > product_prod_nat_nat > ( nat > num > set_Pr1261947904930325089at_nat ) > num ).
thf(func_def_3606,type,
sK986: product_prod_nat_num > product_prod_nat_nat > ( nat > num > set_Pr1261947904930325089at_nat ) > nat ).
thf(func_def_3607,type,
sK987: set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_3608,type,
sK988: ( int > set_Product_unit ) > set_int > int ).
thf(func_def_3609,type,
sK989: ( rat > int ) > ( int > rat ) > int ).
thf(func_def_3610,type,
sK990: ( char > nat ) > ( nat > nat > $o ) > nat ).
thf(func_def_3611,type,
sK991: set_o > ( $o > set_int ) > $o ).
thf(func_def_3612,type,
sK992: ( char > nat ) > ( char > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_3613,type,
sK993: ( char > nat ) > ( char > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_3614,type,
sK994: set_nat > product_prod_nat_int > ( nat > set_int ) > nat ).
thf(func_def_3615,type,
sK995: set_nat > product_prod_nat_int > ( nat > set_int ) > int ).
thf(func_def_3616,type,
sK996: ( nat > nat ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_3617,type,
sK997: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3618,type,
sK998: set_set_int > int > set_int ).
thf(func_def_3619,type,
sK999: ( int > int > set_nat ) > product_prod_int_int > nat > int ).
thf(func_def_3620,type,
sK1000: ( int > int > set_nat ) > product_prod_int_int > nat > int ).
thf(func_def_3621,type,
sK1001: set_o > set_nat > ( $o > set_nat ) > $o ).
thf(func_def_3622,type,
sK1002: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3623,type,
sK1003: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3624,type,
sK1004: set_nat > ( int > set_nat ) > set_int > int ).
thf(func_def_3625,type,
sK1005: ( $o > product_unit ) > product_unit > set_o > $o ).
thf(func_def_3626,type,
sK1006: ( $o > product_unit ) > product_unit > set_o > $o ).
thf(func_def_3627,type,
sK1007: ( nat > $o ) > ( int > nat ) > set_int > int ).
thf(func_def_3628,type,
sK1008: ( nat > int ) > set_nat > ( int > $o ) > nat ).
thf(func_def_3629,type,
sK1009: ( $o > product_unit ) > set_o > ( $o > product_unit ) > $o ).
thf(func_def_3630,type,
sK1010: nat > set_int > ( int > nat ) > int ).
thf(func_def_3631,type,
sK1011: set_nat > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3632,type,
sK1012: ( char > nat ) > ( nat > int > $o ) > ( nat > int > $o ) > ( char > int ) > nat ).
thf(func_def_3633,type,
sK1013: ( char > nat ) > ( nat > int > $o ) > ( nat > int > $o ) > ( char > int ) > int ).
thf(func_def_3634,type,
sK1014: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_3635,type,
sK1015: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > set_nat > product_prod_nat_nat ).
thf(func_def_3636,type,
sK1016: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3637,type,
sK1017: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3638,type,
sK1018: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3639,type,
sK1019: ( char > nat ) > ( nat > char ) > char ).
thf(func_def_3640,type,
sK1020: ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > int > $o ) > ( int > nat ) > int ).
thf(func_def_3641,type,
sK1021: ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > int > $o ) > ( int > nat ) > product_prod_nat_nat ).
thf(func_def_3642,type,
sK1022: set_nat > set_int > nat > int ).
thf(func_def_3643,type,
sK1023: ( int > set_nat ) > ( int > set_nat ) > set_int > int ).
thf(func_def_3644,type,
sK1024: set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat ).
thf(func_def_3645,type,
sK1025: set_nat > ( nat > nat ) > set_nat > nat ).
thf(func_def_3646,type,
sK1026: ( nat > set_nat ) > set_nat > set_nat > nat ).
thf(func_def_3647,type,
sK1027: set_int > nat > int ).
thf(func_def_3648,type,
sK1028: set_nat > ( int > set_nat ) > set_int > int ).
thf(func_def_3649,type,
sK1029: ( int > nat ) > ( nat > int ) > nat ).
thf(func_def_3650,type,
sK1030: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3651,type,
sK1031: set_o > ( $o > int ) > ( $o > int ) > $o ).
thf(func_def_3652,type,
sK1032: ( $o > $o ) > product_unit ).
thf(func_def_3653,type,
sK1033: set_nat > ( nat > nat ) > set_nat > set_nat ).
thf(func_def_3654,type,
sK1034: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > product_unit ) > product_unit > produc3843707927480180839at_nat ).
thf(func_def_3655,type,
sK1035: ( int > int > $o ) > ( int > int ) > ( int > int ) > int > product_prod_int_int ).
thf(func_def_3656,type,
sK1036: ( char > nat ) > ( nat > nat > $o ) > ( char > nat ) > char > product_prod_nat_nat ).
thf(func_def_3657,type,
sK1037: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_3658,type,
sK1038: ( int > rat ) > ( rat > int ) > rat ).
thf(func_def_3659,type,
sK1039: ( rat > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_3660,type,
sK1040: ( nat > char ) > char ).
thf(func_def_3661,type,
sK1041: char > ( nat > char ) > nat ).
thf(func_def_3662,type,
sK1042: nat > ( nat > $o ) > $o > nat ).
thf(func_def_3663,type,
sK1043: ( nat > $o ) > $o > nat ).
thf(func_def_3664,type,
sK1044: ( int > int ) > set_int > int ).
thf(func_def_3665,type,
sK1045: product_unit > set_int > ( int > product_unit ) > product_unit ).
thf(func_def_3666,type,
sK1046: product_unit > set_int > ( int > product_unit ) > int ).
thf(func_def_3667,type,
sK1047: set_o > ( $o > nat > nat ) > $o ).
thf(func_def_3668,type,
sK1048: set_o > ( $o > nat > nat ) > $o ).
thf(func_def_3669,type,
sK1049: ( $o > $o ) > ( $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_3670,type,
sK1050: ( $o > $o ) > ( $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_3671,type,
sK1051: set_nat > set_int > ( int > set_nat ) > int ).
thf(func_def_3672,type,
sK1052: set_Product_unit > product_unit ).
thf(func_def_3673,type,
sK1053: ( int > product_unit ) > set_int > ( int > product_unit ) > int ).
thf(func_def_3674,type,
sK1054: $o > ( char > $o ) > char ).
thf(func_def_3675,type,
sK1055: ( char > int ) > ( int > nat > $o ) > ( char > nat ) > ( int > nat > $o ) > int ).
thf(func_def_3676,type,
sK1056: ( char > int ) > ( int > nat > $o ) > ( char > nat ) > ( int > nat > $o ) > nat ).
thf(func_def_3677,type,
sK1057: ( num > num > $o ) > ( int > num ) > ( int > num ) > ( int > int > $o ) > int ).
thf(func_def_3678,type,
sK1058: ( num > num > $o ) > ( int > num ) > ( int > num ) > ( int > int > $o ) > int ).
thf(func_def_3679,type,
sK1059: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3680,type,
sK1060: ( nat > $o > $o ) > ( char > $o ) > ( char > nat ) > ( nat > $o > $o ) > $o ).
thf(func_def_3681,type,
sK1061: ( nat > $o > $o ) > ( char > $o ) > ( char > nat ) > ( nat > $o > $o ) > nat ).
thf(func_def_3682,type,
sK1062: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3683,type,
sK1063: nat > ( nat > nat ) > set_nat > nat ).
thf(func_def_3684,type,
sK1064: ( $o > set_o ) > set_o > $o ).
thf(func_def_3685,type,
sK1065: ( int > nat ) > set_int > nat ).
thf(func_def_3686,type,
sK1066: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3687,type,
sK1067: set_int > nat > ( int > nat ) > int ).
thf(func_def_3688,type,
sK1068: ( int > nat ) > set_int > nat ).
thf(func_def_3689,type,
sK1069: produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3690,type,
sK1070: produc3843707927480180839at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3691,type,
sK1071: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3692,type,
sK1072: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3693,type,
sK1073: int > set_nat > ( nat > int ) > nat ).
thf(func_def_3694,type,
sK1074: product_unit > set_set_Product_unit > set_Product_unit ).
thf(func_def_3695,type,
sK1075: set_o > ( int > $o ) > $o > set_int > set_int ).
thf(func_def_3696,type,
sK1076: set_o > ( int > $o ) > $o > set_int > int ).
thf(func_def_3697,type,
sK1077: product_unit > ( product_unit > product_unit ) > set_Product_unit > product_unit ).
thf(func_def_3698,type,
sK1078: set_se5479201105039950375at_nat > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3699,type,
sK1079: ( char > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_3700,type,
sK1080: set_o > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_3701,type,
sK1081: ( $o > set_nat ) > ( $o > set_nat ) > set_o > $o ).
thf(func_def_3702,type,
sK1082: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > nat ).
thf(func_def_3703,type,
sK1083: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > nat ).
thf(func_def_3704,type,
sK1084: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat ).
thf(func_def_3705,type,
sK1085: ( int > set_int ) > set_int > int ).
thf(func_def_3706,type,
sK1086: set_nat > ( nat > nat ) > set_nat > nat ).
thf(func_def_3707,type,
sK1087: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_3708,type,
sK1088: $o > set_o > ( $o > set_o ) > $o ).
thf(func_def_3709,type,
sK1089: product_prod_nat_num > set_Pr6200539531224447659at_num > ( num > num ) > ( nat > nat ) > nat ).
thf(func_def_3710,type,
sK1090: product_prod_nat_num > set_Pr6200539531224447659at_num > ( num > num ) > ( nat > nat ) > num ).
thf(func_def_3711,type,
sK1091: set_Product_unit > product_unit > ( product_unit > product_unit ) > product_unit ).
thf(func_def_3712,type,
sK1092: set_Product_unit > ( product_unit > set_Product_unit ) > product_unit ).
thf(func_def_3713,type,
sK1093: set_nat > ( nat > $o ) > $o ).
thf(func_def_3714,type,
sK1094: rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_3715,type,
sK1095: set_nat > ( nat > rat ) > set_rat > rat ).
thf(func_def_3716,type,
sK1096: set_int > ( int > int ) > set_int > set_int ).
thf(func_def_3717,type,
sK1097: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > product_unit > product_prod_nat_nat ).
thf(func_def_3718,type,
sK1098: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_unit ) > product_unit > product_prod_nat_nat ).
thf(func_def_3719,type,
sK1099: ( nat > nat > product_prod_nat_nat > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3720,type,
sK1100: ( nat > nat > product_prod_nat_nat > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_3721,type,
sK1101: ( int > nat ) > ( int > nat ) > ( int > int ) > int ).
thf(func_def_3722,type,
sK1102: product_prod_nat_num > ( nat > num > $o ) > nat ).
thf(func_def_3723,type,
sK1103: product_prod_nat_num > ( nat > num > $o ) > num ).
thf(func_def_3724,type,
sK1104: set_o > ( $o > set_Product_unit ) > $o ).
thf(func_def_3725,type,
sK1105: ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ).
thf(func_def_3726,type,
sK1106: ( nat > $o ) > set_nat > $o ).
thf(func_def_3727,type,
sK1107: set_int > ( nat > int ) > set_nat > set_nat ).
thf(func_def_3728,type,
sK1108: ( $o > set_int ) > set_o > int > $o ).
thf(func_def_3729,type,
sK1109: ( nat > product_prod_nat_nat ) > ( set_Pr1261947904930325089at_nat > $o ) > set_nat > set_nat ).
thf(func_def_3730,type,
sK1110: ( nat > product_prod_nat_nat ) > ( set_Pr1261947904930325089at_nat > $o ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3731,type,
sK1111: product_prod_nat_nat > ( nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_3732,type,
sK1112: product_prod_nat_nat > ( nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_3733,type,
sK1113: set_Product_unit > ( product_unit > set_int ) > product_unit ).
thf(func_def_3734,type,
sK1114: set_nat > ( nat > set_nat ) > set_nat > set_nat ).
thf(func_def_3735,type,
sK1115: set_nat > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_3736,type,
sK1116: ( $o > rat ) > rat > set_o > $o ).
thf(func_def_3737,type,
sK1117: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_3738,type,
sK1118: product_unit > ( nat > product_unit ) > set_nat > nat ).
thf(func_def_3739,type,
sK1119: set_nat > set_int > nat > int ).
thf(func_def_3740,type,
sK1120: set_int > ( int > set_nat ) > int ).
thf(func_def_3741,type,
sK1121: set_Pr4329608150637261639at_nat > set_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3742,type,
sK1122: ( nat > nat ) > set_nat > nat > nat ).
thf(func_def_3743,type,
sK1123: ( nat > rat ) > rat ).
thf(func_def_3744,type,
sK1124: rat > ( nat > rat ) > nat ).
thf(func_def_3745,type,
sK1125: product_unit > ( $o > product_unit ) > set_o > set_Product_unit > $o ).
thf(func_def_3746,type,
sK1126: product_unit > ( $o > product_unit ) > set_o > set_Product_unit > set_o ).
thf(func_def_3747,type,
sK1127: ( nat > int ) > set_nat > set_int > int ).
thf(func_def_3748,type,
sK1128: int > ( nat > int ) > set_nat > nat ).
thf(func_def_3749,type,
sK1129: product_prod_nat_nat > int > ( nat > nat > set_int ) > nat ).
thf(func_def_3750,type,
sK1130: product_prod_nat_nat > int > ( nat > nat > set_int ) > nat ).
thf(func_def_3751,type,
sK1131: set_int > ( int > nat > nat ) > int ).
thf(func_def_3752,type,
sK1132: set_int > ( int > nat > nat ) > int ).
thf(func_def_3753,type,
sK1133: set_o > ( $o > int ) > int > $o ).
thf(func_def_3754,type,
sK1134: ( char > int ) > ( char > int ) > ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3755,type,
sK1135: ( char > int ) > ( char > int ) > ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3756,type,
sK1136: ( nat > int ) > set_nat > ( nat > int ) > nat ).
thf(func_def_3757,type,
sK1137: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3758,type,
sK1138: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
thf(func_def_3759,type,
sK1139: ( char > nat ) > nat > char ).
thf(func_def_3760,type,
sK1140: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3761,type,
sK1141: set_nat > set_nat > ( nat > set_nat ) > nat ).
thf(func_def_3762,type,
sK1142: ( $o > set_nat ) > ( $o > set_nat ) > set_o > $o ).
thf(func_def_3763,type,
sK1143: product_prod_nat_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).
thf(func_def_3764,type,
sK1144: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).
thf(func_def_3765,type,
sK1145: ( int > int ) > set_int > ( int > int ) > int ).
thf(func_def_3766,type,
sK1146: ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3767,type,
sK1147: ( int > int > $o ) > ( int > int > $o ) > int ).
thf(func_def_3768,type,
sK1148: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3769,type,
sK1149: ( num > num > $o ) > ( num > num > $o ) > num ).
thf(func_def_3770,type,
sK1150: int > ( nat > num > set_int ) > product_prod_nat_num > num ).
thf(func_def_3771,type,
sK1151: int > ( nat > num > set_int ) > product_prod_nat_num > nat ).
thf(func_def_3772,type,
sK1152: ( rat > $o ) > $o > rat ).
thf(func_def_3773,type,
sK1153: nat > ( $o > set_nat ) > set_o > $o ).
thf(func_def_3774,type,
sK1154: ( rat > int ) > int > rat ).
thf(func_def_3775,type,
sK1155: ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_3776,type,
sK1156: product_prod_nat_nat > ( nat > product_prod_nat_nat ) > set_nat > nat ).
thf(func_def_3777,type,
sK1157: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat ).
thf(func_def_3778,type,
sK1158: ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat ).
thf(func_def_3779,type,
sK1159: int > ( int > int ) > set_int > int ).
thf(func_def_3780,type,
sK1160: ( int > int ) > set_int > set_int > int ).
thf(func_def_3781,type,
sK1161: nat > ( nat > int ) > int > nat ).
thf(func_def_3782,type,
sK1162: ( nat > int ) > int > nat ).
thf(func_def_3783,type,
sK1163: ( $o > $o > $o ) > ( rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > $o ).
thf(func_def_3784,type,
sK1164: ( $o > $o > $o ) > ( rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > $o ).
thf(func_def_3785,type,
sK1165: set_Product_prod_o_o > set_o ).
thf(func_def_3786,type,
sK1166: $o > set_Product_prod_o_o > $o ).
thf(func_def_3787,type,
sK1167: set_o > set_Product_prod_o_o > $o ).
thf(func_def_3788,type,
sK1168: set_int > set_o > ( $o > product_unit ) > ( int > product_unit ) > $o ).
thf(func_def_3789,type,
sK1169: set_int > set_o > ( $o > product_unit ) > ( int > product_unit ) > int ).
thf(func_def_3790,type,
sK1170: set_int > ( int > nat ) > nat ).
thf(func_def_3791,type,
sK1171: ( $o > set_Product_unit ) > set_o > $o ).
thf(func_def_3792,type,
sK1172: set_int > set_nat > int > nat ).
thf(func_def_3793,type,
sK1173: set_int > ( int > int ) > set_nat > ( nat > int ) > int ).
thf(func_def_3794,type,
sK1174: product_prod_nat_nat > ( nat > nat > set_o ) > $o > nat ).
thf(func_def_3795,type,
sK1175: product_prod_nat_nat > ( nat > nat > set_o ) > $o > nat ).
thf(func_def_3796,type,
sK1176: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_3797,type,
sK1177: rat > ( nat > rat ) > set_nat > nat ).
thf(func_def_3798,type,
sK1178: set_int > ( nat > product_unit ) > set_nat > ( int > product_unit ) > nat ).
thf(func_def_3799,type,
sK1179: set_int > ( nat > product_unit ) > set_nat > ( int > product_unit ) > int ).
thf(func_def_3800,type,
sK1180: set_int > ( int > $o ) > int ).
thf(func_def_3801,type,
sK1181: nat > ( int > nat ) > set_int > int ).
thf(func_def_3802,type,
sK1182: set_nat > set_nat > nat > nat ).
thf(func_def_3803,type,
sK1183: set_nat > set_nat > nat > nat ).
thf(func_def_3804,type,
sK1184: ( int > int > set_nat ) > product_prod_int_int > nat > int ).
thf(func_def_3805,type,
sK1185: ( int > int > set_nat ) > product_prod_int_int > nat > int ).
thf(func_def_3806,type,
sK1186: set_o > ( $o > int ) > int > $o ).
thf(func_def_3807,type,
sK1187: product_unit > ( product_prod_nat_nat > product_unit ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3808,type,
sK1188: ( $o > product_unit ) > ( $o > product_unit ) > set_o > set_o > $o ).
thf(func_def_3809,type,
sK1189: ( $o > product_unit ) > ( $o > product_unit ) > set_o > set_o > $o ).
thf(func_def_3810,type,
sK1190: ( nat > $o ) > set_int > ( int > nat ) > nat ).
thf(func_def_3811,type,
sK1191: ( nat > int ) > ( nat > int ) > set_nat > nat ).
thf(func_def_3812,type,
sK1192: code_integer > ( $o > code_integer ) > set_o > $o ).
thf(func_def_3813,type,
sK1193: ( nat > set_int ) > set_nat > int > nat ).
thf(func_def_3814,type,
sK1194: set_rat > ( nat > rat ) > set_nat > set_nat ).
thf(func_def_3815,type,
sK1195: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > set_nat ) > product_prod_nat_nat ).
thf(func_def_3816,type,
sK1196: ( nat > rat ) > set_nat > rat ).
thf(func_def_3817,type,
sK1197: set_nat > ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3818,type,
sK1198: set_nat > set_rat > nat > rat ).
thf(func_def_3819,type,
sK1199: ( rat > int ) > ( rat > int ) > ( int > int > $o ) > rat > product_prod_int_int ).
thf(func_def_3820,type,
sK1200: ( nat > int ) > ( nat > int ) > set_nat > nat ).
thf(func_def_3821,type,
sK1201: set_nat > ( nat > product_prod_nat_nat ) > product_prod_nat_nat ).
thf(func_def_3822,type,
sK1202: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_3823,type,
sK1203: rat > ( nat > rat ) > nat ).
thf(func_def_3824,type,
sK1204: ( product_prod_nat_nat > set_nat ) > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3825,type,
sK1205: set_int > ( int > set_nat ) > set_nat > int ).
thf(func_def_3826,type,
sK1206: ( nat > nat ) > set_nat > nat ).
thf(func_def_3827,type,
sK1207: product_prod_nat_num > nat ).
thf(func_def_3828,type,
sK1208: product_prod_nat_num > num ).
thf(func_def_3829,type,
sK1209: set_nat > ( product_unit > nat ) > nat > set_Product_unit > product_unit ).
thf(func_def_3830,type,
sK1210: set_nat > ( product_unit > nat ) > nat > set_Product_unit > set_Product_unit ).
thf(func_def_3831,type,
sK1211: set_Pr4329608150637261639at_nat > set_nat > ( produc3843707927480180839at_nat > set_nat ) > produc3843707927480180839at_nat ).
thf(func_def_3832,type,
sK1212: ( int > nat ) > ( int > nat ) > set_int > int ).
thf(func_def_3833,type,
sK1213: ( $o > set_nat ) > set_o > set_nat > $o ).
thf(func_def_3834,type,
sK1214: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_3835,type,
sK1215: set_int > product_unit > ( int > product_unit ) > int ).
thf(func_def_3836,type,
sK1216: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_3837,type,
sK1217: ( $o > product_unit ) > ( $o > product_unit ) > set_o > $o ).
thf(func_def_3838,type,
sK1218: set_nat > ( nat > nat ) > ( nat > $o ) > nat ).
thf(func_def_3839,type,
sK1219: ( nat > int ) > set_nat > ( nat > int ) > nat ).
thf(func_def_3841,type,
ph1221:
!>[X0: $tType] : X0 ).
thf(func_def_3842,type,
sK1222: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat ).
thf(f31075,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26897,f26902,f30799,f31074]) ).
thf(f31074,plain,
( spl1220_26
| ~ spl1220_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f31073]) ).
thf(f31073,plain,
( $false
| spl1220_26
| ~ spl1220_28 ),
inference(subsumption_resolution,[status(thm)],[f31059,f26888]) ).
thf(f26888,plain,
( ( h2
!= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
| spl1220_26 ),
inference(avatar_component_clause,[status(thm)],[f26886]) ).
thf(f26886,definition,
( spl1220_26
<=> ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1220_26])],[avatar_definition]) ).
thf(f31059,plain,
( ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
| ~ spl1220_28 ),
inference(trivial_inequality_removal,[status(thm)],[f31044]) ).
thf(f31044,plain,
( ( $true != $true )
| ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
| ~ spl1220_28 ),
inference(superposition,[status(thm)],[f27028,f30834]) ).
thf(f30834,plain,
( ( ( heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) @ r )
= $true )
| ~ spl1220_28 ),
inference(forward_demodulation,[status(thm)],[f30833,f26947]) ).
thf(f26947,plain,
! [X1: a] :
( ( ref_a2 @ X1 )
= ( heap_heap_ref_a @ ( alloc_a @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26946]) ).
thf(f26946,plain,
! [X1: a] :
( ( ref_a2 @ X1 )
= ( ^ [Y0: a] : ( heap_heap_ref_a @ ( alloc_a @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f19965]) ).
thf(f19965,plain,
( ref_a2
= ( ^ [Y0: a] : ( heap_heap_ref_a @ ( alloc_a @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10389]) ).
thf(f10389,plain,
( ref_a2
= ( ^ [Y0: a] : ( heap_heap_ref_a @ ( alloc_a @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10388]) ).
thf(f10388,plain,
( ( ^ [X0: a] : ( heap_heap_ref_a @ ( alloc_a @ X0 ) ) )
= ref_a2 ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
( ( ^ [X22: a] : ( heap_heap_ref_a @ ( alloc_a @ X22 ) ) )
= ref_a2 ),
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_23_ref__def) ).
thf(f30833,plain,
( ( $true
= ( heap_effect_ref_a @ ( heap_heap_ref_a @ ( alloc_a @ x ) ) @ h @ ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) @ r ) )
| ~ spl1220_28 ),
inference(superposition,[status(thm)],[f25914,f26895]) ).
thf(f26895,plain,
( ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
| ~ spl1220_28 ),
inference(avatar_component_clause,[status(thm)],[f26894]) ).
thf(f26894,definition,
( spl1220_28
<=> ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1220_28])],[avatar_definition]) ).
thf(f25914,plain,
! [X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X1: heap_e7401611519738050253t_unit] :
( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ ( produc1126150082675451753t_unit @ ( X3 @ X1 ) ) @ ( produc473321116828791851t_unit @ ( X3 @ X1 ) ) )
= $true ),
inference(equality_resolution,[status(thm)],[f25913]) ).
thf(f25913,plain,
! [X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X1: heap_e7401611519738050253t_unit] :
( ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ ( produc473321116828791851t_unit @ ( X3 @ X1 ) ) )
= $true )
| ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
!= X2 ) ),
inference(equality_resolution,[status(thm)],[f23922]) ).
thf(f23922,plain,
! [X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X0: ref_a,X1: heap_e7401611519738050253t_unit] :
( ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ X0 )
= $true )
| ( ( produc473321116828791851t_unit @ ( X3 @ X1 ) )
!= X0 )
| ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
!= X2 ) ),
inference(cnf_transformation,[status(thm)],[f13403]) ).
thf(f13403,plain,
! [X0: ref_a,X1: heap_e7401611519738050253t_unit,X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ X0 )
= $true )
| ( ( produc473321116828791851t_unit @ ( X3 @ X1 ) )
!= X0 )
| ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
!= X2 ) ),
inference(flattening,[status(thm)],[f13402]) ).
thf(f13402,plain,
! [X0: ref_a,X1: heap_e7401611519738050253t_unit,X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ X0 )
= $true )
| ( ( produc473321116828791851t_unit @ ( X3 @ X1 ) )
!= X0 )
| ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f5338]) ).
thf(f5338,plain,
! [X0: ref_a,X1: heap_e7401611519738050253t_unit,X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
= X2 )
=> ( ( ( produc473321116828791851t_unit @ ( X3 @ X1 ) )
= X0 )
=> ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5337]) ).
thf(f5337,plain,
! [X0: ref_a,X1: heap_e7401611519738050253t_unit,X2: heap_e7401611519738050253t_unit,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( produc1126150082675451753t_unit @ ( X3 @ X1 ) )
= X2 )
=> ( ( ( produc473321116828791851t_unit @ ( X3 @ X1 ) )
= X0 )
=> ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X1 @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f150]) ).
thf(f150,axiom,
! [X16: ref_a,X12: heap_e7401611519738050253t_unit,X18: heap_e7401611519738050253t_unit,X19: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( produc1126150082675451753t_unit @ ( X19 @ X12 ) )
= X18 )
=> ( ( ( produc473321116828791851t_unit @ ( X19 @ X12 ) )
= X16 )
=> ( heap_effect_ref_a @ ( heap_heap_ref_a @ X19 ) @ X12 @ X18 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_149_effect__heapI) ).
thf(f27028,plain,
! [X0: heap_e7401611519738050253t_unit,X1: ref_a] :
( ( $true
!= ( heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ X0 @ X1 ) )
| ( h2 = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f27027]) ).
thf(f27027,plain,
! [X0: heap_e7401611519738050253t_unit,X1: ref_a] :
( ( h2 = X0 )
| ( $true != $true )
| ( $true
!= ( heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f21964,f24381]) ).
thf(f24381,plain,
( ( heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ h2 @ r )
= $true ),
inference(cnf_transformation,[status(thm)],[f6686]) ).
thf(f6686,plain,
( ( heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ h2 @ r )
= $true ),
inference(fool_elimination,[status(thm)],[f6685]) ).
thf(f6685,plain,
heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ h2 @ r,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ h2 @ r,
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_1_assms) ).
thf(f21964,plain,
! [X2: heap_e7401611519738050253t_unit,X3: ref_a,X0: heap_e7401611519738050253t_unit,X1: heap_Heap_ref_a,X4: ref_a,X5: heap_e7401611519738050253t_unit] :
( ( ( heap_effect_ref_a @ X1 @ X2 @ X5 @ X4 )
!= $true )
| ( ( heap_effect_ref_a @ X1 @ X2 @ X0 @ X3 )
!= $true )
| ( X0 = X5 ) ),
inference(cnf_transformation,[status(thm)],[f14332]) ).
thf(f14332,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_Heap_ref_a,X2: heap_e7401611519738050253t_unit,X3: ref_a,X4: ref_a,X5: heap_e7401611519738050253t_unit] :
( ( ( heap_effect_ref_a @ X1 @ X2 @ X5 @ X4 )
!= $true )
| ( X0 = X5 )
| ( ( heap_effect_ref_a @ X1 @ X2 @ X0 @ X3 )
!= $true ) ),
inference(flattening,[status(thm)],[f14331]) ).
thf(f14331,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_Heap_ref_a,X2: heap_e7401611519738050253t_unit,X3: ref_a,X4: ref_a,X5: heap_e7401611519738050253t_unit] :
( ( X0 = X5 )
| ( ( heap_effect_ref_a @ X1 @ X2 @ X0 @ X3 )
!= $true )
| ( ( heap_effect_ref_a @ X1 @ X2 @ X5 @ X4 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11037]) ).
thf(f11037,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_Heap_ref_a,X2: heap_e7401611519738050253t_unit,X3: ref_a,X4: ref_a,X5: heap_e7401611519738050253t_unit] :
( ( ( heap_effect_ref_a @ X1 @ X2 @ X5 @ X4 )
= $true )
=> ( ( ( heap_effect_ref_a @ X1 @ X2 @ X0 @ X3 )
= $true )
=> ( X0 = X5 ) ) ),
inference(fool_elimination,[status(thm)],[f11036]) ).
thf(f11036,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_Heap_ref_a,X2: heap_e7401611519738050253t_unit,X3: ref_a,X4: ref_a,X5: heap_e7401611519738050253t_unit] :
( ( heap_effect_ref_a @ X1 @ X2 @ X5 @ X4 )
=> ( ( heap_effect_ref_a @ X1 @ X2 @ X0 @ X3 )
=> ( X0 = X5 ) ) ),
inference(rectify,[status(thm)],[f184]) ).
thf(f184,axiom,
! [X43: heap_e7401611519738050253t_unit,X19: heap_Heap_ref_a,X12: heap_e7401611519738050253t_unit,X28: ref_a,X27: ref_a,X18: heap_e7401611519738050253t_unit] :
( ( heap_effect_ref_a @ X19 @ X12 @ X18 @ X27 )
=> ( ( heap_effect_ref_a @ X19 @ X12 @ X43 @ X28 )
=> ( X18 = X43 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_183_effect__deterministic_I2_J) ).
thf(f30799,plain,
spl1220_28,
inference(avatar_split_clause,[status(thm)],[f30797,f26894]) ).
thf(f30797,plain,
( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f30783]) ).
thf(f30783,plain,
( ( $true != $true )
| ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) ) ),
inference(superposition,[status(thm)],[f27921,f24381]) ).
thf(f27921,plain,
! [X2: heap_e7401611519738050253t_unit,X3: ref_a,X0: a,X1: heap_e7401611519738050253t_unit] :
( ( $true
!= ( heap_effect_ref_a @ ( ref_a2 @ X0 ) @ X1 @ X2 @ X3 ) )
| ( ( produc473321116828791851t_unit @ ( alloc_a @ X0 @ X1 ) )
= X3 ) ),
inference(superposition,[status(thm)],[f21547,f26947]) ).
thf(f21547,plain,
! [X2: ref_a,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X0: heap_e7401611519738050253t_unit,X1: heap_e7401611519738050253t_unit] :
( ( $true
!= ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X0 @ X1 @ X2 ) )
| ( ( produc473321116828791851t_unit @ ( X3 @ X0 ) )
= X2 ) ),
inference(cnf_transformation,[status(thm)],[f14497]) ).
thf(f14497,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_e7401611519738050253t_unit,X2: ref_a,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( ( ( produc1126150082675451753t_unit @ ( X3 @ X0 ) )
= X1 )
& ( ( produc473321116828791851t_unit @ ( X3 @ X0 ) )
= X2 ) )
| ( $true
!= ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X0 @ X1 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f6334]) ).
thf(f6334,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_e7401611519738050253t_unit,X2: ref_a,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( $true
= ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X0 @ X1 @ X2 ) )
=> ~ ( ( ( produc1126150082675451753t_unit @ ( X3 @ X0 ) )
= X1 )
=> ( ( produc473321116828791851t_unit @ ( X3 @ X0 ) )
!= X2 ) ) ),
inference(fool_elimination,[status(thm)],[f6333]) ).
thf(f6333,plain,
! [X0: heap_e7401611519738050253t_unit,X1: heap_e7401611519738050253t_unit,X2: ref_a,X3: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X3 ) @ X0 @ X1 @ X2 )
=> ~ ( ( ( produc1126150082675451753t_unit @ ( X3 @ X0 ) )
= X1 )
=> ( ( produc473321116828791851t_unit @ ( X3 @ X0 ) )
!= X2 ) ) ),
inference(rectify,[status(thm)],[f149]) ).
thf(f149,axiom,
! [X12: heap_e7401611519738050253t_unit,X18: heap_e7401611519738050253t_unit,X16: ref_a,X19: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] :
( ( heap_effect_ref_a @ ( heap_heap_ref_a @ X19 ) @ X12 @ X18 @ X16 )
=> ~ ( ( ( produc1126150082675451753t_unit @ ( X19 @ X12 ) )
= X18 )
=> ( ( produc473321116828791851t_unit @ ( X19 @ X12 ) )
!= X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_148_effect__heapE) ).
thf(f26902,plain,
~ spl1220_27,
inference(avatar_split_clause,[status(thm)],[f21552,f26890]) ).
thf(f26890,definition,
( spl1220_27
<=> ( thesis = $true ) ),
introduced(definition,[new_symbols(naming,[spl1220_27])],[avatar_definition]) ).
thf(f21552,plain,
thesis != $true,
inference(cnf_transformation,[status(thm)],[f11980]) ).
thf(f11980,plain,
thesis != $true,
inference(flattening,[status(thm)],[f9695]) ).
thf(f9695,plain,
thesis != $true,
inference(fool_elimination,[status(thm)],[f9694]) ).
thf(f9694,plain,
~ thesis,
inference(rectify,[status(thm)],[f4331]) ).
thf(f4331,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f4330]) ).
thf(f4330,conjecture,
thesis,
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',conj_1) ).
thf(f26897,plain,
( ~ spl1220_26
| spl1220_27
| ~ spl1220_28 ),
inference(avatar_split_clause,[status(thm)],[f24204,f26894,f26890,f26886]) ).
thf(f24204,plain,
( ( r
!= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
| ( h2
!= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
| ( thesis = $true ) ),
inference(cnf_transformation,[status(thm)],[f14477]) ).
thf(f14477,plain,
( ( r
!= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
| ( thesis = $true )
| ( h2
!= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) ) ),
inference(flattening,[status(thm)],[f14476]) ).
thf(f14476,plain,
( ( thesis = $true )
| ( h2
!= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
| ( r
!= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6624]) ).
thf(f6624,plain,
( ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
=> ( ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
=> ( thesis = $true ) ) ),
inference(fool_elimination,[status(thm)],[f6623]) ).
thf(f6623,plain,
( ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
=> ( ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
=> thesis ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( r
= ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
=> ( ( h2
= ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
=> thesis ) ),
file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_0_that) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP206^3 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:29:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 ---- Original DTF file ---
% 0.10/0.39 thf(spec,logic,$$dhol).
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 % File : ITP206^3 : TPTP v9.2.1. Released v8.1.0.
% 0.10/0.39 % Domain : Interactive Theorem Proving
% 0.10/0.39 % Problem : Sledgehammer problem Imperative_HOL_Add 00014_000455
% 0.10/0.39 % Version : [Des22] axioms.
% 0.10/0.39 % English :
% 0.10/0.39
% 0.10/0.39 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.10/0.39 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.10/0.39 % Source : [Des22]
% 0.10/0.39 % Names : 0017_Imperative_HOL_Add_00014_000455 [Des22]
% 0.10/0.39
% 0.10/0.39 % Status : Theorem
% 0.10/0.39 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.62 v8.1.0
% 0.10/0.39 % Syntax : Number of formulae : 6932 (1744 unt;2602 typ; 0 def)
% 0.10/0.39 % Number of atoms : 13690 (5570 equ; 1 cnn)
% 0.10/0.39 % Maximal formula atoms : 11 ( 3 avg)
% 0.10/0.39 % Number of connectives : 50597 (1150 ~; 79 |; 813 &;43012 @)
% 0.10/0.39 % ( 0 <=>;5543 =>; 0 <=; 0 <~>)
% 0.10/0.39 % Maximal formula depth : 18 ( 7 avg)
% 0.10/0.39 % Number of types : 205 ( 204 usr)
% 0.10/0.39 % Number of type conns : 17027 (17027 >; 0 *; 0 +; 0 <<)
% 0.10/0.39 % Number of symbols : 2402 (2398 usr; 114 con; 0-5 aty)
% 0.10/0.39 % Number of variables : 15786 (2761 ^;12753 !; 272 ?;15786 :)
% 0.10/0.39 % SPC : TH0_THM_EQU_NAR
% 0.10/0.39
% 0.10/0.39 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.10/0.39 % from the van Emde Boas Trees session in the Archive of Formal
% 0.10/0.39 % proofs -
% 0.10/0.39 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.10/0.39 % 2022-02-17 13:39:20.935
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 % Could-be-implicit typings (204)
% 0.10/0.39 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J_J,type,
% 0.10/0.39 set_se7592288975875140775at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_M_Eo_J_J,type,
% 0.10/0.39 set_Pr7669914128964046860_nat_o: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
% 0.10/0.39 set_Pr7459493094073627847at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J_J_J,type,
% 0.10/0.39 set_se7255092946006855566_nat_o: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.39 produc1319942482725812455at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_I_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_M_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_J,type,
% 0.10/0.39 produc101387210554329899nteger: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.39 set_Pr5564308138774400199at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_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_Mt__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,
% 0.10/0.39 produc1906917888121415911at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.10/0.39 set_Pr553994874890374343at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.39 produc349518998152878311at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 0.10/0.39 produc2296667697112141421t_unit: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.39 produc4041253808165279839at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.39 set_se5479201105039950375at_nat: $tType ).
% 0.10/0.39
% 0.10/0.39 thf(ty_n_t__Set__Oset_I_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,
% 0.10/0.39 set_Pr7010166363911110284_nat_o: $tType ).
% 0.10/0.39
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% 0.10/0.39 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Rat__Orat,type,
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% 0.10/0.39 thf(sy_c_BNF__Def_OGr_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
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% 0.10/0.39 bNF_Gr1453458339979195462nteger: set_Co4375521073081744395nteger > ( ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.10/0.39 bNF_Gr4092539093814444494nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
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% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001_Eo_001_Eo,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr6591314147588017797at_nat: set_int > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Rat__Orat,type,
% 0.10/0.39 bNF_Grp_int_rat: set_int > ( int > rat ) > int > rat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__String__Ochar,type,
% 0.10/0.39 bNF_Grp_int_char: set_int > ( int > char ) > int > char > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 bNF_Grp_list_nat_int: set_list_nat > ( list_nat > int ) > list_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr600725020315365264st_nat: set_list_nat > ( list_nat > list_nat ) > list_nat > list_nat > $o ).
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% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr4119388860389678161at_nat: set_list_nat > ( list_nat > product_prod_nat_nat ) > list_nat > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_Grp_nat_o: set_nat > ( nat > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_Grp_nat_num: set_nat > ( nat > num ) > nat > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 0.10/0.39 bNF_Gr1993012052113314029t_unit: set_nat > ( nat > product_unit ) > nat > product_unit > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Rat__Orat,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__String__Ochar,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_Grp_num_num: set_num > ( num > num ) > num > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 0.10/0.39 bNF_Gr5237703264515865432t_unit: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J,type,
% 0.10/0.39 bNF_Gr5964920315653434322_ref_a: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > ref_a > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.10/0.39 bNF_Gr2749509334501985047nt_int: set_Pr958786334691620121nt_int > ( product_prod_int_int > int ) > product_prod_int_int > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Num__Onum,type,
% 0.10/0.39 bNF_Gr8532703628021589765nt_num: set_Pr958786334691620121nt_int > ( product_prod_int_int > num ) > product_prod_int_int > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 bNF_Gr8859634586176591525_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 bNF_Gr190934199572118623at_int: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > int ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.39 bNF_Gr193424670081168899at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 0.10/0.39 bNF_Gr5974128493091723341at_num: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > num ) > product_prod_nat_nat > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr7275288873855648526at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Int__Oint,type,
% 0.10/0.39 bNF_Grp_rat_int: set_rat > ( rat > int ) > rat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_Grp_rat_nat: set_rat > ( rat > nat ) > rat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr6883301533820405721at_nat: set_rat > ( rat > product_prod_nat_nat ) > rat > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.10/0.39 bNF_Grp_rat_rat: set_rat > ( rat > rat ) > rat > rat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__String__Ochar,type,
% 0.10/0.39 bNF_Grp_rat_char: set_rat > ( rat > char ) > rat > char > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_Gr6677838525845560078at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Int__Oint,type,
% 0.10/0.39 bNF_Grp_char_int: set_char > ( char > int ) > char > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Nat__Onat,type,
% 0.10/0.39 bNF_Grp_char_nat: set_char > ( char > nat ) > char > nat > $o ).
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% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_Gr8982933507515605408at_nat: set_char > ( char > product_prod_nat_nat ) > char > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Rat__Orat,type,
% 0.10/0.39 bNF_Grp_char_rat: set_char > ( char > rat ) > char > rat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__String__Ochar,type,
% 0.10/0.39 bNF_Grp_char_char: set_char > ( char > char ) > char > char > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_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,type,
% 0.10/0.39 bNF_co1764293801198077070nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > produc101387210554329899nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_Eo_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_convol_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > product_prod_o_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_Eo_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_convol_o_o_nat: ( $o > $o ) > ( $o > nat ) > $o > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_convol_o_nat_o: ( $o > nat ) > ( $o > $o ) > $o > product_prod_nat_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_convol_o_nat_nat: ( $o > nat ) > ( $o > nat ) > $o > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_convol_o_num_nat: ( $o > num ) > ( $o > nat ) > $o > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.39 bNF_co6169604788974073338nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > produc723880050079548563nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_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_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,type,
% 0.10/0.39 bNF_co3156833790671340178nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc101387210554329899nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_co2174166945328636015nt_int: ( int > int ) > ( int > int ) > int > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co2176657415837686291nt_nat: ( int > int ) > ( int > nat ) > int > product_prod_int_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 bNF_co1174813233427581459at_int: ( int > nat ) > ( int > int ) > int > product_prod_nat_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co1177303703936631735at_nat: ( int > nat ) > ( int > nat ) > int > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_co6958007526947186177at_num: ( int > nat ) > ( int > num ) > int > product_prod_nat_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co8531006144098876929um_nat: ( int > num ) > ( int > nat ) > int > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_co5088337930254655563um_num: ( int > num ) > ( int > num ) > int > product_prod_num_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_convol_nat_o_o: ( nat > $o ) > ( nat > $o ) > nat > product_prod_o_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_convol_nat_nat_o: ( nat > nat ) > ( nat > $o ) > nat > product_prod_nat_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co805650143699787099at_nat: ( nat > nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co8159352583862032293um_nat: ( nat > num ) > ( nat > nat ) > nat > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_co4716684370017810927um_num: ( nat > num ) > ( nat > num ) > nat > product_prod_num_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_convol_num_o_nat: ( num > $o ) > ( num > nat ) > num > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co7969830008525221797at_nat: ( num > nat ) > ( num > nat ) > num > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co6100160411832691183um_nat: ( num > num ) > ( num > nat ) > num > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_co6607689160745551784nt_int: ( produc7812382424243267045t_unit > int ) > ( produc7812382424243267045t_unit > int ) > produc7812382424243267045t_unit > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co5610825919353547504at_nat: ( produc7812382424243267045t_unit > nat ) > ( produc7812382424243267045t_unit > nat ) > produc7812382424243267045t_unit > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_co3748779267718262122nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co2751916026326257842at_nat: ( product_prod_int_int > nat ) > ( product_prod_int_int > nat ) > product_prod_int_int > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_co49787548815638194nt_int: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_co8276296344278409722at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Oconvol_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_co147202357524637304at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.39 bNF_cs4943907971211754724nteger: set_Pr8415741480598773322nteger > ( product_prod_int_int > int ) > ( produc2963269191615333738nteger > int ) > ( produc2963269191615333738nteger > product_prod_int_int ) > ( produc2963269191615333738nteger > produc2963269191615333738nteger ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 0.10/0.39 bNF_cs7194553038297458973at_int: set_Pr49084382684228242at_int > ( produc859450856879609959at_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > ( produc4196048018000912732at_int > produc859450856879609959at_nat ) > ( produc4196048018000912732at_int > produc4196048018000912732at_int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 0.10/0.39 bNF_fs409234558581511823t_unit: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_fs4543836202474805097nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_fs8167890477030535480nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_fs6799373675401686564at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_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,
% 0.10/0.39 bNF_fs6342258632037972510at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc859450856879609959at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OfstOp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_fs1946732770515719151at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Opick__middlep_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_pi4515785505327359899nteger: ( int > int > $o ) > ( int > code_integer > $o ) > int > code_integer > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Opick__middlep_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,
% 0.10/0.39 bNF_pi770922605693484880at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.10/0.39 bNF_re6580757339198446453_nat_o: ( ( $o > $o ) > ( $o > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re7413876800493218871nt_nat: ( ( $o > $o ) > ( int > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re1515921786380824775at_nat: ( ( $o > $o ) > ( nat > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re7387973359137000979nt_num: ( ( $o > $o ) > ( nat > num ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re2961086658867094474nt_num: ( ( int > int ) > ( int > code_integer ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re2034674868506727813nt_nat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re7492190849051111027nt_num: ( ( int > int ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > num ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re5502197115626545091er_num: ( ( int > nat ) > ( code_integer > nat ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re3642433447925381491nt_nat: ( ( int > nat ) > ( int > int ) > $o ) > ( ( int > num ) > ( int > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re6307232852808291833nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re4099335476084980305nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re7435575058205011731_nat_o: ( ( int > nat ) > ( nat > $o ) > $o ) > ( ( int > num ) > ( nat > $o ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re717418264989850719at_nat: ( ( int > nat ) > ( nat > nat ) > $o ) > ( ( int > num ) > ( nat > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re4310571189260822741nt_num: ( ( int > nat ) > ( nat > num ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re7839584876883444355nt_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ) > ( ( int > num ) > ( int > int ) > int > num ) > ( ( code_integer > num ) > ( int > code_integer ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re6292805115969292119er_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re4768042542643474933nt_num: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re1982657550219213441nt_nat: ( ( nat > $o ) > ( int > int ) > $o ) > ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re4102725726183926567nt_num: ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > ( int > num ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re2144779315220482269at_nat: ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.10/0.39 bNF_re3930744952143938759_nat_o: ( ( nat > nat ) > ( $o > $o ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re8622501330148003679nt_num: ( ( nat > nat ) > ( int > nat ) > $o ) > ( ( nat > nat ) > ( int > num ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re7744223787735169245_nat_o: ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re3262823321055862553at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re1160762158786734233nt_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ) > ( ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( nat > nat ) > ( int > nat ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re239970166668089693at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re584878643992547173nt_num: ( ( nat > nat ) > ( nat > num ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.10/0.39 bNF_re3931674169038344211_nat_o: ( ( nat > num ) > ( $o > $o ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re5843449549409830101nt_nat: ( ( nat > num ) > ( int > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re6524732562925676389at_nat: ( ( nat > num ) > ( nat > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_M_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re2655444144887082515er_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( code_integer > nat ) > code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re2742285375668209089nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_M_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re4105200416192800571er_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( code_integer > num ) > code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 0.10/0.39 bNF_re5446066262214944985nt_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( int > num ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re3284331099615978085nt_nat: ( ( product_prod_nat_nat > int ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re8419181437172746013nt_nat: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.39 bNF_re2682547871993127601nt_num: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > num ) > ( int > num ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_rel_fun_o_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4895681925607069953_o_nat: ( $o > int > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4209105892566519389_o_nat: ( $o > nat > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_Eo_001t__Num__Onum,type,
% 0.10/0.39 bNF_re766437678722298023_o_num: ( $o > nat > $o ) > ( $o > num > $o ) > ( $o > $o ) > ( nat > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.10/0.39 bNF_re1181178334029315097nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re40212662316476751um_num: ( code_integer > code_integer > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re8313794964846168862um_num: ( code_integer > int > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 0.10/0.39 bNF_re1366391616432607057unit_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( ref_a > ref_a > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.10/0.39 bNF_re5775369113877777_int_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ref_a > int > $o ) > ( heap_e7401611519738050253t_unit > int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re9202112420002600977_nat_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ref_a > nat > $o ) > ( heap_e7401611519738050253t_unit > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re1850668159662942673it_o_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( $o > $o > $o ) > ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 bNF_re2828929484557863493at_int: ( int > code_integer > $o ) > ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 0.10/0.39 bNF_re5404797796594736747unit_o: ( int > int > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( int > ref_a > $o ) > ( int > heap_e7401611519738050253t_unit > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.10/0.39 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4715010359784256181nt_nat: ( int > int > $o ) > ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 bNF_re3713166177374151349at_int: ( int > int > $o ) > ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_re272988434038980259at_num: ( int > int > $o ) > ( nat > num > $o ) > ( int > nat ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re1845987051190671011um_nat: ( int > int > $o ) > ( num > nat > $o ) > ( int > num ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_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,type,
% 0.10/0.39 bNF_re8766404587435608311at_nat: ( int > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_re4914077030771115051_nat_o: ( int > nat > $o ) > ( nat > $o > $o ) > ( int > nat ) > ( nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re3344003087646356989at_nat: ( int > nat > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_re9124706910656911431at_num: ( int > nat > $o ) > ( nat > num > $o ) > ( int > nat ) > ( nat > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 0.10/0.39 bNF_re3760060065607074657_num_o: ( int > nat > $o ) > ( num > $o > $o ) > ( int > num ) > ( nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re1474333490953826375um_nat: ( int > nat > $o ) > ( num > nat > $o ) > ( int > num ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4629543205785817921at_nat: ( list_nat > list_nat > $o ) > ( nat > nat > $o ) > ( list_nat > nat ) > ( list_nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_re439150893885221597_nat_o: ( nat > $o > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( $o > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001t__Num__Onum_001_Eo,type,
% 0.10/0.39 bNF_re8508505965575957011_num_o: ( nat > $o > $o ) > ( num > $o > $o ) > ( nat > num ) > ( $o > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
% 0.10/0.39 bNF_re8207659476513966505_o_int: ( nat > int > $o ) > ( $o > int > $o ) > ( nat > $o ) > ( int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re8210149947023016781_o_nat: ( nat > int > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Num__Onum,type,
% 0.10/0.39 bNF_re4767481733178795415_o_num: ( nat > int > $o ) > ( $o > num > $o ) > ( nat > $o ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re6025474579976152573at_nat: ( nat > int > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_re2582806366131931207at_num: ( nat > int > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4155804983283621959um_nat: ( nat > int > $o ) > ( num > nat > $o ) > ( nat > num ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 0.10/0.39 bNF_re5655699643857186083unit_o: ( nat > nat > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( nat > ref_a > $o ) > ( nat > heap_e7401611519738050253t_unit > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.10/0.39 bNF_re605504016728627135_int_o: ( nat > nat > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( nat > int > $o ) > ( nat > int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.10/0.39 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re7523573913982466217_o_nat: ( nat > nat > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_re1402873238235875719_nat_o: ( nat > nat > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 bNF_re2211152805895086571at_num: ( nat > nat > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( nat > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re3784151423046777323um_nat: ( nat > nat > $o ) > ( num > nat > $o ) > ( nat > num ) > ( nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.10/0.39 bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re4736500879113541833um_num: ( num > num > $o ) > ( num > num > $o ) > ( num > num ) > ( num > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.10/0.39 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.10/0.39 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_re6202762543029211035nteger: ( product_prod_nat_nat > int > $o ) > ( int > code_integer > $o ) > ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re5552630237950767466nt_int: ( product_prod_nat_nat > int > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 bNF_re8466801222876787014um_num: ( product_prod_nat_nat > int > $o ) > ( num > num > $o ) > ( product_prod_nat_nat > num ) > ( int > num ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.10/0.39 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re20414067882207223nt_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re1865807574169326223at_o_o: ( rat > rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re7554818335971813481nt_int: ( rat > rat > $o ) > ( int > int > $o ) > ( rat > int ) > ( rat > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re6557955094579809201at_nat: ( rat > rat > $o ) > ( nat > nat > $o ) > ( rat > nat ) > ( rat > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_re1692451286490762625ar_o_o: ( char > char > $o ) > ( $o > $o > $o ) > ( char > $o ) > ( char > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001t__Int__Oint,type,
% 0.10/0.39 bNF_re4780507660726531203_o_int: ( char > char > $o ) > ( $o > int > $o ) > ( char > $o ) > ( char > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4782998131235581479_o_nat: ( char > char > $o ) > ( $o > nat > $o ) > ( char > $o ) > ( char > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_re6064627146911078825_int_o: ( char > char > $o ) > ( int > $o > $o ) > ( char > int ) > ( char > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_re4731199128827642459nt_int: ( char > char > $o ) > ( int > int > $o ) > ( char > int ) > ( char > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re4733689599336692735nt_nat: ( char > char > $o ) > ( int > nat > $o ) > ( char > int ) > ( char > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_re7885669492343766789_nat_o: ( char > char > $o ) > ( nat > $o > $o ) > ( char > nat ) > ( char > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 bNF_re3731845416926587903at_int: ( char > char > $o ) > ( nat > int > $o ) > ( char > nat ) > ( char > int ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_re3734335887435638179at_nat: ( char > char > $o ) > ( nat > nat > $o ) > ( char > nat ) > ( char > nat ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_001t__Heap__Oref_Itf__a_J_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 0.10/0.39 bNF_sn8323453914685745821t_unit: ( ref_a > ref_a > $o ) > ( ref_a > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 bNF_sn8000174127721201323nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > produc2963269191615333738nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_sn1062102010912252026nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 bNF_sn8916957246138178918at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_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,
% 0.10/0.39 bNF_sn649997494946348640at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc4196048018000912732at_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 bNF_sn1857951156667551021at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Heap__Oref_Itf__a_J_001t__Int__Oint_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi7828673959370436579_int_o: ( ref_a > int ) > ( heap_e7401611519738050253t_unit > int ) > ( int > int > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Heap__Oref_Itf__a_J_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi4623496019404053219_nat_o: ( ref_a > nat ) > ( heap_e7401611519738050253t_unit > nat ) > ( nat > nat > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_Eo,type,
% 0.10/0.39 bNF_vi699694178825965831eger_o: ( int > int ) > ( code_integer > code_integer ) > ( int > code_integer > $o ) > int > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi2125572119366604152_int_o: ( int > int ) > ( code_integer > int ) > ( int > int > $o ) > int > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi3884084463199473129_int_o: ( int > int ) > ( int > int ) > ( int > int > $o ) > int > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi3197508430158922565_int_o: ( int > int ) > ( nat > int ) > ( int > int > $o ) > int > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi5018550775591610529_nat_o: ( int > int ) > ( nat > nat ) > ( int > nat > $o ) > int > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Rat__Orat_001_Eo,type,
% 0.10/0.39 bNF_vi1281217848275042457_rat_o: ( int > int ) > ( nat > rat ) > ( int > rat > $o ) > int > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__String__Ochar_001_Eo,type,
% 0.10/0.39 bNF_vi9149698133064535136char_o: ( int > int ) > ( nat > char ) > ( int > char > $o ) > int > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi2193923016096921761_nat_o: ( int > nat ) > ( int > nat ) > ( nat > nat > $o ) > int > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__Rat__Orat_001_Eo,type,
% 0.10/0.39 bNF_vi7769575839906753835_rat_o: ( int > nat ) > ( num > rat ) > ( nat > rat > $o ) > int > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__String__Ochar_001_Eo,type,
% 0.10/0.39 bNF_vi1300075849944819442char_o: ( int > nat ) > ( num > char ) > ( nat > char > $o ) > int > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum_001_Eo,type,
% 0.10/0.39 bNF_vi2326032003723069084_num_o: ( int > num ) > ( code_integer > num ) > ( num > num > $o ) > int > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum_001_Eo,type,
% 0.10/0.39 bNF_vi2107963681178519309_num_o: ( int > num ) > ( int > num ) > ( num > num > $o ) > int > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi2881549544236934259_int_o: ( int > product_prod_nat_nat ) > ( code_integer > int ) > ( product_prod_nat_nat > int > $o ) > int > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 bNF_vi1204582724742824157_nat_o: ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__List__Olist_It__Nat__Onat_J_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi467646977814820164_int_o: ( list_nat > int ) > ( code_integer > int ) > ( int > int > $o ) > list_nat > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 bNF_vi5202502398764838569_nat_o: ( list_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > list_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__Product____Type__Ounit_001_Eo,type,
% 0.10/0.39 bNF_vi5856767400800367702unit_o: ( nat > $o ) > ( $o > product_unit ) > ( $o > product_unit > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__Rat__Orat_001_Eo,type,
% 0.10/0.39 bNF_vi3868162310295888627_rat_o: ( nat > $o ) > ( $o > rat ) > ( $o > rat > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__String__Ochar_001_Eo,type,
% 0.10/0.39 bNF_vi8816436626763797690char_o: ( nat > $o ) > ( $o > char ) > ( $o > char > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi7331807916455492308_int_o: ( nat > int ) > ( code_integer > int ) > ( int > int > $o ) > nat > code_integer > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi8357618154448083105_int_o: ( nat > int ) > ( nat > int ) > ( int > int > $o ) > nat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi1731478210338170163_nat_o: ( nat > int ) > ( num > nat ) > ( int > nat > $o ) > nat > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_vi6818137723729380987_o_o_o: ( nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001t__Product____Type__Ounit_001_Eo,type,
% 0.10/0.39 bNF_vi1443435967014148806unit_o: ( nat > nat ) > ( $o > product_unit ) > ( nat > product_unit > $o ) > nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi6667456707345531737_nat_o: ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > nat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001_Eo,type,
% 0.10/0.39 bNF_vi2930123780028963665_rat_o: ( nat > nat ) > ( nat > rat ) > ( nat > rat > $o ) > nat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__String__Ochar_001_Eo,type,
% 0.10/0.39 bNF_vi8943400373106913048char_o: ( nat > nat ) > ( nat > char ) > ( nat > char > $o ) > nat > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 bNF_vi190728152058600505_nat_o: ( nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi1633389952966819264_nat_o: ( product_prod_int_int > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_int_int > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_Eo,type,
% 0.10/0.39 bNF_vi5082502771524357669nt_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 0.10/0.39 bNF_vi8966365312794588230_int_o: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo,type,
% 0.10/0.39 bNF_vi33923956287962137eger_o: ( product_prod_nat_nat > int ) > ( int > code_integer ) > ( int > code_integer > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi9094538908245281400_nat_o: ( product_prod_nat_nat > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_nat_nat > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi2682369418337388893_int_o: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > ( int > int > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001_Eo_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_vi9025507403824386624_o_o_o: ( product_prod_nat_nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > product_prod_nat_nat > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 bNF_vi5493721401438417730_nat_o: ( product_prod_nat_nat > nat ) > ( int > nat ) > ( nat > nat > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi5426221348228882691_int_o: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 bNF_vi763171854521451549_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 ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Def_Ovimage2p_001t__Rat__Orat_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 bNF_vi508398028314858188_int_o: ( rat > int ) > ( code_integer > int ) > ( int > int > $o ) > rat > code_integer > $o ).
% 0.10/0.39
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% 0.10/0.39 bNF_vi2997284877290766385_nat_o: ( rat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > rat > int > $o ).
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% 0.10/0.39 bNF_vi7262943168399475603_int_o: ( char > int ) > ( code_integer > int ) > ( int > int > $o ) > char > code_integer > $o ).
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% 0.10/0.39 bNF_vi728936465572800120_nat_o: ( char > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > char > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 bNF_Gr2943678036615987864nt_int: set_o > ( $o > int ) > ( $o > int ) > set_Pr958786334691620121nt_int ).
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_001t__Int__Oint_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 0.10/0.39 bNF_Gr7020624548710275655nt_num: ( int > num ) > ( int > num ) > ( int > int > $o ) > num > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J,type,
% 0.10/0.39 bNF_Gr364077372107685167_int_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.10/0.39 bNF_Gr1354378531936274772nt_int: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
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% 0.10/0.39 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 bNF_Gr6955563364113978072nt_nat: ( product_prod_nat_nat > nat ) > ( int > nat ) > ( product_prod_nat_nat > int > $o ) > nat > nat > $o ).
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc_001_Eo_001_Eo,type,
% 0.10/0.39 bNF_We7690717809131995284nc_o_o: set_o > set_o > set_o_o ).
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc_001_Eo_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc_001t__Int__Oint_001t__Rat__Orat,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc_001t__Rat__Orat_001_Eo,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Constructions_OFunc__map_001t__Int__Oint_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
% 0.10/0.39 bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
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% 0.10/0.39 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
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% 0.10/0.39 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_Finite__Set_Ofinite_001t__String__Ochar,type,
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% 0.10/0.39 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.39 comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_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,type,
% 0.10/0.39 comp_C7826480081638475456nteger: ( ( code_integer > code_integer ) > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_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_M_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_J_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 comp_C6484513282182537548nteger: ( ( code_integer > code_integer ) > produc101387210554329899nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc101387210554329899nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_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_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,
% 0.10/0.39 comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Int__Oint,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
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% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Num__Onum,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_int_set_nat_int: ( int > set_nat ) > ( int > int ) > int > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.10/0.39 comp_nat_o_o: ( nat > $o ) > ( $o > nat ) > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_o_int: ( nat > $o ) > ( int > nat ) > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_n1662990198670838940at_nat: ( nat > $o ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
% 0.10/0.39 comp_nat_int_o: ( nat > int ) > ( $o > nat ) > $o > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_int_int: ( nat > int ) > ( int > nat ) > int > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum,type,
% 0.10/0.39 comp_nat_int_num: ( nat > int ) > ( num > nat ) > num > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_n5749082658982224864at_nat: ( nat > int ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Rat__Orat,type,
% 0.10/0.39 comp_nat_int_rat: ( nat > int ) > ( rat > nat ) > rat > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__String__Ochar,type,
% 0.10/0.39 comp_nat_int_char: ( nat > int ) > ( char > nat ) > char > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 comp_nat_nat_o: ( nat > nat ) > ( $o > nat ) > $o > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_nat_int: ( nat > nat ) > ( int > nat ) > int > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 comp_nat_nat_num: ( nat > nat ) > ( num > nat ) > num > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_n2711240574518091068at_nat: ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.10/0.39 comp_nat_nat_rat: ( nat > nat ) > ( rat > nat ) > rat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__String__Ochar,type,
% 0.10/0.39 comp_nat_nat_char: ( nat > nat ) > ( char > nat ) > char > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 comp_n2103536230552569900nteger: ( nat > num ) > ( code_integer > nat ) > code_integer > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_num_nat: ( nat > num ) > ( nat > nat ) > nat > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 comp_nat_num_num: ( nat > num ) > ( num > nat ) > num > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_n8649498751204056690at_nat: ( nat > num ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_n8574565218330151774at_nat: ( nat > product_prod_nat_nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Int__Oint,type,
% 0.10/0.39 comp_n8531277669757933902um_int: ( nat > product_prod_num_num ) > ( int > nat ) > int > product_prod_num_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_rat_int: ( nat > rat ) > ( int > nat ) > int > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.10/0.39 comp_nat_rat_rat: ( nat > rat ) > ( rat > nat ) > rat > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__String__Ochar,type,
% 0.10/0.39 comp_nat_rat_char: ( nat > rat ) > ( char > nat ) > char > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_set_nat_int: ( nat > set_nat ) > ( int > nat ) > int > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_set_nat_nat: ( nat > set_nat ) > ( nat > nat ) > nat > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_nat_set_rat_int: ( nat > set_rat ) > ( int > nat ) > int > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_nat_set_rat_nat: ( nat > set_rat ) > ( nat > nat ) > nat > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__String__Ochar_001t__String__Ochar,type,
% 0.10/0.39 comp_nat_char_char: ( nat > char ) > ( char > nat ) > char > char ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001_Eo,type,
% 0.10/0.39 comp_num_o_o: ( num > $o ) > ( $o > num ) > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Int__Oint,type,
% 0.10/0.39 comp_num_o_int: ( num > $o ) > ( int > num ) > int > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 comp_num_o_nat: ( num > $o ) > ( nat > num ) > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Num__Onum,type,
% 0.10/0.39 comp_num_o_num: ( num > $o ) > ( num > num ) > num > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 comp_num_nat_int: ( num > nat ) > ( int > num ) > int > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 comp_num_nat_nat: ( num > nat ) > ( nat > num ) > nat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.39 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 0.10/0.39 comp_num_num_o: ( num > num ) > ( $o > num ) > $o > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 comp_n8557746072492896886nteger: ( num > num ) > ( code_integer > num ) > code_integer > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint,type,
% 0.10/0.39 comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint,type,
% 0.10/0.39 comp_num_set_int_int: ( num > set_int ) > ( int > num ) > int > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_num_set_nat_int: ( num > set_nat ) > ( int > num ) > int > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_num_set_rat_int: ( num > set_rat ) > ( int > num ) > int > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_I_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_M_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_J_001t__Code____Numeral__Ointeger,type,
% 0.10/0.39 comp_P8564252314792299288nteger: ( produc723880050079548563nteger > produc101387210554329899nteger ) > ( code_integer > produc723880050079548563nteger ) > code_integer > produc101387210554329899nteger ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001_Eo,type,
% 0.10/0.39 comp_P2137996956111167876_o_o_o: ( product_prod_o_o > $o ) > ( $o > product_prod_o_o ) > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
% 0.10/0.39 comp_P551574746845053877_o_o_o: ( product_prod_o_o > product_prod_o_o ) > ( $o > product_prod_o_o ) > $o > product_prod_o_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_P7034811116587396339_o_nat: ( product_prod_o_o > product_prod_o_o ) > ( nat > product_prod_o_o ) > nat > product_prod_o_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P4785046977597218846at_nat: ( product_prod_o_o > product_prod_o_o ) > ( product_prod_nat_nat > product_prod_o_o ) > product_prod_nat_nat > product_prod_o_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001_Eo,type,
% 0.10/0.39 comp_P1471321874221585045at_o_o: ( product_prod_o_o > product_prod_nat_o ) > ( $o > product_prod_o_o ) > $o > product_prod_nat_o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P465755969289462830at_int: ( product_prod_o_int > product_prod_o_nat ) > ( product_prod_nat_int > product_prod_o_int ) > product_prod_nat_int > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 comp_P1422407636550552773_nat_o: ( product_prod_o_nat > product_prod_o_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_P1391661485614827491at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( nat > product_prod_o_nat ) > nat > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P4962864564169660718at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( product_prod_nat_nat > product_prod_o_nat ) > product_prod_nat_nat > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P9057111047297513408at_int: ( product_prod_o_nat > product_prod_o_num ) > ( product_prod_nat_int > product_prod_o_nat ) > product_prod_nat_int > product_prod_o_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 comp_P196761593691424337_nat_o: ( product_prod_o_nat > product_prod_nat_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 comp_P972951341003599239_nat_o: ( product_prod_o_nat > product_prod_num_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.39 comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 0.10/0.39 comp_P8237986404257982958t_unit: ( produc8126358835630522215t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc8126358835630522215t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 0.10/0.39 comp_P3239167524078694454t_unit: ( produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J,type,
% 0.10/0.39 comp_P2006160480335490974_ref_a: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( produc1799199577659733785_ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J,type,
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% 0.10/0.39
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% 0.10/0.39 comp_P4044372497395451596t_unit: ( produc7812382424243267045t_unit > ref_a ) > ( produc7812382424243267045t_unit > produc7812382424243267045t_unit ) > produc7812382424243267045t_unit > ref_a ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.10/0.39 comp_P6653955642190706324nt_nat: ( product_prod_int_int > int ) > ( nat > product_prod_int_int ) > nat > int ).
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% 0.10/0.39 comp_P4161745170962941589t_char: ( product_prod_int_int > int ) > ( char > product_prod_int_int ) > char > int ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P2318390481314533713nt_int: ( product_prod_int_int > nat ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > nat ).
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% 0.10/0.39 comp_P2788356708182965334nt_int: ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
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% 0.10/0.39 comp_P2134349925370910487at_int: ( product_prod_int_int > product_prod_nat_nat ) > ( int > product_prod_int_int ) > int > product_prod_nat_nat ).
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% 0.10/0.39 comp_P3488689526429045841nt_nat: ( product_prod_int_nat > nat ) > ( product_prod_int_nat > product_prod_int_nat ) > product_prod_int_nat > nat ).
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% 0.10/0.39 comp_P1145193044942399421um_int: ( product_prod_int_nat > product_prod_nat_num ) > ( int > product_prod_int_nat ) > int > product_prod_nat_num ).
% 0.10/0.39
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% 0.10/0.39 comp_P5799945282029801519_o_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_nat_o ).
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% 0.10/0.39 comp_P8901546994122883554at_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( product_prod_nat_nat > product_prod_nat_o ) > product_prod_nat_nat > product_prod_nat_o ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Num__Onum_M_Eo_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_P6576135029341976421_o_nat: ( product_prod_nat_o > product_prod_num_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_num_o ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Num__Onum_M_Eo_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P5807473265676440968nt_nat: ( product_prod_nat_o > product_prod_num_o ) > ( product_prod_int_nat > product_prod_nat_o ) > product_prod_int_nat > product_prod_num_o ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P397146161216181329at_int: ( product_prod_nat_int > nat ) > ( product_prod_nat_int > product_prod_nat_int ) > product_prod_nat_int > nat ).
% 0.10/0.39
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% 0.10/0.39 comp_P8376639181999047357at_int: ( product_prod_nat_int > product_prod_num_nat ) > ( int > product_prod_nat_int ) > int > product_prod_num_nat ).
% 0.10/0.39
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% 0.10/0.39 comp_P3772045228931366376nt_int: ( product_prod_nat_int > product_prod_num_nat ) > ( product_prod_int_int > product_prod_nat_int ) > product_prod_int_int > product_prod_num_nat ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P2002127591014248037at_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 ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P7900071416159368952at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > $o ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P3913276677246710332at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P4524073163769703009at_int: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P4605287290794827253at_nat: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int ).
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% 0.10/0.39 comp_P1953119740877977564at_int: ( product_prod_nat_nat > nat ) > ( int > product_prod_nat_nat ) > int > nat ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.10/0.39 comp_P1320480151300532104at_rat: ( product_prod_nat_nat > nat ) > ( rat > product_prod_nat_nat ) > rat > nat ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__String__Ochar,type,
% 0.10/0.39 comp_P1491501995297412481t_char: ( product_prod_nat_nat > nat ) > ( char > product_prod_nat_nat ) > char > nat ).
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% 0.10/0.39 thf(sy_c_Fun_Ocomp_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,
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% 0.10/0.39 comp_P7387482301570536291um_int: ( product_prod_nat_nat > product_prod_num_num ) > ( int > product_prod_nat_nat ) > int > product_prod_num_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.10/0.39 comp_P9218946435557410242nt_int: ( product_prod_nat_nat > product_prod_num_num ) > ( product_prod_int_int > product_prod_nat_nat ) > product_prod_int_int > product_prod_num_num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P8336958949797789649um_nat: ( product_prod_nat_num > nat ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Num__Onum_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J,type,
% 0.10/0.39 comp_P5051845089628979463um_nat: ( product_prod_nat_num > num ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 0.10/0.39 comp_P3192427084145116251at_num: ( product_prod_num_nat > product_prod_o_nat ) > ( num > product_prod_num_nat ) > num > product_prod_o_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 0.10/0.39 comp_P2539519431309506803at_num: ( product_prod_num_nat > product_prod_nat_nat ) > ( num > product_prod_num_nat ) > num > product_prod_nat_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 0.10/0.39 comp_P480327259280165693at_num: ( product_prod_num_nat > product_prod_num_nat ) > ( num > product_prod_num_nat ) > num > product_prod_num_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Int__Oint,type,
% 0.10/0.39 comp_P4305060815297604026um_int: ( product_prod_num_num > num ) > ( int > product_prod_num_num ) > int > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_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__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_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,
% 0.10/0.39 comp_P4974406650942564362at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_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__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.39 comp_P4528037747288561284at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.39 comp_P3728553842126764068at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( produc1319942482725812455at_nat > produc1319942482725812455at_nat ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.10/0.39 comp_P8235817900121468292at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_Eo_001_Eo,type,
% 0.10/0.39 comp_P5156358013004227690it_o_o: ( product_unit > $o ) > ( $o > product_unit ) > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 comp_P4985893458130756478_o_nat: ( product_unit > $o ) > ( nat > product_unit ) > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001_Eo_001_Eo,type,
% 0.10/0.39 comp_rat_o_o: ( rat > $o ) > ( $o > rat ) > $o > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001_Eo_001t__Nat__Onat,type,
% 0.10/0.39 comp_rat_o_nat: ( rat > $o ) > ( nat > rat ) > nat > $o ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.39 comp_rat_int_int: ( rat > int ) > ( int > rat ) > int > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.39 comp_rat_int_nat: ( rat > int ) > ( nat > rat ) > nat > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__String__Ochar,type,
% 0.10/0.39 comp_rat_int_char: ( rat > int ) > ( char > rat ) > char > int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001_Eo,type,
% 0.10/0.39 comp_rat_nat_o: ( rat > nat ) > ( $o > rat ) > $o > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.39 comp_rat_nat_int: ( rat > nat ) > ( int > rat ) > int > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.39 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.10/0.39 comp_rat_nat_rat: ( rat > nat ) > ( rat > rat ) > rat > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__String__Ochar,type,
% 0.10/0.39 comp_rat_nat_char: ( rat > nat ) > ( char > rat ) > char > nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.39 comp_rat_num_nat: ( rat > num ) > ( nat > rat ) > nat > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.39 comp_rat_num_num: ( rat > num ) > ( num > rat ) > num > num ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.10/0.39 comp_rat_rat_nat: ( rat > rat ) > ( nat > rat ) > nat > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__String__Ochar,type,
% 0.10/0.39 comp_rat_rat_char: ( rat > rat ) > ( char > rat ) > char > rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__String__Ochar_001t__String__Ochar,type,
% 0.10/0.39 comp_rat_char_char: ( rat > char ) > ( char > rat ) > char > char ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Set__Oset_I_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_J,type,
% 0.10/0.39 comp_s4786119426940707554nteger: ( set_Co726186806682698383nteger > set_Code_integer ) > ( set_Pr4111642102156807771nteger > set_Co726186806682698383nteger ) > set_Pr4111642102156807771nteger > set_Code_integer ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_I_Eo_J,type,
% 0.10/0.39 comp_s9189197539837705563_set_o: ( set_o > set_nat ) > ( set_o > set_o ) > set_o > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.10/0.39 comp_s7717450105097109807et_nat: ( set_int > set_int ) > ( set_nat > set_int ) > set_nat > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.10/0.39 comp_s2487324123861929025et_int: ( set_int > set_int ) > ( set_set_int > set_int ) > set_set_int > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.10/0.39 comp_s5712175470073906149et_int: ( set_int > set_nat ) > ( set_set_int > set_int ) > set_set_int > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001_Eo,type,
% 0.10/0.39 comp_s7011316712748663051_int_o: ( set_nat > set_int ) > ( $o > set_nat ) > $o > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint,type,
% 0.10/0.39 comp_s5617672292595496825nt_int: ( set_nat > set_int ) > ( int > set_nat ) > int > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_s5620162763104547101nt_nat: ( set_nat > set_int ) > ( nat > set_nat ) > nat > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Num__Onum_J,type,
% 0.10/0.39 comp_s6458263553158497821et_num: ( set_nat > set_int ) > ( set_num > set_nat ) > set_num > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.10/0.39 comp_s3768223441818958217et_nat: ( set_nat > set_int ) > ( set_set_nat > set_nat ) > set_set_nat > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
% 0.10/0.39 comp_s33089643564333159_nat_o: ( set_nat > set_nat ) > ( $o > set_nat ) > $o > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_s3430750717902475037at_int: ( set_nat > set_nat ) > ( int > set_nat ) > int > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_s3433241188411525313at_nat: ( set_nat > set_nat ) > ( nat > set_nat ) > nat > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.10/0.39 comp_s8964582002068861047et_nat: ( set_nat > set_nat ) > ( set_nat > set_nat ) > set_nat > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.10/0.39 comp_s6993074788030935341et_nat: ( set_nat > set_nat ) > ( set_set_nat > set_nat ) > set_set_nat > set_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001_Eo,type,
% 0.10/0.39 comp_s8507027185284273247_rat_o: ( set_nat > set_rat ) > ( $o > set_nat ) > $o > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 0.10/0.39 comp_s8253438564248248613at_int: ( set_nat > set_rat ) > ( int > set_nat ) > int > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 0.10/0.39 comp_s8255929034757298889at_nat: ( set_nat > set_rat ) > ( nat > set_nat ) > nat > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.10/0.39 comp_s6435139744279249717et_nat: ( set_nat > set_rat ) > ( set_set_nat > set_nat ) > set_set_nat > set_rat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.39 comp_s7355055891894327172at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.10/0.39 comp_s8709038167382007543et_int: ( set_set_int > set_int ) > ( set_set_int > set_set_int ) > set_set_int > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.10/0.39 comp_s1975749275458958491et_nat: ( set_set_int > set_int ) > ( set_set_nat > set_set_int ) > set_set_nat > set_int ).
% 0.10/0.39
% 0.10/0.39 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
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% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 0.10/0.40 inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
% 0.10/0.40 inf_inf_rat: rat > rat > rat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 0.10/0.40 inf_inf_set_o: set_o > set_o > set_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 0.10/0.40 inf_inf_set_int: set_int > set_int > set_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.10/0.40 inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 0.10/0.40 inf_in7510916698018314649at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.40 inf_in4302113700860409141at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 0.10/0.40
% 0.10/0.40 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,
% 0.10/0.40 inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
% 0.10/0.40 inf_in2456762090751560885at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.10/0.40 inf_in4660618365625256667t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.10/0.40 inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__String__Ochar_J,type,
% 0.10/0.40 inf_inf_set_char: set_char > set_char > set_char ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_062_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
% 0.10/0.40 sup_su1544571744061072657eger_o: ( int > code_integer > $o ) > ( int > code_integer > $o ) > int > code_integer > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.10/0.40 sup_sup_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.10/0.40 sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Num__Onum_M_Eo_J_J,type,
% 0.10/0.40 sup_sup_nat_num_o: ( nat > num > $o ) > ( nat > num > $o ) > nat > num > $o ).
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% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.10/0.40 sup_su5231854730092680051_int_o: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_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,
% 0.10/0.40 sup_su362511073950362882_nat_o: ( 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 > $o ).
% 0.10/0.40
% 0.10/0.40 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,
% 0.10/0.40 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 ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
% 0.10/0.40 sup_su6164525874564267778_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 0.10/0.40 sup_sup_int: int > int > int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.10/0.40 sup_sup_nat: nat > nat > nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 0.10/0.40 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 0.10/0.40 sup_sup_rat: rat > rat > rat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 0.10/0.40 sup_sup_set_o: set_o > set_o > set_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 0.10/0.40 sup_sup_set_int: set_int > set_int > set_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.10/0.40 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 0.10/0.40 sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Ounit_J_J,type,
% 0.10/0.40 sup_su4058753791541417424t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.10/0.40 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 0.10/0.40 sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 0.10/0.40 sup_su2042722026077122175at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Ounit_J_J,type,
% 0.10/0.40 sup_su4209953369189666580t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.40 sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_M_Eo_J_J,type,
% 0.10/0.40 sup_su2851927382625014182unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 sup_su1639320892072265582it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 0.10/0.40 sup_su6481247232241170203t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.10/0.40 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
% 0.10/0.40 sup_su5395584912770621083at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.10/0.40 sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.10/0.40 sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 0.10/0.40 sup_sup_set_set_o: set_set_o > set_set_o > set_set_o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.10/0.40 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.40 sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.10/0.40 sup_su474284620922681339at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
% 0.10/0.40 sup_su5975557051335651745t_unit: set_set_Product_unit > set_set_Product_unit > set_set_Product_unit ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 0.10/0.40 lattic8265883725875713057ax_nat: set_nat > nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lifting_OQuotient_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 0.10/0.40 quotie9062115205763428814nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > code_integer > $o ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lifting_OQuotient_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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.40 quotie8207154290130328982nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lifting_OQuotient_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,
% 0.10/0.40 quotie8803226531959296410nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lifting_OQuotient_001_Eo_001_Eo,type,
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% 0.10/0.40
% 0.10/0.40 thf(sy_c_Lifting_OQuotient_001_Eo_001t__Nat__Onat,type,
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% 0.10/0.40 quotie4166942682936818134at_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 ) > $o ).
% 0.10/0.40
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% 0.10/0.40 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
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% 0.10/0.40 id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_OId__on_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,
% 0.10/0.40 id_on_3275838214495744996at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.10/0.40 conver1062113817206378758nt_int: ( ( int > product_prod_int_int ) > ( int > int ) > $o ) > ( int > int ) > ( int > product_prod_int_int ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver1572571282669976050nt_nat: ( ( int > product_prod_nat_nat ) > ( int > nat ) > $o ) > ( int > nat ) > ( int > product_prod_nat_nat ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 0.10/0.40 conver5699786650113435344nt_num: ( ( int > product_prod_num_num ) > ( int > num ) > $o ) > ( int > num ) > ( int > product_prod_num_num ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver6066198818478722162at_nat: ( ( list_nat > product_prod_nat_nat ) > ( list_nat > nat ) > $o ) > ( list_nat > nat ) > ( list_nat > product_prod_nat_nat ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.10/0.40 conver2987682522074450438at_int: ( ( nat > product_prod_int_int ) > ( nat > int ) > $o ) > ( nat > int ) > ( nat > product_prod_int_int ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver3498139987538047730at_nat: ( ( nat > product_prod_nat_nat ) > ( nat > nat ) > $o ) > ( nat > nat ) > ( nat > product_prod_nat_nat ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.10/0.40 conver3229387634306789365nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Rat__Orat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Int__Oint_J,type,
% 0.10/0.40 conver6967689361887734790at_int: ( ( rat > product_prod_int_int ) > ( rat > int ) > $o ) > ( rat > int ) > ( rat > product_prod_int_int ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__Rat__Orat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Rat__Orat_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver7478146827351332082at_nat: ( ( rat > product_prod_nat_nat ) > ( rat > nat ) > $o ) > ( rat > nat ) > ( rat > product_prod_nat_nat ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__String__Ochar_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__String__Ochar_Mt__Int__Oint_J,type,
% 0.10/0.40 conver1155128050257070662ar_int: ( ( char > product_prod_int_int ) > ( char > int ) > $o ) > ( char > int ) > ( char > product_prod_int_int ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_062_It__String__Ochar_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__String__Ochar_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver5210974729819302706ar_nat: ( ( char > product_prod_nat_nat ) > ( char > nat ) > $o ) > ( char > nat ) > ( char > product_prod_nat_nat ) > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001_Eo_001_Eo,type,
% 0.10/0.40 conversep_o_o: ( $o > $o > $o ) > $o > $o > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.10/0.40 conver1462408618118490240er_int: ( code_integer > int > $o ) > int > code_integer > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.10/0.40 conver2101108097643427968nteger: ( int > code_integer > $o ) > code_integer > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.40 conversep_int_int: ( int > int > $o ) > int > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.40 conversep_int_nat: ( int > nat > $o ) > nat > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver1866313717161370910at_nat: ( int > product_prod_nat_nat > $o ) > product_prod_nat_nat > int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.10/0.40 conver909888920752868663st_nat: ( list_nat > list_nat > $o ) > list_nat > list_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001_Eo,type,
% 0.10/0.40 conversep_nat_o: ( nat > $o > $o ) > $o > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.40 conversep_nat_int: ( nat > int > $o ) > int > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.40 conversep_nat_nat: ( nat > nat > $o ) > nat > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Num__Onum,type,
% 0.10/0.40 conversep_nat_num: ( nat > num > $o ) > num > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.10/0.40 conversep_nat_rat: ( nat > rat > $o ) > rat > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__String__Ochar,type,
% 0.10/0.40 conversep_nat_char: ( nat > char > $o ) > char > nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Num__Onum_001t__Nat__Onat,type,
% 0.10/0.40 conversep_num_nat: ( num > nat > $o ) > nat > num > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Num__Onum_001t__Num__Onum,type,
% 0.10/0.40 conversep_num_num: ( num > num > $o ) > num > num > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J,type,
% 0.10/0.40 conver4368408235330554745_ref_a: ( produc7812382424243267045t_unit > ref_a > $o ) > ref_a > produc7812382424243267045t_unit > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 0.10/0.40 conver7247880940930113968nt_int: ( product_prod_int_int > int > $o ) > int > product_prod_int_int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.10/0.40 conver4689305806000247544at_int: ( product_prod_nat_nat > int > $o ) > int > product_prod_nat_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.10/0.40 conver4691796276509297820at_nat: ( product_prod_nat_nat > nat > $o ) > nat > product_prod_nat_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.40 conver6965824823119931701at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Int__Oint,type,
% 0.10/0.40 conversep_rat_int: ( rat > int > $o ) > int > rat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Nat__Onat,type,
% 0.10/0.40 conversep_rat_nat: ( rat > nat > $o ) > nat > rat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.10/0.40 conversep_rat_rat: ( rat > rat > $o ) > rat > rat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__String__Ochar,type,
% 0.10/0.40 conversep_rat_char: ( rat > char > $o ) > char > rat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 conver5243090411617913141at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.10/0.40 conver9095369822871743413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Int__Oint,type,
% 0.10/0.40 conversep_char_int: ( char > int > $o ) > int > char > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Nat__Onat,type,
% 0.10/0.40 conversep_char_nat: ( char > nat > $o ) > nat > char > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Rat__Orat,type,
% 0.10/0.40 conversep_char_rat: ( char > rat > $o ) > rat > char > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__String__Ochar,type,
% 0.10/0.40 conversep_char_char: ( char > char > $o ) > char > char > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Int__Oint,type,
% 0.10/0.40 inv_image_int_int: set_Pr958786334691620121nt_int > ( int > int ) > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Nat__Onat,type,
% 0.10/0.40 inv_image_int_nat: set_Pr958786334691620121nt_int > ( nat > int ) > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 inv_im8510909985083594081at_nat: set_Pr958786334691620121nt_int > ( set_Pr1261947904930325089at_nat > int ) > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Int__Oint,type,
% 0.10/0.40 inv_image_nat_int: set_Pr1261947904930325089at_nat > ( int > nat ) > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.10/0.40 inv_image_nat_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 inv_im6750873321330482877at_nat: set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_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,
% 0.10/0.40 inv_im2354225701593503139at_nat: set_Pr1261947904930325089at_nat > ( set_Pr4329608150637261639at_nat > nat ) > set_Pr7459493094073627847at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Int__Oint,type,
% 0.10/0.40 inv_im4434751243573137211at_int: set_Pr4329608150637261639at_nat > ( int > set_Pr1261947904930325089at_nat ) > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 0.10/0.40 inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Int__Oint,type,
% 0.10/0.40 inv_im2900519150384625825at_int: set_Pr7459493094073627847at_nat > ( int > set_Pr4329608150637261639at_nat ) > set_Pr958786334691620121nt_int ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Nat__Onat,type,
% 0.10/0.40 inv_im2903009620893676101at_nat: set_Pr7459493094073627847at_nat > ( nat > set_Pr4329608150637261639at_nat ) > set_Pr1261947904930325089at_nat ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001_Eo,type,
% 0.10/0.40 refl_on_o: set_o > set_Product_prod_o_o > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Int__Oint,type,
% 0.10/0.40 refl_on_int: set_int > set_Pr958786334691620121nt_int > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
% 0.10/0.40 refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.10/0.40 refl_o7122697186039111552at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.10/0.40 refl_o7446464703481863270at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Product____Type__Ounit,type,
% 0.10/0.40 refl_on_Product_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).
% 0.10/0.40
% 0.10/0.40 thf(sy_c_Relation_Orefl__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.10/0.40 refl_o6955724340487615712at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).
% 0.10/0.40
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% 0.10/0.40 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 0.10/0.40 thf(sy_c_Relation_Orelcompp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
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% 0.10/0.41
% 0.10/0.41 thf(sy_v_x,type,
% 0.10/0.41 x: a ).
% 0.10/0.41
% 0.10/0.41 % Relevant facts (4289)
% 0.10/0.41 thf(fact_0_that,axiom,
% 0.10/0.41 ( ( r
% 0.10/0.41 = ( produc473321116828791851t_unit @ ( alloc_a @ x @ h ) ) )
% 0.10/0.41 => ( ( h2
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( alloc_a @ x @ h ) ) )
% 0.10/0.41 => thesis ) ) ).
% 0.10/0.41
% 0.10/0.41 % that
% 0.10/0.41 thf(fact_1_assms,axiom,
% 0.10/0.41 heap_effect_ref_a @ ( ref_a2 @ x ) @ h @ h2 @ r ).
% 0.10/0.41
% 0.10/0.41 % assms
% 0.10/0.41 thf(fact_2_prod_Oexpand,axiom,
% 0.10/0.41 ! [Prod: produc7812382424243267045t_unit,Prod2: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( ( ( produc473321116828791851t_unit @ Prod )
% 0.10/0.41 = ( produc473321116828791851t_unit @ Prod2 ) )
% 0.10/0.41 & ( ( produc1126150082675451753t_unit @ Prod )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ Prod2 ) ) )
% 0.10/0.41 => ( Prod = Prod2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.expand
% 0.10/0.41 thf(fact_3_prod__eqI,axiom,
% 0.10/0.41 ! [P: produc7812382424243267045t_unit,Q: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( ( produc473321116828791851t_unit @ P )
% 0.10/0.41 = ( produc473321116828791851t_unit @ Q ) )
% 0.10/0.41 => ( ( ( produc1126150082675451753t_unit @ P )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ Q ) )
% 0.10/0.41 => ( P = Q ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_eqI
% 0.10/0.41 thf(fact_4_exE__realizer_H,axiom,
% 0.10/0.41 ! [P2: heap_e7401611519738050253t_unit > ref_a > $o,P: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( P2 @ ( produc1126150082675451753t_unit @ P ) @ ( produc473321116828791851t_unit @ P ) )
% 0.10/0.41 => ~ ! [X: ref_a,Y: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ~ ( P2 @ Y @ X ) ) ).
% 0.10/0.41
% 0.10/0.41 % exE_realizer'
% 0.10/0.41 thf(fact_5_prod__eq__iff,axiom,
% 0.10/0.41 ( ( ^ [Y2: produc7812382424243267045t_unit,Z: produc7812382424243267045t_unit] : ( Y2 = Z ) )
% 0.10/0.41 = ( ^ [S: produc7812382424243267045t_unit,T: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( ( produc473321116828791851t_unit @ S )
% 0.10/0.41 = ( produc473321116828791851t_unit @ T ) )
% 0.10/0.41 & ( ( produc1126150082675451753t_unit @ S )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ T ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_eq_iff
% 0.10/0.41 thf(fact_6_Ref_Oget__alloc,axiom,
% 0.10/0.41 ! [X2: a,H: heap_e7401611519738050253t_unit,X3: a] :
% 0.10/0.41 ( ( get_a @ ( produc1126150082675451753t_unit @ ( alloc_a @ X2 @ H ) ) @ ( produc473321116828791851t_unit @ ( alloc_a @ X3 @ H ) ) )
% 0.10/0.41 = X2 ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.get_alloc
% 0.10/0.41 thf(fact_7_set__alloc,axiom,
% 0.10/0.41 ! [V: a,H: heap_e7401611519738050253t_unit,V2: a] :
% 0.10/0.41 ( ( set_a @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) @ V2 @ ( produc1126150082675451753t_unit @ ( alloc_a @ V @ H ) ) )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( alloc_a @ V2 @ H ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % set_alloc
% 0.10/0.41 thf(fact_8_Ref_Opresent__alloc,axiom,
% 0.10/0.41 ! [H: heap_e7401611519738050253t_unit,R: ref_a,V: a] :
% 0.10/0.41 ( ( present_a @ H @ R )
% 0.10/0.41 => ( present_a @ ( produc1126150082675451753t_unit @ ( alloc_a @ V @ H ) ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.present_alloc
% 0.10/0.41 thf(fact_9_Ref_Onot__present__alloc,axiom,
% 0.10/0.41 ! [H: heap_e7401611519738050253t_unit,V: a] :
% 0.10/0.41 ~ ( present_a @ H @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.not_present_alloc
% 0.10/0.41 thf(fact_10_Ref_Oset__same,axiom,
% 0.10/0.41 ! [R: ref_a,X2: a,Y3: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( set_a @ R @ X2 @ ( set_a @ R @ Y3 @ H ) )
% 0.10/0.41 = ( set_a @ R @ X2 @ H ) ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.set_same
% 0.10/0.41 thf(fact_11_Ref_Oget__set__eq,axiom,
% 0.10/0.41 ! [R: ref_a,X2: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( get_a @ ( set_a @ R @ X2 @ H ) @ R )
% 0.10/0.41 = X2 ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.get_set_eq
% 0.10/0.41 thf(fact_12_present__set,axiom,
% 0.10/0.41 ! [R: ref_a,V: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( present_a @ ( set_a @ R @ V @ H ) )
% 0.10/0.41 = ( present_a @ H ) ) ).
% 0.10/0.41
% 0.10/0.41 % present_set
% 0.10/0.41 thf(fact_13_effect__refE,axiom,
% 0.10/0.41 ! [V: a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( ref_a2 @ V ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( ( get_a @ H2 @ R )
% 0.10/0.41 = V )
% 0.10/0.41 => ( ( present_a @ H2 @ R )
% 0.10/0.41 => ( present_a @ H @ R ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_refE
% 0.10/0.41 thf(fact_14_alloc__set,axiom,
% 0.10/0.41 ! [X2: a,R: ref_a,X3: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( produc473321116828791851t_unit @ ( alloc_a @ X2 @ ( set_a @ R @ X3 @ H ) ) )
% 0.10/0.41 = ( produc473321116828791851t_unit @ ( alloc_a @ X2 @ H ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % alloc_set
% 0.10/0.41 thf(fact_15_ref_H__def,axiom,
% 0.10/0.41 ref_a3 = ref_a2 ).
% 0.10/0.41
% 0.10/0.41 % ref'_def
% 0.10/0.41 thf(fact_16_get__alloc__neq,axiom,
% 0.10/0.41 ! [R: ref_a,V: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( noteq_a_a @ R @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) )
% 0.10/0.41 => ( ( get_a @ ( produc1126150082675451753t_unit @ ( alloc_a @ V @ H ) ) @ R )
% 0.10/0.41 = ( get_a @ H @ R ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % get_alloc_neq
% 0.10/0.41 thf(fact_17_effect__changeE,axiom,
% 0.10/0.41 ! [F: a > a,R2: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: a] :
% 0.10/0.41 ( ( heap_effect_a @ ( change_a @ F @ R2 ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( H2
% 0.10/0.41 = ( set_a @ R2 @ ( F @ ( get_a @ H @ R2 ) ) @ H ) )
% 0.10/0.41 => ( R
% 0.10/0.41 != ( F @ ( get_a @ H @ R2 ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_changeE
% 0.10/0.41 thf(fact_18_effect__changeE,axiom,
% 0.10/0.41 ! [F: ref_a > ref_a,R2: ref_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( change_ref_a @ F @ R2 ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( H2
% 0.10/0.41 = ( set_ref_a2 @ R2 @ ( F @ ( get_ref_a @ H @ R2 ) ) @ H ) )
% 0.10/0.41 => ( R
% 0.10/0.41 != ( F @ ( get_ref_a @ H @ R2 ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_changeE
% 0.10/0.41 thf(fact_19_effect__changeI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,R: ref_a,F: a > a,H: heap_e7401611519738050253t_unit,X2: a] :
% 0.10/0.41 ( ( H2
% 0.10/0.41 = ( set_a @ R @ ( F @ ( get_a @ H @ R ) ) @ H ) )
% 0.10/0.41 => ( ( X2
% 0.10/0.41 = ( F @ ( get_a @ H @ R ) ) )
% 0.10/0.41 => ( heap_effect_a @ ( change_a @ F @ R ) @ H @ H2 @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_changeI
% 0.10/0.41 thf(fact_20_effect__changeI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,R: ref_ref_a,F: ref_a > ref_a,H: heap_e7401611519738050253t_unit,X2: ref_a] :
% 0.10/0.41 ( ( H2
% 0.10/0.41 = ( set_ref_a2 @ R @ ( F @ ( get_ref_a @ H @ R ) ) @ H ) )
% 0.10/0.41 => ( ( X2
% 0.10/0.41 = ( F @ ( get_ref_a @ H @ R ) ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( change_ref_a @ F @ R ) @ H @ H2 @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_changeI
% 0.10/0.41 thf(fact_21_present__alloc__neq,axiom,
% 0.10/0.41 ! [H: heap_e7401611519738050253t_unit,R: ref_a,V: a] :
% 0.10/0.41 ( ( present_a @ H @ R )
% 0.10/0.41 => ( noteq_a_a @ R @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % present_alloc_neq
% 0.10/0.41 thf(fact_22_Ref_Oget__set__neq,axiom,
% 0.10/0.41 ! [R: ref_a,S2: ref_a,X2: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( noteq_a_a @ R @ S2 )
% 0.10/0.41 => ( ( get_a @ ( set_a @ S2 @ X2 @ H ) @ R )
% 0.10/0.41 = ( get_a @ H @ R ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.get_set_neq
% 0.10/0.41 thf(fact_23_ref__def,axiom,
% 0.10/0.41 ( ref_a2
% 0.10/0.41 = ( ^ [V3: a] : ( heap_heap_ref_a @ ( alloc_a @ V3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ref_def
% 0.10/0.41 thf(fact_24_effect__lookupE,axiom,
% 0.10/0.41 ! [R: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: a] :
% 0.10/0.41 ( ( heap_effect_a @ ( lookup_a @ R ) @ H @ H2 @ X2 )
% 0.10/0.41 => ~ ( ( H2 = H )
% 0.10/0.41 => ( X2
% 0.10/0.41 != ( get_a @ H @ R ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_lookupE
% 0.10/0.41 thf(fact_25_effect__lookupE,axiom,
% 0.10/0.41 ! [R: ref_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( lookup_ref_a @ R ) @ H @ H2 @ X2 )
% 0.10/0.41 => ~ ( ( H2 = H )
% 0.10/0.41 => ( X2
% 0.10/0.41 != ( get_ref_a @ H @ R ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_lookupE
% 0.10/0.41 thf(fact_26_effect__lookupI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,X2: a,R: ref_a] :
% 0.10/0.41 ( ( H2 = H )
% 0.10/0.41 => ( ( X2
% 0.10/0.41 = ( get_a @ H @ R ) )
% 0.10/0.41 => ( heap_effect_a @ ( lookup_a @ R ) @ H @ H2 @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_lookupI
% 0.10/0.41 thf(fact_27_effect__lookupI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,X2: ref_a,R: ref_ref_a] :
% 0.10/0.41 ( ( H2 = H )
% 0.10/0.41 => ( ( X2
% 0.10/0.41 = ( get_ref_a @ H @ R ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( lookup_ref_a @ R ) @ H @ H2 @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_lookupI
% 0.10/0.41 thf(fact_28_effect__refI,axiom,
% 0.10/0.41 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,V: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 0.10/0.41 = ( alloc_a @ V @ H ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( ref_a2 @ V ) @ H @ H2 @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_refI
% 0.10/0.41 thf(fact_29_snd__swap,axiom,
% 0.10/0.41 ! [X2: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( produc6369869760173755749_ref_a @ ( produc970745769005243767t_unit @ X2 ) )
% 0.10/0.41 = ( produc473321116828791851t_unit @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_swap
% 0.10/0.41 thf(fact_30_snd__swap,axiom,
% 0.10/0.41 ! [X2: produc1799199577659733785_ref_a] :
% 0.10/0.41 ( ( produc1126150082675451753t_unit @ ( produc6214465446503547763_ref_a @ X2 ) )
% 0.10/0.41 = ( produc5717040794327095847_ref_a @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_swap
% 0.10/0.41 thf(fact_31_fst__swap,axiom,
% 0.10/0.41 ! [X2: produc1799199577659733785_ref_a] :
% 0.10/0.41 ( ( produc473321116828791851t_unit @ ( produc6214465446503547763_ref_a @ X2 ) )
% 0.10/0.41 = ( produc6369869760173755749_ref_a @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_swap
% 0.10/0.41 thf(fact_32_fst__swap,axiom,
% 0.10/0.41 ! [X2: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( produc5717040794327095847_ref_a @ ( produc970745769005243767t_unit @ X2 ) )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_swap
% 0.10/0.41 thf(fact_33_prod_Oinject,axiom,
% 0.10/0.41 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat,Y1: set_Pr4329608150637261639at_nat,Y22: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( ( produc9060074326276436823at_nat @ X1 @ X22 )
% 0.10/0.41 = ( produc9060074326276436823at_nat @ Y1 @ Y22 ) )
% 0.10/0.41 = ( ( X1 = Y1 )
% 0.10/0.41 & ( X22 = Y22 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.inject
% 0.10/0.41 thf(fact_34_prod_Oinject,axiom,
% 0.10/0.41 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat,Y1: set_Pr1261947904930325089at_nat,Y22: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( ( produc2922128104949294807at_nat @ X1 @ X22 )
% 0.10/0.41 = ( produc2922128104949294807at_nat @ Y1 @ Y22 ) )
% 0.10/0.41 = ( ( X1 = Y1 )
% 0.10/0.41 & ( X22 = Y22 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.inject
% 0.10/0.41 thf(fact_35_prod_Oinject,axiom,
% 0.10/0.41 ! [X1: nat,X22: num,Y1: nat,Y22: num] :
% 0.10/0.41 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 0.10/0.41 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 0.10/0.41 = ( ( X1 = Y1 )
% 0.10/0.41 & ( X22 = Y22 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.inject
% 0.10/0.41 thf(fact_36_prod_Oinject,axiom,
% 0.10/0.41 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 0.10/0.41 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.10/0.41 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 0.10/0.41 = ( ( X1 = Y1 )
% 0.10/0.41 & ( X22 = Y22 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.inject
% 0.10/0.41 thf(fact_37_prod_Oinject,axiom,
% 0.10/0.41 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 0.10/0.41 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 0.10/0.41 = ( ( X1 = Y1 )
% 0.10/0.41 & ( X22 = Y22 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.inject
% 0.10/0.41 thf(fact_38_old_Oprod_Oinject,axiom,
% 0.10/0.41 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( ( produc9060074326276436823at_nat @ A @ B )
% 0.10/0.41 = ( produc9060074326276436823at_nat @ A2 @ B2 ) )
% 0.10/0.41 = ( ( A = A2 )
% 0.10/0.41 & ( B = B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.inject
% 0.10/0.41 thf(fact_39_old_Oprod_Oinject,axiom,
% 0.10/0.41 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 0.10/0.41 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 0.10/0.41 = ( ( A = A2 )
% 0.10/0.41 & ( B = B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.inject
% 0.10/0.41 thf(fact_40_old_Oprod_Oinject,axiom,
% 0.10/0.41 ! [A: nat,B: num,A2: nat,B2: num] :
% 0.10/0.41 ( ( ( product_Pair_nat_num @ A @ B )
% 0.10/0.41 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 0.10/0.41 = ( ( A = A2 )
% 0.10/0.41 & ( B = B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.inject
% 0.10/0.41 thf(fact_41_old_Oprod_Oinject,axiom,
% 0.10/0.41 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.10/0.41 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.10/0.41 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.10/0.41 = ( ( A = A2 )
% 0.10/0.41 & ( B = B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.inject
% 0.10/0.41 thf(fact_42_old_Oprod_Oinject,axiom,
% 0.10/0.41 ! [A: int,B: int,A2: int,B2: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ A @ B )
% 0.10/0.41 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.10/0.41 = ( ( A = A2 )
% 0.10/0.41 & ( B = B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.inject
% 0.10/0.41 thf(fact_43_swap__simp,axiom,
% 0.10/0.41 ! [X2: num,Y3: nat] :
% 0.10/0.41 ( ( product_swap_num_nat @ ( product_Pair_num_nat @ X2 @ Y3 ) )
% 0.10/0.41 = ( product_Pair_nat_num @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_44_swap__simp,axiom,
% 0.10/0.41 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( produc5396952528824381687at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = ( produc9060074326276436823at_nat @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_45_swap__simp,axiom,
% 0.10/0.41 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( produc3946833401584108663at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = ( produc2922128104949294807at_nat @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_46_swap__simp,axiom,
% 0.10/0.41 ! [X2: nat,Y3: num] :
% 0.10/0.41 ( ( product_swap_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.41 = ( product_Pair_num_nat @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_47_swap__simp,axiom,
% 0.10/0.41 ! [X2: nat,Y3: nat] :
% 0.10/0.41 ( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.41 = ( product_Pair_nat_nat @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_48_swap__simp,axiom,
% 0.10/0.41 ! [X2: int,Y3: int] :
% 0.10/0.41 ( ( product_swap_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.41 = ( product_Pair_int_int @ Y3 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % swap_simp
% 0.10/0.41 thf(fact_49_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: produc1319942482725812455at_nat] :
% 0.10/0.41 ( ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ Prod ) @ ( produc826222791318859909at_nat @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_50_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: produc3843707927480180839at_nat] :
% 0.10/0.41 ( ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ Prod ) @ ( produc2937545259423399429at_nat @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_51_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: product_prod_nat_num] :
% 0.10/0.41 ( ( product_Pair_nat_num @ ( product_fst_nat_num @ Prod ) @ ( product_snd_nat_num @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_52_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: product_prod_nat_nat] :
% 0.10/0.41 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_53_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: product_prod_int_int] :
% 0.10/0.41 ( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_54_prod_Ocollapse,axiom,
% 0.10/0.41 ! [Prod: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ Prod ) @ ( produc1126150082675451753t_unit @ Prod ) )
% 0.10/0.41 = Prod ) ).
% 0.10/0.41
% 0.10/0.41 % prod.collapse
% 0.10/0.41 thf(fact_55_old_Oprod_Oexhaust,axiom,
% 0.10/0.41 ! [Y3: produc1319942482725812455at_nat] :
% 0.10/0.41 ~ ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( Y3
% 0.10/0.41 != ( produc9060074326276436823at_nat @ A3 @ B3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.exhaust
% 0.10/0.41 thf(fact_56_old_Oprod_Oexhaust,axiom,
% 0.10/0.41 ! [Y3: produc3843707927480180839at_nat] :
% 0.10/0.41 ~ ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( Y3
% 0.10/0.41 != ( produc2922128104949294807at_nat @ A3 @ B3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.exhaust
% 0.10/0.41 thf(fact_57_old_Oprod_Oexhaust,axiom,
% 0.10/0.41 ! [Y3: product_prod_nat_num] :
% 0.10/0.41 ~ ! [A3: nat,B3: num] :
% 0.10/0.41 ( Y3
% 0.10/0.41 != ( product_Pair_nat_num @ A3 @ B3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.exhaust
% 0.10/0.41 thf(fact_58_old_Oprod_Oexhaust,axiom,
% 0.10/0.41 ! [Y3: product_prod_nat_nat] :
% 0.10/0.41 ~ ! [A3: nat,B3: nat] :
% 0.10/0.41 ( Y3
% 0.10/0.41 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.exhaust
% 0.10/0.41 thf(fact_59_old_Oprod_Oexhaust,axiom,
% 0.10/0.41 ! [Y3: product_prod_int_int] :
% 0.10/0.41 ~ ! [A3: int,B3: int] :
% 0.10/0.41 ( Y3
% 0.10/0.41 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.exhaust
% 0.10/0.41 thf(fact_60_surj__pair,axiom,
% 0.10/0.41 ! [P: produc1319942482725812455at_nat] :
% 0.10/0.41 ? [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc9060074326276436823at_nat @ X @ Y ) ) ).
% 0.10/0.41
% 0.10/0.41 % surj_pair
% 0.10/0.41 thf(fact_61_surj__pair,axiom,
% 0.10/0.41 ! [P: produc3843707927480180839at_nat] :
% 0.10/0.41 ? [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc2922128104949294807at_nat @ X @ Y ) ) ).
% 0.10/0.41
% 0.10/0.41 % surj_pair
% 0.10/0.41 thf(fact_62_surj__pair,axiom,
% 0.10/0.41 ! [P: product_prod_nat_num] :
% 0.10/0.41 ? [X: nat,Y: num] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_num @ X @ Y ) ) ).
% 0.10/0.41
% 0.10/0.41 % surj_pair
% 0.10/0.41 thf(fact_63_surj__pair,axiom,
% 0.10/0.41 ! [P: product_prod_nat_nat] :
% 0.10/0.41 ? [X: nat,Y: nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ X @ Y ) ) ).
% 0.10/0.41
% 0.10/0.41 % surj_pair
% 0.10/0.41 thf(fact_64_surj__pair,axiom,
% 0.10/0.41 ! [P: product_prod_int_int] :
% 0.10/0.41 ? [X: int,Y: int] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_int_int @ X @ Y ) ) ).
% 0.10/0.41
% 0.10/0.41 % surj_pair
% 0.10/0.41 thf(fact_65_prod__cases,axiom,
% 0.10/0.41 ! [P2: produc1319942482725812455at_nat > $o,P: produc1319942482725812455at_nat] :
% 0.10/0.41 ( ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( P2 @ ( produc9060074326276436823at_nat @ A3 @ B3 ) )
% 0.10/0.41 => ( P2 @ P ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_cases
% 0.10/0.41 thf(fact_66_prod__cases,axiom,
% 0.10/0.41 ! [P2: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
% 0.10/0.41 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P2 @ ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 0.10/0.41 => ( P2 @ P ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_cases
% 0.10/0.41 thf(fact_67_prod__cases,axiom,
% 0.10/0.41 ! [P2: product_prod_nat_num > $o,P: product_prod_nat_num] :
% 0.10/0.41 ( ! [A3: nat,B3: num] : ( P2 @ ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.10/0.41 => ( P2 @ P ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_cases
% 0.10/0.41 thf(fact_68_prod__cases,axiom,
% 0.10/0.41 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 0.10/0.41 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.10/0.41 => ( P2 @ P ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_cases
% 0.10/0.41 thf(fact_69_prod__cases,axiom,
% 0.10/0.41 ! [P2: product_prod_int_int > $o,P: product_prod_int_int] :
% 0.10/0.41 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 0.10/0.41 => ( P2 @ P ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod_cases
% 0.10/0.41 thf(fact_70_Pair__inject,axiom,
% 0.10/0.41 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( ( produc9060074326276436823at_nat @ A @ B )
% 0.10/0.41 = ( produc9060074326276436823at_nat @ A2 @ B2 ) )
% 0.10/0.41 => ~ ( ( A = A2 )
% 0.10/0.41 => ( B != B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Pair_inject
% 0.10/0.41 thf(fact_71_Pair__inject,axiom,
% 0.10/0.41 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 0.10/0.41 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 0.10/0.41 => ~ ( ( A = A2 )
% 0.10/0.41 => ( B != B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Pair_inject
% 0.10/0.41 thf(fact_72_Pair__inject,axiom,
% 0.10/0.41 ! [A: nat,B: num,A2: nat,B2: num] :
% 0.10/0.41 ( ( ( product_Pair_nat_num @ A @ B )
% 0.10/0.41 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 0.10/0.41 => ~ ( ( A = A2 )
% 0.10/0.41 => ( B != B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Pair_inject
% 0.10/0.41 thf(fact_73_Pair__inject,axiom,
% 0.10/0.41 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.10/0.41 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.10/0.41 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.10/0.41 => ~ ( ( A = A2 )
% 0.10/0.41 => ( B != B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Pair_inject
% 0.10/0.41 thf(fact_74_Pair__inject,axiom,
% 0.10/0.41 ! [A: int,B: int,A2: int,B2: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ A @ B )
% 0.10/0.41 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.10/0.41 => ~ ( ( A = A2 )
% 0.10/0.41 => ( B != B2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Pair_inject
% 0.10/0.41 thf(fact_75_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: produc3843707927480180839at_nat,P2: produc3843707927480180839at_nat > $o] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ A @ ( collec6321179662152712658at_nat @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_76_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: $o,P2: $o > $o] :
% 0.10/0.41 ( ( member_o @ A @ ( collect_o @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_77_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: int,P2: int > $o] :
% 0.10/0.41 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_78_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_79_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: nat,P2: nat > $o] :
% 0.10/0.41 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_80_mem__Collect__eq,axiom,
% 0.10/0.41 ! [A: product_prod_int_int,P2: product_prod_int_int > $o] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P2 ) )
% 0.10/0.41 = ( P2 @ A ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_Collect_eq
% 0.10/0.41 thf(fact_81_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( collec6321179662152712658at_nat
% 0.10/0.41 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_82_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_o] :
% 0.10/0.41 ( ( collect_o
% 0.10/0.41 @ ^ [X4: $o] : ( member_o @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_83_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_int] :
% 0.10/0.41 ( ( collect_int
% 0.10/0.41 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_84_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( collec3392354462482085612at_nat
% 0.10/0.41 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_85_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_nat] :
% 0.10/0.41 ( ( collect_nat
% 0.10/0.41 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_86_Collect__mem__eq,axiom,
% 0.10/0.41 ! [A4: set_Pr958786334691620121nt_int] :
% 0.10/0.41 ( ( collec213857154873943460nt_int
% 0.10/0.41 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A4 ) )
% 0.10/0.41 = A4 ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_mem_eq
% 0.10/0.41 thf(fact_87_Collect__cong,axiom,
% 0.10/0.41 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.10/0.41 ( ! [X: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ X )
% 0.10/0.41 = ( Q2 @ X ) )
% 0.10/0.41 => ( ( collec3392354462482085612at_nat @ P2 )
% 0.10/0.41 = ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_cong
% 0.10/0.41 thf(fact_88_Collect__cong,axiom,
% 0.10/0.41 ! [P2: nat > $o,Q2: nat > $o] :
% 0.10/0.41 ( ! [X: nat] :
% 0.10/0.41 ( ( P2 @ X )
% 0.10/0.41 = ( Q2 @ X ) )
% 0.10/0.41 => ( ( collect_nat @ P2 )
% 0.10/0.41 = ( collect_nat @ Q2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_cong
% 0.10/0.41 thf(fact_89_Collect__cong,axiom,
% 0.10/0.41 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > $o] :
% 0.10/0.41 ( ! [X: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ X )
% 0.10/0.41 = ( Q2 @ X ) )
% 0.10/0.41 => ( ( collec213857154873943460nt_int @ P2 )
% 0.10/0.41 = ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_cong
% 0.10/0.41 thf(fact_90_fst__eqD,axiom,
% 0.10/0.41 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_91_fst__eqD,axiom,
% 0.10/0.41 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_92_fst__eqD,axiom,
% 0.10/0.41 ! [X2: nat,Y3: num,A: nat] :
% 0.10/0.41 ( ( ( product_fst_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_93_fst__eqD,axiom,
% 0.10/0.41 ! [X2: nat,Y3: nat,A: nat] :
% 0.10/0.41 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_94_fst__eqD,axiom,
% 0.10/0.41 ! [X2: int,Y3: int,A: int] :
% 0.10/0.41 ( ( ( product_fst_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_95_fst__eqD,axiom,
% 0.10/0.41 ! [X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: ref_a] :
% 0.10/0.41 ( ( ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( X2 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_eqD
% 0.10/0.41 thf(fact_96_fst__conv,axiom,
% 0.10/0.41 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_97_fst__conv,axiom,
% 0.10/0.41 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_98_fst__conv,axiom,
% 0.10/0.41 ! [X1: nat,X22: num] :
% 0.10/0.41 ( ( product_fst_nat_num @ ( product_Pair_nat_num @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_99_fst__conv,axiom,
% 0.10/0.41 ! [X1: nat,X22: nat] :
% 0.10/0.41 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_100_fst__conv,axiom,
% 0.10/0.41 ! [X1: int,X22: int] :
% 0.10/0.41 ( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_101_fst__conv,axiom,
% 0.10/0.41 ! [X1: ref_a,X22: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X1 @ X22 ) )
% 0.10/0.41 = X1 ) ).
% 0.10/0.41
% 0.10/0.41 % fst_conv
% 0.10/0.41 thf(fact_102_snd__eqD,axiom,
% 0.10/0.41 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_103_snd__eqD,axiom,
% 0.10/0.41 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_104_snd__eqD,axiom,
% 0.10/0.41 ! [X2: nat,Y3: num,A: num] :
% 0.10/0.41 ( ( ( product_snd_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_105_snd__eqD,axiom,
% 0.10/0.41 ! [X2: nat,Y3: nat,A: nat] :
% 0.10/0.41 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_106_snd__eqD,axiom,
% 0.10/0.41 ! [X2: int,Y3: int,A: int] :
% 0.10/0.41 ( ( ( product_snd_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_107_snd__eqD,axiom,
% 0.10/0.41 ! [X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 0.10/0.41 = A )
% 0.10/0.41 => ( Y3 = A ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_eqD
% 0.10/0.41 thf(fact_108_snd__conv,axiom,
% 0.10/0.41 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_109_snd__conv,axiom,
% 0.10/0.41 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_110_snd__conv,axiom,
% 0.10/0.41 ! [X1: nat,X22: num] :
% 0.10/0.41 ( ( product_snd_nat_num @ ( product_Pair_nat_num @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_111_snd__conv,axiom,
% 0.10/0.41 ! [X1: nat,X22: nat] :
% 0.10/0.41 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_112_snd__conv,axiom,
% 0.10/0.41 ! [X1: int,X22: int] :
% 0.10/0.41 ( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_113_snd__conv,axiom,
% 0.10/0.41 ! [X1: ref_a,X22: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X1 @ X22 ) )
% 0.10/0.41 = X22 ) ).
% 0.10/0.41
% 0.10/0.41 % snd_conv
% 0.10/0.41 thf(fact_114_prod_Oswap__def,axiom,
% 0.10/0.41 ( produc5396952528824381687at_nat
% 0.10/0.41 = ( ^ [P3: produc1319942482725812455at_nat] : ( produc9060074326276436823at_nat @ ( produc826222791318859909at_nat @ P3 ) @ ( produc4486455499028916547at_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_115_prod_Oswap__def,axiom,
% 0.10/0.41 ( produc3946833401584108663at_nat
% 0.10/0.41 = ( ^ [P3: produc3843707927480180839at_nat] : ( produc2922128104949294807at_nat @ ( produc2937545259423399429at_nat @ P3 ) @ ( produc6011863565407846595at_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_116_prod_Oswap__def,axiom,
% 0.10/0.41 ( product_swap_num_nat
% 0.10/0.41 = ( ^ [P3: product_prod_num_nat] : ( product_Pair_nat_num @ ( product_snd_num_nat @ P3 ) @ ( product_fst_num_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_117_prod_Oswap__def,axiom,
% 0.10/0.41 ( product_swap_nat_nat
% 0.10/0.41 = ( ^ [P3: product_prod_nat_nat] : ( product_Pair_nat_nat @ ( product_snd_nat_nat @ P3 ) @ ( product_fst_nat_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_118_prod_Oswap__def,axiom,
% 0.10/0.41 ( product_swap_int_int
% 0.10/0.41 = ( ^ [P3: product_prod_int_int] : ( product_Pair_int_int @ ( product_snd_int_int @ P3 ) @ ( product_fst_int_int @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_119_prod_Oswap__def,axiom,
% 0.10/0.41 ( produc970745769005243767t_unit
% 0.10/0.41 = ( ^ [P3: produc7812382424243267045t_unit] : ( produc2564672488694626579_ref_a @ ( produc1126150082675451753t_unit @ P3 ) @ ( produc473321116828791851t_unit @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.swap_def
% 0.10/0.41 thf(fact_120_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: produc1319942482725812455at_nat] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ Prod ) @ ( produc826222791318859909at_nat @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_121_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: produc3843707927480180839at_nat] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ Prod ) @ ( produc2937545259423399429at_nat @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_122_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: product_prod_nat_num] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( product_Pair_nat_num @ ( product_fst_nat_num @ Prod ) @ ( product_snd_nat_num @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_123_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: product_prod_nat_nat] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_124_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: product_prod_int_int] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_125_prod_Oexhaust__sel,axiom,
% 0.10/0.41 ! [Prod: produc7812382424243267045t_unit] :
% 0.10/0.41 ( Prod
% 0.10/0.41 = ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ Prod ) @ ( produc1126150082675451753t_unit @ Prod ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.exhaust_sel
% 0.10/0.41 thf(fact_126_exI__realizer,axiom,
% 0.10/0.41 ! [P2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) @ ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_127_exI__realizer,axiom,
% 0.10/0.41 ! [P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Y3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) @ ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_128_exI__realizer,axiom,
% 0.10/0.41 ! [P2: num > nat > $o,Y3: num,X2: nat] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( product_snd_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) ) @ ( product_fst_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_129_exI__realizer,axiom,
% 0.10/0.41 ! [P2: nat > nat > $o,Y3: nat,X2: nat] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_130_exI__realizer,axiom,
% 0.10/0.41 ! [P2: int > int > $o,Y3: int,X2: int] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( product_snd_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_131_exI__realizer,axiom,
% 0.10/0.41 ! [P2: heap_e7401611519738050253t_unit > ref_a > $o,Y3: heap_e7401611519738050253t_unit,X2: ref_a] :
% 0.10/0.41 ( ( P2 @ Y3 @ X2 )
% 0.10/0.41 => ( P2 @ ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) ) @ ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % exI_realizer
% 0.10/0.41 thf(fact_132_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: set_Pr4329608150637261639at_nat > $o,P: set_Pr4329608150637261639at_nat,Q2: set_Pr4329608150637261639at_nat > $o,Q: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_133_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: set_Pr1261947904930325089at_nat > $o,P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat > $o,Q: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_134_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: nat > $o,P: nat,Q2: num > $o,Q: num] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( product_fst_nat_num @ ( product_Pair_nat_num @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( product_snd_nat_num @ ( product_Pair_nat_num @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_135_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: nat > $o,P: nat,Q2: nat > $o,Q: nat] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_136_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: int > $o,P: int,Q2: int > $o,Q: int] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( product_fst_int_int @ ( product_Pair_int_int @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( product_snd_int_int @ ( product_Pair_int_int @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_137_conjI__realizer,axiom,
% 0.10/0.41 ! [P2: ref_a > $o,P: ref_a,Q2: heap_e7401611519738050253t_unit > $o,Q: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( P2 @ P )
% 0.10/0.41 => ( ( Q2 @ Q )
% 0.10/0.41 => ( ( P2 @ ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ P @ Q ) ) )
% 0.10/0.41 & ( Q2 @ ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ P @ Q ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % conjI_realizer
% 0.10/0.41 thf(fact_138_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: produc1319942482725812455at_nat] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ T2 ) @ ( produc826222791318859909at_nat @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_139_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: produc3843707927480180839at_nat] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ T2 ) @ ( produc2937545259423399429at_nat @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_140_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: product_prod_nat_num] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( product_Pair_nat_num @ ( product_fst_nat_num @ T2 ) @ ( product_snd_nat_num @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_141_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: product_prod_nat_nat] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T2 ) @ ( product_snd_nat_nat @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_142_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: product_prod_int_int] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ T2 ) @ ( product_snd_int_int @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_143_surjective__pairing,axiom,
% 0.10/0.41 ! [T2: produc7812382424243267045t_unit] :
% 0.10/0.41 ( T2
% 0.10/0.41 = ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ T2 ) @ ( produc1126150082675451753t_unit @ T2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % surjective_pairing
% 0.10/0.41 thf(fact_144_Ref_Oset__set__swap,axiom,
% 0.10/0.41 ! [R: ref_a,R2: ref_a,X2: a,X3: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( noteq_a_a @ R @ R2 )
% 0.10/0.41 => ( ( set_a @ R @ X2 @ ( set_a @ R2 @ X3 @ H ) )
% 0.10/0.41 = ( set_a @ R2 @ X3 @ ( set_a @ R @ X2 @ H ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Ref.set_set_swap
% 0.10/0.41 thf(fact_145_next__fresh,axiom,
% 0.10/0.41 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,X2: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 0.10/0.41 = ( alloc_a @ X2 @ H ) )
% 0.10/0.41 => ~ ( present_a @ H @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % next_fresh
% 0.10/0.41 thf(fact_146_next__present,axiom,
% 0.10/0.41 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,X2: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 0.10/0.41 = ( alloc_a @ X2 @ H ) )
% 0.10/0.41 => ( present_a @ H2 @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % next_present
% 0.10/0.41 thf(fact_147_noteq__I,axiom,
% 0.10/0.41 ! [H: heap_e7401611519738050253t_unit,R: ref_a,R2: ref_a] :
% 0.10/0.41 ( ( present_a @ H @ R )
% 0.10/0.41 => ( ~ ( present_a @ H @ R2 )
% 0.10/0.41 => ( noteq_a_a @ R @ R2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % noteq_I
% 0.10/0.41 thf(fact_148_effect__heapE,axiom,
% 0.10/0.41 ! [F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ F ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( H2
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( R
% 0.10/0.41 != ( produc473321116828791851t_unit @ ( F @ H ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_heapE
% 0.10/0.41 thf(fact_149_effect__heapI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( H2
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( ( R
% 0.10/0.41 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( heap_heap_ref_a @ F ) @ H @ H2 @ R ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_heapI
% 0.10/0.41 thf(fact_150_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: produc1319942482725812455at_nat] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( produc4486455499028916547at_nat @ A ) @ ( produc826222791318859909at_nat @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_151_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: produc3843707927480180839at_nat] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( produc6011863565407846595at_nat @ A ) @ ( produc2937545259423399429at_nat @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_152_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: nat > num > $o,X2: nat,Y3: num,A: product_prod_nat_num] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( product_fst_nat_num @ A ) @ ( product_snd_nat_num @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_153_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: nat > nat > $o,X2: nat,Y3: nat,A: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_154_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: int > int > $o,X2: int,Y3: int,A: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( product_fst_int_int @ A ) @ ( product_snd_int_int @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_155_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.10/0.41 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o,X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( P2 @ X2 @ Y3 )
% 0.10/0.41 => ( ( A
% 0.10/0.41 = ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 0.10/0.41 => ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( produc1126150082675451753t_unit @ A ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % BNF_Greatest_Fixpoint.subst_Pair
% 0.10/0.41 thf(fact_156_sndI,axiom,
% 0.10/0.41 ! [X2: produc1319942482725812455at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc9060074326276436823at_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc826222791318859909at_nat @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_157_sndI,axiom,
% 0.10/0.41 ! [X2: produc3843707927480180839at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc2922128104949294807at_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc2937545259423399429at_nat @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_158_sndI,axiom,
% 0.10/0.41 ! [X2: product_prod_nat_num,Y3: nat,Z2: num] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_nat_num @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_snd_nat_num @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_159_sndI,axiom,
% 0.10/0.41 ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_snd_nat_nat @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_160_sndI,axiom,
% 0.10/0.41 ! [X2: product_prod_int_int,Y3: int,Z2: int] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_int_int @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_snd_int_int @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_161_sndI,axiom,
% 0.10/0.41 ! [X2: produc7812382424243267045t_unit,Y3: ref_a,Z2: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc6544324848051098391t_unit @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc1126150082675451753t_unit @ X2 )
% 0.10/0.41 = Z2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndI
% 0.10/0.41 thf(fact_162_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( produc826222791318859909at_nat @ P ) )
% 0.10/0.41 = ( ? [A5: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc9060074326276436823at_nat @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_163_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( produc2937545259423399429at_nat @ P ) )
% 0.10/0.41 = ( ? [A5: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc2922128104949294807at_nat @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_164_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: num,P: product_prod_nat_num] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( product_snd_nat_num @ P ) )
% 0.10/0.41 = ( ? [A5: nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_num @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_165_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: nat,P: product_prod_nat_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( product_snd_nat_nat @ P ) )
% 0.10/0.41 = ( ? [A5: nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_166_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: int,P: product_prod_int_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( product_snd_int_int @ P ) )
% 0.10/0.41 = ( ? [A5: int] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_int_int @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_167_eq__snd__iff,axiom,
% 0.10/0.41 ! [B: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( produc1126150082675451753t_unit @ P ) )
% 0.10/0.41 = ( ? [A5: ref_a] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc6544324848051098391t_unit @ A5 @ B ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_snd_iff
% 0.10/0.41 thf(fact_168_fstI,axiom,
% 0.10/0.41 ! [X2: produc1319942482725812455at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc9060074326276436823at_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc4486455499028916547at_nat @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_169_fstI,axiom,
% 0.10/0.41 ! [X2: produc3843707927480180839at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc2922128104949294807at_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc6011863565407846595at_nat @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_170_fstI,axiom,
% 0.10/0.41 ! [X2: product_prod_nat_num,Y3: nat,Z2: num] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_nat_num @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_fst_nat_num @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_171_fstI,axiom,
% 0.10/0.41 ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_fst_nat_nat @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_172_fstI,axiom,
% 0.10/0.41 ! [X2: product_prod_int_int,Y3: int,Z2: int] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( product_Pair_int_int @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( product_fst_int_int @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_173_fstI,axiom,
% 0.10/0.41 ! [X2: produc7812382424243267045t_unit,Y3: ref_a,Z2: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( X2
% 0.10/0.41 = ( produc6544324848051098391t_unit @ Y3 @ Z2 ) )
% 0.10/0.41 => ( ( produc473321116828791851t_unit @ X2 )
% 0.10/0.41 = Y3 ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstI
% 0.10/0.41 thf(fact_174_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( produc4486455499028916547at_nat @ P ) )
% 0.10/0.41 = ( ? [B4: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc9060074326276436823at_nat @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_175_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( produc6011863565407846595at_nat @ P ) )
% 0.10/0.41 = ( ? [B4: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc2922128104949294807at_nat @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_176_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: nat,P: product_prod_nat_num] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( product_fst_nat_num @ P ) )
% 0.10/0.41 = ( ? [B4: num] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_num @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_177_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: nat,P: product_prod_nat_nat] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( product_fst_nat_nat @ P ) )
% 0.10/0.41 = ( ? [B4: nat] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_178_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: int,P: product_prod_int_int] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( product_fst_int_int @ P ) )
% 0.10/0.41 = ( ? [B4: int] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( product_Pair_int_int @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_179_eq__fst__iff,axiom,
% 0.10/0.41 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 0.10/0.41 ( ( A
% 0.10/0.41 = ( produc473321116828791851t_unit @ P ) )
% 0.10/0.41 = ( ? [B4: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( P
% 0.10/0.41 = ( produc6544324848051098391t_unit @ A @ B4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % eq_fst_iff
% 0.10/0.41 thf(fact_180_effect__guardE,axiom,
% 0.10/0.41 ! [P2: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( heap_guard_ref_a @ P2 @ F ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( H2
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( ( R
% 0.10/0.41 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ~ ( P2 @ H ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_guardE
% 0.10/0.41 thf(fact_181_effect__guardI,axiom,
% 0.10/0.41 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,R: ref_a] :
% 0.10/0.41 ( ( P2 @ H )
% 0.10/0.41 => ( ( H2
% 0.10/0.41 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( ( R
% 0.10/0.41 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( heap_guard_ref_a @ P2 @ F ) @ H @ H2 @ R ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_guardI
% 0.10/0.41 thf(fact_182_effect__ifI,axiom,
% 0.10/0.41 ! [C: $o,T2: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a,E: heap_Heap_ref_a] :
% 0.10/0.41 ( ( C
% 0.10/0.41 => ( heap_effect_ref_a @ T2 @ H @ H2 @ R ) )
% 0.10/0.41 => ( ( ~ C
% 0.10/0.41 => ( heap_effect_ref_a @ E @ H @ H2 @ R ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( if_Heap_Heap_ref_a @ C @ T2 @ E ) @ H @ H2 @ R ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_ifI
% 0.10/0.41 thf(fact_183_effect__deterministic_I2_J,axiom,
% 0.10/0.41 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,A: ref_a,H3: heap_e7401611519738050253t_unit,B: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ F @ H @ H2 @ A )
% 0.10/0.41 => ( ( heap_effect_ref_a @ F @ H @ H3 @ B )
% 0.10/0.41 => ( H2 = H3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_deterministic(2)
% 0.10/0.41 thf(fact_184_effect__deterministic_I1_J,axiom,
% 0.10/0.41 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,A: ref_a,H3: heap_e7401611519738050253t_unit,B: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ F @ H @ H2 @ A )
% 0.10/0.41 => ( ( heap_effect_ref_a @ F @ H @ H3 @ B )
% 0.10/0.41 => ( A = B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_deterministic(1)
% 0.10/0.41 thf(fact_185_effect__ifE,axiom,
% 0.10/0.41 ! [C: $o,T2: heap_Heap_ref_a,E: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( if_Heap_Heap_ref_a @ C @ T2 @ E ) @ H @ H2 @ R )
% 0.10/0.41 => ( ( C
% 0.10/0.41 => ~ ( heap_effect_ref_a @ T2 @ H @ H2 @ R ) )
% 0.10/0.41 => ~ ( ~ C
% 0.10/0.41 => ~ ( heap_effect_ref_a @ E @ H @ H2 @ R ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_ifE
% 0.10/0.41 thf(fact_186_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: $o > nat,X2: $o,C: num,G: $o > num,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr7727518618234538026at_num @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_187_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: nat > nat,X2: nat,C: num,G: nat > num,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr3875488559241464598at_num @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_188_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: int > nat,X2: int,C: num,G: int > num,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr4247142119478309234at_num @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_189_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: $o > nat,X2: $o,C: nat,G: $o > nat,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr1946814795223983584at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_190_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: nat > nat,X2: nat,C: nat,G: nat > nat,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr7318156773085685964at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_191_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: int > nat,X2: int,C: nat,G: int > nat,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr7689810333322530600at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_192_image2__eqI,axiom,
% 0.10/0.41 ! [B: int,F: $o > int,X2: $o,C: int,G: $o > int,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr2943678036615987864nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_193_image2__eqI,axiom,
% 0.10/0.41 ! [B: int,F: nat > int,X2: nat,C: int,G: nat > int,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr8315020014477690244nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_194_image2__eqI,axiom,
% 0.10/0.41 ! [B: int,F: int > int,X2: int,C: int,G: int > int,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr8686673574714534880nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_195_image2__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: product_prod_nat_nat > nat,X2: product_prod_nat_nat,C: num,G: product_prod_nat_nat > num,A4: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( C
% 0.10/0.41 = ( G @ X2 ) )
% 0.10/0.41 => ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 0.10/0.41 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr5511461681843259283at_num @ A4 @ F @ G ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image2_eqI
% 0.10/0.41 thf(fact_196_lim__set,axiom,
% 0.10/0.41 ! [R: ref_a,V: a,H: heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( lim_Product_unit @ ( set_a @ R @ V @ H ) )
% 0.10/0.41 = ( lim_Product_unit @ H ) ) ).
% 0.10/0.41
% 0.10/0.41 % lim_set
% 0.10/0.41 thf(fact_197_prod_Osplit__sel__asm,axiom,
% 0.10/0.41 ! [P2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 0.10/0.41 = ( ~ ( ( Prod
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.10/0.41 & ~ ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel_asm
% 0.10/0.41 thf(fact_198_prod_Osplit__sel__asm,axiom,
% 0.10/0.41 ! [P2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.10/0.41 = ( ~ ( ( Prod
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.10/0.41 & ~ ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel_asm
% 0.10/0.41 thf(fact_199_prod_Osplit__sel__asm,axiom,
% 0.10/0.41 ! [P2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.10/0.41 = ( ~ ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel_asm
% 0.10/0.41 thf(fact_200_prod_Osplit__sel__asm,axiom,
% 0.10/0.41 ! [P2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 0.10/0.41 = ( ~ ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel_asm
% 0.10/0.41 thf(fact_201_prod_Osplit__sel__asm,axiom,
% 0.10/0.41 ! [P2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.10/0.41 = ( ~ ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel_asm
% 0.10/0.41 thf(fact_202_prod_Osplit__sel,axiom,
% 0.10/0.41 ! [P2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 0.10/0.41 = ( ( Prod
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.10/0.41 => ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel
% 0.10/0.41 thf(fact_203_prod_Osplit__sel,axiom,
% 0.10/0.41 ! [P2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.10/0.41 ( ( P2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.10/0.41 = ( ( Prod
% 0.10/0.41 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 0.10/0.41 => ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel
% 0.10/0.41 thf(fact_204_prod_Osplit__sel,axiom,
% 0.10/0.41 ! [P2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.10/0.41 = ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel
% 0.10/0.41 thf(fact_205_prod_Osplit__sel,axiom,
% 0.10/0.41 ! [P2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 0.10/0.41 = ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel
% 0.10/0.41 thf(fact_206_prod_Osplit__sel,axiom,
% 0.10/0.41 ! [P2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 0.10/0.41 ( ( P2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.10/0.41 = ( ( Prod
% 0.10/0.41 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 0.10/0.41 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % prod.split_sel
% 0.10/0.41 thf(fact_207_ssubst__Pair__rhs,axiom,
% 0.10/0.41 ! [R: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat,S3: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ R @ S2 ) @ R3 )
% 0.10/0.41 => ( ( S3 = S2 )
% 0.10/0.41 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ R @ S3 ) @ R3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ssubst_Pair_rhs
% 0.10/0.41 thf(fact_208_ssubst__Pair__rhs,axiom,
% 0.10/0.41 ! [R: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,S3: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S2 ) @ R3 )
% 0.10/0.41 => ( ( S3 = S2 )
% 0.10/0.41 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S3 ) @ R3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ssubst_Pair_rhs
% 0.10/0.41 thf(fact_209_ssubst__Pair__rhs,axiom,
% 0.10/0.41 ! [R: nat,S2: num,R3: set_Pr6200539531224447659at_num,S3: num] :
% 0.10/0.41 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ R @ S2 ) @ R3 )
% 0.10/0.41 => ( ( S3 = S2 )
% 0.10/0.41 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ R @ S3 ) @ R3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ssubst_Pair_rhs
% 0.10/0.41 thf(fact_210_ssubst__Pair__rhs,axiom,
% 0.10/0.41 ! [R: nat,S2: nat,R3: set_Pr1261947904930325089at_nat,S3: nat] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S2 ) @ R3 )
% 0.10/0.41 => ( ( S3 = S2 )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S3 ) @ R3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ssubst_Pair_rhs
% 0.10/0.41 thf(fact_211_ssubst__Pair__rhs,axiom,
% 0.10/0.41 ! [R: int,S2: int,R3: set_Pr958786334691620121nt_int,S3: int] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S2 ) @ R3 )
% 0.10/0.41 => ( ( S3 = S2 )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S3 ) @ R3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % ssubst_Pair_rhs
% 0.10/0.41 thf(fact_212_effect__raiseE,axiom,
% 0.10/0.41 ! [X2: literal,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ~ ( heap_effect_ref_a @ ( heap_raise_ref_a @ X2 ) @ H @ H2 @ R ) ).
% 0.10/0.41
% 0.10/0.41 % effect_raiseE
% 0.10/0.41 thf(fact_213_effect__updateE,axiom,
% 0.10/0.41 ! [R2: ref_a,V: a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: product_unit] :
% 0.10/0.41 ( ( heap_e2830298082929533060t_unit @ ( update_a @ R2 @ V ) @ H @ H2 @ R )
% 0.10/0.41 => ( H2
% 0.10/0.41 = ( set_a @ R2 @ V @ H ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_updateE
% 0.10/0.41 thf(fact_214_curryI,axiom,
% 0.10/0.41 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( F @ ( produc9060074326276436823at_nat @ A @ B ) )
% 0.10/0.41 => ( produc447603880154497357_nat_o @ F @ A @ B ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryI
% 0.10/0.41 thf(fact_215_curryI,axiom,
% 0.10/0.41 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( F @ ( produc2922128104949294807at_nat @ A @ B ) )
% 0.10/0.41 => ( produc7820828192191229133_nat_o @ F @ A @ B ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryI
% 0.10/0.41 thf(fact_216_curryI,axiom,
% 0.10/0.41 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 0.10/0.41 ( ( F @ ( product_Pair_nat_num @ A @ B ) )
% 0.10/0.41 => ( produc156083480235303841_num_o @ F @ A @ B ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryI
% 0.10/0.41 thf(fact_217_curryI,axiom,
% 0.10/0.41 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.10/0.41 ( ( F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.10/0.41 => ( produc1310100445399344235_nat_o @ F @ A @ B ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryI
% 0.10/0.41 thf(fact_218_curryI,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 0.10/0.41 ( ( F @ ( product_Pair_int_int @ A @ B ) )
% 0.10/0.41 => ( produc175634133007206835_int_o @ F @ A @ B ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryI
% 0.10/0.41 thf(fact_219_case__prod__curry,axiom,
% 0.10/0.41 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.10/0.41 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_curry
% 0.10/0.41 thf(fact_220_case__prod__curry,axiom,
% 0.10/0.41 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.10/0.41 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_curry
% 0.10/0.41 thf(fact_221_case__prod__curry,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > product_prod_int_int] :
% 0.10/0.41 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_curry
% 0.10/0.41 thf(fact_222_case__prod__curry,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > $o] :
% 0.10/0.41 ( ( produc4947309494688390418_int_o @ ( produc175634133007206835_int_o @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_curry
% 0.10/0.41 thf(fact_223_case__prod__curry,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > int] :
% 0.10/0.41 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_curry
% 0.10/0.41 thf(fact_224_curry__case__prod,axiom,
% 0.10/0.41 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.10/0.41 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % curry_case_prod
% 0.10/0.41 thf(fact_225_curry__case__prod,axiom,
% 0.10/0.41 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 0.10/0.41 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % curry_case_prod
% 0.10/0.41 thf(fact_226_curry__case__prod,axiom,
% 0.10/0.41 ! [F: int > int > product_prod_int_int] :
% 0.10/0.41 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % curry_case_prod
% 0.10/0.41 thf(fact_227_curry__case__prod,axiom,
% 0.10/0.41 ! [F: int > int > $o] :
% 0.10/0.41 ( ( produc175634133007206835_int_o @ ( produc4947309494688390418_int_o @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % curry_case_prod
% 0.10/0.41 thf(fact_228_curry__case__prod,axiom,
% 0.10/0.41 ! [F: int > int > int] :
% 0.10/0.41 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 0.10/0.41 = F ) ).
% 0.10/0.41
% 0.10/0.41 % curry_case_prod
% 0.10/0.41 thf(fact_229_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: $o,C: nat > num > set_o,P: product_prod_nat_num] :
% 0.10/0.41 ( ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: num] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_num @ X @ Y ) )
% 0.10/0.41 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_230_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: nat,C: nat > num > set_nat,P: product_prod_nat_num] :
% 0.10/0.41 ( ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: num] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_num @ X @ Y ) )
% 0.10/0.41 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_231_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: int,C: nat > num > set_int,P: product_prod_nat_num] :
% 0.10/0.41 ( ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: num] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_num @ X @ Y ) )
% 0.10/0.41 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_232_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: $o,C: nat > nat > set_o,P: product_prod_nat_nat] :
% 0.10/0.41 ( ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: nat] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.10/0.41 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_233_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: nat,C: nat > nat > set_nat,P: product_prod_nat_nat] :
% 0.10/0.41 ( ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: nat] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.10/0.41 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_234_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: int,C: nat > nat > set_int,P: product_prod_nat_nat] :
% 0.10/0.41 ( ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: nat] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.10/0.41 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_235_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: $o,C: int > int > set_o,P: product_prod_int_int] :
% 0.10/0.41 ( ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ P ) )
% 0.10/0.41 => ~ ! [X: int,Y: int] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_int_int @ X @ Y ) )
% 0.10/0.41 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_236_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: nat,C: int > int > set_nat,P: product_prod_int_int] :
% 0.10/0.41 ( ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P ) )
% 0.10/0.41 => ~ ! [X: int,Y: int] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_int_int @ X @ Y ) )
% 0.10/0.41 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_237_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: int,C: int > int > set_int,P: product_prod_int_int] :
% 0.10/0.41 ( ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P ) )
% 0.10/0.41 => ~ ! [X: int,Y: int] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_int_int @ X @ Y ) )
% 0.10/0.41 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_238_mem__case__prodE,axiom,
% 0.10/0.41 ! [Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat,P: product_prod_nat_num] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ P ) )
% 0.10/0.41 => ~ ! [X: nat,Y: num] :
% 0.10/0.41 ( ( P
% 0.10/0.41 = ( product_Pair_nat_num @ X @ Y ) )
% 0.10/0.41 => ~ ( member8440522571783428010at_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % mem_case_prodE
% 0.10/0.41 thf(fact_239_old_Oprod_Ocase,axiom,
% 0.10/0.41 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 0.10/0.41 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.10/0.41 = ( F @ X1 @ X22 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.case
% 0.10/0.41 thf(fact_240_old_Oprod_Ocase,axiom,
% 0.10/0.41 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 0.10/0.41 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.10/0.41 = ( F @ X1 @ X22 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.case
% 0.10/0.41 thf(fact_241_old_Oprod_Ocase,axiom,
% 0.10/0.41 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 0.10/0.41 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.10/0.41 = ( F @ X1 @ X22 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.case
% 0.10/0.41 thf(fact_242_old_Oprod_Ocase,axiom,
% 0.10/0.41 ! [F: int > int > $o,X1: int,X22: int] :
% 0.10/0.41 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.10/0.41 = ( F @ X1 @ X22 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.case
% 0.10/0.41 thf(fact_243_old_Oprod_Ocase,axiom,
% 0.10/0.41 ! [F: int > int > int,X1: int,X22: int] :
% 0.10/0.41 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.10/0.41 = ( F @ X1 @ X22 ) ) ).
% 0.10/0.41
% 0.10/0.41 % old.prod.case
% 0.10/0.41 thf(fact_244_curryD,axiom,
% 0.10/0.41 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( produc447603880154497357_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryD
% 0.10/0.41 thf(fact_245_curryD,axiom,
% 0.10/0.41 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( produc7820828192191229133_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryD
% 0.10/0.41 thf(fact_246_curryD,axiom,
% 0.10/0.41 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 0.10/0.41 ( ( produc156083480235303841_num_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryD
% 0.10/0.41 thf(fact_247_curryD,axiom,
% 0.10/0.41 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.10/0.41 ( ( produc1310100445399344235_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryD
% 0.10/0.41 thf(fact_248_curryD,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 0.10/0.41 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryD
% 0.10/0.41 thf(fact_249_curryE,axiom,
% 0.10/0.41 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( produc447603880154497357_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryE
% 0.10/0.41 thf(fact_250_curryE,axiom,
% 0.10/0.41 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( produc7820828192191229133_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryE
% 0.10/0.41 thf(fact_251_curryE,axiom,
% 0.10/0.41 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 0.10/0.41 ( ( produc156083480235303841_num_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryE
% 0.10/0.41 thf(fact_252_curryE,axiom,
% 0.10/0.41 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.10/0.41 ( ( produc1310100445399344235_nat_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryE
% 0.10/0.41 thf(fact_253_curryE,axiom,
% 0.10/0.41 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 0.10/0.41 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 0.10/0.41 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % curryE
% 0.10/0.41 thf(fact_254_Product__Type_OCollect__case__prodD,axiom,
% 0.10/0.41 ! [X2: produc3843707927480180839at_nat,A4: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ X2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ A4 ) ) )
% 0.10/0.41 => ( A4 @ ( produc6011863565407846595at_nat @ X2 ) @ ( produc2937545259423399429at_nat @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Product_Type.Collect_case_prodD
% 0.10/0.41 thf(fact_255_Product__Type_OCollect__case__prodD,axiom,
% 0.10/0.41 ! [X2: product_prod_nat_nat,A4: nat > nat > $o] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ X2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A4 ) ) )
% 0.10/0.41 => ( A4 @ ( product_fst_nat_nat @ X2 ) @ ( product_snd_nat_nat @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Product_Type.Collect_case_prodD
% 0.10/0.41 thf(fact_256_Product__Type_OCollect__case__prodD,axiom,
% 0.10/0.41 ! [X2: produc7812382424243267045t_unit,A4: ref_a > heap_e7401611519738050253t_unit > $o] :
% 0.10/0.41 ( ( member7849944260330398460t_unit @ X2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ A4 ) ) )
% 0.10/0.41 => ( A4 @ ( produc473321116828791851t_unit @ X2 ) @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Product_Type.Collect_case_prodD
% 0.10/0.41 thf(fact_257_Product__Type_OCollect__case__prodD,axiom,
% 0.10/0.41 ! [X2: product_prod_int_int,A4: int > int > $o] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ X2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) )
% 0.10/0.41 => ( A4 @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Product_Type.Collect_case_prodD
% 0.10/0.41 thf(fact_258_effect__returnI,axiom,
% 0.10/0.41 ! [H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: ref_a] :
% 0.10/0.41 ( ( H = H2 )
% 0.10/0.41 => ( heap_effect_ref_a @ ( heap_return_ref_a @ X2 ) @ H @ H2 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_returnI
% 0.10/0.41 thf(fact_259_effect__returnE,axiom,
% 0.10/0.41 ! [X2: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( heap_return_ref_a @ X2 ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( R = X2 )
% 0.10/0.41 => ( H2 != H ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_returnE
% 0.10/0.41 thf(fact_260_split__beta,axiom,
% 0.10/0.41 ( produc27273713700761075at_nat
% 0.10/0.41 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod3 ) @ ( product_snd_nat_nat @ Prod3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_beta
% 0.10/0.41 thf(fact_261_split__beta,axiom,
% 0.10/0.41 ( produc8739625826339149834_nat_o
% 0.10/0.41 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,Prod3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod3 ) @ ( product_snd_nat_nat @ Prod3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_beta
% 0.10/0.41 thf(fact_262_split__beta,axiom,
% 0.10/0.41 ( produc4245557441103728435nt_int
% 0.10/0.41 = ( ^ [F2: int > int > product_prod_int_int,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_beta
% 0.10/0.41 thf(fact_263_split__beta,axiom,
% 0.10/0.41 ( produc4947309494688390418_int_o
% 0.10/0.41 = ( ^ [F2: int > int > $o,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_beta
% 0.10/0.41 thf(fact_264_split__beta,axiom,
% 0.10/0.41 ( produc8211389475949308722nt_int
% 0.10/0.41 = ( ^ [F2: int > int > int,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_beta
% 0.10/0.41 thf(fact_265_case__prod__beta,axiom,
% 0.10/0.41 ( produc27273713700761075at_nat
% 0.10/0.41 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_beta
% 0.10/0.41 thf(fact_266_case__prod__beta,axiom,
% 0.10/0.41 ( produc8739625826339149834_nat_o
% 0.10/0.41 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_beta
% 0.10/0.41 thf(fact_267_case__prod__beta,axiom,
% 0.10/0.41 ( produc4245557441103728435nt_int
% 0.10/0.41 = ( ^ [F2: int > int > product_prod_int_int,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_beta
% 0.10/0.41 thf(fact_268_case__prod__beta,axiom,
% 0.10/0.41 ( produc4947309494688390418_int_o
% 0.10/0.41 = ( ^ [F2: int > int > $o,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_beta
% 0.10/0.41 thf(fact_269_case__prod__beta,axiom,
% 0.10/0.41 ( produc8211389475949308722nt_int
% 0.10/0.41 = ( ^ [F2: int > int > int,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % case_prod_beta
% 0.10/0.41 thf(fact_270_internal__case__prod__def,axiom,
% 0.10/0.41 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 0.10/0.41
% 0.10/0.41 % internal_case_prod_def
% 0.10/0.41 thf(fact_271_internal__case__prod__def,axiom,
% 0.10/0.41 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 0.10/0.41
% 0.10/0.41 % internal_case_prod_def
% 0.10/0.41 thf(fact_272_internal__case__prod__def,axiom,
% 0.10/0.41 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 0.10/0.41
% 0.10/0.41 % internal_case_prod_def
% 0.10/0.41 thf(fact_273_internal__case__prod__def,axiom,
% 0.10/0.41 produc8005341501107743676_int_o = produc4947309494688390418_int_o ).
% 0.10/0.41
% 0.10/0.41 % internal_case_prod_def
% 0.10/0.41 thf(fact_274_internal__case__prod__def,axiom,
% 0.10/0.41 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 0.10/0.41
% 0.10/0.41 % internal_case_prod_def
% 0.10/0.41 thf(fact_275_effect__updateI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,R: ref_a,V: a,H: heap_e7401611519738050253t_unit,X2: product_unit] :
% 0.10/0.41 ( ( H2
% 0.10/0.41 = ( set_a @ R @ V @ H ) )
% 0.10/0.41 => ( heap_e2830298082929533060t_unit @ ( update_a @ R @ V ) @ H @ H2 @ X2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_updateI
% 0.10/0.41 thf(fact_276_split__cong,axiom,
% 0.10/0.41 ! [Q: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P: product_prod_nat_nat] :
% 0.10/0.41 ( ! [X: nat,Y: nat] :
% 0.10/0.41 ( ( ( product_Pair_nat_nat @ X @ Y )
% 0.10/0.41 = Q )
% 0.10/0.41 => ( ( F @ X @ Y )
% 0.10/0.41 = ( G @ X @ Y ) ) )
% 0.10/0.41 => ( ( P = Q )
% 0.10/0.41 => ( ( produc27273713700761075at_nat @ F @ P )
% 0.10/0.41 = ( produc27273713700761075at_nat @ G @ Q ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_cong
% 0.10/0.41 thf(fact_277_split__cong,axiom,
% 0.10/0.41 ! [Q: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 0.10/0.41 ( ! [X: nat,Y: nat] :
% 0.10/0.41 ( ( ( product_Pair_nat_nat @ X @ Y )
% 0.10/0.41 = Q )
% 0.10/0.41 => ( ( F @ X @ Y )
% 0.10/0.41 = ( G @ X @ Y ) ) )
% 0.10/0.41 => ( ( P = Q )
% 0.10/0.41 => ( ( produc8739625826339149834_nat_o @ F @ P )
% 0.10/0.41 = ( produc8739625826339149834_nat_o @ G @ Q ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_cong
% 0.10/0.41 thf(fact_278_split__cong,axiom,
% 0.10/0.41 ! [Q: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P: product_prod_int_int] :
% 0.10/0.41 ( ! [X: int,Y: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ X @ Y )
% 0.10/0.41 = Q )
% 0.10/0.41 => ( ( F @ X @ Y )
% 0.10/0.41 = ( G @ X @ Y ) ) )
% 0.10/0.41 => ( ( P = Q )
% 0.10/0.41 => ( ( produc4245557441103728435nt_int @ F @ P )
% 0.10/0.41 = ( produc4245557441103728435nt_int @ G @ Q ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_cong
% 0.10/0.41 thf(fact_279_split__cong,axiom,
% 0.10/0.41 ! [Q: product_prod_int_int,F: int > int > $o,G: int > int > $o,P: product_prod_int_int] :
% 0.10/0.41 ( ! [X: int,Y: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ X @ Y )
% 0.10/0.41 = Q )
% 0.10/0.41 => ( ( F @ X @ Y )
% 0.10/0.41 = ( G @ X @ Y ) ) )
% 0.10/0.41 => ( ( P = Q )
% 0.10/0.41 => ( ( produc4947309494688390418_int_o @ F @ P )
% 0.10/0.41 = ( produc4947309494688390418_int_o @ G @ Q ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_cong
% 0.10/0.41 thf(fact_280_split__cong,axiom,
% 0.10/0.41 ! [Q: product_prod_int_int,F: int > int > int,G: int > int > int,P: product_prod_int_int] :
% 0.10/0.41 ( ! [X: int,Y: int] :
% 0.10/0.41 ( ( ( product_Pair_int_int @ X @ Y )
% 0.10/0.41 = Q )
% 0.10/0.41 => ( ( F @ X @ Y )
% 0.10/0.41 = ( G @ X @ Y ) ) )
% 0.10/0.41 => ( ( P = Q )
% 0.10/0.41 => ( ( produc8211389475949308722nt_int @ F @ P )
% 0.10/0.41 = ( produc8211389475949308722nt_int @ G @ Q ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % split_cong
% 0.10/0.41 thf(fact_281_csquare__fstOp__sndOp,axiom,
% 0.10/0.41 ! [F: ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > $o,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] : ( bNF_cs7194553038297458973at_int @ ( collec2851339944984316337at_int @ ( F @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) @ produc6408287024330202629at_nat @ produc4619704898428564714at_int @ ( bNF_fs6342258632037972510at_int @ P2 @ Q2 ) @ ( bNF_sn649997494946348640at_int @ P2 @ Q2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % csquare_fstOp_sndOp
% 0.10/0.41 thf(fact_282_csquare__fstOp__sndOp,axiom,
% 0.10/0.41 ! [F: ( int > code_integer > $o ) > produc2963269191615333738nteger > $o,P2: int > int > $o,Q2: int > code_integer > $o] : ( bNF_cs4943907971211754724nteger @ ( collec7215431352809750357nteger @ ( F @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) @ product_snd_int_int @ produc45500017171379470nteger @ ( bNF_fs4543836202474805097nteger @ P2 @ Q2 ) @ ( bNF_sn8000174127721201323nteger @ P2 @ Q2 ) ) ).
% 0.10/0.41
% 0.10/0.41 % csquare_fstOp_sndOp
% 0.10/0.41 thf(fact_283_effect__tapI,axiom,
% 0.10/0.41 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,R: ref_a,F: heap_e7401611519738050253t_unit > ref_a] :
% 0.10/0.41 ( ( H2 = H )
% 0.10/0.41 => ( ( R
% 0.10/0.41 = ( F @ H ) )
% 0.10/0.41 => ( heap_effect_ref_a @ ( heap_tap_ref_a @ F ) @ H @ H2 @ R ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_tapI
% 0.10/0.41 thf(fact_284_effect__tapE,axiom,
% 0.10/0.41 ! [F: heap_e7401611519738050253t_unit > ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( heap_tap_ref_a @ F ) @ H @ H2 @ R )
% 0.10/0.41 => ~ ( ( H2 = H )
% 0.10/0.41 => ( R
% 0.10/0.41 != ( F @ H ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_tapE
% 0.10/0.41 thf(fact_285_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: num,X2: nat,A4: set_Pr6200539531224447659at_num] :
% 0.10/0.41 ( ( member6570852975090897396um_nat @ ( product_Pair_num_nat @ Y3 @ X2 ) @ ( image_2347970371937200581um_nat @ product_swap_nat_num @ A4 ) )
% 0.10/0.41 = ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_286_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,A4: set_Pr7459493094073627847at_nat] :
% 0.10/0.41 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y3 @ X2 ) @ ( image_3313167189156628421at_nat @ produc5396952528824381687at_nat @ A4 ) )
% 0.10/0.41 = ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_287_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X2 ) @ ( image_960689587819713477at_nat @ produc3946833401584108663at_nat @ A4 ) )
% 0.10/0.41 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_288_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: nat,X2: num,A4: set_Pr3280342998896498603um_nat] :
% 0.10/0.41 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ Y3 @ X2 ) @ ( image_7762062833379733445at_num @ product_swap_num_nat @ A4 ) )
% 0.10/0.41 = ( member6570852975090897396um_nat @ ( product_Pair_num_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_289_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: nat,X2: nat,A4: set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ ( image_5168914502847457605at_nat @ product_swap_nat_nat @ A4 ) )
% 0.10/0.41 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_290_pair__in__swap__image,axiom,
% 0.10/0.41 ! [Y3: int,X2: int,A4: set_Pr958786334691620121nt_int] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ ( image_2653370878348428101nt_int @ product_swap_int_int @ A4 ) )
% 0.10/0.41 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ A4 ) ) ).
% 0.10/0.41
% 0.10/0.41 % pair_in_swap_image
% 0.10/0.41 thf(fact_291_snd__sndOp,axiom,
% 0.10/0.41 ! [P2: ref_a > ref_a > $o,Q2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 0.10/0.41 ( produc1126150082675451753t_unit
% 0.10/0.41 = ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( bNF_sn8323453914685745821t_unit @ P2 @ Q2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_sndOp
% 0.10/0.41 thf(fact_292_comp__cong,axiom,
% 0.10/0.41 ! [F: $o > $o,G: nat > $o,X2: nat,F3: $o > $o,G2: nat > $o,X3: nat] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_o_o_nat @ F @ G @ X2 )
% 0.10/0.41 = ( comp_o_o_nat @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_293_comp__cong,axiom,
% 0.10/0.41 ! [F: nat > num,G: int > nat,X2: int,F3: nat > num,G2: int > nat,X3: int] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_nat_num_int @ F @ G @ X2 )
% 0.10/0.41 = ( comp_nat_num_int @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_294_comp__cong,axiom,
% 0.10/0.41 ! [F: nat > nat,G: nat > nat,X2: nat,F3: nat > nat,G2: nat > nat,X3: nat] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 0.10/0.41 = ( comp_nat_nat_nat @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_295_comp__cong,axiom,
% 0.10/0.41 ! [F: nat > nat,G: nat > nat,X2: nat,F3: int > nat,G2: int > int,X3: int] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 0.10/0.41 = ( comp_int_nat_int @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_296_comp__cong,axiom,
% 0.10/0.41 ! [F: int > nat,G: int > int,X2: int,F3: nat > nat,G2: nat > nat,X3: nat] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 0.10/0.41 = ( comp_nat_nat_nat @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_297_comp__cong,axiom,
% 0.10/0.41 ! [F: int > nat,G: int > int,X2: int,F3: int > nat,G2: int > int,X3: int] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 0.10/0.41 = ( comp_int_nat_int @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_298_comp__cong,axiom,
% 0.10/0.41 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( F3 @ ( G2 @ X3 ) ) )
% 0.10/0.41 => ( ( comp_C8797469213163452608nteger @ F @ G @ X2 )
% 0.10/0.41 = ( comp_C8797469213163452608nteger @ F3 @ G2 @ X3 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_cong
% 0.10/0.41 thf(fact_299_comp__apply__eq,axiom,
% 0.10/0.41 ! [F: $o > $o,G: nat > $o,X2: nat,H: $o > $o,K: nat > $o] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( H @ ( K @ X2 ) ) )
% 0.10/0.41 => ( ( comp_o_o_nat @ F @ G @ X2 )
% 0.10/0.41 = ( comp_o_o_nat @ H @ K @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply_eq
% 0.10/0.41 thf(fact_300_comp__apply__eq,axiom,
% 0.10/0.41 ! [F: nat > num,G: int > nat,X2: int,H: nat > num,K: int > nat] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( H @ ( K @ X2 ) ) )
% 0.10/0.41 => ( ( comp_nat_num_int @ F @ G @ X2 )
% 0.10/0.41 = ( comp_nat_num_int @ H @ K @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply_eq
% 0.10/0.41 thf(fact_301_comp__apply__eq,axiom,
% 0.10/0.41 ! [F: nat > nat,G: nat > nat,X2: nat,H: nat > nat,K: nat > nat] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( H @ ( K @ X2 ) ) )
% 0.10/0.41 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 0.10/0.41 = ( comp_nat_nat_nat @ H @ K @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply_eq
% 0.10/0.41 thf(fact_302_comp__apply__eq,axiom,
% 0.10/0.41 ! [F: int > nat,G: int > int,X2: int,H: int > nat,K: int > int] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( H @ ( K @ X2 ) ) )
% 0.10/0.41 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 0.10/0.41 = ( comp_int_nat_int @ H @ K @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply_eq
% 0.10/0.41 thf(fact_303_comp__apply__eq,axiom,
% 0.10/0.41 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,H: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 0.10/0.41 ( ( ( F @ ( G @ X2 ) )
% 0.10/0.41 = ( H @ ( K @ X2 ) ) )
% 0.10/0.41 => ( ( comp_C8797469213163452608nteger @ F @ G @ X2 )
% 0.10/0.41 = ( comp_C8797469213163452608nteger @ H @ K @ X2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply_eq
% 0.10/0.41 thf(fact_304_pick__middlep,axiom,
% 0.10/0.41 ! [P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o,A: product_prod_nat_nat,C: int] :
% 0.10/0.41 ( ( relcom8911704206367525917at_int @ P2 @ Q2 @ A @ C )
% 0.10/0.41 => ( ( P2 @ A @ ( bNF_pi770922605693484880at_int @ P2 @ Q2 @ A @ C ) )
% 0.10/0.41 & ( Q2 @ ( bNF_pi770922605693484880at_int @ P2 @ Q2 @ A @ C ) @ C ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % pick_middlep
% 0.10/0.41 thf(fact_305_pick__middlep,axiom,
% 0.10/0.41 ! [P2: int > int > $o,Q2: int > code_integer > $o,A: int,C: code_integer] :
% 0.10/0.41 ( ( relcom967497705283160040nteger @ P2 @ Q2 @ A @ C )
% 0.10/0.41 => ( ( P2 @ A @ ( bNF_pi4515785505327359899nteger @ P2 @ Q2 @ A @ C ) )
% 0.10/0.41 & ( Q2 @ ( bNF_pi4515785505327359899nteger @ P2 @ Q2 @ A @ C ) @ C ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % pick_middlep
% 0.10/0.41 thf(fact_306_sndOp__in,axiom,
% 0.10/0.41 ! [Ac: produc3843707927480180839at_nat,P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Q2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ Ac @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( relcom8363394528208558896at_nat @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8757157785044589968at_nat @ ( bNF_sn1857951156667551021at_nat @ P2 @ Q2 @ Ac ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ Q2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndOp_in
% 0.10/0.41 thf(fact_307_sndOp__in,axiom,
% 0.10/0.41 ! [Ac: product_prod_nat_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ Ac @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( bNF_sn8916957246138178918at_nat @ P2 @ Q2 @ Ac ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndOp_in
% 0.10/0.41 thf(fact_308_sndOp__in,axiom,
% 0.10/0.41 ! [Ac: produc4196048018000912732at_int,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] :
% 0.10/0.41 ( ( member8394280151737582451at_int @ Ac @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8394280151737582451at_int @ ( bNF_sn649997494946348640at_int @ P2 @ Q2 @ Ac ) @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ Q2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndOp_in
% 0.10/0.41 thf(fact_309_sndOp__in,axiom,
% 0.10/0.41 ! [Ac: produc2963269191615333738nteger,P2: int > int > $o,Q2: int > code_integer > $o] :
% 0.10/0.41 ( ( member4345257455949424659nteger @ Ac @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member4345257455949424659nteger @ ( bNF_sn8000174127721201323nteger @ P2 @ Q2 @ Ac ) @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ Q2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndOp_in
% 0.10/0.41 thf(fact_310_sndOp__in,axiom,
% 0.10/0.41 ! [Ac: product_prod_int_int,P2: int > int > $o,Q2: int > int > $o] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ Ac @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( relcompp_int_int_int @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( bNF_sn1062102010912252026nt_int @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % sndOp_in
% 0.10/0.41 thf(fact_311_fstOp__in,axiom,
% 0.10/0.41 ! [Ac: produc3843707927480180839at_nat,P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Q2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ Ac @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( relcom8363394528208558896at_nat @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8757157785044589968at_nat @ ( bNF_fs1946732770515719151at_nat @ P2 @ Q2 @ Ac ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ P2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstOp_in
% 0.10/0.41 thf(fact_312_fstOp__in,axiom,
% 0.10/0.41 ! [Ac: product_prod_nat_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ Ac @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8440522571783428010at_nat @ ( bNF_fs6799373675401686564at_nat @ P2 @ Q2 @ Ac ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstOp_in
% 0.10/0.41 thf(fact_313_fstOp__in,axiom,
% 0.10/0.41 ! [Ac: produc4196048018000912732at_int,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] :
% 0.10/0.41 ( ( member8394280151737582451at_int @ Ac @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member8206827879206165904at_nat @ ( bNF_fs6342258632037972510at_int @ P2 @ Q2 @ Ac ) @ ( collec7088162979684241874at_nat @ ( produc6590410687421337004_nat_o @ P2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstOp_in
% 0.10/0.41 thf(fact_314_fstOp__in,axiom,
% 0.10/0.41 ! [Ac: produc2963269191615333738nteger,P2: int > int > $o,Q2: int > code_integer > $o] :
% 0.10/0.41 ( ( member4345257455949424659nteger @ Ac @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( bNF_fs4543836202474805097nteger @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstOp_in
% 0.10/0.41 thf(fact_315_fstOp__in,axiom,
% 0.10/0.41 ! [Ac: product_prod_int_int,P2: int > int > $o,Q2: int > int > $o] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ Ac @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( relcompp_int_int_int @ P2 @ Q2 ) ) ) )
% 0.10/0.41 => ( member5262025264175285858nt_int @ ( bNF_fs8167890477030535480nt_int @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fstOp_in
% 0.10/0.41 thf(fact_316_effect__bindE,axiom,
% 0.10/0.41 ! [F: heap_Heap_ref_a,G: ref_a > heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ ( heap_b146640354529102224_ref_a @ F @ G ) @ H @ H3 @ R2 )
% 0.10/0.41 => ~ ! [H4: heap_e7401611519738050253t_unit,R4: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ F @ H @ H4 @ R4 )
% 0.10/0.41 => ~ ( heap_effect_ref_a @ ( G @ R4 ) @ H4 @ H3 @ R2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_bindE
% 0.10/0.41 thf(fact_317_effect__bindI,axiom,
% 0.10/0.41 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a,G: ref_a > heap_Heap_ref_a,H3: heap_e7401611519738050253t_unit,R2: ref_a] :
% 0.10/0.41 ( ( heap_effect_ref_a @ F @ H @ H2 @ R )
% 0.10/0.41 => ( ( heap_effect_ref_a @ ( G @ R ) @ H2 @ H3 @ R2 )
% 0.10/0.41 => ( heap_effect_ref_a @ ( heap_b146640354529102224_ref_a @ F @ G ) @ H @ H3 @ R2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % effect_bindI
% 0.10/0.41 thf(fact_318_fst__fstOp,axiom,
% 0.10/0.41 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o,Q2: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o] :
% 0.10/0.41 ( produc473321116828791851t_unit
% 0.10/0.41 = ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( bNF_fs409234558581511823t_unit @ P2 @ Q2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_fstOp
% 0.10/0.41 thf(fact_319_comp__apply,axiom,
% 0.10/0.41 ( comp_o_o_nat
% 0.10/0.41 = ( ^ [F2: $o > $o,G3: nat > $o,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply
% 0.10/0.41 thf(fact_320_comp__apply,axiom,
% 0.10/0.41 ( comp_nat_num_int
% 0.10/0.41 = ( ^ [F2: nat > num,G3: int > nat,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply
% 0.10/0.41 thf(fact_321_comp__apply,axiom,
% 0.10/0.41 ( comp_nat_nat_nat
% 0.10/0.41 = ( ^ [F2: nat > nat,G3: nat > nat,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply
% 0.10/0.41 thf(fact_322_comp__apply,axiom,
% 0.10/0.41 ( comp_int_nat_int
% 0.10/0.41 = ( ^ [F2: int > nat,G3: int > int,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply
% 0.10/0.41 thf(fact_323_comp__apply,axiom,
% 0.10/0.41 ( comp_C8797469213163452608nteger
% 0.10/0.41 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X4: code_integer] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % comp_apply
% 0.10/0.41 thf(fact_324_image__eqI,axiom,
% 0.10/0.41 ! [B: $o,F: $o > $o,X2: $o,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_325_image__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: $o > nat,X2: $o,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member_nat @ B @ ( image_o_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_326_image__eqI,axiom,
% 0.10/0.41 ! [B: int,F: $o > int,X2: $o,A4: set_o] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_o @ X2 @ A4 )
% 0.10/0.41 => ( member_int @ B @ ( image_o_int @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_327_image__eqI,axiom,
% 0.10/0.41 ! [B: rat,F: nat > rat,X2: nat,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_328_image__eqI,axiom,
% 0.10/0.41 ! [B: $o,F: nat > $o,X2: nat,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member_o @ B @ ( image_nat_o @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_329_image__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: nat > nat,X2: nat,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_330_image__eqI,axiom,
% 0.10/0.41 ! [B: int,F: nat > int,X2: nat,A4: set_nat] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_nat @ X2 @ A4 )
% 0.10/0.41 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_331_image__eqI,axiom,
% 0.10/0.41 ! [B: $o,F: int > $o,X2: int,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member_o @ B @ ( image_int_o @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_332_image__eqI,axiom,
% 0.10/0.41 ! [B: nat,F: int > nat,X2: int,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member_nat @ B @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_333_image__eqI,axiom,
% 0.10/0.41 ! [B: int,F: int > int,X2: int,A4: set_int] :
% 0.10/0.41 ( ( B
% 0.10/0.41 = ( F @ X2 ) )
% 0.10/0.41 => ( ( member_int @ X2 @ A4 )
% 0.10/0.41 => ( member_int @ B @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eqI
% 0.10/0.41 thf(fact_334_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_335_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_rat > rat,G: rat > rat,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_rat_rat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_rat @ ( comp_rat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_336_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_nat > nat,G: rat > nat,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_337_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_int > int,G: rat > int,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_338_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_rat > rat,G: int > rat,F: nat > int,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_int_rat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_rat @ ( comp_int_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_339_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_num > num,G: nat > num,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Inf @ ( image_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_340_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_rat > rat,G: nat > rat,F: nat > nat,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_nat_rat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_rat @ ( comp_nat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_341_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_rat > rat,G: nat > rat,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Inf @ ( image_nat_rat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_int_rat @ ( comp_nat_rat_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_342_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
% 0.10/0.41 ( ( Inf @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_343_Inf_OINF__image,axiom,
% 0.10/0.41 ! [Inf: set_nat > nat,G: nat > nat,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Inf @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Inf @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Inf.INF_image
% 0.10/0.41 thf(fact_344_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_345_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_rat > rat,G: rat > rat,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_rat_rat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_rat @ ( comp_rat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_346_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_nat > nat,G: rat > nat,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_347_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_int > int,G: rat > int,F: nat > rat,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_348_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_rat > rat,G: int > rat,F: nat > int,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_int_rat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_rat @ ( comp_int_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_349_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_num > num,G: nat > num,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Sup @ ( image_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_350_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_rat > rat,G: nat > rat,F: nat > nat,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_nat_rat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_rat @ ( comp_nat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_351_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_rat > rat,G: nat > rat,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Sup @ ( image_nat_rat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_int_rat @ ( comp_nat_rat_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_352_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
% 0.10/0.41 ( ( Sup @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_353_Sup_OSUP__image,axiom,
% 0.10/0.41 ! [Sup: set_nat > nat,G: nat > nat,F: int > nat,A4: set_int] :
% 0.10/0.41 ( ( Sup @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.10/0.41 = ( Sup @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Sup.SUP_image
% 0.10/0.41 thf(fact_354_image__comp,axiom,
% 0.10/0.41 ! [F: $o > $o,G: nat > $o,R: set_nat] :
% 0.10/0.41 ( ( image_o_o @ F @ ( image_nat_o @ G @ R ) )
% 0.10/0.41 = ( image_nat_o @ ( comp_o_o_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_355_image__comp,axiom,
% 0.10/0.41 ! [F: rat > rat,G: nat > rat,R: set_nat] :
% 0.10/0.41 ( ( image_rat_rat @ F @ ( image_nat_rat @ G @ R ) )
% 0.10/0.41 = ( image_nat_rat @ ( comp_rat_rat_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_356_image__comp,axiom,
% 0.10/0.41 ! [F: rat > nat,G: nat > rat,R: set_nat] :
% 0.10/0.41 ( ( image_rat_nat @ F @ ( image_nat_rat @ G @ R ) )
% 0.10/0.41 = ( image_nat_nat @ ( comp_rat_nat_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_357_image__comp,axiom,
% 0.10/0.41 ! [F: rat > int,G: nat > rat,R: set_nat] :
% 0.10/0.41 ( ( image_rat_int @ F @ ( image_nat_rat @ G @ R ) )
% 0.10/0.41 = ( image_nat_int @ ( comp_rat_int_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_358_image__comp,axiom,
% 0.10/0.41 ! [F: int > rat,G: nat > int,R: set_nat] :
% 0.10/0.41 ( ( image_int_rat @ F @ ( image_nat_int @ G @ R ) )
% 0.10/0.41 = ( image_nat_rat @ ( comp_int_rat_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_359_image__comp,axiom,
% 0.10/0.41 ! [F: nat > num,G: int > nat,R: set_int] :
% 0.10/0.41 ( ( image_nat_num @ F @ ( image_int_nat @ G @ R ) )
% 0.10/0.41 = ( image_int_num @ ( comp_nat_num_int @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_360_image__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,G: nat > nat,R: set_nat] :
% 0.10/0.41 ( ( image_nat_rat @ F @ ( image_nat_nat @ G @ R ) )
% 0.10/0.41 = ( image_nat_rat @ ( comp_nat_rat_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_361_image__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,G: int > nat,R: set_int] :
% 0.10/0.41 ( ( image_nat_rat @ F @ ( image_int_nat @ G @ R ) )
% 0.10/0.41 = ( image_int_rat @ ( comp_nat_rat_int @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_362_image__comp,axiom,
% 0.10/0.41 ! [F: nat > nat,G: nat > nat,R: set_nat] :
% 0.10/0.41 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ R ) )
% 0.10/0.41 = ( image_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_363_image__comp,axiom,
% 0.10/0.41 ! [F: nat > nat,G: int > nat,R: set_int] :
% 0.10/0.41 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ R ) )
% 0.10/0.41 = ( image_int_nat @ ( comp_nat_nat_int @ F @ G ) @ R ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_comp
% 0.10/0.41 thf(fact_364_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat,H: $o > $o] :
% 0.10/0.41 ( ( ( image_nat_o @ F @ A4 )
% 0.10/0.41 = ( image_nat_o @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_o @ ( comp_o_o_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_o @ ( comp_o_o_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_365_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: int > rat,A4: set_int,G: nat > rat,B5: set_nat,H: rat > nat] :
% 0.10/0.41 ( ( ( image_int_rat @ F @ A4 )
% 0.10/0.41 = ( image_nat_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_int_nat @ ( comp_rat_nat_int @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_nat @ ( comp_rat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_366_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: int > rat,A4: set_int,G: nat > rat,B5: set_nat,H: rat > int] :
% 0.10/0.41 ( ( ( image_int_rat @ F @ A4 )
% 0.10/0.41 = ( image_nat_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_int_int @ ( comp_rat_int_int @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_int @ ( comp_rat_int_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_367_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,A4: set_nat,G: int > rat,B5: set_int,H: rat > nat] :
% 0.10/0.41 ( ( ( image_nat_rat @ F @ A4 )
% 0.10/0.41 = ( image_int_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_nat @ ( comp_rat_nat_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_int_nat @ ( comp_rat_nat_int @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_368_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,A4: set_nat,G: int > rat,B5: set_int,H: rat > int] :
% 0.10/0.41 ( ( ( image_nat_rat @ F @ A4 )
% 0.10/0.41 = ( image_int_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_int @ ( comp_rat_int_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_int_int @ ( comp_rat_int_int @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_369_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > rat] :
% 0.10/0.41 ( ( ( image_nat_rat @ F @ A4 )
% 0.10/0.41 = ( image_nat_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_rat @ ( comp_rat_rat_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_rat @ ( comp_rat_rat_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_370_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > nat] :
% 0.10/0.41 ( ( ( image_nat_rat @ F @ A4 )
% 0.10/0.41 = ( image_nat_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_nat @ ( comp_rat_nat_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_nat @ ( comp_rat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_371_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > int] :
% 0.10/0.41 ( ( ( image_nat_rat @ F @ A4 )
% 0.10/0.41 = ( image_nat_rat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_int @ ( comp_rat_int_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_int @ ( comp_rat_int_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_372_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > rat] :
% 0.10/0.41 ( ( ( image_nat_nat @ F @ A4 )
% 0.10/0.41 = ( image_nat_nat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_rat @ ( comp_nat_rat_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_rat @ ( comp_nat_rat_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_373_image__eq__imp__comp,axiom,
% 0.10/0.41 ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > nat] :
% 0.10/0.41 ( ( ( image_nat_nat @ F @ A4 )
% 0.10/0.41 = ( image_nat_nat @ G @ B5 ) )
% 0.10/0.41 => ( ( image_nat_nat @ ( comp_nat_nat_nat @ H @ F ) @ A4 )
% 0.10/0.41 = ( image_nat_nat @ ( comp_nat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % image_eq_imp_comp
% 0.10/0.41 thf(fact_374_snd__comp__apsnd,axiom,
% 0.10/0.41 ! [F: code_integer > code_integer] :
% 0.10/0.41 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F ) )
% 0.10/0.41 = ( comp_C1043215000170864188nteger @ F @ produc6174133586879617921nteger ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_comp_apsnd
% 0.10/0.41 thf(fact_375_snd__comp__apsnd,axiom,
% 0.10/0.41 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc3038839249364385243_ref_a @ F ) )
% 0.10/0.41 = ( comp_h4837689053573563144t_unit @ F @ produc1126150082675451753t_unit ) ) ).
% 0.10/0.41
% 0.10/0.41 % snd_comp_apsnd
% 0.10/0.41 thf(fact_376_fst__comp__apfst,axiom,
% 0.10/0.41 ! [F: ref_a > ref_a] :
% 0.10/0.41 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc4508741384315284437t_unit @ F ) )
% 0.10/0.41 = ( comp_r2143332150499412868t_unit @ F @ produc473321116828791851t_unit ) ) ).
% 0.10/0.41
% 0.10/0.41 % fst_comp_apfst
% 0.10/0.41 thf(fact_377_Collect__case__prod__Grp__eqD,axiom,
% 0.10/0.41 ! [Z2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.10/0.41 ( ( member8757157785044589968at_nat @ Z2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ F ) ) ) )
% 0.10/0.41 => ( ( comp_s7355055891894327172at_nat @ F @ produc6011863565407846595at_nat @ Z2 )
% 0.10/0.41 = ( produc2937545259423399429at_nat @ Z2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_case_prod_Grp_eqD
% 0.10/0.41 thf(fact_378_Collect__case__prod__Grp__eqD,axiom,
% 0.10/0.41 ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
% 0.10/0.41 ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
% 0.10/0.41 => ( ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat @ Z2 )
% 0.10/0.41 = ( product_snd_nat_nat @ Z2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_case_prod_Grp_eqD
% 0.10/0.41 thf(fact_379_Collect__case__prod__Grp__eqD,axiom,
% 0.10/0.41 ! [Z2: produc7812382424243267045t_unit,A4: set_ref_a,F: ref_a > heap_e7401611519738050253t_unit] :
% 0.10/0.41 ( ( member7849944260330398460t_unit @ Z2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_Gr6510375311308651680t_unit @ A4 @ F ) ) ) )
% 0.10/0.41 => ( ( comp_r3604920825623061426t_unit @ F @ produc473321116828791851t_unit @ Z2 )
% 0.10/0.41 = ( produc1126150082675451753t_unit @ Z2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_case_prod_Grp_eqD
% 0.10/0.41 thf(fact_380_Collect__case__prod__Grp__eqD,axiom,
% 0.10/0.41 ! [Z2: product_prod_int_int,A4: set_int,F: int > int] :
% 0.10/0.41 ( ( member5262025264175285858nt_int @ Z2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ F ) ) ) )
% 0.10/0.41 => ( ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int @ Z2 )
% 0.10/0.41 = ( product_snd_int_int @ Z2 ) ) ) ).
% 0.10/0.41
% 0.10/0.41 % Collect_case_prod_Grp_eqD
% 0.10/0.41 thf(fact_381_Collect__split__mono__strong,axiom,
% 0.10/0.41 ! [X5: set_nat,A4: set_Pr1261947904930325089at_nat,Y4: set_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 0.10/0.41 ( ( X5
% 0.10/0.41 = ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A4 ) )
% 0.10/0.41 => ( ( Y4
% 0.10/0.41 = ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A4 ) )
% 0.10/0.41 => ( ! [X: nat] :
% 0.10/0.41 ( ( member_nat @ X @ X5 )
% 0.10/0.42 => ! [Xa: nat] :
% 0.10/0.42 ( ( member_nat @ Xa @ Y4 )
% 0.10/0.42 => ( ( P2 @ X @ Xa )
% 0.10/0.42 => ( Q2 @ X @ Xa ) ) ) )
% 0.10/0.42 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) )
% 0.10/0.42 => ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q2 ) ) ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_split_mono_strong
% 0.10/0.42 thf(fact_382_Collect__split__mono__strong,axiom,
% 0.10/0.42 ! [X5: set_ref_a,A4: set_Pr1133966238863718811t_unit,Y4: set_he8644174446132254637t_unit,P2: ref_a > heap_e7401611519738050253t_unit > $o,Q2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 0.10/0.42 ( ( X5
% 0.10/0.42 = ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ A4 ) )
% 0.10/0.42 => ( ( Y4
% 0.10/0.42 = ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ A4 ) )
% 0.10/0.42 => ( ! [X: ref_a] :
% 0.10/0.42 ( ( member_ref_a @ X @ X5 )
% 0.10/0.42 => ! [Xa: heap_e7401611519738050253t_unit] :
% 0.10/0.42 ( ( member242389114213480694t_unit @ Xa @ Y4 )
% 0.10/0.42 => ( ( P2 @ X @ Xa )
% 0.10/0.42 => ( Q2 @ X @ Xa ) ) ) )
% 0.10/0.42 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ P2 ) ) )
% 0.10/0.42 => ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ Q2 ) ) ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_split_mono_strong
% 0.10/0.42 thf(fact_383_Collect__split__mono__strong,axiom,
% 0.10/0.42 ! [X5: set_int,A4: set_Pr958786334691620121nt_int,Y4: set_int,P2: int > int > $o,Q2: int > int > $o] :
% 0.10/0.42 ( ( X5
% 0.10/0.42 = ( image_5042161079198086560nt_int @ product_fst_int_int @ A4 ) )
% 0.10/0.42 => ( ( Y4
% 0.10/0.42 = ( image_5042161079198086560nt_int @ product_snd_int_int @ A4 ) )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ X5 )
% 0.10/0.42 => ! [Xa: int] :
% 0.10/0.42 ( ( member_int @ Xa @ Y4 )
% 0.10/0.42 => ( ( P2 @ X @ Xa )
% 0.10/0.42 => ( Q2 @ X @ Xa ) ) ) )
% 0.10/0.42 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) )
% 0.10/0.42 => ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q2 ) ) ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_split_mono_strong
% 0.10/0.42 thf(fact_384_snd__comp__map__prod,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 0.10/0.42 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc3456481717235892722t_unit @ F @ G ) )
% 0.10/0.42 = ( comp_h4837689053573563144t_unit @ G @ produc1126150082675451753t_unit ) ) ).
% 0.10/0.42
% 0.10/0.42 % snd_comp_map_prod
% 0.10/0.42 thf(fact_385_fst__comp__map__prod,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 0.10/0.42 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc3456481717235892722t_unit @ F @ G ) )
% 0.10/0.42 = ( comp_r2143332150499412868t_unit @ F @ produc473321116828791851t_unit ) ) ).
% 0.10/0.42
% 0.10/0.42 % fst_comp_map_prod
% 0.10/0.42 thf(fact_386_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: num > num,A: nat,B: num] :
% 0.10/0.42 ( ( produc1665548884793878990um_num @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_387_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: num > nat,A: nat,B: num] :
% 0.10/0.42 ( ( produc5108217098638100356um_nat @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_388_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > int,G: num > int,A: nat,B: num] :
% 0.10/0.42 ( ( produc5477380188365894716um_int @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_389_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > num,A: nat,B: nat] :
% 0.10/0.42 ( ( produc3535218481486409604at_num @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_390_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > nat,A: nat,B: nat] :
% 0.10/0.42 ( ( produc6977886695330630970at_nat @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_391_map__prod__simp,axiom,
% 0.10/0.42 ! [F: nat > int,G: nat > int,A: nat,B: nat] :
% 0.10/0.42 ( ( produc7347049785058425330at_int @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_392_map__prod__simp,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > num,A: int,B: int] :
% 0.10/0.42 ( ( produc2224754261294513212nt_num @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_393_map__prod__simp,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > nat,A: int,B: int] :
% 0.10/0.42 ( ( produc5667422475138734578nt_nat @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_394_map__prod__simp,axiom,
% 0.10/0.42 ! [F: int > int,G: int > int,A: int,B: int] :
% 0.10/0.42 ( ( produc6036585564866528938nt_int @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_395_map__prod__simp,axiom,
% 0.10/0.42 ! [F: set_Pr1261947904930325089at_nat > nat,G: set_Pr1261947904930325089at_nat > num,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( produc3932168101365401472at_num @ F @ G @ ( produc2922128104949294807at_nat @ A @ B ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_simp
% 0.10/0.42 thf(fact_396_fst__map__prod,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc473321116828791851t_unit @ ( produc3456481717235892722t_unit @ F @ G @ X2 ) )
% 0.10/0.42 = ( F @ ( produc473321116828791851t_unit @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % fst_map_prod
% 0.10/0.42 thf(fact_397_snd__map__prod,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc1126150082675451753t_unit @ ( produc3456481717235892722t_unit @ F @ G @ X2 ) )
% 0.10/0.42 = ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % snd_map_prod
% 0.10/0.42 thf(fact_398_apfst__conv,axiom,
% 0.10/0.42 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.10/0.42 ( ( produc6529295065807390923at_nat @ F @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( produc9060074326276436823at_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_conv
% 0.10/0.42 thf(fact_399_apfst__conv,axiom,
% 0.10/0.42 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( produc5380969780118646373at_nat @ F @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( produc2922128104949294807at_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_conv
% 0.10/0.42 thf(fact_400_apfst__conv,axiom,
% 0.10/0.42 ! [F: nat > nat,X2: nat,Y3: num] :
% 0.10/0.42 ( ( produc6767424583952363640at_num @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ X2 ) @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_conv
% 0.10/0.42 thf(fact_401_apfst__conv,axiom,
% 0.10/0.42 ! [F: nat > nat,X2: nat,Y3: nat] :
% 0.10/0.42 ( ( produc986720760941809198at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_conv
% 0.10/0.42 thf(fact_402_apfst__conv,axiom,
% 0.10/0.42 ! [F: int > int,X2: int,Y3: int] :
% 0.10/0.42 ( ( produc2355237562570658114nt_int @ F @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ X2 ) @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_conv
% 0.10/0.42 thf(fact_403_apsnd__conv,axiom,
% 0.10/0.42 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.10/0.42 ( ( produc8057050257526108681at_nat @ F @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( produc9060074326276436823at_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_404_apsnd__conv,axiom,
% 0.10/0.42 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( produc6468969725218530979at_nat @ F @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( produc2922128104949294807at_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_405_apsnd__conv,axiom,
% 0.10/0.42 ! [F: num > num,X2: nat,Y3: num] :
% 0.10/0.42 ( ( produc8389275579088931588um_nat @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_num @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_406_apsnd__conv,axiom,
% 0.10/0.42 ! [F: num > nat,X2: nat,Y3: num] :
% 0.10/0.42 ( ( produc1035573138926686394at_nat @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_407_apsnd__conv,axiom,
% 0.10/0.42 ! [F: nat > num,X2: nat,Y3: nat] :
% 0.10/0.42 ( ( produc1225095714263496890um_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_num @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_408_apsnd__conv,axiom,
% 0.10/0.42 ! [F: nat > nat,X2: nat,Y3: nat] :
% 0.10/0.42 ( ( produc3094765310956027504at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_409_apsnd__conv,axiom,
% 0.10/0.42 ! [F: int > int,X2: int,Y3: int] :
% 0.10/0.42 ( ( produc4463282112584876420nt_int @ F @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.10/0.42 = ( product_Pair_int_int @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_410_apsnd__conv,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,X2: code_integer,Y3: code_integer] :
% 0.10/0.42 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X2 @ Y3 ) )
% 0.10/0.42 = ( produc1086072967326762835nteger @ X2 @ ( F @ Y3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_conv
% 0.10/0.42 thf(fact_411_fst__apfst,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc473321116828791851t_unit @ ( produc4508741384315284437t_unit @ F @ X2 ) )
% 0.10/0.42 = ( F @ ( produc473321116828791851t_unit @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % fst_apfst
% 0.10/0.42 thf(fact_412_snd__apfst,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc1126150082675451753t_unit @ ( produc4508741384315284437t_unit @ F @ X2 ) )
% 0.10/0.42 = ( produc1126150082675451753t_unit @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % snd_apfst
% 0.10/0.42 thf(fact_413_fst__apsnd,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 0.10/0.42 ( ( produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F @ X2 ) )
% 0.10/0.42 = ( produc8508995932063986495nteger @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % fst_apsnd
% 0.10/0.42 thf(fact_414_fst__apsnd,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc473321116828791851t_unit @ ( produc3038839249364385243_ref_a @ F @ X2 ) )
% 0.10/0.42 = ( produc473321116828791851t_unit @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % fst_apsnd
% 0.10/0.42 thf(fact_415_snd__apsnd,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 0.10/0.42 ( ( produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F @ X2 ) )
% 0.10/0.42 = ( F @ ( produc6174133586879617921nteger @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % snd_apsnd
% 0.10/0.42 thf(fact_416_snd__apsnd,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc1126150082675451753t_unit @ ( produc3038839249364385243_ref_a @ F @ X2 ) )
% 0.10/0.42 = ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % snd_apsnd
% 0.10/0.42 thf(fact_417_apsnd__eq__conv,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger,G: code_integer > code_integer] :
% 0.10/0.42 ( ( ( produc6499014454317279255nteger @ F @ X2 )
% 0.10/0.42 = ( produc6499014454317279255nteger @ G @ X2 ) )
% 0.10/0.42 = ( ( F @ ( produc6174133586879617921nteger @ X2 ) )
% 0.10/0.42 = ( G @ ( produc6174133586879617921nteger @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_eq_conv
% 0.10/0.42 thf(fact_418_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > nat,G: num > num] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 0.10/0.42 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_4925883905578568901at_num @ ( produc1665548884793878990um_num @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_419_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > nat,G: num > nat] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 0.10/0.42 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_4217639968629731195at_nat @ ( produc5108217098638100356um_nat @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_420_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > int,G: num > int] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 0.10/0.42 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_1039142661021589043nt_int @ ( produc5477380188365894716um_int @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_421_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > nat,G: nat > num] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 0.10/0.42 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_5877158439796295311at_num @ ( produc3535218481486409604at_num @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_422_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > nat,G: nat > nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 0.10/0.42 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_423_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > int,G: nat > int] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 0.10/0.42 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_424_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > nat,G: int > num] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 0.10/0.42 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_6540112122905407959at_num @ ( produc2224754261294513212nt_num @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_425_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > nat,G: int > nat] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 0.10/0.42 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_426_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > int,G: int > int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 0.10/0.42 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_427_map__prod__imageI,axiom,
% 0.10/0.42 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > nat,G: set_Pr1261947904930325089at_nat > num] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R3 )
% 0.10/0.42 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_8033574621161215657at_num @ ( produc3932168101365401472at_num @ F @ G ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_imageI
% 0.10/0.42 thf(fact_428_snd__comp__apfst,axiom,
% 0.10/0.42 ! [F: ref_a > ref_a] :
% 0.10/0.42 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc4508741384315284437t_unit @ F ) )
% 0.10/0.42 = produc1126150082675451753t_unit ) ).
% 0.10/0.42
% 0.10/0.42 % snd_comp_apfst
% 0.10/0.42 thf(fact_429_fst__comp__apsnd,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer] :
% 0.10/0.42 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F ) )
% 0.10/0.42 = produc8508995932063986495nteger ) ).
% 0.10/0.42
% 0.10/0.42 % fst_comp_apsnd
% 0.10/0.42 thf(fact_430_fst__comp__apsnd,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 0.10/0.42 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc3038839249364385243_ref_a @ F ) )
% 0.10/0.42 = produc473321116828791851t_unit ) ).
% 0.10/0.42
% 0.10/0.42 % fst_comp_apsnd
% 0.10/0.42 thf(fact_431_apfst__apsnd,axiom,
% 0.10/0.42 ! [F: ref_a > set_Pr4329608150637261639at_nat,G: heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc2316621926130398489at_nat @ F @ ( produc5080965012319039829_ref_a @ G @ X2 ) )
% 0.10/0.42 = ( produc9060074326276436823at_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_apsnd
% 0.10/0.42 thf(fact_432_apfst__apsnd,axiom,
% 0.10/0.42 ! [F: ref_a > set_Pr1261947904930325089at_nat,G: heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc4016808307611786905at_nat @ F @ ( produc2928627021203296111_ref_a @ G @ X2 ) )
% 0.10/0.42 = ( produc2922128104949294807at_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_apsnd
% 0.10/0.42 thf(fact_433_apfst__apsnd,axiom,
% 0.10/0.42 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > num,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc1704413584773205829at_num @ F @ ( produc7633249859560231688_ref_a @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_apsnd
% 0.10/0.42 thf(fact_434_apfst__apsnd,axiom,
% 0.10/0.42 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc5147081798617427195at_nat @ F @ ( produc8366372614399963582_ref_a @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_apsnd
% 0.10/0.42 thf(fact_435_apfst__apsnd,axiom,
% 0.10/0.42 ! [F: ref_a > int,G: heap_e7401611519738050253t_unit > int,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc6143945040009431475nt_int @ F @ ( produc3558794870892339738_ref_a @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_apsnd
% 0.10/0.42 thf(fact_436_apsnd__apfst,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat,G: ref_a > set_Pr4329608150637261639at_nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc5990651871820846223at_nat @ F @ ( produc5988837738927868575t_unit @ G @ X2 ) )
% 0.10/0.42 = ( produc9060074326276436823at_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst
% 0.10/0.42 thf(fact_437_apsnd__apfst,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat,G: ref_a > set_Pr1261947904930325089at_nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc8705118745468743695at_nat @ F @ ( produc5323809043756447493t_unit @ G @ X2 ) )
% 0.10/0.42 = ( produc2922128104949294807at_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst
% 0.10/0.42 thf(fact_438_apsnd__apfst,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > num,G: ref_a > nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc3902377510303101371um_nat @ F @ ( produc6942186945380262242t_unit @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_nat_num @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst
% 0.10/0.42 thf(fact_439_apsnd__apfst,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > nat,G: ref_a > nat,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc5772047106995631985at_nat @ F @ ( produc6942186945380262242t_unit @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_nat_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst
% 0.10/0.42 thf(fact_440_apsnd__apfst,axiom,
% 0.10/0.42 ! [F: heap_e7401611519738050253t_unit > int,G: ref_a > int,X2: produc7812382424243267045t_unit] :
% 0.10/0.42 ( ( produc6768910348387636265nt_int @ F @ ( produc5845103964736263686t_unit @ G @ X2 ) )
% 0.10/0.42 = ( product_Pair_int_int @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst
% 0.10/0.42 thf(fact_441_apsnd__apfst__commute,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,G: code_integer > code_integer,P: produc8923325533196201883nteger] :
% 0.10/0.42 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ P ) )
% 0.10/0.42 = ( produc3195571438000033749nteger @ G @ ( produc6499014454317279255nteger @ F @ P ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_apfst_commute
% 0.10/0.42 thf(fact_442_subset__image__iff,axiom,
% 0.10/0.42 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 = ( ? [AA: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.10/0.42 & ( B5
% 0.10/0.42 = ( image_nat_rat @ F @ AA ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_image_iff
% 0.10/0.42 thf(fact_443_subset__image__iff,axiom,
% 0.10/0.42 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 = ( ? [AA: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.10/0.42 & ( B5
% 0.10/0.42 = ( image_nat_nat @ F @ AA ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_image_iff
% 0.10/0.42 thf(fact_444_subset__image__iff,axiom,
% 0.10/0.42 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 = ( ? [AA: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.10/0.42 & ( B5
% 0.10/0.42 = ( image_nat_int @ F @ AA ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_image_iff
% 0.10/0.42 thf(fact_445_subset__image__iff,axiom,
% 0.10/0.42 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 = ( ? [AA: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ AA @ A4 )
% 0.10/0.42 & ( B5
% 0.10/0.42 = ( image_int_nat @ F @ AA ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_image_iff
% 0.10/0.42 thf(fact_446_subset__image__iff,axiom,
% 0.10/0.42 ! [B5: set_int,F: int > int,A4: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 = ( ? [AA: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ AA @ A4 )
% 0.10/0.42 & ( B5
% 0.10/0.42 = ( image_int_int @ F @ AA ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_image_iff
% 0.10/0.42 thf(fact_447_image__subset__iff,axiom,
% 0.10/0.42 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.10/0.42 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.10/0.42 = ( ! [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 => ( member_rat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subset_iff
% 0.10/0.42 thf(fact_448_image__subset__iff,axiom,
% 0.10/0.42 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.10/0.42 = ( ! [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subset_iff
% 0.10/0.42 thf(fact_449_image__subset__iff,axiom,
% 0.10/0.42 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.10/0.42 = ( ! [X4: int] :
% 0.10/0.42 ( ( member_int @ X4 @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subset_iff
% 0.10/0.42 thf(fact_450_image__subset__iff,axiom,
% 0.10/0.42 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.10/0.42 = ( ! [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subset_iff
% 0.10/0.42 thf(fact_451_image__subset__iff,axiom,
% 0.10/0.42 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.10/0.42 = ( ! [X4: int] :
% 0.10/0.42 ( ( member_int @ X4 @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subset_iff
% 0.10/0.42 thf(fact_452_subset__imageE,axiom,
% 0.10/0.42 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 => ~ ! [C2: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.10/0.42 => ( B5
% 0.10/0.42 != ( image_nat_rat @ F @ C2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_imageE
% 0.10/0.42 thf(fact_453_subset__imageE,axiom,
% 0.10/0.42 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 => ~ ! [C2: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.10/0.42 => ( B5
% 0.10/0.42 != ( image_nat_nat @ F @ C2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_imageE
% 0.10/0.42 thf(fact_454_subset__imageE,axiom,
% 0.10/0.42 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 => ~ ! [C2: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.10/0.42 => ( B5
% 0.10/0.42 != ( image_nat_int @ F @ C2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_imageE
% 0.10/0.42 thf(fact_455_subset__imageE,axiom,
% 0.10/0.42 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 => ~ ! [C2: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 0.10/0.42 => ( B5
% 0.10/0.42 != ( image_int_nat @ F @ C2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_imageE
% 0.10/0.42 thf(fact_456_subset__imageE,axiom,
% 0.10/0.42 ! [B5: set_int,F: int > int,A4: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 => ~ ! [C2: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 0.10/0.42 => ( B5
% 0.10/0.42 != ( image_int_int @ F @ C2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % subset_imageE
% 0.10/0.42 thf(fact_457_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_o,F: $o > $o,B5: set_o] :
% 0.10/0.42 ( ! [X: $o] :
% 0.10/0.42 ( ( member_o @ X @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_458_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_o,F: $o > nat,B5: set_nat] :
% 0.10/0.42 ( ! [X: $o] :
% 0.10/0.42 ( ( member_o @ X @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_nat @ ( image_o_nat @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_459_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_o,F: $o > int,B5: set_int] :
% 0.10/0.42 ( ! [X: $o] :
% 0.10/0.42 ( ( member_o @ X @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_int @ ( image_o_int @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_460_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_nat,F: nat > rat,B5: set_rat] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 => ( member_rat @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_461_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_nat,F: nat > $o,B5: set_o] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_462_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_463_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_nat,F: nat > int,B5: set_int] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_464_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_int,F: int > $o,B5: set_o] :
% 0.10/0.42 ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_o @ ( image_int_o @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_465_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_int,F: int > nat,B5: set_nat] :
% 0.10/0.42 ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_466_image__subsetI,axiom,
% 0.10/0.42 ! [A4: set_int,F: int > int,B5: set_int] :
% 0.10/0.42 ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.10/0.42 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_subsetI
% 0.10/0.42 thf(fact_467_image__mono,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.10/0.42 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_mono
% 0.10/0.42 thf(fact_468_image__mono,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.10/0.42 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_mono
% 0.10/0.42 thf(fact_469_image__mono,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,F: nat > int] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.10/0.42 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_mono
% 0.10/0.42 thf(fact_470_image__mono,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,F: int > nat] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.10/0.42 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_mono
% 0.10/0.42 thf(fact_471_image__mono,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,F: int > int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.10/0.42 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_mono
% 0.10/0.42 thf(fact_472_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,H: nat > $o,I: nat > $o] :
% 0.10/0.42 ( ( comp_P4785046977597218846at_nat @ ( produc1928436952130685430_o_o_o @ F @ G ) @ ( produc6957950696844810486_nat_o @ H @ I ) )
% 0.10/0.42 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_473_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > num,H: nat > $o,I: int > nat] :
% 0.10/0.42 ( ( comp_P9057111047297513408at_int @ ( produc3628557804203378146at_num @ F @ G ) @ ( produc8250590009387450446nt_nat @ H @ I ) )
% 0.10/0.42 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_474_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > nat,H: nat > $o,I: nat > nat] :
% 0.10/0.42 ( ( comp_P4962864564169660718at_nat @ ( produc7071226018047599512at_nat @ F @ G ) @ ( produc7251236297486395890at_nat @ H @ I ) )
% 0.10/0.42 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_475_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: int > nat,H: nat > $o,I: int > int] :
% 0.10/0.42 ( ( comp_P465755969289462830at_int @ ( produc8070579729948654068nt_nat @ F @ G ) @ ( produc8248099538878400170nt_int @ H @ I ) )
% 0.10/0.42 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_int_nat_int @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_476_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > num,G: $o > $o,H: int > nat,I: nat > $o] :
% 0.10/0.42 ( ( comp_P5807473265676440968nt_nat @ ( produc3264868786340801506um_o_o @ F @ G ) @ ( produc8298419091753553490_nat_o @ H @ I ) )
% 0.10/0.42 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_477_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > num,H: int > nat,I: int > nat] :
% 0.10/0.42 ( ( comp_P9218946435557410242nt_int @ ( produc1476026309457068494at_num @ F @ G ) @ ( produc5667422475138734578nt_nat @ H @ I ) )
% 0.10/0.42 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_478_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,H: int > nat,I: nat > nat] :
% 0.10/0.42 ( ( comp_P5124699952429557552nt_nat @ ( produc4918694523301289860at_nat @ F @ G ) @ ( produc4668068763237680022at_nat @ H @ I ) )
% 0.10/0.42 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_479_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > num,G: int > nat,H: int > nat,I: int > int] :
% 0.10/0.42 ( ( comp_P3772045228931366376nt_int @ ( produc5918048235202344416nt_nat @ F @ G ) @ ( produc5664932004629684302nt_int @ H @ I ) )
% 0.10/0.42 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_int_nat_int @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_480_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: $o > $o,H: nat > nat,I: nat > $o] :
% 0.10/0.42 ( ( comp_P8901546994122883554at_nat @ ( produc2001155298098703512at_o_o @ F @ G ) @ ( produc4787215299218314158_nat_o @ H @ I ) )
% 0.10/0.42 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_481_map__prod_Ocomp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > num,H: nat > nat,I: int > nat] :
% 0.10/0.42 ( ( comp_P6334688330072917552at_int @ ( produc3535218481486409604at_num @ F @ G ) @ ( produc7977240407231685526nt_nat @ H @ I ) )
% 0.10/0.42 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.comp
% 0.10/0.42 thf(fact_482_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,H: nat > $o,I: nat > $o,Prod: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc1928436952130685430_o_o_o @ F @ G @ ( produc6957950696844810486_nat_o @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_483_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > num,H: nat > $o,I: int > nat,Prod: product_prod_nat_int] :
% 0.10/0.42 ( ( produc3628557804203378146at_num @ F @ G @ ( produc8250590009387450446nt_nat @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_484_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > nat,H: nat > $o,I: nat > nat,Prod: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc7071226018047599512at_nat @ F @ G @ ( produc7251236297486395890at_nat @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_485_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: $o > $o,G: int > nat,H: nat > $o,I: int > int,Prod: product_prod_nat_int] :
% 0.10/0.42 ( ( produc8070579729948654068nt_nat @ F @ G @ ( produc8248099538878400170nt_int @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_int_nat_int @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_486_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > num,G: $o > $o,H: int > nat,I: nat > $o,Prod: product_prod_int_nat] :
% 0.10/0.42 ( ( produc3264868786340801506um_o_o @ F @ G @ ( produc8298419091753553490_nat_o @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_487_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > num,H: int > nat,I: int > nat,Prod: product_prod_int_int] :
% 0.10/0.42 ( ( produc1476026309457068494at_num @ F @ G @ ( produc5667422475138734578nt_nat @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_488_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,H: int > nat,I: nat > nat,Prod: product_prod_int_nat] :
% 0.10/0.42 ( ( produc4918694523301289860at_nat @ F @ G @ ( produc4668068763237680022at_nat @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_489_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > num,G: int > nat,H: int > nat,I: int > int,Prod: product_prod_int_int] :
% 0.10/0.42 ( ( produc5918048235202344416nt_nat @ F @ G @ ( produc5664932004629684302nt_int @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_int_nat_int @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_490_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > nat,G: $o > $o,H: nat > nat,I: nat > $o,Prod: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc2001155298098703512at_o_o @ F @ G @ ( produc4787215299218314158_nat_o @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_491_map__prod_Ocompositionality,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > num,H: nat > nat,I: int > nat,Prod: product_prod_nat_int] :
% 0.10/0.42 ( ( produc3535218481486409604at_num @ F @ G @ ( produc7977240407231685526nt_nat @ H @ I @ Prod ) )
% 0.10/0.42 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod.compositionality
% 0.10/0.42 thf(fact_492_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: $o > $o,F22: nat > $o,G1: $o > $o,G22: nat > $o] :
% 0.10/0.42 ( ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P4785046977597218846at_nat @ ( produc1928436952130685430_o_o_o @ F1 @ G1 ) @ ( produc6957950696844810486_nat_o @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_493_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: $o > $o,F22: nat > $o,G1: nat > num,G22: int > nat] :
% 0.10/0.42 ( ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P9057111047297513408at_int @ ( produc3628557804203378146at_num @ F1 @ G1 ) @ ( produc8250590009387450446nt_nat @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_494_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: $o > $o,F22: nat > $o,G1: nat > nat,G22: nat > nat] :
% 0.10/0.42 ( ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_nat_nat_nat @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P4962864564169660718at_nat @ ( produc7071226018047599512at_nat @ F1 @ G1 ) @ ( produc7251236297486395890at_nat @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_495_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: $o > $o,F22: nat > $o,G1: int > nat,G22: int > int] :
% 0.10/0.42 ( ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_int_nat_int @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P465755969289462830at_int @ ( produc8070579729948654068nt_nat @ F1 @ G1 ) @ ( produc8248099538878400170nt_int @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_496_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > num,F22: int > nat,G1: $o > $o,G22: nat > $o] :
% 0.10/0.42 ( ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P5807473265676440968nt_nat @ ( produc3264868786340801506um_o_o @ F1 @ G1 ) @ ( produc8298419091753553490_nat_o @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_497_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > num,F22: int > nat,G1: nat > num,G22: int > nat] :
% 0.10/0.42 ( ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P9218946435557410242nt_int @ ( produc1476026309457068494at_num @ F1 @ G1 ) @ ( produc5667422475138734578nt_nat @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_498_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > num,F22: int > nat,G1: nat > nat,G22: nat > nat] :
% 0.10/0.42 ( ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_nat_nat_nat @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P5124699952429557552nt_nat @ ( produc4918694523301289860at_nat @ F1 @ G1 ) @ ( produc4668068763237680022at_nat @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_499_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > num,F22: int > nat,G1: int > nat,G22: int > int] :
% 0.10/0.42 ( ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_int_nat_int @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P3772045228931366376nt_int @ ( produc5918048235202344416nt_nat @ F1 @ G1 ) @ ( produc5664932004629684302nt_int @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_500_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > nat,F22: nat > nat,G1: $o > $o,G22: nat > $o] :
% 0.10/0.42 ( ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P8901546994122883554at_nat @ ( produc2001155298098703512at_o_o @ F1 @ G1 ) @ ( produc4787215299218314158_nat_o @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_501_map__prod__compose,axiom,
% 0.10/0.42 ! [F1: nat > nat,F22: nat > nat,G1: nat > num,G22: int > nat] :
% 0.10/0.42 ( ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 0.10/0.42 = ( comp_P6334688330072917552at_int @ ( produc3535218481486409604at_num @ F1 @ G1 ) @ ( produc7977240407231685526nt_nat @ F22 @ G22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_compose
% 0.10/0.42 thf(fact_502_apsnd__compose,axiom,
% 0.10/0.42 ! [F: code_integer > code_integer,G: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 0.10/0.42 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X2 ) )
% 0.10/0.42 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_compose
% 0.10/0.42 thf(fact_503_Collect__case__prod__Grp__in,axiom,
% 0.10/0.42 ! [Z2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ Z2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ F ) ) ) )
% 0.10/0.42 => ( member2643936169264416010at_nat @ ( produc6011863565407846595at_nat @ Z2 ) @ A4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_Grp_in
% 0.10/0.42 thf(fact_504_Collect__case__prod__Grp__in,axiom,
% 0.10/0.42 ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
% 0.10/0.42 => ( member_nat @ ( product_fst_nat_nat @ Z2 ) @ A4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_Grp_in
% 0.10/0.42 thf(fact_505_Collect__case__prod__Grp__in,axiom,
% 0.10/0.42 ! [Z2: produc7812382424243267045t_unit,A4: set_ref_a,F: ref_a > heap_e7401611519738050253t_unit] :
% 0.10/0.42 ( ( member7849944260330398460t_unit @ Z2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_Gr6510375311308651680t_unit @ A4 @ F ) ) ) )
% 0.10/0.42 => ( member_ref_a @ ( produc473321116828791851t_unit @ Z2 ) @ A4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_Grp_in
% 0.10/0.42 thf(fact_506_Collect__case__prod__Grp__in,axiom,
% 0.10/0.42 ! [Z2: product_prod_int_int,A4: set_int,F: int > int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ Z2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ F ) ) ) )
% 0.10/0.42 => ( member_int @ ( product_fst_int_int @ Z2 ) @ A4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_Grp_in
% 0.10/0.42 thf(fact_507_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_num,F: nat > nat,G: num > num,R3: set_Pr6200539531224447659at_num] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ C @ ( image_4925883905578568901at_num @ ( produc1665548884793878990um_num @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: num] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_508_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_num,F: nat > nat,G: nat > num,R3: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ C @ ( image_5877158439796295311at_num @ ( produc3535218481486409604at_num @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_509_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_num,F: int > nat,G: int > num,R3: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ C @ ( image_6540112122905407959at_num @ ( produc2224754261294513212nt_num @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: int,Y: int] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_510_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_nat,F: nat > nat,G: num > nat,R3: set_Pr6200539531224447659at_num] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ C @ ( image_4217639968629731195at_nat @ ( produc5108217098638100356um_nat @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: num] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_511_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_nat,F: nat > nat,G: nat > nat,R3: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ C @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_512_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_nat_nat,F: int > nat,G: int > nat,R3: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ C @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: int,Y: int] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_513_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_int_int,F: nat > int,G: num > int,R3: set_Pr6200539531224447659at_num] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ C @ ( image_1039142661021589043nt_int @ ( produc5477380188365894716um_int @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: num] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_514_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_int_int,F: nat > int,G: nat > int,R3: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ C @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_515_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: product_prod_int_int,F: int > int,G: int > int,R3: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ C @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: int,Y: int] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_516_prod__fun__imageE,axiom,
% 0.10/0.42 ! [C: produc3843707927480180839at_nat,F: nat > set_Pr1261947904930325089at_nat,G: num > set_Pr1261947904930325089at_nat,R3: set_Pr6200539531224447659at_num] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ C @ ( image_2708129733610033121at_nat @ ( produc170006858110003436at_nat @ F @ G ) @ R3 ) )
% 0.10/0.42 => ~ ! [X: nat,Y: num] :
% 0.10/0.42 ( ( C
% 0.10/0.42 = ( produc2922128104949294807at_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod_fun_imageE
% 0.10/0.42 thf(fact_517_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,B: $o,F: $o > $o] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_518_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,B: nat,F: $o > nat] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_nat @ B @ ( image_o_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_519_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,B: int,F: $o > int] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_int @ B @ ( image_o_int @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_520_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,B: rat,F: nat > rat] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_521_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,B: $o,F: nat > $o] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_o @ B @ ( image_nat_o @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_522_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,B: nat,F: nat > nat] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_523_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,B: int,F: nat > int] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_524_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,B: $o,F: int > $o] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_o @ B @ ( image_int_o @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_525_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,B: nat,F: int > nat] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_nat @ B @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_526_rev__image__eqI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,B: int,F: int > int] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( ( B
% 0.10/0.42 = ( F @ X2 ) )
% 0.10/0.42 => ( member_int @ B @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rev_image_eqI
% 0.10/0.42 thf(fact_527_ball__imageD,axiom,
% 0.10/0.42 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 0.10/0.42 ( ! [X: rat] :
% 0.10/0.42 ( ( member_rat @ X @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ X ) )
% 0.10/0.42 => ! [X6: nat] :
% 0.10/0.42 ( ( member_nat @ X6 @ A4 )
% 0.10/0.42 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % ball_imageD
% 0.10/0.42 thf(fact_528_ball__imageD,axiom,
% 0.10/0.42 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ X ) )
% 0.10/0.42 => ! [X6: nat] :
% 0.10/0.42 ( ( member_nat @ X6 @ A4 )
% 0.10/0.42 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % ball_imageD
% 0.10/0.42 thf(fact_529_ball__imageD,axiom,
% 0.10/0.42 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 0.10/0.42 ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ X ) )
% 0.10/0.42 => ! [X6: nat] :
% 0.10/0.42 ( ( member_nat @ X6 @ A4 )
% 0.10/0.42 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % ball_imageD
% 0.10/0.42 thf(fact_530_ball__imageD,axiom,
% 0.10/0.42 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 0.10/0.42 ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ X ) )
% 0.10/0.42 => ! [X6: int] :
% 0.10/0.42 ( ( member_int @ X6 @ A4 )
% 0.10/0.42 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % ball_imageD
% 0.10/0.42 thf(fact_531_ball__imageD,axiom,
% 0.10/0.42 ! [F: int > int,A4: set_int,P2: int > $o] :
% 0.10/0.42 ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ X ) )
% 0.10/0.42 => ! [X6: int] :
% 0.10/0.42 ( ( member_int @ X6 @ A4 )
% 0.10/0.42 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % ball_imageD
% 0.10/0.42 thf(fact_532_image__cong,axiom,
% 0.10/0.42 ! [M: set_nat,N: set_nat,F: nat > rat,G: nat > rat] :
% 0.10/0.42 ( ( M = N )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ N )
% 0.10/0.42 => ( ( F @ X )
% 0.10/0.42 = ( G @ X ) ) )
% 0.10/0.42 => ( ( image_nat_rat @ F @ M )
% 0.10/0.42 = ( image_nat_rat @ G @ N ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_cong
% 0.10/0.42 thf(fact_533_image__cong,axiom,
% 0.10/0.42 ! [M: set_nat,N: set_nat,F: nat > nat,G: nat > nat] :
% 0.10/0.42 ( ( M = N )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ N )
% 0.10/0.42 => ( ( F @ X )
% 0.10/0.42 = ( G @ X ) ) )
% 0.10/0.42 => ( ( image_nat_nat @ F @ M )
% 0.10/0.42 = ( image_nat_nat @ G @ N ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_cong
% 0.10/0.42 thf(fact_534_image__cong,axiom,
% 0.10/0.42 ! [M: set_nat,N: set_nat,F: nat > int,G: nat > int] :
% 0.10/0.42 ( ( M = N )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ N )
% 0.10/0.42 => ( ( F @ X )
% 0.10/0.42 = ( G @ X ) ) )
% 0.10/0.42 => ( ( image_nat_int @ F @ M )
% 0.10/0.42 = ( image_nat_int @ G @ N ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_cong
% 0.10/0.42 thf(fact_535_image__cong,axiom,
% 0.10/0.42 ! [M: set_int,N: set_int,F: int > nat,G: int > nat] :
% 0.10/0.42 ( ( M = N )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ N )
% 0.10/0.42 => ( ( F @ X )
% 0.10/0.42 = ( G @ X ) ) )
% 0.10/0.42 => ( ( image_int_nat @ F @ M )
% 0.10/0.42 = ( image_int_nat @ G @ N ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_cong
% 0.10/0.42 thf(fact_536_image__cong,axiom,
% 0.10/0.42 ! [M: set_int,N: set_int,F: int > int,G: int > int] :
% 0.10/0.42 ( ( M = N )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ N )
% 0.10/0.42 => ( ( F @ X )
% 0.10/0.42 = ( G @ X ) ) )
% 0.10/0.42 => ( ( image_int_int @ F @ M )
% 0.10/0.42 = ( image_int_int @ G @ N ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_cong
% 0.10/0.42 thf(fact_537_bex__imageD,axiom,
% 0.10/0.42 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 0.10/0.42 ( ? [X6: rat] :
% 0.10/0.42 ( ( member_rat @ X6 @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 & ( P2 @ X6 ) )
% 0.10/0.42 => ? [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % bex_imageD
% 0.10/0.42 thf(fact_538_bex__imageD,axiom,
% 0.10/0.42 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 0.10/0.42 ( ? [X6: nat] :
% 0.10/0.42 ( ( member_nat @ X6 @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 & ( P2 @ X6 ) )
% 0.10/0.42 => ? [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % bex_imageD
% 0.10/0.42 thf(fact_539_bex__imageD,axiom,
% 0.10/0.42 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 0.10/0.42 ( ? [X6: int] :
% 0.10/0.42 ( ( member_int @ X6 @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 & ( P2 @ X6 ) )
% 0.10/0.42 => ? [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ A4 )
% 0.10/0.42 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % bex_imageD
% 0.10/0.42 thf(fact_540_bex__imageD,axiom,
% 0.10/0.42 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 0.10/0.42 ( ? [X6: nat] :
% 0.10/0.42 ( ( member_nat @ X6 @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 & ( P2 @ X6 ) )
% 0.10/0.42 => ? [X: int] :
% 0.10/0.42 ( ( member_int @ X @ A4 )
% 0.10/0.42 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % bex_imageD
% 0.10/0.42 thf(fact_541_bex__imageD,axiom,
% 0.10/0.42 ! [F: int > int,A4: set_int,P2: int > $o] :
% 0.10/0.42 ( ? [X6: int] :
% 0.10/0.42 ( ( member_int @ X6 @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 & ( P2 @ X6 ) )
% 0.10/0.42 => ? [X: int] :
% 0.10/0.42 ( ( member_int @ X @ A4 )
% 0.10/0.42 & ( P2 @ ( F @ X ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % bex_imageD
% 0.10/0.42 thf(fact_542_image__iff,axiom,
% 0.10/0.42 ! [Z2: rat,F: nat > rat,A4: set_nat] :
% 0.10/0.42 ( ( member_rat @ Z2 @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 = ( ? [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 & ( Z2
% 0.10/0.42 = ( F @ X4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_iff
% 0.10/0.42 thf(fact_543_image__iff,axiom,
% 0.10/0.42 ! [Z2: nat,F: nat > nat,A4: set_nat] :
% 0.10/0.42 ( ( member_nat @ Z2 @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 = ( ? [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 & ( Z2
% 0.10/0.42 = ( F @ X4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_iff
% 0.10/0.42 thf(fact_544_image__iff,axiom,
% 0.10/0.42 ! [Z2: nat,F: int > nat,A4: set_int] :
% 0.10/0.42 ( ( member_nat @ Z2 @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 = ( ? [X4: int] :
% 0.10/0.42 ( ( member_int @ X4 @ A4 )
% 0.10/0.42 & ( Z2
% 0.10/0.42 = ( F @ X4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_iff
% 0.10/0.42 thf(fact_545_image__iff,axiom,
% 0.10/0.42 ! [Z2: int,F: nat > int,A4: set_nat] :
% 0.10/0.42 ( ( member_int @ Z2 @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 = ( ? [X4: nat] :
% 0.10/0.42 ( ( member_nat @ X4 @ A4 )
% 0.10/0.42 & ( Z2
% 0.10/0.42 = ( F @ X4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_iff
% 0.10/0.42 thf(fact_546_image__iff,axiom,
% 0.10/0.42 ! [Z2: int,F: int > int,A4: set_int] :
% 0.10/0.42 ( ( member_int @ Z2 @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 = ( ? [X4: int] :
% 0.10/0.42 ( ( member_int @ X4 @ A4 )
% 0.10/0.42 & ( Z2
% 0.10/0.42 = ( F @ X4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_iff
% 0.10/0.42 thf(fact_547_imageI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,F: $o > $o] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_548_imageI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,F: $o > nat] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X2 ) @ ( image_o_nat @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_549_imageI,axiom,
% 0.10/0.42 ! [X2: $o,A4: set_o,F: $o > int] :
% 0.10/0.42 ( ( member_o @ X2 @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X2 ) @ ( image_o_int @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_550_imageI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,F: nat > rat] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( member_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_551_imageI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,F: nat > $o] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X2 ) @ ( image_nat_o @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_552_imageI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_553_imageI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,F: nat > int] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X2 ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_554_imageI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,F: int > $o] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( member_o @ ( F @ X2 ) @ ( image_int_o @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_555_imageI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,F: int > nat] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( member_nat @ ( F @ X2 ) @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_556_imageI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,F: int > int] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( member_int @ ( F @ X2 ) @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % imageI
% 0.10/0.42 thf(fact_557_Sup_OSUP__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > rat,D: nat > rat,Sup: set_rat > rat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Sup @ ( image_nat_rat @ C3 @ A4 ) )
% 0.10/0.42 = ( Sup @ ( image_nat_rat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Sup.SUP_cong
% 0.10/0.42 thf(fact_558_Sup_OSUP__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Sup: set_nat > nat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Sup @ ( image_nat_nat @ C3 @ A4 ) )
% 0.10/0.42 = ( Sup @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Sup.SUP_cong
% 0.10/0.42 thf(fact_559_Sup_OSUP__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int,Sup: set_int > int] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Sup @ ( image_nat_int @ C3 @ A4 ) )
% 0.10/0.42 = ( Sup @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Sup.SUP_cong
% 0.10/0.42 thf(fact_560_Sup_OSUP__cong,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat,Sup: set_nat > nat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Sup @ ( image_int_nat @ C3 @ A4 ) )
% 0.10/0.42 = ( Sup @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Sup.SUP_cong
% 0.10/0.42 thf(fact_561_Sup_OSUP__cong,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int,Sup: set_int > int] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Sup @ ( image_int_int @ C3 @ A4 ) )
% 0.10/0.42 = ( Sup @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Sup.SUP_cong
% 0.10/0.42 thf(fact_562_Inf_OINF__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > rat,D: nat > rat,Inf: set_rat > rat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Inf @ ( image_nat_rat @ C3 @ A4 ) )
% 0.10/0.42 = ( Inf @ ( image_nat_rat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Inf.INF_cong
% 0.10/0.42 thf(fact_563_Inf_OINF__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Inf: set_nat > nat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Inf @ ( image_nat_nat @ C3 @ A4 ) )
% 0.10/0.42 = ( Inf @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Inf.INF_cong
% 0.10/0.42 thf(fact_564_Inf_OINF__cong,axiom,
% 0.10/0.42 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int,Inf: set_int > int] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: nat] :
% 0.10/0.42 ( ( member_nat @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Inf @ ( image_nat_int @ C3 @ A4 ) )
% 0.10/0.42 = ( Inf @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Inf.INF_cong
% 0.10/0.42 thf(fact_565_Inf_OINF__cong,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat,Inf: set_nat > nat] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Inf @ ( image_int_nat @ C3 @ A4 ) )
% 0.10/0.42 = ( Inf @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Inf.INF_cong
% 0.10/0.42 thf(fact_566_Inf_OINF__cong,axiom,
% 0.10/0.42 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int,Inf: set_int > int] :
% 0.10/0.42 ( ( A4 = B5 )
% 0.10/0.42 => ( ! [X: int] :
% 0.10/0.42 ( ( member_int @ X @ B5 )
% 0.10/0.42 => ( ( C3 @ X )
% 0.10/0.42 = ( D @ X ) ) )
% 0.10/0.42 => ( ( Inf @ ( image_int_int @ C3 @ A4 ) )
% 0.10/0.42 = ( Inf @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Inf.INF_cong
% 0.10/0.42 thf(fact_567_comp__eq__dest__lhs,axiom,
% 0.10/0.42 ! [A: $o > $o,B: nat > $o,C: nat > $o,V: nat] :
% 0.10/0.42 ( ( ( comp_o_o_nat @ A @ B )
% 0.10/0.42 = C )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ V ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest_lhs
% 0.10/0.42 thf(fact_568_comp__eq__dest__lhs,axiom,
% 0.10/0.42 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 0.10/0.42 ( ( ( comp_nat_num_int @ A @ B )
% 0.10/0.42 = C )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ V ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest_lhs
% 0.10/0.42 thf(fact_569_comp__eq__dest__lhs,axiom,
% 0.10/0.42 ! [A: nat > nat,B: nat > nat,C: nat > nat,V: nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_nat @ A @ B )
% 0.10/0.42 = C )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ V ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest_lhs
% 0.10/0.42 thf(fact_570_comp__eq__dest__lhs,axiom,
% 0.10/0.42 ! [A: int > nat,B: int > int,C: int > nat,V: int] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ A @ B )
% 0.10/0.42 = C )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ V ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest_lhs
% 0.10/0.42 thf(fact_571_comp__eq__dest__lhs,axiom,
% 0.10/0.42 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.10/0.42 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.10/0.42 = C )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ V ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest_lhs
% 0.10/0.42 thf(fact_572_comp__eq__elim,axiom,
% 0.10/0.42 ! [A: $o > $o,B: nat > $o,C: $o > $o,D2: nat > $o] :
% 0.10/0.42 ( ( ( comp_o_o_nat @ A @ B )
% 0.10/0.42 = ( comp_o_o_nat @ C @ D2 ) )
% 0.10/0.42 => ! [V4: nat] :
% 0.10/0.42 ( ( A @ ( B @ V4 ) )
% 0.10/0.42 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_elim
% 0.10/0.42 thf(fact_573_comp__eq__elim,axiom,
% 0.10/0.42 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat] :
% 0.10/0.42 ( ( ( comp_nat_num_int @ A @ B )
% 0.10/0.42 = ( comp_nat_num_int @ C @ D2 ) )
% 0.10/0.42 => ! [V4: int] :
% 0.10/0.42 ( ( A @ ( B @ V4 ) )
% 0.10/0.42 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_elim
% 0.10/0.42 thf(fact_574_comp__eq__elim,axiom,
% 0.10/0.42 ! [A: nat > nat,B: nat > nat,C: nat > nat,D2: nat > nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_nat @ A @ B )
% 0.10/0.42 = ( comp_nat_nat_nat @ C @ D2 ) )
% 0.10/0.42 => ! [V4: nat] :
% 0.10/0.42 ( ( A @ ( B @ V4 ) )
% 0.10/0.42 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_elim
% 0.10/0.42 thf(fact_575_comp__eq__elim,axiom,
% 0.10/0.42 ! [A: int > nat,B: int > int,C: int > nat,D2: int > int] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ A @ B )
% 0.10/0.42 = ( comp_int_nat_int @ C @ D2 ) )
% 0.10/0.42 => ! [V4: int] :
% 0.10/0.42 ( ( A @ ( B @ V4 ) )
% 0.10/0.42 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_elim
% 0.10/0.42 thf(fact_576_comp__eq__elim,axiom,
% 0.10/0.42 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.10/0.42 => ! [V4: code_integer] :
% 0.10/0.42 ( ( A @ ( B @ V4 ) )
% 0.10/0.42 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_elim
% 0.10/0.42 thf(fact_577_comp__eq__dest,axiom,
% 0.10/0.42 ! [A: $o > $o,B: nat > $o,C: $o > $o,D2: nat > $o,V: nat] :
% 0.10/0.42 ( ( ( comp_o_o_nat @ A @ B )
% 0.10/0.42 = ( comp_o_o_nat @ C @ D2 ) )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest
% 0.10/0.42 thf(fact_578_comp__eq__dest,axiom,
% 0.10/0.42 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat,V: int] :
% 0.10/0.42 ( ( ( comp_nat_num_int @ A @ B )
% 0.10/0.42 = ( comp_nat_num_int @ C @ D2 ) )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest
% 0.10/0.42 thf(fact_579_comp__eq__dest,axiom,
% 0.10/0.42 ! [A: nat > nat,B: nat > nat,C: nat > nat,D2: nat > nat,V: nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_nat @ A @ B )
% 0.10/0.42 = ( comp_nat_nat_nat @ C @ D2 ) )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest
% 0.10/0.42 thf(fact_580_comp__eq__dest,axiom,
% 0.10/0.42 ! [A: int > nat,B: int > int,C: int > nat,D2: int > int,V: int] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ A @ B )
% 0.10/0.42 = ( comp_int_nat_int @ C @ D2 ) )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest
% 0.10/0.42 thf(fact_581_comp__eq__dest,axiom,
% 0.10/0.42 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 0.10/0.42 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 0.10/0.42 => ( ( A @ ( B @ V ) )
% 0.10/0.42 = ( C @ ( D2 @ V ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_eq_dest
% 0.10/0.42 thf(fact_582_comp__assoc,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > $o,H: nat > nat] :
% 0.10/0.42 ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_o_nat @ F @ ( comp_nat_o_nat @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_583_comp__assoc,axiom,
% 0.10/0.42 ! [F: nat > num,G: int > nat,H: int > int] :
% 0.10/0.42 ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_584_comp__assoc,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,H: nat > $o] :
% 0.10/0.42 ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_585_comp__assoc,axiom,
% 0.10/0.42 ! [F: num > num,G: nat > num,H: int > nat] :
% 0.10/0.42 ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_586_comp__assoc,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,H: int > nat] :
% 0.10/0.42 ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_587_comp__assoc,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > nat,H: nat > nat] :
% 0.10/0.42 ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_588_comp__assoc,axiom,
% 0.10/0.42 ! [F: nat > nat,G: int > nat,H: int > int] :
% 0.10/0.42 ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_int @ F @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_589_comp__assoc,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > int,H: int > int] :
% 0.10/0.42 ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_nat_int @ F @ ( comp_int_int_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_590_comp__assoc,axiom,
% 0.10/0.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,H: code_integer > code_integer] :
% 0.10/0.42 ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_591_comp__assoc,axiom,
% 0.10/0.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,H: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_assoc
% 0.10/0.42 thf(fact_592_comp__def,axiom,
% 0.10/0.42 ( comp_o_o_nat
% 0.10/0.42 = ( ^ [F2: $o > $o,G3: nat > $o,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_def
% 0.10/0.42 thf(fact_593_comp__def,axiom,
% 0.10/0.42 ( comp_nat_num_int
% 0.10/0.42 = ( ^ [F2: nat > num,G3: int > nat,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_def
% 0.10/0.42 thf(fact_594_comp__def,axiom,
% 0.10/0.42 ( comp_nat_nat_nat
% 0.10/0.42 = ( ^ [F2: nat > nat,G3: nat > nat,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_def
% 0.10/0.42 thf(fact_595_comp__def,axiom,
% 0.10/0.42 ( comp_int_nat_int
% 0.10/0.42 = ( ^ [F2: int > nat,G3: int > int,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_def
% 0.10/0.42 thf(fact_596_comp__def,axiom,
% 0.10/0.42 ( comp_C8797469213163452608nteger
% 0.10/0.42 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X4: code_integer] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % comp_def
% 0.10/0.42 thf(fact_597_apfst__convE,axiom,
% 0.10/0.42 ! [Q: produc1319942482725812455at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 0.10/0.42 ( ( Q
% 0.10/0.42 = ( produc6529295065807390923at_nat @ F @ P ) )
% 0.10/0.42 => ~ ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.10/0.42 ( ( P
% 0.10/0.42 = ( produc9060074326276436823at_nat @ X @ Y ) )
% 0.10/0.42 => ( Q
% 0.10/0.42 != ( produc9060074326276436823at_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_convE
% 0.10/0.42 thf(fact_598_apfst__convE,axiom,
% 0.10/0.42 ! [Q: produc3843707927480180839at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 0.10/0.42 ( ( Q
% 0.10/0.42 = ( produc5380969780118646373at_nat @ F @ P ) )
% 0.10/0.42 => ~ ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( P
% 0.10/0.42 = ( produc2922128104949294807at_nat @ X @ Y ) )
% 0.10/0.42 => ( Q
% 0.10/0.42 != ( produc2922128104949294807at_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_convE
% 0.10/0.42 thf(fact_599_apfst__convE,axiom,
% 0.10/0.42 ! [Q: product_prod_nat_num,F: nat > nat,P: product_prod_nat_num] :
% 0.10/0.42 ( ( Q
% 0.10/0.42 = ( produc6767424583952363640at_num @ F @ P ) )
% 0.10/0.42 => ~ ! [X: nat,Y: num] :
% 0.10/0.42 ( ( P
% 0.10/0.42 = ( product_Pair_nat_num @ X @ Y ) )
% 0.10/0.42 => ( Q
% 0.10/0.42 != ( product_Pair_nat_num @ ( F @ X ) @ Y ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_convE
% 0.10/0.42 thf(fact_600_apfst__convE,axiom,
% 0.10/0.42 ! [Q: product_prod_nat_nat,F: nat > nat,P: product_prod_nat_nat] :
% 0.10/0.42 ( ( Q
% 0.10/0.42 = ( produc986720760941809198at_nat @ F @ P ) )
% 0.10/0.42 => ~ ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( P
% 0.10/0.42 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.10/0.42 => ( Q
% 0.10/0.42 != ( product_Pair_nat_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_convE
% 0.10/0.42 thf(fact_601_apfst__convE,axiom,
% 0.10/0.42 ! [Q: product_prod_int_int,F: int > int,P: product_prod_int_int] :
% 0.10/0.42 ( ( Q
% 0.10/0.42 = ( produc2355237562570658114nt_int @ F @ P ) )
% 0.10/0.42 => ~ ! [X: int,Y: int] :
% 0.10/0.42 ( ( P
% 0.10/0.42 = ( product_Pair_int_int @ X @ Y ) )
% 0.10/0.42 => ( Q
% 0.10/0.42 != ( product_Pair_int_int @ ( F @ X ) @ Y ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % apfst_convE
% 0.10/0.42 thf(fact_602_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: $o > $o,G22: $o > $o,F1: nat > $o,F22: nat > $o,V: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc1928436952130685430_o_o_o @ G1 @ G22 @ ( produc6957950696844810486_nat_o @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_603_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: $o > $o,G22: nat > num,F1: nat > $o,F22: int > nat,V: product_prod_nat_int] :
% 0.10/0.42 ( ( produc3628557804203378146at_num @ G1 @ G22 @ ( produc8250590009387450446nt_nat @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_604_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: $o > $o,G22: nat > nat,F1: nat > $o,F22: nat > nat,V: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc7071226018047599512at_nat @ G1 @ G22 @ ( produc7251236297486395890at_nat @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_nat_nat_nat @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_605_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: $o > $o,G22: int > nat,F1: nat > $o,F22: int > int,V: product_prod_nat_int] :
% 0.10/0.42 ( ( produc8070579729948654068nt_nat @ G1 @ G22 @ ( produc8248099538878400170nt_int @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_int_nat_int @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_606_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > num,G22: $o > $o,F1: int > nat,F22: nat > $o,V: product_prod_int_nat] :
% 0.10/0.42 ( ( produc3264868786340801506um_o_o @ G1 @ G22 @ ( produc8298419091753553490_nat_o @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_607_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > num,G22: nat > num,F1: int > nat,F22: int > nat,V: product_prod_int_int] :
% 0.10/0.42 ( ( produc1476026309457068494at_num @ G1 @ G22 @ ( produc5667422475138734578nt_nat @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_608_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > num,G22: nat > nat,F1: int > nat,F22: nat > nat,V: product_prod_int_nat] :
% 0.10/0.42 ( ( produc4918694523301289860at_nat @ G1 @ G22 @ ( produc4668068763237680022at_nat @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_nat_nat_nat @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_609_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > num,G22: int > nat,F1: int > nat,F22: int > int,V: product_prod_int_int] :
% 0.10/0.42 ( ( produc5918048235202344416nt_nat @ G1 @ G22 @ ( produc5664932004629684302nt_int @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_int_nat_int @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_610_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > nat,G22: $o > $o,F1: nat > nat,F22: nat > $o,V: product_prod_nat_nat] :
% 0.10/0.42 ( ( produc2001155298098703512at_o_o @ G1 @ G22 @ ( produc4787215299218314158_nat_o @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_611_prod_Omap__comp,axiom,
% 0.10/0.42 ! [G1: nat > nat,G22: nat > num,F1: nat > nat,F22: int > nat,V: product_prod_nat_int] :
% 0.10/0.42 ( ( produc3535218481486409604at_num @ G1 @ G22 @ ( produc7977240407231685526nt_nat @ F1 @ F22 @ V ) )
% 0.10/0.42 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.map_comp
% 0.10/0.42 thf(fact_612_subrelI,axiom,
% 0.10/0.42 ! [R: set_Pr7459493094073627847at_nat,S2: set_Pr7459493094073627847at_nat] :
% 0.10/0.42 ( ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.10/0.42 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ R )
% 0.10/0.42 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ S2 ) )
% 0.10/0.42 => ( ord_le5997549366648089703at_nat @ R @ S2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % subrelI
% 0.10/0.42 thf(fact_613_subrelI,axiom,
% 0.10/0.42 ! [R: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 0.10/0.42 ( ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
% 0.10/0.42 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ S2 ) )
% 0.10/0.42 => ( ord_le1268244103169919719at_nat @ R @ S2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % subrelI
% 0.10/0.42 thf(fact_614_subrelI,axiom,
% 0.10/0.42 ! [R: set_Pr6200539531224447659at_num,S2: set_Pr6200539531224447659at_num] :
% 0.10/0.42 ( ! [X: nat,Y: num] :
% 0.10/0.42 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R )
% 0.10/0.42 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ S2 ) )
% 0.10/0.42 => ( ord_le8085105155179020875at_num @ R @ S2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % subrelI
% 0.10/0.42 thf(fact_615_subrelI,axiom,
% 0.10/0.42 ! [R: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.10/0.42 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ S2 ) )
% 0.10/0.42 => ( ord_le3146513528884898305at_nat @ R @ S2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % subrelI
% 0.10/0.42 thf(fact_616_subrelI,axiom,
% 0.10/0.42 ! [R: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ! [X: int,Y: int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.10/0.42 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ S2 ) )
% 0.10/0.42 => ( ord_le2843351958646193337nt_int @ R @ S2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % subrelI
% 0.10/0.42 thf(fact_617_all__subset__image,axiom,
% 0.10/0.42 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 0.10/0.42 ( ( ! [B6: set_rat] :
% 0.10/0.42 ( ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ B6 ) ) )
% 0.10/0.42 = ( ! [B6: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.10/0.42 => ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % all_subset_image
% 0.10/0.42 thf(fact_618_all__subset__image,axiom,
% 0.10/0.42 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.10/0.42 ( ( ! [B6: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ B6 ) ) )
% 0.10/0.42 = ( ! [B6: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.10/0.42 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % all_subset_image
% 0.10/0.42 thf(fact_619_all__subset__image,axiom,
% 0.10/0.42 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 0.10/0.42 ( ( ! [B6: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ B6 ) ) )
% 0.10/0.42 = ( ! [B6: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.10/0.42 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % all_subset_image
% 0.10/0.42 thf(fact_620_all__subset__image,axiom,
% 0.10/0.42 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.10/0.42 ( ( ! [B6: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ B6 ) ) )
% 0.10/0.42 = ( ! [B6: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 0.10/0.42 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % all_subset_image
% 0.10/0.42 thf(fact_621_all__subset__image,axiom,
% 0.10/0.42 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 0.10/0.42 ( ( ! [B6: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 0.10/0.42 => ( P2 @ B6 ) ) )
% 0.10/0.42 = ( ! [B6: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 0.10/0.42 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % all_subset_image
% 0.10/0.42 thf(fact_622_rel__fun__Collect__case__prodD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 0.10/0.42 ( ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 0.10/0.42 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 0.10/0.42 => ( B5 @ ( comp_P8635049891247748876at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i5627883460353289149at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_Collect_case_prodD
% 0.10/0.42 thf(fact_623_rel__fun__Collect__case__prodD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 0.10/0.42 ( ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 0.10/0.42 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 0.10/0.42 => ( B5 @ ( comp_P4524073163769703009at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i4519014998770822500at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_Collect_case_prodD
% 0.10/0.42 thf(fact_624_rel__fun__Collect__case__prodD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 0.10/0.42 ( ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 0.10/0.42 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 0.10/0.42 => ( B5 @ ( comp_P7900071416159368952at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i653165354545908656at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_Collect_case_prodD
% 0.10/0.42 thf(fact_625_rel__fun__Collect__case__prodD,axiom,
% 0.10/0.42 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num,X5: set_Pr8415741480598773322nteger,X2: produc2963269191615333738nteger] :
% 0.10/0.42 ( ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( ord_le2638047946463454698nteger @ X5 @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ A4 ) ) )
% 0.10/0.42 => ( ( member4345257455949424659nteger @ X2 @ X5 )
% 0.10/0.42 => ( B5 @ ( comp_i3846818780818535807nteger @ F @ produc45500017171379470nteger @ X2 ) @ ( comp_C8580465762518603278nteger @ G @ produc2153544567185597776nteger @ X2 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_Collect_case_prodD
% 0.10/0.42 thf(fact_626_rel__fun__Collect__case__prodD,axiom,
% 0.10/0.42 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num,X5: set_Pr958786334691620121nt_int,X2: product_prod_int_int] :
% 0.10/0.42 ( ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) )
% 0.10/0.42 => ( ( member5262025264175285858nt_int @ X2 @ X5 )
% 0.10/0.42 => ( B5 @ ( comp_i7231038107349025742nt_int @ F @ product_fst_int_int @ X2 ) @ ( comp_i7231038107349025742nt_int @ G @ product_snd_int_int @ X2 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_Collect_case_prodD
% 0.10/0.42 thf(fact_627_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ ( bNF_co8276296344278409722at_nat @ ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat ) @ ( comp_n2711240574518091068at_nat @ G @ product_snd_nat_nat ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_vi6667456707345531737_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_628_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_4710180989675653397at_nat @ ( bNF_co5610825919353547504at_nat @ ( comp_r8155216869944865719t_unit @ F @ produc473321116828791851t_unit ) @ ( comp_h8354993580257045729t_unit @ G @ produc1126150082675451753t_unit ) ) @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_vi4623496019404053219_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_629_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: nat > int,G: nat > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_1990417195239315453nt_int @ ( bNF_co49787548815638194nt_int @ ( comp_n5749082658982224864at_nat @ F @ product_fst_nat_nat ) @ ( comp_n5749082658982224864at_nat @ G @ product_snd_nat_nat ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_vi8357618154448083105_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_630_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: ref_a > int,G: heap_e7401611519738050253t_unit > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_1531683682067511245nt_int @ ( bNF_co6607689160745551784nt_int @ ( comp_r7249815618783853587t_unit @ F @ produc473321116828791851t_unit ) @ ( comp_h7449592329096033597t_unit @ G @ produc1126150082675451753t_unit ) ) @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_vi7828673959370436579_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_631_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_5831868185956570253at_nat @ ( bNF_co2751916026326257842at_nat @ ( comp_i1292779930663060120nt_int @ F @ product_fst_int_int ) @ ( comp_i1292779930663060120nt_int @ G @ product_snd_int_int ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_vi2193923016096921761_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_632_convol__image__vimage2p,axiom,
% 0.10/0.42 ! [F: int > int,G: int > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ ( bNF_co3748779267718262122nt_int @ ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) @ ( comp_i4330622015127193916nt_int @ G @ product_snd_int_int ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_vi3884084463199473129_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_image_vimage2p
% 0.10/0.42 thf(fact_633_prod_Osize__gen__o__map,axiom,
% 0.10/0.42 ! [F: nat > nat,Fa: nat > nat,G: nat > nat,Ga: nat > nat] :
% 0.10/0.42 ( ( comp_P1567445206330693457at_nat @ ( basic_876126793109182934at_nat @ F @ Fa ) @ ( produc6977886695330630970at_nat @ G @ Ga ) )
% 0.10/0.42 = ( basic_876126793109182934at_nat @ ( comp_nat_nat_nat @ F @ G ) @ ( comp_nat_nat_nat @ Fa @ Ga ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.size_gen_o_map
% 0.10/0.42 thf(fact_634_prod_Osize__gen__o__map,axiom,
% 0.10/0.42 ! [F: nat > nat,Fa: int > nat,G: nat > nat,Ga: int > int] :
% 0.10/0.42 ( ( comp_P397146161216181329at_int @ ( basic_873636322600132658at_int @ F @ Fa ) @ ( produc7974749936722635250nt_int @ G @ Ga ) )
% 0.10/0.42 = ( basic_873636322600132658at_int @ ( comp_nat_nat_nat @ F @ G ) @ ( comp_int_nat_int @ Fa @ Ga ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.size_gen_o_map
% 0.10/0.42 thf(fact_635_prod_Osize__gen__o__map,axiom,
% 0.10/0.42 ! [F: int > nat,Fa: nat > nat,G: int > int,Ga: nat > nat] :
% 0.10/0.42 ( ( comp_P3488689526429045841nt_nat @ ( basic_1875480505010237490nt_nat @ F @ Fa ) @ ( produc5039722323474524658at_nat @ G @ Ga ) )
% 0.10/0.42 = ( basic_1875480505010237490nt_nat @ ( comp_int_nat_int @ F @ G ) @ ( comp_nat_nat_nat @ Fa @ Ga ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.size_gen_o_map
% 0.10/0.42 thf(fact_636_prod_Osize__gen__o__map,axiom,
% 0.10/0.42 ! [F: int > nat,Fa: int > nat,G: int > int,Ga: int > int] :
% 0.10/0.42 ( ( comp_P2318390481314533713nt_int @ ( basic_1872990034501187214nt_int @ F @ Fa ) @ ( produc6036585564866528938nt_int @ G @ Ga ) )
% 0.10/0.42 = ( basic_1872990034501187214nt_int @ ( comp_int_nat_int @ F @ G ) @ ( comp_int_nat_int @ Fa @ Ga ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % prod.size_gen_o_map
% 0.10/0.42 thf(fact_637_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca968750328013420230at_nat
% 0.10/0.42 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > nat] :
% 0.10/0.42 ! [I2: nat,J: nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_638_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca1968104039914474786nt_nat
% 0.10/0.42 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > nat] :
% 0.10/0.42 ! [I2: int,J: int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_639_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca966259857504369954at_int
% 0.10/0.42 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > int] :
% 0.10/0.42 ! [I2: nat,J: nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_640_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca1965613569405424510nt_int
% 0.10/0.42 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > int] :
% 0.10/0.42 ! [I2: int,J: int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_641_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca333620267926924494at_rat
% 0.10/0.42 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > rat] :
% 0.10/0.42 ! [I2: nat,J: nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_rat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_642_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca1332973979827979050nt_rat
% 0.10/0.42 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > rat] :
% 0.10/0.42 ! [I2: int,J: int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_rat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_643_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca30959104405961555nteger
% 0.10/0.42 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > code_integer] :
% 0.10/0.42 ! [I2: nat,J: nat] :
% 0.10/0.42 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_le3102999989581377725nteger @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_644_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca402612664642806191nteger
% 0.10/0.42 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > code_integer] :
% 0.10/0.42 ! [I2: int,J: int] :
% 0.10/0.42 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_le3102999989581377725nteger @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_645_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca4949091444211332621at_nat
% 0.10/0.42 = ( ^ [R5: set_Pr4329608150637261639at_nat,As: set_Pr1261947904930325089at_nat > nat] :
% 0.10/0.42 ! [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_646_relChain__def,axiom,
% 0.10/0.42 ( bNF_Ca4946600973702282345at_int
% 0.10/0.42 = ( ^ [R5: set_Pr4329608150637261639at_nat,As: set_Pr1261947904930325089at_nat > int] :
% 0.10/0.42 ! [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I2 @ J ) @ R5 )
% 0.10/0.42 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relChain_def
% 0.10/0.42 thf(fact_647_Collect__case__prod__in__rel__leI,axiom,
% 0.10/0.42 ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( ord_le3146513528884898305at_nat @ X5 @ Y4 )
% 0.10/0.42 => ( ord_le3146513528884898305at_nat @ X5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( fun_in_rel_nat_nat @ Y4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_in_rel_leI
% 0.10/0.42 thf(fact_648_Collect__case__prod__in__rel__leI,axiom,
% 0.10/0.42 ! [X5: set_Pr958786334691620121nt_int,Y4: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ( ord_le2843351958646193337nt_int @ X5 @ Y4 )
% 0.10/0.42 => ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( fun_in_rel_int_int @ Y4 ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_in_rel_leI
% 0.10/0.42 thf(fact_649_Collect__case__prod__in__rel__leE,axiom,
% 0.10/0.42 ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( ord_le3146513528884898305at_nat @ X5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( fun_in_rel_nat_nat @ Y4 ) ) ) )
% 0.10/0.42 => ( ord_le3146513528884898305at_nat @ X5 @ Y4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_in_rel_leE
% 0.10/0.42 thf(fact_650_Collect__case__prod__in__rel__leE,axiom,
% 0.10/0.42 ! [X5: set_Pr958786334691620121nt_int,Y4: set_Pr958786334691620121nt_int] :
% 0.10/0.42 ( ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( fun_in_rel_int_int @ Y4 ) ) ) )
% 0.10/0.42 => ( ord_le2843351958646193337nt_int @ X5 @ Y4 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_in_rel_leE
% 0.10/0.42 thf(fact_651_relcompp__assoc,axiom,
% 0.10/0.42 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,T2: int > int > $o] :
% 0.10/0.42 ( ( relcom2949942408940504938nt_int @ ( relcom8911704206367525917at_int @ R @ S2 ) @ T2 )
% 0.10/0.42 = ( relcom8911704206367525917at_int @ R @ ( relcom2949942408940504938nt_int @ S2 @ T2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_assoc
% 0.10/0.42 thf(fact_652_relcompp__assoc,axiom,
% 0.10/0.42 ! [R: int > int > $o,S2: int > code_integer > $o,T2: code_integer > code_integer > $o] :
% 0.10/0.42 ( ( relcom8320293257703906841nteger @ ( relcom967497705283160040nteger @ R @ S2 ) @ T2 )
% 0.10/0.42 = ( relcom967497705283160040nteger @ R @ ( relcom8320293257703906841nteger @ S2 @ T2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_assoc
% 0.10/0.42 thf(fact_653_relcompp__assoc,axiom,
% 0.10/0.42 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > product_prod_nat_nat > $o,T2: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( ( relcom8911704206367525917at_int @ ( relcom282571730187242960at_nat @ R @ S2 ) @ T2 )
% 0.10/0.42 = ( relcom8911704206367525917at_int @ R @ ( relcom8911704206367525917at_int @ S2 @ T2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_assoc
% 0.10/0.42 thf(fact_654_relcompp__assoc,axiom,
% 0.10/0.42 ! [R: int > int > $o,S2: int > int > $o,T2: int > code_integer > $o] :
% 0.10/0.42 ( ( relcom967497705283160040nteger @ ( relcompp_int_int_int @ R @ S2 ) @ T2 )
% 0.10/0.42 = ( relcom967497705283160040nteger @ R @ ( relcom967497705283160040nteger @ S2 @ T2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_assoc
% 0.10/0.42 thf(fact_655_relcompp__apply,axiom,
% 0.10/0.42 ( relcom8911704206367525917at_int
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > product_prod_nat_nat > $o,S4: product_prod_nat_nat > int > $o,A5: product_prod_nat_nat,C4: int] :
% 0.10/0.42 ? [B4: product_prod_nat_nat] :
% 0.10/0.42 ( ( R6 @ A5 @ B4 )
% 0.10/0.42 & ( S4 @ B4 @ C4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_apply
% 0.10/0.42 thf(fact_656_relcompp__apply,axiom,
% 0.10/0.42 ( relcom967497705283160040nteger
% 0.10/0.42 = ( ^ [R6: int > int > $o,S4: int > code_integer > $o,A5: int,C4: code_integer] :
% 0.10/0.42 ? [B4: int] :
% 0.10/0.42 ( ( R6 @ A5 @ B4 )
% 0.10/0.42 & ( S4 @ B4 @ C4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_apply
% 0.10/0.42 thf(fact_657_rel__funI,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funI
% 0.10/0.42 thf(fact_658_rel__funI,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funI
% 0.10/0.42 thf(fact_659_rel__funI,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funI
% 0.10/0.42 thf(fact_660_rel__funI,axiom,
% 0.10/0.42 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num] :
% 0.10/0.42 ( ! [X: int,Y: code_integer] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funI
% 0.10/0.42 thf(fact_661_rel__funI,axiom,
% 0.10/0.42 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num] :
% 0.10/0.42 ( ! [X: int,Y: int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.10/0.42 => ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funI
% 0.10/0.42 thf(fact_662_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: $o > $o > $o,Sd: $o > $o > $o] :
% 0.10/0.42 ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re2697311982885662685_nat_o
% 0.10/0.42 @ ( bNF_re4705727531993890431at_o_o
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re4705727531993890431at_o_o
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_o_o_nat
% 0.10/0.42 @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_663_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: $o > nat > $o,Sd: $o > nat > $o] :
% 0.10/0.42 ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re2144779315220482269at_nat
% 0.10/0.42 @ ( bNF_re7523573913982466217_o_nat
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re7523573913982466217_o_nat
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_o_o_nat
% 0.10/0.42 @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_664_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: nat > int > $o,Sd: num > nat > $o] :
% 0.10/0.42 ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re3642433447925381491nt_nat
% 0.10/0.42 @ ( bNF_re3713166177374151349at_int
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re1845987051190671011um_nat
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_nat_num_int
% 0.10/0.42 @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_665_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: nat > $o > $o,Sd: nat > $o > $o] :
% 0.10/0.42 ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re7744223787735169245_nat_o
% 0.10/0.42 @ ( bNF_re1402873238235875719_nat_o
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re1402873238235875719_nat_o
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_nat_nat_nat
% 0.10/0.42 @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_666_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: nat > nat > $o,Sd: nat > nat > $o] :
% 0.10/0.42 ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re239970166668089693at_nat
% 0.10/0.42 @ ( bNF_re5653821019739307937at_nat
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re5653821019739307937at_nat
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_nat_nat_nat
% 0.10/0.42 @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_667_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: int > nat > $o,Sd: nat > num > $o] :
% 0.10/0.42 ( bNF_re4310571189260822741nt_num @ ( bNF_re9124706910656911431at_num @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re7492190849051111027nt_num
% 0.10/0.42 @ ( bNF_re4715010359784256181nt_nat
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re272988434038980259at_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_int_nat_int
% 0.10/0.42 @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_668_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: int > int > $o,Sd: nat > nat > $o] :
% 0.10/0.42 ( bNF_re6307232852808291833nt_nat @ ( bNF_re3715656647883201625at_nat @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re2034674868506727813nt_nat
% 0.10/0.42 @ ( bNF_re4712519889275205905nt_int
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re3715656647883201625at_nat
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_int_nat_int
% 0.10/0.42 @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_669_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: nat > nat > $o,Sd: num > num > $o] :
% 0.10/0.42 ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re9099949428469764705nt_num
% 0.10/0.42 @ ( bNF_re3715656647883201625at_nat
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_nat_num_int
% 0.10/0.42 @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_670_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: num > num > $o,Sd: num > num > $o] :
% 0.10/0.42 ( bNF_re5446066262214944985nt_num @ ( bNF_re4736500879113541833um_num @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re4768042542643474933nt_num
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_num_num_int
% 0.10/0.42 @ comp_num_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_671_fun_Omap__transfer,axiom,
% 0.10/0.42 ! [Rb: int > code_integer > $o,Sd: num > num > $o] :
% 0.10/0.42 ( bNF_re7839584876883444355nt_num @ ( bNF_re6718328864250387230um_num @ Rb @ Sd )
% 0.10/0.42 @ ( bNF_re2961086658867094474nt_num
% 0.10/0.42 @ ( bNF_re982302072995117890nteger
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Rb )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ Sd ) )
% 0.10/0.42 @ comp_int_num_int
% 0.10/0.42 @ comp_C2177396528461469320um_int ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_transfer
% 0.10/0.42 thf(fact_672_rel__fun__iff__leq__vimage2p,axiom,
% 0.10/0.42 ( bNF_re4555766996558763186at_nat
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: nat > nat > $o,F2: product_prod_nat_nat > nat,G3: int > nat] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi5493721401438417730_nat_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_leq_vimage2p
% 0.10/0.42 thf(fact_673_rel__fun__iff__leq__vimage2p,axiom,
% 0.10/0.42 ( bNF_re7408651293131936558nt_int
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G3: int > int > int] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi8966365312794588230_int_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_leq_vimage2p
% 0.10/0.42 thf(fact_674_rel__fun__iff__leq__vimage2p,axiom,
% 0.10/0.42 ( bNF_re717283939379294677_int_o
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > $o,G3: int > int > $o] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi5082502771524357669nt_o_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_leq_vimage2p
% 0.10/0.42 thf(fact_675_rel__fun__iff__leq__vimage2p,axiom,
% 0.10/0.42 ( bNF_re6718328864250387230um_num
% 0.10/0.42 = ( ^ [R6: int > code_integer > $o,S4: num > num > $o,F2: int > num,G3: code_integer > num] : ( ord_le996066559646421213eger_o @ R6 @ ( bNF_vi2326032003723069084_num_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_leq_vimage2p
% 0.10/0.42 thf(fact_676_rel__fun__iff__leq__vimage2p,axiom,
% 0.10/0.42 ( bNF_re7626690874201225453um_num
% 0.10/0.42 = ( ^ [R6: int > int > $o,S4: num > num > $o,F2: int > num,G3: int > num] : ( ord_le6741204236512500942_int_o @ R6 @ ( bNF_vi2107963681178519309_num_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_leq_vimage2p
% 0.10/0.42 thf(fact_677_rel__fun__mono_H,axiom,
% 0.10/0.42 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: nat > nat > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( ( bNF_re4555766996558763186at_nat @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( bNF_re4555766996558763186at_nat @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono'
% 0.10/0.42 thf(fact_678_rel__fun__mono_H,axiom,
% 0.10/0.42 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat > product_prod_nat_nat,Y: int > int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( ( bNF_re7408651293131936558nt_int @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( bNF_re7408651293131936558nt_int @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono'
% 0.10/0.42 thf(fact_679_rel__fun__mono_H,axiom,
% 0.10/0.42 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] :
% 0.10/0.42 ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat > $o,Y: int > $o] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( ( bNF_re717283939379294677_int_o @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( bNF_re717283939379294677_int_o @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono'
% 0.10/0.42 thf(fact_680_rel__fun__mono_H,axiom,
% 0.10/0.42 ! [Y4: int > code_integer > $o,X5: int > code_integer > $o,A4: num > num > $o,B5: num > num > $o,F: int > num,G: code_integer > num] :
% 0.10/0.42 ( ! [X: int,Y: code_integer] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: num,Y: num] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( ( bNF_re6718328864250387230um_num @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( bNF_re6718328864250387230um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono'
% 0.10/0.42 thf(fact_681_rel__fun__mono_H,axiom,
% 0.10/0.42 ! [Y4: int > int > $o,X5: int > int > $o,A4: num > num > $o,B5: num > num > $o,F: int > num,G: int > num] :
% 0.10/0.42 ( ! [X: int,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: num,Y: num] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( ( bNF_re7626690874201225453um_num @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( bNF_re7626690874201225453um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono'
% 0.10/0.42 thf(fact_682_rel__fun__mono,axiom,
% 0.10/0.42 ! [X5: product_prod_nat_nat > int > $o,A4: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,Y4: product_prod_nat_nat > int > $o,B5: nat > nat > $o] :
% 0.10/0.42 ( ( bNF_re4555766996558763186at_nat @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: nat,Y: nat] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( bNF_re4555766996558763186at_nat @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono
% 0.10/0.42 thf(fact_683_rel__fun__mono,axiom,
% 0.10/0.42 ! [X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,Y4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o] :
% 0.10/0.42 ( ( bNF_re7408651293131936558nt_int @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat > product_prod_nat_nat,Y: int > int] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( bNF_re7408651293131936558nt_int @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono
% 0.10/0.42 thf(fact_684_rel__fun__mono,axiom,
% 0.10/0.42 ! [X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,Y4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o] :
% 0.10/0.42 ( ( bNF_re717283939379294677_int_o @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: product_prod_nat_nat > $o,Y: int > $o] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( bNF_re717283939379294677_int_o @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono
% 0.10/0.42 thf(fact_685_rel__fun__mono,axiom,
% 0.10/0.42 ! [X5: int > code_integer > $o,A4: num > num > $o,F: int > num,G: code_integer > num,Y4: int > code_integer > $o,B5: num > num > $o] :
% 0.10/0.42 ( ( bNF_re6718328864250387230um_num @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( ! [X: int,Y: code_integer] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: num,Y: num] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( bNF_re6718328864250387230um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono
% 0.10/0.42 thf(fact_686_rel__fun__mono,axiom,
% 0.10/0.42 ! [X5: int > int > $o,A4: num > num > $o,F: int > num,G: int > num,Y4: int > int > $o,B5: num > num > $o] :
% 0.10/0.42 ( ( bNF_re7626690874201225453um_num @ X5 @ A4 @ F @ G )
% 0.10/0.42 => ( ! [X: int,Y: int] :
% 0.10/0.42 ( ( Y4 @ X @ Y )
% 0.10/0.42 => ( X5 @ X @ Y ) )
% 0.10/0.42 => ( ! [X: num,Y: num] :
% 0.10/0.42 ( ( A4 @ X @ Y )
% 0.10/0.42 => ( B5 @ X @ Y ) )
% 0.10/0.42 => ( bNF_re7626690874201225453um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_mono
% 0.10/0.42 thf(fact_687_rel__funD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,X2: product_prod_nat_nat,Y3: int] :
% 0.10/0.42 ( ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( A4 @ X2 @ Y3 )
% 0.10/0.42 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funD
% 0.10/0.42 thf(fact_688_rel__funD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,X2: product_prod_nat_nat,Y3: int] :
% 0.10/0.42 ( ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( A4 @ X2 @ Y3 )
% 0.10/0.42 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funD
% 0.10/0.42 thf(fact_689_rel__funD,axiom,
% 0.10/0.42 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,X2: product_prod_nat_nat,Y3: int] :
% 0.10/0.42 ( ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( A4 @ X2 @ Y3 )
% 0.10/0.42 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funD
% 0.10/0.42 thf(fact_690_rel__funD,axiom,
% 0.10/0.42 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num,X2: int,Y3: code_integer] :
% 0.10/0.42 ( ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( A4 @ X2 @ Y3 )
% 0.10/0.42 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funD
% 0.10/0.42 thf(fact_691_rel__funD,axiom,
% 0.10/0.42 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num,X2: int,Y3: int] :
% 0.10/0.42 ( ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G )
% 0.10/0.42 => ( ( A4 @ X2 @ Y3 )
% 0.10/0.42 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_funD
% 0.10/0.42 thf(fact_692_fun_Orel__compp,axiom,
% 0.10/0.42 ! [R3: num > num > $o,S5: num > num > $o] :
% 0.10/0.42 ( ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ ( relcompp_num_num_num @ R3 @ S5 ) )
% 0.10/0.42 = ( relcom9025577121137075810nt_num
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ R3 )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ S5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.rel_compp
% 0.10/0.42 thf(fact_693_relcompp__mono,axiom,
% 0.10/0.42 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,S3: product_prod_nat_nat > int > $o,S2: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( ( ord_le5604493270027003598_nat_o @ R2 @ R )
% 0.10/0.42 => ( ( ord_le129227817499904167_int_o @ S3 @ S2 )
% 0.10/0.42 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R2 @ S3 ) @ ( relcom8911704206367525917at_int @ R @ S2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_mono
% 0.10/0.42 thf(fact_694_relcompp__mono,axiom,
% 0.10/0.42 ! [R2: int > int > $o,R: int > int > $o,S3: int > code_integer > $o,S2: int > code_integer > $o] :
% 0.10/0.42 ( ( ord_le6741204236512500942_int_o @ R2 @ R )
% 0.10/0.42 => ( ( ord_le996066559646421213eger_o @ S3 @ S2 )
% 0.10/0.42 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R2 @ S3 ) @ ( relcom967497705283160040nteger @ R @ S2 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp_mono
% 0.10/0.42 thf(fact_695_in__rel__def,axiom,
% 0.10/0.42 ( fun_in6812141508599261570at_nat
% 0.10/0.42 = ( ^ [R6: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_def
% 0.10/0.42 thf(fact_696_in__rel__def,axiom,
% 0.10/0.42 ( fun_in8056734985859589634at_nat
% 0.10/0.42 = ( ^ [R6: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_def
% 0.10/0.42 thf(fact_697_in__rel__def,axiom,
% 0.10/0.42 ( fun_in_rel_nat_num
% 0.10/0.42 = ( ^ [R6: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_def
% 0.10/0.42 thf(fact_698_in__rel__def,axiom,
% 0.10/0.42 ( fun_in_rel_nat_nat
% 0.10/0.42 = ( ^ [R6: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_def
% 0.10/0.42 thf(fact_699_in__rel__def,axiom,
% 0.10/0.42 ( fun_in_rel_int_int
% 0.10/0.42 = ( ^ [R6: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_def
% 0.10/0.42 thf(fact_700_in__rel__Collect__case__prod__eq,axiom,
% 0.10/0.42 ! [X5: nat > nat > $o] :
% 0.10/0.42 ( ( fun_in_rel_nat_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ X5 ) ) )
% 0.10/0.42 = X5 ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_Collect_case_prod_eq
% 0.10/0.42 thf(fact_701_in__rel__Collect__case__prod__eq,axiom,
% 0.10/0.42 ! [X5: int > int > $o] :
% 0.10/0.42 ( ( fun_in_rel_int_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ X5 ) ) )
% 0.10/0.42 = X5 ) ).
% 0.10/0.42
% 0.10/0.42 % in_rel_Collect_case_prod_eq
% 0.10/0.42 thf(fact_702_Collect__case__prod__mono,axiom,
% 0.10/0.42 ! [A4: nat > nat > $o,B5: nat > nat > $o] :
% 0.10/0.42 ( ( ord_le2646555220125990790_nat_o @ A4 @ B5 )
% 0.10/0.42 => ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A4 ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_mono
% 0.10/0.42 thf(fact_703_Collect__case__prod__mono,axiom,
% 0.10/0.42 ! [A4: int > int > $o,B5: int > int > $o] :
% 0.10/0.42 ( ( ord_le6741204236512500942_int_o @ A4 @ B5 )
% 0.10/0.42 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B5 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % Collect_case_prod_mono
% 0.10/0.42 thf(fact_704_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: num > num,F: nat > num,V: int > nat] :
% 0.10/0.42 ( ( comp_num_num_int @ G @ ( comp_nat_num_int @ F @ V ) )
% 0.10/0.42 = ( comp_nat_num_int @ ( comp_num_num_nat @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_705_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: nat > nat,F: int > nat,V: int > int] :
% 0.10/0.42 ( ( comp_nat_nat_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 0.10/0.42 = ( comp_int_nat_int @ ( comp_nat_nat_int @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_706_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: $o > $o,F: nat > $o,V: nat > nat] :
% 0.10/0.42 ( ( comp_o_o_nat @ G @ ( comp_nat_o_nat @ F @ V ) )
% 0.10/0.42 = ( comp_nat_o_nat @ ( comp_o_o_nat @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_707_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: $o > $o,F: $o > $o,V: nat > $o] :
% 0.10/0.42 ( ( comp_o_o_nat @ G @ ( comp_o_o_nat @ F @ V ) )
% 0.10/0.42 = ( comp_o_o_nat @ ( comp_o_o_o @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_708_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: nat > num,F: nat > nat,V: int > nat] :
% 0.10/0.42 ( ( comp_nat_num_int @ G @ ( comp_nat_nat_int @ F @ V ) )
% 0.10/0.42 = ( comp_nat_num_int @ ( comp_nat_num_nat @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_709_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: nat > num,F: int > nat,V: int > int] :
% 0.10/0.42 ( ( comp_nat_num_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 0.10/0.42 = ( comp_int_num_int @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_710_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: nat > nat,F: nat > nat,V: nat > nat] :
% 0.10/0.42 ( ( comp_nat_nat_nat @ G @ ( comp_nat_nat_nat @ F @ V ) )
% 0.10/0.42 = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_711_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: int > nat,F: int > int,V: int > int] :
% 0.10/0.42 ( ( comp_int_nat_int @ G @ ( comp_int_int_int @ F @ V ) )
% 0.10/0.42 = ( comp_int_nat_int @ ( comp_int_nat_int @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_712_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: code_integer > code_integer] :
% 0.10/0.42 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2931745410781319416nteger @ F @ V ) )
% 0.10/0.42 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_713_fun_Omap__comp,axiom,
% 0.10/0.42 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer > code_integer,V: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2822359487432382964nteger @ F @ V ) )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ G @ F ) @ V ) ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_comp
% 0.10/0.42 thf(fact_714_relcompp_Ocases,axiom,
% 0.10/0.42 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,A1: product_prod_nat_nat,A22: int] :
% 0.10/0.42 ( ( relcom8911704206367525917at_int @ R @ S2 @ A1 @ A22 )
% 0.10/0.42 => ~ ! [B3: product_prod_nat_nat] :
% 0.10/0.42 ( ( R @ A1 @ B3 )
% 0.10/0.42 => ~ ( S2 @ B3 @ A22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp.cases
% 0.10/0.42 thf(fact_715_relcompp_Ocases,axiom,
% 0.10/0.42 ! [R: int > int > $o,S2: int > code_integer > $o,A1: int,A22: code_integer] :
% 0.10/0.42 ( ( relcom967497705283160040nteger @ R @ S2 @ A1 @ A22 )
% 0.10/0.42 => ~ ! [B3: int] :
% 0.10/0.42 ( ( R @ A1 @ B3 )
% 0.10/0.42 => ~ ( S2 @ B3 @ A22 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp.cases
% 0.10/0.42 thf(fact_716_relcompp_Osimps,axiom,
% 0.10/0.42 ( relcom8911704206367525917at_int
% 0.10/0.42 = ( ^ [R5: product_prod_nat_nat > product_prod_nat_nat > $o,S: product_prod_nat_nat > int > $o,A12: product_prod_nat_nat,A23: int] :
% 0.10/0.42 ? [A5: product_prod_nat_nat,B4: product_prod_nat_nat,C4: int] :
% 0.10/0.42 ( ( A12 = A5 )
% 0.10/0.42 & ( A23 = C4 )
% 0.10/0.42 & ( R5 @ A5 @ B4 )
% 0.10/0.42 & ( S @ B4 @ C4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp.simps
% 0.10/0.42 thf(fact_717_relcompp_Osimps,axiom,
% 0.10/0.42 ( relcom967497705283160040nteger
% 0.10/0.42 = ( ^ [R5: int > int > $o,S: int > code_integer > $o,A12: int,A23: code_integer] :
% 0.10/0.42 ? [A5: int,B4: int,C4: code_integer] :
% 0.10/0.42 ( ( A12 = A5 )
% 0.10/0.42 & ( A23 = C4 )
% 0.10/0.42 & ( R5 @ A5 @ B4 )
% 0.10/0.42 & ( S @ B4 @ C4 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcompp.simps
% 0.10/0.42 thf(fact_718_eq__OO,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( ( relcom8911704206367525917at_int
% 0.10/0.42 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z )
% 0.10/0.42 @ R3 )
% 0.10/0.42 = R3 ) ).
% 0.10/0.42
% 0.10/0.42 % eq_OO
% 0.10/0.42 thf(fact_719_eq__OO,axiom,
% 0.10/0.42 ! [R3: int > code_integer > $o] :
% 0.10/0.42 ( ( relcom967497705283160040nteger
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.10/0.42 @ R3 )
% 0.10/0.42 = R3 ) ).
% 0.10/0.42
% 0.10/0.42 % eq_OO
% 0.10/0.42 thf(fact_720_relcomppE,axiom,
% 0.10/0.42 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,A: product_prod_nat_nat,C: int] :
% 0.10/0.42 ( ( relcom8911704206367525917at_int @ R @ S2 @ A @ C )
% 0.10/0.42 => ~ ! [B3: product_prod_nat_nat] :
% 0.10/0.42 ( ( R @ A @ B3 )
% 0.10/0.42 => ~ ( S2 @ B3 @ C ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcomppE
% 0.10/0.42 thf(fact_721_relcomppE,axiom,
% 0.10/0.42 ! [R: int > int > $o,S2: int > code_integer > $o,A: int,C: code_integer] :
% 0.10/0.42 ( ( relcom967497705283160040nteger @ R @ S2 @ A @ C )
% 0.10/0.42 => ~ ! [B3: int] :
% 0.10/0.42 ( ( R @ A @ B3 )
% 0.10/0.42 => ~ ( S2 @ B3 @ C ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcomppE
% 0.10/0.42 thf(fact_722_relcomppI,axiom,
% 0.10/0.42 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat,S2: product_prod_nat_nat > int > $o,C: int] :
% 0.10/0.42 ( ( R @ A @ B )
% 0.10/0.42 => ( ( S2 @ B @ C )
% 0.10/0.42 => ( relcom8911704206367525917at_int @ R @ S2 @ A @ C ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcomppI
% 0.10/0.42 thf(fact_723_relcomppI,axiom,
% 0.10/0.42 ! [R: int > int > $o,A: int,B: int,S2: int > code_integer > $o,C: code_integer] :
% 0.10/0.42 ( ( R @ A @ B )
% 0.10/0.42 => ( ( S2 @ B @ C )
% 0.10/0.42 => ( relcom967497705283160040nteger @ R @ S2 @ A @ C ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % relcomppI
% 0.10/0.42 thf(fact_724_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: $o > $o,H22: $o > $o,F: nat > $o,G: nat > $o] :
% 0.10/0.42 ( ( comp_P7034811116587396339_o_nat @ ( produc1928436952130685430_o_o_o @ H1 @ H22 ) @ ( bNF_convol_nat_o_o @ F @ G ) )
% 0.10/0.42 = ( bNF_convol_nat_o_o @ ( comp_o_o_nat @ H1 @ F ) @ ( comp_o_o_nat @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_725_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: $o > $o,H22: nat > nat,F: nat > $o,G: nat > nat] :
% 0.10/0.42 ( ( comp_P1391661485614827491at_nat @ ( produc7071226018047599512at_nat @ H1 @ H22 ) @ ( bNF_convol_nat_o_nat @ F @ G ) )
% 0.10/0.42 = ( bNF_convol_nat_o_nat @ ( comp_o_o_nat @ H1 @ F ) @ ( comp_nat_nat_nat @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_726_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: nat > num,H22: nat > num,F: int > nat,G: int > nat] :
% 0.10/0.42 ( ( comp_P7387482301570536291um_int @ ( produc1476026309457068494at_num @ H1 @ H22 ) @ ( bNF_co1177303703936631735at_nat @ F @ G ) )
% 0.10/0.42 = ( bNF_co5088337930254655563um_num @ ( comp_nat_num_int @ H1 @ F ) @ ( comp_nat_num_int @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_727_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: nat > num,H22: int > nat,F: int > nat,G: int > int] :
% 0.10/0.42 ( ( comp_P8376639181999047357at_int @ ( produc5918048235202344416nt_nat @ H1 @ H22 ) @ ( bNF_co1174813233427581459at_int @ F @ G ) )
% 0.10/0.42 = ( bNF_co8531006144098876929um_nat @ ( comp_nat_num_int @ H1 @ F ) @ ( comp_int_nat_int @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_728_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: nat > nat,H22: $o > $o,F: nat > nat,G: nat > $o] :
% 0.10/0.42 ( ( comp_P5799945282029801519_o_nat @ ( produc2001155298098703512at_o_o @ H1 @ H22 ) @ ( bNF_convol_nat_nat_o @ F @ G ) )
% 0.10/0.42 = ( bNF_convol_nat_nat_o @ ( comp_nat_nat_nat @ H1 @ F ) @ ( comp_o_o_nat @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_729_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: nat > nat,H22: nat > nat,F: nat > nat,G: nat > nat] :
% 0.10/0.42 ( ( comp_P7430769850142754163at_nat @ ( produc6977886695330630970at_nat @ H1 @ H22 ) @ ( bNF_co805650143699787099at_nat @ F @ G ) )
% 0.10/0.42 = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ H1 @ F ) @ ( comp_nat_nat_nat @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_730_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: int > nat,H22: nat > num,F: int > int,G: int > nat] :
% 0.10/0.42 ( ( comp_P1145193044942399421um_int @ ( produc1225400549393458656at_num @ H1 @ H22 ) @ ( bNF_co2176657415837686291nt_nat @ F @ G ) )
% 0.10/0.42 = ( bNF_co6958007526947186177at_num @ ( comp_int_nat_int @ H1 @ F ) @ ( comp_nat_num_int @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_731_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: int > nat,H22: int > nat,F: int > int,G: int > int] :
% 0.10/0.42 ( ( comp_P2134349925370910487at_int @ ( produc5667422475138734578nt_nat @ H1 @ H22 ) @ ( bNF_co2174166945328636015nt_int @ F @ G ) )
% 0.10/0.42 = ( bNF_co1177303703936631735at_nat @ ( comp_int_nat_int @ H1 @ F ) @ ( comp_int_nat_int @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_732_map__prod__o__convol,axiom,
% 0.10/0.42 ! [H1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,G: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( comp_P8564252314792299288nteger @ ( produc4724772261320961782nteger @ H1 @ H22 ) @ ( bNF_co6169604788974073338nteger @ F @ G ) )
% 0.10/0.42 = ( bNF_co3156833790671340178nteger @ ( comp_C8797469213163452608nteger @ H1 @ F ) @ ( comp_C8797469213163452608nteger @ H22 @ G ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol
% 0.10/0.42 thf(fact_733_convol__o,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,H: nat > $o] :
% 0.10/0.42 ( ( comp_o7658611401268416066_o_nat @ ( bNF_convol_o_o_o @ F @ G ) @ H )
% 0.10/0.42 = ( bNF_convol_nat_o_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_o
% 0.10/0.42 thf(fact_734_convol__o,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > num,H: int > nat] :
% 0.10/0.42 ( ( comp_n8531277669757933902um_int @ ( bNF_co4716684370017810927um_num @ F @ G ) @ H )
% 0.10/0.42 = ( bNF_co5088337930254655563um_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_o
% 0.10/0.42 thf(fact_735_convol__o,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > nat,H: nat > nat] :
% 0.10/0.42 ( ( comp_n8574565218330151774at_nat @ ( bNF_co805650143699787099at_nat @ F @ G ) @ H )
% 0.10/0.42 = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_o
% 0.10/0.42 thf(fact_736_convol__o,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > nat,H: int > int] :
% 0.10/0.42 ( ( comp_i1108739374719436894at_int @ ( bNF_co1177303703936631735at_nat @ F @ G ) @ H )
% 0.10/0.42 = ( bNF_co1177303703936631735at_nat @ ( comp_int_nat_int @ F @ H ) @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_o
% 0.10/0.42 thf(fact_737_convol__o,axiom,
% 0.10/0.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( comp_C6484513282182537548nteger @ ( bNF_co1764293801198077070nteger @ F @ G ) @ H )
% 0.10/0.42 = ( bNF_co3156833790671340178nteger @ ( comp_C8797469213163452608nteger @ F @ H ) @ ( comp_C8797469213163452608nteger @ G @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_o
% 0.10/0.42 thf(fact_738_vimage2p__relcompp__mono,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat,H: int > int] :
% 0.10/0.42 ( ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ T3 )
% 0.10/0.42 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ ( bNF_vi763171854521451549_nat_o @ F @ G @ R3 ) @ ( bNF_vi5426221348228882691_int_o @ G @ H @ S5 ) ) @ ( bNF_vi5426221348228882691_int_o @ F @ H @ T3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % vimage2p_relcompp_mono
% 0.10/0.42 thf(fact_739_vimage2p__relcompp__mono,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o,F: int > product_prod_nat_nat,G: int > product_prod_nat_nat,H: code_integer > int] :
% 0.10/0.42 ( ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ T3 )
% 0.10/0.42 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ ( bNF_vi1204582724742824157_nat_o @ F @ G @ R3 ) @ ( bNF_vi2881549544236934259_int_o @ G @ H @ S5 ) ) @ ( bNF_vi2881549544236934259_int_o @ F @ H @ T3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % vimage2p_relcompp_mono
% 0.10/0.42 thf(fact_740_vimage2p__relcompp__mono,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o,F: product_prod_nat_nat > int,G: product_prod_nat_nat > int,H: int > code_integer] :
% 0.10/0.42 ( ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ T3 )
% 0.10/0.42 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ ( bNF_vi2682369418337388893_int_o @ F @ G @ R3 ) @ ( bNF_vi33923956287962137eger_o @ G @ H @ S5 ) ) @ ( bNF_vi33923956287962137eger_o @ F @ H @ T3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % vimage2p_relcompp_mono
% 0.10/0.42 thf(fact_741_vimage2p__relcompp__mono,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o,F: int > int,G: int > int,H: code_integer > code_integer] :
% 0.10/0.42 ( ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ T3 )
% 0.10/0.42 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ ( bNF_vi3884084463199473129_int_o @ F @ G @ R3 ) @ ( bNF_vi699694178825965831eger_o @ G @ H @ S5 ) ) @ ( bNF_vi699694178825965831eger_o @ F @ H @ T3 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % vimage2p_relcompp_mono
% 0.10/0.42 thf(fact_742_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > code_integer > $o,S5: num > num > $o,R7: code_integer > code_integer > $o,S6: num > num > $o] : ( ord_le6931201860925936491_num_o @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_743_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > code_integer > $o,S5: num > num > $o,R7: code_integer > int > $o,S6: num > num > $o] : ( ord_le4541714130423454556_num_o @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_744_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: num > num > $o,R7: int > int > $o,S6: num > num > $o] : ( ord_le4541714130423454556_num_o @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_745_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: num > num > $o,R7: int > code_integer > $o,S6: num > num > $o] : ( ord_le6931201860925936491_num_o @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_746_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: int > int > $o,R7: int > code_integer > $o,S6: int > code_integer > $o] : ( ord_le7522433683449569238eger_o @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_747_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > int > $o,S5: nat > nat > $o,R7: int > int > $o,S6: nat > nat > $o] : ( ord_le1714508135640884727_nat_o @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_748_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: nat > nat > $o,R7: product_prod_nat_nat > int > $o,S6: nat > nat > $o] : ( ord_le1714508135640884727_nat_o @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_749_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: int > int > $o,R7: product_prod_nat_nat > int > $o,S6: int > code_integer > $o] : ( ord_le6141271677531915726eger_o @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_750_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: int > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,R7: int > code_integer > $o,S6: product_prod_nat_nat > int > $o] : ( ord_le8615040745438789472_int_o @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_751_pos__fun__distr,axiom,
% 0.10/0.42 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S6: product_prod_nat_nat > int > $o] : ( ord_le2484784447047653514_int_o @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % pos_fun_distr
% 0.10/0.42 thf(fact_752_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: nat > nat > $o] :
% 0.10/0.42 ( bNF_re6580757339198446453_nat_o
% 0.10/0.42 @ ^ [Y2: $o > $o,Z: $o > $o] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re2697311982885662685_nat_o
% 0.10/0.42 @ ( bNF_re4705727531993890431at_o_o @ R1
% 0.10/0.42 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re4705727531993890431at_o_o @ R1
% 0.10/0.42 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_o_o_nat
% 0.10/0.42 @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_753_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: nat > nat > $o] :
% 0.10/0.42 ( bNF_re3262823321055862553at_nat
% 0.10/0.42 @ ^ [Y2: nat > nat,Z: nat > nat] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re239970166668089693at_nat
% 0.10/0.42 @ ( bNF_re5653821019739307937at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re5653821019739307937at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_nat_nat_nat
% 0.10/0.42 @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_754_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: int > int > $o] :
% 0.10/0.42 ( bNF_re6307232852808291833nt_nat
% 0.10/0.42 @ ^ [Y2: int > nat,Z: int > nat] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re2034674868506727813nt_nat
% 0.10/0.42 @ ( bNF_re4712519889275205905nt_int @ R1
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re3715656647883201625at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_int_nat_int
% 0.10/0.42 @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_755_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: int > code_integer > $o] :
% 0.10/0.42 ( bNF_re2655444144887082515er_num
% 0.10/0.42 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re5502197115626545091er_num
% 0.10/0.42 @ ( bNF_re2807294637932363402at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re6718328864250387230um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_nat_num_int
% 0.10/0.42 @ comp_n2103536230552569900nteger ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_756_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: int > int > $o] :
% 0.10/0.42 ( bNF_re3846787885862361009nt_num
% 0.10/0.42 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re9099949428469764705nt_num
% 0.10/0.42 @ ( bNF_re3715656647883201625at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_nat_num_int
% 0.10/0.42 @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_757_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: int > code_integer > $o] :
% 0.10/0.42 ( bNF_re4105200416192800571er_num
% 0.10/0.42 @ ^ [Y2: num > num,Z: num > num] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re6292805115969292119er_num
% 0.10/0.42 @ ( bNF_re6718328864250387230um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re6718328864250387230um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_num_num_int
% 0.10/0.42 @ comp_n8557746072492896886nteger ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_758_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: int > int > $o] :
% 0.10/0.42 ( bNF_re5446066262214944985nt_num
% 0.10/0.42 @ ^ [Y2: num > num,Z: num > num] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re4768042542643474933nt_num
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re7626690874201225453um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_num_num_int
% 0.10/0.42 @ comp_num_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_759_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( bNF_re4099335476084980305nt_nat
% 0.10/0.42 @ ^ [Y2: int > nat,Z: int > nat] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re3284331099615978085nt_nat
% 0.10/0.42 @ ( bNF_re5552630237950767466nt_int @ R1
% 0.10/0.42 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re4555766996558763186at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_i4471277238271202272at_nat
% 0.10/0.42 @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_760_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( bNF_re2742285375668209089nt_num
% 0.10/0.42 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re2682547871993127601nt_num
% 0.10/0.42 @ ( bNF_re4555766996558763186at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re8466801222876787014um_num @ R1
% 0.10/0.42 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_n8649498751204056690at_nat
% 0.10/0.42 @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_761_o__rsp_I2_J,axiom,
% 0.10/0.42 ! [R1: product_prod_nat_nat > int > $o] :
% 0.10/0.42 ( bNF_re1160762158786734233nt_nat
% 0.10/0.42 @ ^ [Y2: nat > nat,Z: nat > nat] : ( Y2 = Z )
% 0.10/0.42 @ ( bNF_re8419181437172746013nt_nat
% 0.10/0.42 @ ( bNF_re4555766996558763186at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.42 @ ( bNF_re4555766996558763186at_nat @ R1
% 0.10/0.42 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 0.10/0.42 @ comp_n2711240574518091068at_nat
% 0.10/0.42 @ comp_nat_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(2)
% 0.10/0.42 thf(fact_762_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: $o > $o > $o,R32: $o > $o > $o,R1: nat > nat > $o] : ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ R22 @ R32 ) @ ( bNF_re2697311982885662685_nat_o @ ( bNF_re4705727531993890431at_o_o @ R1 @ R22 ) @ ( bNF_re4705727531993890431at_o_o @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_763_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: $o > nat > $o,R32: $o > num > $o,R1: nat > int > $o] : ( bNF_re7387973359137000979nt_num @ ( bNF_re766437678722298023_o_num @ R22 @ R32 ) @ ( bNF_re4102725726183926567nt_num @ ( bNF_re8210149947023016781_o_nat @ R1 @ R22 ) @ ( bNF_re4767481733178795415_o_num @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_764_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: $o > nat > $o,R32: $o > nat > $o,R1: nat > nat > $o] : ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ R22 @ R32 ) @ ( bNF_re2144779315220482269at_nat @ ( bNF_re7523573913982466217_o_nat @ R1 @ R22 ) @ ( bNF_re7523573913982466217_o_nat @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_765_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: $o > int > $o,R32: $o > nat > $o,R1: nat > int > $o] : ( bNF_re7413876800493218871nt_nat @ ( bNF_re4895681925607069953_o_nat @ R22 @ R32 ) @ ( bNF_re1982657550219213441nt_nat @ ( bNF_re8207659476513966505_o_int @ R1 @ R22 ) @ ( bNF_re8210149947023016781_o_nat @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_766_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > $o > $o,R32: num > $o > $o,R1: int > nat > $o] : ( bNF_re3931674169038344211_nat_o @ ( bNF_re8508505965575957011_num_o @ R22 @ R32 ) @ ( bNF_re7435575058205011731_nat_o @ ( bNF_re4914077030771115051_nat_o @ R1 @ R22 ) @ ( bNF_re3760060065607074657_num_o @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_767_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > nat > $o,R32: num > nat > $o,R1: int > nat > $o] : ( bNF_re6524732562925676389at_nat @ ( bNF_re3784151423046777323um_nat @ R22 @ R32 ) @ ( bNF_re717418264989850719at_nat @ ( bNF_re3344003087646356989at_nat @ R1 @ R22 ) @ ( bNF_re1474333490953826375um_nat @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_768_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > int > $o,R32: num > nat > $o,R1: int > int > $o] : ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ R22 @ R32 ) @ ( bNF_re3642433447925381491nt_nat @ ( bNF_re3713166177374151349at_int @ R1 @ R22 ) @ ( bNF_re1845987051190671011um_nat @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_769_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > $o > $o,R32: nat > $o > $o,R1: nat > nat > $o] : ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ R22 @ R32 ) @ ( bNF_re7744223787735169245_nat_o @ ( bNF_re1402873238235875719_nat_o @ R1 @ R22 ) @ ( bNF_re1402873238235875719_nat_o @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_770_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > nat > $o,R32: nat > num > $o,R1: nat > int > $o] : ( bNF_re584878643992547173nt_num @ ( bNF_re2211152805895086571at_num @ R22 @ R32 ) @ ( bNF_re8622501330148003679nt_num @ ( bNF_re6025474579976152573at_nat @ R1 @ R22 ) @ ( bNF_re2582806366131931207at_num @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_771_o__rsp_I1_J,axiom,
% 0.10/0.42 ! [R22: nat > nat > $o,R32: nat > nat > $o,R1: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ R22 @ R32 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ R1 @ R22 ) @ ( bNF_re5653821019739307937at_nat @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % o_rsp(1)
% 0.10/0.42 thf(fact_772_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: int > int,H: nat > int,R12: nat > int,R23: nat > nat,F: int > nat,L: nat > nat] :
% 0.10/0.42 ( ( ( comp_int_int_nat @ G @ H )
% 0.10/0.42 = ( comp_nat_int_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_int_nat_nat @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_773_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: nat > int,H: nat > nat,R12: int > int,R23: nat > int,F: int > nat,L: int > nat] :
% 0.10/0.42 ( ( ( comp_nat_int_nat @ G @ H )
% 0.10/0.42 = ( comp_int_int_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_int_nat_int @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_nat_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_774_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: int > int,H: int > int,R12: int > int,R23: int > int,F: int > nat,L: int > nat] :
% 0.10/0.42 ( ( ( comp_int_int_int @ G @ H )
% 0.10/0.42 = ( comp_int_int_int @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_int_nat_int @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_nat_int @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_775_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: nat > $o,H: nat > nat,R12: $o > $o,R23: nat > $o,F: $o > $o,L: $o > $o] :
% 0.10/0.42 ( ( ( comp_nat_o_nat @ G @ H )
% 0.10/0.42 = ( comp_o_o_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_o_o_o @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_o_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_776_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: nat > $o,H: nat > nat,R12: $o > $o,R23: nat > $o,F: $o > nat,L: $o > nat] :
% 0.10/0.42 ( ( ( comp_nat_o_nat @ G @ H )
% 0.10/0.42 = ( comp_o_o_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_o_nat_o @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_nat_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_777_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: int > num,H: int > int,R12: nat > num,R23: int > nat,F: num > nat,L: nat > nat] :
% 0.10/0.42 ( ( ( comp_int_num_int @ G @ H )
% 0.10/0.42 = ( comp_nat_num_int @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_num_nat_nat @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_num_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_int @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_778_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: int > nat,H: nat > int,R12: nat > nat,R23: nat > nat,F: nat > num,L: nat > num] :
% 0.10/0.42 ( ( ( comp_int_nat_nat @ G @ H )
% 0.10/0.42 = ( comp_nat_nat_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_nat_num_nat @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_int_num_nat @ ( comp_nat_num_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_num_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_779_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: $o > nat,H: nat > $o,R12: nat > nat,R23: nat > nat,F: nat > $o,L: nat > $o] :
% 0.10/0.42 ( ( ( comp_o_nat_nat @ G @ H )
% 0.10/0.42 = ( comp_nat_nat_nat @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_nat_o_nat @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_o_o_nat @ ( comp_nat_o_o @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_o_nat @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_780_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: nat > nat,H: int > nat,R12: int > nat,R23: int > int,F: nat > nat,L: int > nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_int @ G @ H )
% 0.10/0.42 = ( comp_int_nat_int @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_nat_nat_int @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_nat_int @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_781_rewriteR__comp__comp2,axiom,
% 0.10/0.42 ! [G: nat > nat,H: int > nat,R12: int > nat,R23: int > int,F: nat > num,L: int > num] :
% 0.10/0.42 ( ( ( comp_nat_nat_int @ G @ H )
% 0.10/0.42 = ( comp_int_nat_int @ R12 @ R23 ) )
% 0.10/0.42 => ( ( ( comp_nat_num_int @ F @ R12 )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_num_int @ L @ R23 ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp2
% 0.10/0.42 thf(fact_782_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: $o > nat,G: $o > $o,L1: nat > nat,L2: $o > nat,H: nat > $o,R: nat > nat] :
% 0.10/0.42 ( ( ( comp_o_nat_o @ F @ G )
% 0.10/0.42 = ( comp_nat_nat_o @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_o_nat_nat @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_o_nat_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 0.10/0.42 = ( comp_nat_nat_nat @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_783_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: num > num,G: nat > num,L1: nat > num,L2: nat > nat,H: int > nat,R: int > nat] :
% 0.10/0.42 ( ( ( comp_num_num_nat @ F @ G )
% 0.10/0.42 = ( comp_nat_num_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_nat_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 0.10/0.42 = ( comp_nat_num_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_784_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: num > nat,G: nat > num,L1: int > nat,L2: nat > int,H: int > nat,R: int > int] :
% 0.10/0.42 ( ( ( comp_num_nat_nat @ F @ G )
% 0.10/0.42 = ( comp_int_nat_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_int_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_num_nat_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 0.10/0.42 = ( comp_int_nat_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_785_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,L1: $o > $o,L2: $o > $o,H: nat > $o,R: nat > $o] :
% 0.10/0.42 ( ( ( comp_o_o_o @ F @ G )
% 0.10/0.42 = ( comp_o_o_o @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_o_o_nat @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 0.10/0.42 = ( comp_o_o_nat @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_786_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: nat > nat,G: $o > nat,L1: $o > nat,L2: $o > $o,H: nat > $o,R: nat > $o] :
% 0.10/0.42 ( ( ( comp_nat_nat_o @ F @ G )
% 0.10/0.42 = ( comp_o_nat_o @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_o_o_nat @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ F @ ( comp_o_nat_nat @ G @ H ) )
% 0.10/0.42 = ( comp_o_nat_nat @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_787_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,L1: num > num,L2: nat > num,H: int > nat,R: int > num] :
% 0.10/0.42 ( ( ( comp_nat_num_nat @ F @ G )
% 0.10/0.42 = ( comp_num_num_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_num_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) )
% 0.10/0.42 = ( comp_num_num_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_788_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: int > nat,G: nat > int,L1: num > nat,L2: nat > num,H: int > nat,R: int > num] :
% 0.10/0.42 ( ( ( comp_int_nat_nat @ F @ G )
% 0.10/0.42 = ( comp_num_nat_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_num_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_int_nat_int @ F @ ( comp_nat_int_int @ G @ H ) )
% 0.10/0.42 = ( comp_num_nat_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_789_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: num > $o,G: nat > num,L1: $o > $o,L2: nat > $o,H: int > nat,R: int > $o] :
% 0.10/0.42 ( ( ( comp_num_o_nat @ F @ G )
% 0.10/0.42 = ( comp_o_o_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_o_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_num_o_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 0.10/0.42 = ( comp_o_o_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_790_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: nat > $o,G: nat > nat,L1: $o > $o,L2: nat > $o,H: nat > nat,R: nat > $o] :
% 0.10/0.42 ( ( ( comp_nat_o_nat @ F @ G )
% 0.10/0.42 = ( comp_o_o_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_o_nat @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_o_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
% 0.10/0.42 = ( comp_o_o_nat @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_791_rewriteL__comp__comp2,axiom,
% 0.10/0.42 ! [F: num > nat,G: nat > num,L1: nat > nat,L2: nat > nat,H: int > nat,R: int > nat] :
% 0.10/0.42 ( ( ( comp_num_nat_nat @ F @ G )
% 0.10/0.42 = ( comp_nat_nat_nat @ L1 @ L2 ) )
% 0.10/0.42 => ( ( ( comp_nat_nat_int @ L2 @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_num_nat_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 0.10/0.42 = ( comp_nat_nat_int @ L1 @ R ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp2
% 0.10/0.42 thf(fact_792_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: nat > $o,H: nat > nat,R: nat > $o,F: $o > $o] :
% 0.10/0.42 ( ( ( comp_nat_o_nat @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_o_nat @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_793_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: nat > nat,H: int > nat,R: int > nat,F: nat > num] :
% 0.10/0.42 ( ( ( comp_nat_nat_int @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_num_int @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_794_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: int > int,H: int > int,R: int > int,F: int > nat] :
% 0.10/0.42 ( ( ( comp_int_int_int @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_int_nat_int @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_795_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: $o > $o,H: nat > $o,R: nat > $o,F: $o > $o] :
% 0.10/0.42 ( ( ( comp_o_o_nat @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ G ) @ H )
% 0.10/0.42 = ( comp_o_o_nat @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_796_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: nat > num,H: int > nat,R: int > num,F: num > num] :
% 0.10/0.42 ( ( ( comp_nat_num_int @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_num_num_int @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_797_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: nat > nat,H: nat > nat,R: nat > nat,F: nat > nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_nat @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_nat @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_798_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: int > nat,H: int > int,R: int > nat,F: nat > num] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_num_int @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_799_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: int > nat,H: int > int,R: int > nat,F: nat > nat] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ G ) @ H )
% 0.10/0.42 = ( comp_nat_nat_int @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_800_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: code_integer > code_integer > code_integer,H: code_integer > code_integer,R: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.10/0.42 ( ( ( comp_C2931745410781319416nteger @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_801_rewriteR__comp__comp,axiom,
% 0.10/0.42 ! [G: ( code_integer > code_integer ) > code_integer > code_integer,H: code_integer > code_integer > code_integer,R: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.10/0.42 ( ( ( comp_C2822359487432382964nteger @ G @ H )
% 0.10/0.42 = R )
% 0.10/0.42 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ F @ R ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteR_comp_comp
% 0.10/0.42 thf(fact_802_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: num > num,G: nat > num,L: nat > num,H: int > nat] :
% 0.10/0.42 ( ( ( comp_num_num_nat @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 0.10/0.42 = ( comp_nat_num_int @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_803_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: int > nat,L: int > nat,H: int > int] :
% 0.10/0.42 ( ( ( comp_nat_nat_int @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_nat_int @ F @ ( comp_int_nat_int @ G @ H ) )
% 0.10/0.42 = ( comp_int_nat_int @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_804_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,L: $o > $o,H: nat > $o] :
% 0.10/0.42 ( ( ( comp_o_o_o @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 0.10/0.42 = ( comp_o_o_nat @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_805_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,L: nat > num,H: int > nat] :
% 0.10/0.42 ( ( ( comp_nat_num_nat @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) )
% 0.10/0.42 = ( comp_nat_num_int @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_806_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: $o > $o,G: nat > $o,L: nat > $o,H: nat > nat] :
% 0.10/0.42 ( ( ( comp_o_o_nat @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_o_o_nat @ F @ ( comp_nat_o_nat @ G @ H ) )
% 0.10/0.42 = ( comp_nat_o_nat @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_807_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: nat > num,G: int > nat,L: int > num,H: int > int] :
% 0.10/0.42 ( ( ( comp_nat_num_int @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H ) )
% 0.10/0.42 = ( comp_int_num_int @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_808_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: nat > nat,G: nat > nat,L: nat > nat,H: nat > nat] :
% 0.10/0.42 ( ( ( comp_nat_nat_nat @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
% 0.10/0.42 = ( comp_nat_nat_nat @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_809_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: int > nat,G: int > int,L: int > nat,H: int > int] :
% 0.10/0.42 ( ( ( comp_int_nat_int @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_int_nat_int @ F @ ( comp_int_int_int @ G @ H ) )
% 0.10/0.42 = ( comp_int_nat_int @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_810_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer] :
% 0.10/0.42 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H ) )
% 0.10/0.42 = ( comp_C1593894019821074884nteger @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_811_rewriteL__comp__comp,axiom,
% 0.10/0.42 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] :
% 0.10/0.42 ( ( ( comp_C3983183376822107068nteger @ F @ G )
% 0.10/0.42 = L )
% 0.10/0.42 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H ) )
% 0.10/0.42 = ( comp_C8797469213163452608nteger @ L @ H ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rewriteL_comp_comp
% 0.10/0.42 thf(fact_812_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: nat > $o,G: nat > nat,X2: nat,N: $o > $o,H: nat > $o,F: $o > $o] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_o_o_nat @ ( comp_o_o_o @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_813_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: int > nat,G: int > int,X2: int,N: nat > nat,H: int > nat,F: nat > num] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_814_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: nat > nat,G: int > nat,X2: int,N: int > nat,H: int > int,F: nat > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_815_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: int > int,G: nat > int,X2: nat,N: nat > int,H: nat > nat,F: int > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_816_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: $o > $o,G: nat > $o,X2: nat,N: nat > $o,H: nat > nat,F: $o > $o] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_817_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: nat > nat,G: int > nat,X2: int,N: int > nat,H: int > int,F: nat > num] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_int_num_int @ ( comp_nat_num_int @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_818_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: nat > int,G: nat > nat,X2: nat,N: int > int,H: nat > int,F: int > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_819_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: nat > nat,G: nat > nat,X2: nat,N: nat > nat,H: nat > nat,F: nat > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_820_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: int > nat,G: int > int,X2: int,N: nat > nat,H: int > nat,F: nat > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_821_type__copy__map__cong0,axiom,
% 0.10/0.42 ! [M: int > int,G: int > int,X2: int,N: int > int,H: int > int,F: int > nat] :
% 0.10/0.42 ( ( ( M @ ( G @ X2 ) )
% 0.10/0.42 = ( N @ ( H @ X2 ) ) )
% 0.10/0.42 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ M ) @ G @ X2 )
% 0.10/0.42 = ( comp_int_nat_int @ ( comp_int_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % type_copy_map_cong0
% 0.10/0.42 thf(fact_822_comp__transfer,axiom,
% 0.10/0.42 ! [B5: $o > $o > $o,C3: $o > $o > $o,A4: nat > nat > $o] : ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ B5 @ C3 ) @ ( bNF_re2697311982885662685_nat_o @ ( bNF_re4705727531993890431at_o_o @ A4 @ B5 ) @ ( bNF_re4705727531993890431at_o_o @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_823_comp__transfer,axiom,
% 0.10/0.42 ! [B5: $o > nat > $o,C3: $o > num > $o,A4: nat > int > $o] : ( bNF_re7387973359137000979nt_num @ ( bNF_re766437678722298023_o_num @ B5 @ C3 ) @ ( bNF_re4102725726183926567nt_num @ ( bNF_re8210149947023016781_o_nat @ A4 @ B5 ) @ ( bNF_re4767481733178795415_o_num @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_824_comp__transfer,axiom,
% 0.10/0.42 ! [B5: $o > nat > $o,C3: $o > nat > $o,A4: nat > nat > $o] : ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ B5 @ C3 ) @ ( bNF_re2144779315220482269at_nat @ ( bNF_re7523573913982466217_o_nat @ A4 @ B5 ) @ ( bNF_re7523573913982466217_o_nat @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_825_comp__transfer,axiom,
% 0.10/0.42 ! [B5: $o > int > $o,C3: $o > nat > $o,A4: nat > int > $o] : ( bNF_re7413876800493218871nt_nat @ ( bNF_re4895681925607069953_o_nat @ B5 @ C3 ) @ ( bNF_re1982657550219213441nt_nat @ ( bNF_re8207659476513966505_o_int @ A4 @ B5 ) @ ( bNF_re8210149947023016781_o_nat @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_826_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > $o > $o,C3: num > $o > $o,A4: int > nat > $o] : ( bNF_re3931674169038344211_nat_o @ ( bNF_re8508505965575957011_num_o @ B5 @ C3 ) @ ( bNF_re7435575058205011731_nat_o @ ( bNF_re4914077030771115051_nat_o @ A4 @ B5 ) @ ( bNF_re3760060065607074657_num_o @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_827_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > nat > $o,C3: num > nat > $o,A4: int > nat > $o] : ( bNF_re6524732562925676389at_nat @ ( bNF_re3784151423046777323um_nat @ B5 @ C3 ) @ ( bNF_re717418264989850719at_nat @ ( bNF_re3344003087646356989at_nat @ A4 @ B5 ) @ ( bNF_re1474333490953826375um_nat @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_828_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > int > $o,C3: num > nat > $o,A4: int > int > $o] : ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ B5 @ C3 ) @ ( bNF_re3642433447925381491nt_nat @ ( bNF_re3713166177374151349at_int @ A4 @ B5 ) @ ( bNF_re1845987051190671011um_nat @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_int_nat_int ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_829_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > $o > $o,C3: nat > $o > $o,A4: nat > nat > $o] : ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ B5 @ C3 ) @ ( bNF_re7744223787735169245_nat_o @ ( bNF_re1402873238235875719_nat_o @ A4 @ B5 ) @ ( bNF_re1402873238235875719_nat_o @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_o_o_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_830_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > nat > $o,C3: nat > num > $o,A4: nat > int > $o] : ( bNF_re584878643992547173nt_num @ ( bNF_re2211152805895086571at_num @ B5 @ C3 ) @ ( bNF_re8622501330148003679nt_num @ ( bNF_re6025474579976152573at_nat @ A4 @ B5 ) @ ( bNF_re2582806366131931207at_num @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_nat_num_int ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_831_comp__transfer,axiom,
% 0.10/0.42 ! [B5: nat > nat > $o,C3: nat > nat > $o,A4: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ B5 @ C3 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ A4 @ B5 ) @ ( bNF_re5653821019739307937at_nat @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % comp_transfer
% 0.10/0.42 thf(fact_832_rel__fun__iff__geq__image2p,axiom,
% 0.10/0.42 ( bNF_re4555766996558763186at_nat
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: nat > nat > $o,F2: product_prod_nat_nat > nat,G3: int > nat] : ( ord_le2646555220125990790_nat_o @ ( bNF_Gr6955563364113978072nt_nat @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_geq_image2p
% 0.10/0.42 thf(fact_833_rel__fun__iff__geq__image2p,axiom,
% 0.10/0.42 ( bNF_re7408651293131936558nt_int
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G3: int > int > int] : ( ord_le2484784447047653514_int_o @ ( bNF_Gr1354378531936274772nt_int @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_geq_image2p
% 0.10/0.42 thf(fact_834_rel__fun__iff__geq__image2p,axiom,
% 0.10/0.42 ( bNF_re717283939379294677_int_o
% 0.10/0.42 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > $o,G3: int > int > $o] : ( ord_le2932013042137311317nt_o_o @ ( bNF_Gr364077372107685167_int_o @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_geq_image2p
% 0.10/0.42 thf(fact_835_rel__fun__iff__geq__image2p,axiom,
% 0.10/0.42 ( bNF_re6718328864250387230um_num
% 0.10/0.42 = ( ^ [R6: int > code_integer > $o,S4: num > num > $o,F2: int > num,G3: code_integer > num] : ( ord_le6124364862034508274_num_o @ ( bNF_Gr166583433173494904er_num @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_geq_image2p
% 0.10/0.42 thf(fact_836_rel__fun__iff__geq__image2p,axiom,
% 0.10/0.42 ( bNF_re7626690874201225453um_num
% 0.10/0.42 = ( ^ [R6: int > int > $o,S4: num > num > $o,F2: int > num,G3: int > num] : ( ord_le6124364862034508274_num_o @ ( bNF_Gr7020624548710275655nt_num @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % rel_fun_iff_geq_image2p
% 0.10/0.42 thf(fact_837_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > nat,X2: nat] :
% 0.10/0.42 ( ( comp_P5371577678113413053at_nat @ ( produc4918694523301289860at_nat @ F @ id_nat ) @ ( bNF_co805650143699787099at_nat @ id_nat @ G ) @ X2 )
% 0.10/0.42 = ( bNF_co8159352583862032293um_nat @ ( comp_num_num_nat @ id_num @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_838_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: $o > nat,G: $o > nat,X2: $o] :
% 0.10/0.42 ( ( comp_P196761593691424337_nat_o @ ( produc6587185857518356756at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_o_nat_nat @ ( comp_nat_nat_o @ id_nat @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_839_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > nat,X2: $o] :
% 0.10/0.42 ( ( comp_P1422407636550552773_nat_o @ ( produc7071226018047599512at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_o_o_nat @ ( comp_o_o_o @ id_o @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_840_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: $o > num,G: $o > nat,X2: $o] :
% 0.10/0.42 ( ( comp_P972951341003599239_nat_o @ ( produc4527993685489015646at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_o_num_nat @ ( comp_num_num_o @ id_num @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_841_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: num > nat,G: num > nat,X2: num] :
% 0.10/0.42 ( ( comp_P2539519431309506803at_num @ ( produc4208724500416182148at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 0.10/0.42 = ( bNF_co7969830008525221797at_nat @ ( comp_nat_nat_num @ id_nat @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_842_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: num > $o,G: num > nat,X2: num] :
% 0.10/0.42 ( ( comp_P3192427084145116251at_num @ ( produc8319293927732033832at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_num_o_nat @ ( comp_o_o_num @ id_o @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_843_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: num > num,G: num > nat,X2: num] :
% 0.10/0.42 ( ( comp_P480327259280165693at_num @ ( produc2149532328386841038at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 0.10/0.42 = ( bNF_co6100160411832691183um_nat @ ( comp_num_num_num @ id_num @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_844_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: nat > num,G: nat > $o,X2: nat] :
% 0.10/0.42 ( ( comp_P6576135029341976421_o_nat @ ( produc3264868786340801506um_o_o @ F @ id_o ) @ ( bNF_convol_nat_nat_o @ id_nat @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_nat_num_o @ ( comp_num_num_nat @ id_num @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_845_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: $o > nat,G: $o > $o,X2: $o] :
% 0.10/0.42 ( ( comp_P1471321874221585045at_o_o @ ( produc9141321880750005618at_o_o @ F @ id_o ) @ ( bNF_convol_o_o_o @ id_o @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_o_nat_o @ ( comp_nat_nat_o @ id_nat @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_846_map__prod__o__convol__id,axiom,
% 0.10/0.42 ! [F: $o > $o,G: $o > $o,X2: $o] :
% 0.10/0.42 ( ( comp_P551574746845053877_o_o_o @ ( produc1928436952130685430_o_o_o @ F @ id_o ) @ ( bNF_convol_o_o_o @ id_o @ G ) @ X2 )
% 0.10/0.42 = ( bNF_convol_o_o_o @ ( comp_o_o_o @ id_o @ F ) @ G @ X2 ) ) ).
% 0.10/0.42
% 0.10/0.42 % map_prod_o_convol_id
% 0.10/0.42 thf(fact_847_image__Fpow__mono,axiom,
% 0.10/0.42 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.10/0.42 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.10/0.42 => ( ord_le513522071413781156et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_rat @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_Fpow_mono
% 0.10/0.42 thf(fact_848_image__Fpow__mono,axiom,
% 0.10/0.42 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.10/0.42 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_nat @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_Fpow_mono
% 0.10/0.42 thf(fact_849_image__Fpow__mono,axiom,
% 0.10/0.42 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.10/0.42 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_int @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_Fpow_mono
% 0.10/0.42 thf(fact_850_image__Fpow__mono,axiom,
% 0.10/0.42 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.10/0.42 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.10/0.42 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_nat @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_Fpow_mono
% 0.10/0.42 thf(fact_851_image__Fpow__mono,axiom,
% 0.10/0.42 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.10/0.42 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.10/0.42 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_int @ B5 ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % image_Fpow_mono
% 0.10/0.42 thf(fact_852_convol__mem__GrpI,axiom,
% 0.10/0.42 ! [X2: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,G: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.10/0.42 ( ( member2643936169264416010at_nat @ X2 @ A4 )
% 0.10/0.42 => ( member8757157785044589968at_nat @ ( bNF_co147202357524637304at_nat @ id_set2334057505560298834at_nat @ G @ X2 ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ G ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_mem_GrpI
% 0.10/0.42 thf(fact_853_convol__mem__GrpI,axiom,
% 0.10/0.42 ! [X2: nat,A4: set_nat,G: nat > nat] :
% 0.10/0.42 ( ( member_nat @ X2 @ A4 )
% 0.10/0.42 => ( member8440522571783428010at_nat @ ( bNF_co805650143699787099at_nat @ id_nat @ G @ X2 ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ G ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_mem_GrpI
% 0.10/0.42 thf(fact_854_convol__mem__GrpI,axiom,
% 0.10/0.42 ! [X2: int,A4: set_int,G: int > int] :
% 0.10/0.42 ( ( member_int @ X2 @ A4 )
% 0.10/0.42 => ( member5262025264175285858nt_int @ ( bNF_co2174166945328636015nt_int @ id_int @ G @ X2 ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ G ) ) ) ) ) ).
% 0.10/0.42
% 0.10/0.42 % convol_mem_GrpI
% 0.10/0.42 thf(fact_855_image__id,axiom,
% 0.10/0.42 ( ( image_o_o @ id_o )
% 0.10/0.42 = id_set_o ) ).
% 0.10/0.42
% 0.10/0.42 % image_id
% 0.10/0.42 thf(fact_856_image__id,axiom,
% 0.10/0.42 ( ( image_num_num @ id_num )
% 0.10/0.42 = id_set_num ) ).
% 0.10/0.42
% 0.10/0.42 % image_id
% 0.10/0.42 thf(fact_857_image__id,axiom,
% 0.10/0.42 ( ( image_nat_nat @ id_nat )
% 0.10/0.42 = id_set_nat ) ).
% 0.10/0.42
% 0.10/0.42 % image_id
% 0.10/0.42 thf(fact_858_image__id,axiom,
% 0.10/0.42 ( ( image_int_int @ id_int )
% 0.10/0.42 = id_set_int ) ).
% 0.10/0.42
% 0.10/0.42 % image_id
% 0.10/0.42 thf(fact_859_fun_Omap__id,axiom,
% 0.10/0.42 ! [T2: nat > $o] :
% 0.10/0.42 ( ( comp_o_o_nat @ id_o @ T2 )
% 0.10/0.42 = T2 ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_id
% 0.10/0.42 thf(fact_860_fun_Omap__id,axiom,
% 0.10/0.42 ! [T2: nat > nat] :
% 0.10/0.42 ( ( comp_nat_nat_nat @ id_nat @ T2 )
% 0.10/0.42 = T2 ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_id
% 0.10/0.42 thf(fact_861_comp__id,axiom,
% 0.10/0.42 ! [F: nat > nat] :
% 0.10/0.42 ( ( comp_nat_nat_nat @ F @ id_nat )
% 0.10/0.42 = F ) ).
% 0.10/0.42
% 0.10/0.42 % comp_id
% 0.10/0.42 thf(fact_862_comp__id,axiom,
% 0.10/0.42 ! [F: int > nat] :
% 0.10/0.42 ( ( comp_int_nat_int @ F @ id_int )
% 0.10/0.42 = F ) ).
% 0.10/0.42
% 0.10/0.42 % comp_id
% 0.10/0.42 thf(fact_863_id__comp,axiom,
% 0.10/0.42 ! [G: nat > $o] :
% 0.10/0.42 ( ( comp_o_o_nat @ id_o @ G )
% 0.10/0.42 = G ) ).
% 0.10/0.42
% 0.10/0.42 % id_comp
% 0.10/0.42 thf(fact_864_id__comp,axiom,
% 0.10/0.42 ! [G: nat > nat] :
% 0.10/0.42 ( ( comp_nat_nat_nat @ id_nat @ G )
% 0.10/0.42 = G ) ).
% 0.10/0.42
% 0.10/0.42 % id_comp
% 0.10/0.42 thf(fact_865_case__prod__Pair,axiom,
% 0.10/0.42 ( ( produc5456455677105495163at_nat @ produc9060074326276436823at_nat )
% 0.10/0.42 = id_Pro6043886709289754456at_nat ) ).
% 0.10/0.42
% 0.10/0.42 % case_prod_Pair
% 0.10/0.42 thf(fact_866_case__prod__Pair,axiom,
% 0.10/0.42 ( ( produc7548845685434208379at_nat @ produc2922128104949294807at_nat )
% 0.10/0.42 = id_Pro8722402698821300696at_nat ) ).
% 0.10/0.42
% 0.10/0.42 % case_prod_Pair
% 0.10/0.42 thf(fact_867_case__prod__Pair,axiom,
% 0.10/0.42 ( ( produc49306077274653107at_num @ product_Pair_nat_num )
% 0.10/0.42 = id_Pro8267972854940751164at_num ) ).
% 0.10/0.42
% 0.10/0.42 % case_prod_Pair
% 0.10/0.42 thf(fact_868_case__prod__Pair,axiom,
% 0.10/0.42 ( ( produc2626176000494625587at_nat @ product_Pair_nat_nat )
% 0.10/0.42 = id_Pro7559728917991913458at_nat ) ).
% 0.10/0.42
% 0.10/0.42 % case_prod_Pair
% 0.10/0.42 thf(fact_869_case__prod__Pair,axiom,
% 0.10/0.42 ( ( produc4245557441103728435nt_int @ product_Pair_int_int )
% 0.10/0.42 = id_Pro4381231610383771306nt_int ) ).
% 0.10/0.42
% 0.10/0.42 % case_prod_Pair
% 0.10/0.42 thf(fact_870_apsnd__id,axiom,
% 0.10/0.42 ( ( produc6499014454317279255nteger @ id_Code_integer )
% 0.10/0.42 = id_Pro2309048762231606924nteger ) ).
% 0.10/0.42
% 0.10/0.42 % apsnd_id
% 0.10/0.42 thf(fact_871_range__fst,axiom,
% 0.10/0.42 ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ top_to2503719809363509323t_unit )
% 0.10/0.42 = top_top_set_ref_a ) ).
% 0.10/0.42
% 0.10/0.42 % range_fst
% 0.10/0.42 thf(fact_872_range__snd,axiom,
% 0.10/0.42 ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ top_to2503719809363509323t_unit )
% 0.10/0.42 = top_to3956321331435058429t_unit ) ).
% 0.10/0.42
% 0.10/0.42 % range_snd
% 0.10/0.42 thf(fact_873_fun_Omap__id0,axiom,
% 0.10/0.42 ( ( comp_o_o_nat @ id_o )
% 0.10/0.42 = id_nat_o ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_id0
% 0.10/0.42 thf(fact_874_fun_Omap__id0,axiom,
% 0.10/0.42 ( ( comp_nat_nat_nat @ id_nat )
% 0.10/0.42 = id_nat_nat ) ).
% 0.10/0.42
% 0.10/0.42 % fun.map_id0
% 0.10/0.42 thf(fact_875_surj__id,axiom,
% 0.10/0.42 ( ( image_o_o @ id_o @ top_top_set_o )
% 0.10/0.42 = top_top_set_o ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_876_surj__id,axiom,
% 0.10/0.42 ( ( image_num_num @ id_num @ top_top_set_num )
% 0.10/0.42 = top_top_set_num ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_877_surj__id,axiom,
% 0.10/0.42 ( ( image_char_char @ id_char @ top_top_set_char )
% 0.10/0.42 = top_top_set_char ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_878_surj__id,axiom,
% 0.10/0.42 ( ( image_7976474329151083847st_nat @ id_list_nat @ top_top_set_list_nat )
% 0.10/0.42 = top_top_set_list_nat ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_879_surj__id,axiom,
% 0.10/0.42 ( ( image_rat_rat @ id_rat @ top_top_set_rat )
% 0.10/0.42 = top_top_set_rat ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_880_surj__id,axiom,
% 0.10/0.42 ( ( image_nat_nat @ id_nat @ top_top_set_nat )
% 0.10/0.42 = top_top_set_nat ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_881_surj__id,axiom,
% 0.10/0.42 ( ( image_int_int @ id_int @ top_top_set_int )
% 0.10/0.42 = top_top_set_int ) ).
% 0.10/0.42
% 0.10/0.42 % surj_id
% 0.10/0.42 thf(fact_882_Grp__UNIV__idI,axiom,
% 0.10/0.42 ! [X2: $o,Y3: $o] :
% 0.10/0.42 ( ( X2 = Y3 )
% 0.10/0.42 => ( bNF_Grp_o_o @ top_top_set_o @ id_o @ X2 @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Grp_UNIV_idI
% 0.10/0.42 thf(fact_883_Grp__UNIV__idI,axiom,
% 0.10/0.42 ! [X2: num,Y3: num] :
% 0.10/0.42 ( ( X2 = Y3 )
% 0.10/0.42 => ( bNF_Grp_num_num @ top_top_set_num @ id_num @ X2 @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Grp_UNIV_idI
% 0.10/0.42 thf(fact_884_Grp__UNIV__idI,axiom,
% 0.10/0.42 ! [X2: char,Y3: char] :
% 0.10/0.42 ( ( X2 = Y3 )
% 0.10/0.42 => ( bNF_Grp_char_char @ top_top_set_char @ id_char @ X2 @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Grp_UNIV_idI
% 0.10/0.42 thf(fact_885_Grp__UNIV__idI,axiom,
% 0.10/0.42 ! [X2: list_nat,Y3: list_nat] :
% 0.10/0.42 ( ( X2 = Y3 )
% 0.10/0.42 => ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ id_list_nat @ X2 @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Grp_UNIV_idI
% 0.10/0.42 thf(fact_886_Grp__UNIV__idI,axiom,
% 0.10/0.42 ! [X2: rat,Y3: rat] :
% 0.10/0.42 ( ( X2 = Y3 )
% 0.10/0.42 => ( bNF_Grp_rat_rat @ top_top_set_rat @ id_rat @ X2 @ Y3 ) ) ).
% 0.10/0.42
% 0.10/0.42 % Grp_UNIV_idI
% 0.10/0.43 thf(fact_887_Grp__UNIV__idI,axiom,
% 0.10/0.43 ! [X2: nat,Y3: nat] :
% 0.10/0.43 ( ( X2 = Y3 )
% 0.10/0.43 => ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat @ X2 @ Y3 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Grp_UNIV_idI
% 0.10/0.43 thf(fact_888_Grp__UNIV__idI,axiom,
% 0.10/0.43 ! [X2: int,Y3: int] :
% 0.10/0.43 ( ( X2 = Y3 )
% 0.10/0.43 => ( bNF_Grp_int_int @ top_top_set_int @ id_int @ X2 @ Y3 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Grp_UNIV_idI
% 0.10/0.43 thf(fact_889_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_o_o @ top_top_set_o @ id_o ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_890_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_num_num @ top_top_set_num @ id_num ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_891_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: char,Z: char] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_char_char @ top_top_set_char @ id_char ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_892_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ id_list_nat ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_893_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: rat,Z: rat] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_rat_rat @ top_top_set_rat @ id_rat ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_894_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_895_eq__alt,axiom,
% 0.10/0.43 ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 0.10/0.43 = ( bNF_Grp_int_int @ top_top_set_int @ id_int ) ) ).
% 0.10/0.43
% 0.10/0.43 % eq_alt
% 0.10/0.43 thf(fact_896_Inf_OINF__id__eq,axiom,
% 0.10/0.43 ! [Inf: set_o > $o,A4: set_o] :
% 0.10/0.43 ( ( Inf @ ( image_o_o @ id_o @ A4 ) )
% 0.10/0.43 = ( Inf @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Inf.INF_id_eq
% 0.10/0.43 thf(fact_897_Inf_OINF__id__eq,axiom,
% 0.10/0.43 ! [Inf: set_num > num,A4: set_num] :
% 0.10/0.43 ( ( Inf @ ( image_num_num @ id_num @ A4 ) )
% 0.10/0.43 = ( Inf @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Inf.INF_id_eq
% 0.10/0.43 thf(fact_898_Inf_OINF__id__eq,axiom,
% 0.10/0.43 ! [Inf: set_nat > nat,A4: set_nat] :
% 0.10/0.43 ( ( Inf @ ( image_nat_nat @ id_nat @ A4 ) )
% 0.10/0.43 = ( Inf @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Inf.INF_id_eq
% 0.10/0.43 thf(fact_899_Inf_OINF__id__eq,axiom,
% 0.10/0.43 ! [Inf: set_int > int,A4: set_int] :
% 0.10/0.43 ( ( Inf @ ( image_int_int @ id_int @ A4 ) )
% 0.10/0.43 = ( Inf @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Inf.INF_id_eq
% 0.10/0.43 thf(fact_900_Sup_OSUP__id__eq,axiom,
% 0.10/0.43 ! [Sup: set_o > $o,A4: set_o] :
% 0.10/0.43 ( ( Sup @ ( image_o_o @ id_o @ A4 ) )
% 0.10/0.43 = ( Sup @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Sup.SUP_id_eq
% 0.10/0.43 thf(fact_901_Sup_OSUP__id__eq,axiom,
% 0.10/0.43 ! [Sup: set_num > num,A4: set_num] :
% 0.10/0.43 ( ( Sup @ ( image_num_num @ id_num @ A4 ) )
% 0.10/0.43 = ( Sup @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Sup.SUP_id_eq
% 0.10/0.43 thf(fact_902_Sup_OSUP__id__eq,axiom,
% 0.10/0.43 ! [Sup: set_nat > nat,A4: set_nat] :
% 0.10/0.43 ( ( Sup @ ( image_nat_nat @ id_nat @ A4 ) )
% 0.10/0.43 = ( Sup @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Sup.SUP_id_eq
% 0.10/0.43 thf(fact_903_Sup_OSUP__id__eq,axiom,
% 0.10/0.43 ! [Sup: set_int > int,A4: set_int] :
% 0.10/0.43 ( ( Sup @ ( image_int_int @ id_int @ A4 ) )
% 0.10/0.43 = ( Sup @ A4 ) ) ).
% 0.10/0.43
% 0.10/0.43 % Sup.SUP_id_eq
% 0.10/0.43 thf(fact_904_comp__eq__id__dest,axiom,
% 0.10/0.43 ! [A: $o > $o,B: nat > $o,C: nat > $o,V: nat] :
% 0.10/0.43 ( ( ( comp_o_o_nat @ A @ B )
% 0.10/0.43 = ( comp_o_o_nat @ id_o @ C ) )
% 0.10/0.43 => ( ( A @ ( B @ V ) )
% 0.10/0.43 = ( C @ V ) ) ) ).
% 0.10/0.43
% 0.10/0.43 % comp_eq_id_dest
% 0.10/0.43 thf(fact_905_comp__eq__id__dest,axiom,
% 0.10/0.43 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 0.10/0.43 ( ( ( comp_nat_num_int @ A @ B )
% 0.10/0.43 = ( comp_num_num_int @ id_num @ C ) )
% 0.10/0.43 => ( ( A @ ( B @ V ) )
% 0.10/0.43 = ( C @ V ) ) ) ).
% 0.10/0.43
% 0.10/0.43 % comp_eq_id_dest
% 0.10/0.43 thf(fact_906_comp__eq__id__dest,axiom,
% 0.10/0.43 ! [A: nat > nat,B: nat > nat,C: nat > nat,V: nat] :
% 0.10/0.43 ( ( ( comp_nat_nat_nat @ A @ B )
% 0.10/0.43 = ( comp_nat_nat_nat @ id_nat @ C ) )
% 0.10/0.43 => ( ( A @ ( B @ V ) )
% 0.10/0.43 = ( C @ V ) ) ) ).
% 0.10/0.43
% 0.10/0.43 % comp_eq_id_dest
% 0.10/0.43 thf(fact_907_comp__eq__id__dest,axiom,
% 0.10/0.43 ! [A: int > nat,B: int > int,C: int > nat,V: int] :
% 0.10/0.43 ( ( ( comp_int_nat_int @ A @ B )
% 0.10/0.43 = ( comp_nat_nat_int @ id_nat @ C ) )
% 0.10/0.43 => ( ( A @ ( B @ V ) )
% 0.10/0.43 = ( C @ V ) ) ) ).
% 0.10/0.43
% 0.10/0.43 % comp_eq_id_dest
% 0.10/0.43 thf(fact_908_comp__eq__id__dest,axiom,
% 0.10/0.43 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 0.10/0.43 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 0.10/0.43 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 0.14/0.43 => ( ( A @ ( B @ V ) )
% 0.14/0.43 = ( C @ V ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_eq_id_dest
% 0.14/0.43 thf(fact_909_pointfree__idE,axiom,
% 0.14/0.43 ! [F: nat > nat,G: nat > nat,X2: nat] :
% 0.14/0.43 ( ( ( comp_nat_nat_nat @ F @ G )
% 0.14/0.43 = id_nat )
% 0.14/0.43 => ( ( F @ ( G @ X2 ) )
% 0.14/0.43 = X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pointfree_idE
% 0.14/0.43 thf(fact_910_surjD,axiom,
% 0.14/0.43 ! [F: char > char,Y3: char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ? [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_911_surjD,axiom,
% 0.14/0.43 ! [F: char > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ? [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_912_surjD,axiom,
% 0.14/0.43 ! [F: char > nat,Y3: nat] :
% 0.14/0.43 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ? [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_913_surjD,axiom,
% 0.14/0.43 ! [F: char > int,Y3: int] :
% 0.14/0.43 ( ( ( image_char_int @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ? [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_914_surjD,axiom,
% 0.14/0.43 ! [F: rat > char,Y3: char] :
% 0.14/0.43 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ? [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_915_surjD,axiom,
% 0.14/0.43 ! [F: rat > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ? [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_916_surjD,axiom,
% 0.14/0.43 ! [F: rat > nat,Y3: nat] :
% 0.14/0.43 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ? [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_917_surjD,axiom,
% 0.14/0.43 ! [F: rat > int,Y3: int] :
% 0.14/0.43 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ? [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_918_surjD,axiom,
% 0.14/0.43 ! [F: nat > char,Y3: char] :
% 0.14/0.43 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ? [X: nat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_919_surjD,axiom,
% 0.14/0.43 ! [F: nat > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ? [X: nat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 = ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjD
% 0.14/0.43 thf(fact_920_surjE,axiom,
% 0.14/0.43 ! [F: char > char,Y3: char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_921_surjE,axiom,
% 0.14/0.43 ! [F: char > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_922_surjE,axiom,
% 0.14/0.43 ! [F: char > nat,Y3: nat] :
% 0.14/0.43 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_923_surjE,axiom,
% 0.14/0.43 ! [F: char > int,Y3: int] :
% 0.14/0.43 ( ( ( image_char_int @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_924_surjE,axiom,
% 0.14/0.43 ! [F: rat > char,Y3: char] :
% 0.14/0.43 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_925_surjE,axiom,
% 0.14/0.43 ! [F: rat > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_926_surjE,axiom,
% 0.14/0.43 ! [F: rat > nat,Y3: nat] :
% 0.14/0.43 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_927_surjE,axiom,
% 0.14/0.43 ! [F: rat > int,Y3: int] :
% 0.14/0.43 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_928_surjE,axiom,
% 0.14/0.43 ! [F: nat > char,Y3: char] :
% 0.14/0.43 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_929_surjE,axiom,
% 0.14/0.43 ! [F: nat > rat,Y3: rat] :
% 0.14/0.43 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( Y3
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjE
% 0.14/0.43 thf(fact_930_surjI,axiom,
% 0.14/0.43 ! [G: char > char,F: char > char] :
% 0.14/0.43 ( ! [X: char] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_char_char @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_931_surjI,axiom,
% 0.14/0.43 ! [G: char > rat,F: rat > char] :
% 0.14/0.43 ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_char_rat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_932_surjI,axiom,
% 0.14/0.43 ! [G: char > nat,F: nat > char] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_char_nat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_933_surjI,axiom,
% 0.14/0.43 ! [G: char > int,F: int > char] :
% 0.14/0.43 ( ! [X: int] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_char_int @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_int ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_934_surjI,axiom,
% 0.14/0.43 ! [G: rat > char,F: char > rat] :
% 0.14/0.43 ( ! [X: char] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_rat_char @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_935_surjI,axiom,
% 0.14/0.43 ! [G: rat > rat,F: rat > rat] :
% 0.14/0.43 ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_rat_rat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_936_surjI,axiom,
% 0.14/0.43 ! [G: rat > nat,F: nat > rat] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_rat_nat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_937_surjI,axiom,
% 0.14/0.43 ! [G: rat > int,F: int > rat] :
% 0.14/0.43 ( ! [X: int] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_rat_int @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_938_surjI,axiom,
% 0.14/0.43 ! [G: nat > char,F: char > nat] :
% 0.14/0.43 ( ! [X: char] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_nat_char @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_939_surjI,axiom,
% 0.14/0.43 ! [G: nat > rat,F: rat > nat] :
% 0.14/0.43 ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( ( image_nat_rat @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % surjI
% 0.14/0.43 thf(fact_940_rangeI,axiom,
% 0.14/0.43 ! [F: char > $o,X2: char] : ( member_o @ ( F @ X2 ) @ ( image_char_o @ F @ top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_941_rangeI,axiom,
% 0.14/0.43 ! [F: char > nat,X2: char] : ( member_nat @ ( F @ X2 ) @ ( image_char_nat @ F @ top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_942_rangeI,axiom,
% 0.14/0.43 ! [F: char > int,X2: char] : ( member_int @ ( F @ X2 ) @ ( image_char_int @ F @ top_top_set_char ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_943_rangeI,axiom,
% 0.14/0.43 ! [F: rat > $o,X2: rat] : ( member_o @ ( F @ X2 ) @ ( image_rat_o @ F @ top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_944_rangeI,axiom,
% 0.14/0.43 ! [F: rat > nat,X2: rat] : ( member_nat @ ( F @ X2 ) @ ( image_rat_nat @ F @ top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_945_rangeI,axiom,
% 0.14/0.43 ! [F: rat > int,X2: rat] : ( member_int @ ( F @ X2 ) @ ( image_rat_int @ F @ top_top_set_rat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_946_rangeI,axiom,
% 0.14/0.43 ! [F: nat > rat,X2: nat] : ( member_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_947_rangeI,axiom,
% 0.14/0.43 ! [F: nat > $o,X2: nat] : ( member_o @ ( F @ X2 ) @ ( image_nat_o @ F @ top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_948_rangeI,axiom,
% 0.14/0.43 ! [F: nat > nat,X2: nat] : ( member_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_949_rangeI,axiom,
% 0.14/0.43 ! [F: nat > int,X2: nat] : ( member_int @ ( F @ X2 ) @ ( image_nat_int @ F @ top_top_set_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeI
% 0.14/0.43 thf(fact_950_surj__def,axiom,
% 0.14/0.43 ! [F: char > char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 = ( ! [Y5: char] :
% 0.14/0.43 ? [X4: char] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_951_surj__def,axiom,
% 0.14/0.43 ! [F: char > rat] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 = ( ! [Y5: rat] :
% 0.14/0.43 ? [X4: char] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_952_surj__def,axiom,
% 0.14/0.43 ! [F: char > nat] :
% 0.14/0.43 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 = ( ! [Y5: nat] :
% 0.14/0.43 ? [X4: char] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_953_surj__def,axiom,
% 0.14/0.43 ! [F: char > int] :
% 0.14/0.43 ( ( ( image_char_int @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 = ( ! [Y5: int] :
% 0.14/0.43 ? [X4: char] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_954_surj__def,axiom,
% 0.14/0.43 ! [F: rat > char] :
% 0.14/0.43 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 = ( ! [Y5: char] :
% 0.14/0.43 ? [X4: rat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_955_surj__def,axiom,
% 0.14/0.43 ! [F: rat > rat] :
% 0.14/0.43 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 = ( ! [Y5: rat] :
% 0.14/0.43 ? [X4: rat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_956_surj__def,axiom,
% 0.14/0.43 ! [F: rat > nat] :
% 0.14/0.43 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 = ( ! [Y5: nat] :
% 0.14/0.43 ? [X4: rat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_957_surj__def,axiom,
% 0.14/0.43 ! [F: rat > int] :
% 0.14/0.43 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 = ( ! [Y5: int] :
% 0.14/0.43 ? [X4: rat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_958_surj__def,axiom,
% 0.14/0.43 ! [F: nat > char] :
% 0.14/0.43 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 = ( ! [Y5: char] :
% 0.14/0.43 ? [X4: nat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_959_surj__def,axiom,
% 0.14/0.43 ! [F: nat > rat] :
% 0.14/0.43 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 = ( ! [Y5: rat] :
% 0.14/0.43 ? [X4: nat] :
% 0.14/0.43 ( Y5
% 0.14/0.43 = ( F @ X4 ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_def
% 0.14/0.43 thf(fact_960_range__eqI,axiom,
% 0.14/0.43 ! [B: $o,F: char > $o,X2: char] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_961_range__eqI,axiom,
% 0.14/0.43 ! [B: nat,F: char > nat,X2: char] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_962_range__eqI,axiom,
% 0.14/0.43 ! [B: int,F: char > int,X2: char] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_963_range__eqI,axiom,
% 0.14/0.43 ! [B: $o,F: rat > $o,X2: rat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_964_range__eqI,axiom,
% 0.14/0.43 ! [B: nat,F: rat > nat,X2: rat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_965_range__eqI,axiom,
% 0.14/0.43 ! [B: int,F: rat > int,X2: rat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_966_range__eqI,axiom,
% 0.14/0.43 ! [B: rat,F: nat > rat,X2: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_967_range__eqI,axiom,
% 0.14/0.43 ! [B: $o,F: nat > $o,X2: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_968_range__eqI,axiom,
% 0.14/0.43 ! [B: nat,F: nat > nat,X2: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_969_range__eqI,axiom,
% 0.14/0.43 ! [B: int,F: nat > int,X2: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X2 ) )
% 0.14/0.43 => ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_eqI
% 0.14/0.43 thf(fact_970_effect__success,axiom,
% 0.14/0.43 ! [C: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 0.14/0.43 ( ( heap_effect_ref_a @ C @ H @ H2 @ R )
% 0.14/0.43 => ( heap_success_ref_a @ C @ H ) ) ).
% 0.14/0.43
% 0.14/0.43 % effect_success
% 0.14/0.43 thf(fact_971_success__effectE,axiom,
% 0.14/0.43 ! [C: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit] :
% 0.14/0.43 ( ( heap_success_ref_a @ C @ H )
% 0.14/0.43 => ~ ! [R4: ref_a,H4: heap_e7401611519738050253t_unit] :
% 0.14/0.43 ~ ( heap_effect_ref_a @ C @ H @ H4 @ R4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % success_effectE
% 0.14/0.43 thf(fact_972_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_char @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_7676512070627423941r_char @ ( produc7830753070125841726r_char @ F @ G ) @ top_to1235241553633177651r_char )
% 0.14/0.43 = top_to1235241553633177651r_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_973_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > rat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_rat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_7275072250160737868ar_rat @ ( produc5209943433214700613ar_rat @ F @ G ) @ top_to1235241553633177651r_char )
% 0.14/0.43 = top_to8437673547576850234ar_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_974_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > nat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_nat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( image_1559928771699358788ar_nat @ ( produc5845073493301196349ar_nat @ F @ G ) @ top_to1235241553633177651r_char )
% 0.14/0.43 = top_to5594287848199751986ar_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_975_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > int] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_int @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ( image_6605449789044937888ar_int @ ( produc5842583022792146073ar_int @ F @ G ) @ top_to1235241553633177651r_char )
% 0.14/0.43 = top_to3104204703268025230ar_int ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_976_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: rat > char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_rat_char @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_8036680598759533694r_char @ ( produc5432746246116964165t_char @ F @ G ) @ top_to8437673547576850234ar_rat )
% 0.14/0.43 = top_to1235241553633177651r_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_977_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: rat > rat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_rat_rat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_5644637116751559941ar_rat @ ( produc1230515432254573900at_rat @ F @ G ) @ top_to8437673547576850234ar_rat )
% 0.14/0.43 = top_to8437673547576850234ar_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_978_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: rat > nat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_rat_nat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( image_9152865675144956669ar_nat @ ( produc1865645492341069636at_nat @ F @ G ) @ top_to8437673547576850234ar_rat )
% 0.14/0.43 = top_to5594287848199751986ar_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_979_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: rat > int] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_rat_int @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ( image_4975014655635759961ar_int @ ( produc1863155021832019360at_int @ F @ G ) @ top_to8437673547576850234ar_rat )
% 0.14/0.43 = top_to3104204703268025230ar_int ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_980_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: nat > char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_nat_char @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_5973708714899544198r_char @ ( produc8759894717825771837t_char @ F @ G ) @ top_to5594287848199751986ar_nat )
% 0.14/0.43 = top_to1235241553633177651r_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_981_map__prod__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: nat > rat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_nat_rat @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_2699825501378146573ar_rat @ ( produc1547070076189439812at_rat @ F @ G ) @ top_to5594287848199751986ar_nat )
% 0.14/0.43 = top_to8437673547576850234ar_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % map_prod_surj
% 0.14/0.43 thf(fact_982_GrD1,axiom,
% 0.14/0.43 ! [X2: set_Pr4329608150637261639at_nat,Fx: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Fx ) @ ( bNF_Gr7888059597227825506at_nat @ A4 @ F ) )
% 0.14/0.43 => ( member6273874620674182256at_nat @ X2 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD1
% 0.14/0.43 thf(fact_983_GrD1,axiom,
% 0.14/0.43 ! [X2: set_Pr1261947904930325089at_nat,Fx: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Fx ) @ ( bNF_Gr1527221351080490466at_nat @ A4 @ F ) )
% 0.14/0.43 => ( member2643936169264416010at_nat @ X2 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD1
% 0.14/0.43 thf(fact_984_GrD1,axiom,
% 0.14/0.43 ! [X2: nat,Fx: num,A4: set_nat,F: nat > num] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Fx ) @ ( bNF_Gr_nat_num @ A4 @ F ) )
% 0.14/0.43 => ( member_nat @ X2 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD1
% 0.14/0.43 thf(fact_985_GrD1,axiom,
% 0.14/0.43 ! [X2: nat,Fx: nat,A4: set_nat,F: nat > nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Fx ) @ ( bNF_Gr_nat_nat @ A4 @ F ) )
% 0.14/0.43 => ( member_nat @ X2 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD1
% 0.14/0.43 thf(fact_986_GrD1,axiom,
% 0.14/0.43 ! [X2: int,Fx: int,A4: set_int,F: int > int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Fx ) @ ( bNF_Gr_int_int @ A4 @ F ) )
% 0.14/0.43 => ( member_int @ X2 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD1
% 0.14/0.43 thf(fact_987_GrD2,axiom,
% 0.14/0.43 ! [X2: set_Pr4329608150637261639at_nat,Fx: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Fx ) @ ( bNF_Gr7888059597227825506at_nat @ A4 @ F ) )
% 0.14/0.43 => ( ( F @ X2 )
% 0.14/0.43 = Fx ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD2
% 0.14/0.43 thf(fact_988_GrD2,axiom,
% 0.14/0.43 ! [X2: set_Pr1261947904930325089at_nat,Fx: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Fx ) @ ( bNF_Gr1527221351080490466at_nat @ A4 @ F ) )
% 0.14/0.43 => ( ( F @ X2 )
% 0.14/0.43 = Fx ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD2
% 0.14/0.43 thf(fact_989_GrD2,axiom,
% 0.14/0.43 ! [X2: nat,Fx: num,A4: set_nat,F: nat > num] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Fx ) @ ( bNF_Gr_nat_num @ A4 @ F ) )
% 0.14/0.43 => ( ( F @ X2 )
% 0.14/0.43 = Fx ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD2
% 0.14/0.43 thf(fact_990_GrD2,axiom,
% 0.14/0.43 ! [X2: nat,Fx: nat,A4: set_nat,F: nat > nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Fx ) @ ( bNF_Gr_nat_nat @ A4 @ F ) )
% 0.14/0.43 => ( ( F @ X2 )
% 0.14/0.43 = Fx ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD2
% 0.14/0.43 thf(fact_991_GrD2,axiom,
% 0.14/0.43 ! [X2: int,Fx: int,A4: set_int,F: int > int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Fx ) @ ( bNF_Gr_int_int @ A4 @ F ) )
% 0.14/0.43 => ( ( F @ X2 )
% 0.14/0.43 = Fx ) ) ).
% 0.14/0.43
% 0.14/0.43 % GrD2
% 0.14/0.43 thf(fact_992_success__refI,axiom,
% 0.14/0.43 ! [V: a,H: heap_e7401611519738050253t_unit] : ( heap_success_ref_a @ ( ref_a2 @ V ) @ H ) ).
% 0.14/0.43
% 0.14/0.43 % success_refI
% 0.14/0.43 thf(fact_993_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > $o,Ya: char > $o,Y3: char > $o,Xa2: char > $o,R3: $o > $o > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re1692451286490762625ar_o_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re1692451286490762625ar_o_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_994_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > $o,Ya: char > $o,Y3: char > nat,Xa2: char > nat,R3: $o > nat > $o,Ra: $o > nat > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: nat] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re4782998131235581479_o_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re4782998131235581479_o_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_995_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > $o,Ya: char > $o,Y3: char > int,Xa2: char > int,R3: $o > int > $o,Ra: $o > int > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: int] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re4780507660726531203_o_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re4780507660726531203_o_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_996_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > nat,Ya: char > nat,Y3: char > $o,Xa2: char > $o,R3: nat > $o > $o,Ra: nat > $o > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: $o] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re7885669492343766789_nat_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re7885669492343766789_nat_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_997_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > nat,Ya: char > nat,Y3: char > nat,Xa2: char > nat,R3: nat > nat > $o,Ra: nat > nat > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_998_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > nat,Ya: char > nat,Y3: char > int,Xa2: char > int,R3: nat > int > $o,Ra: nat > int > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: int] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re3731845416926587903at_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re3731845416926587903at_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_999_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > int,Ya: char > int,Y3: char > $o,Xa2: char > $o,R3: int > $o > $o,Ra: int > $o > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: int,Yb: $o] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re6064627146911078825_int_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re6064627146911078825_int_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_1000_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > int,Ya: char > int,Y3: char > nat,Xa2: char > nat,R3: int > nat > $o,Ra: int > nat > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: int,Yb: nat] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re4733689599336692735nt_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re4733689599336692735nt_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_1001_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: char > int,Ya: char > int,Y3: char > int,Xa2: char > int,R3: int > int > $o,Ra: int > int > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: int,Yb: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_1002_fun_Orel__cong,axiom,
% 0.14/0.43 ! [X2: rat > $o,Ya: rat > $o,Y3: rat > $o,Xa2: rat > $o,R3: $o > $o > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ( Y3 = Xa2 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_rat_o @ Ya @ top_top_set_rat ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_rat_o @ Xa2 @ top_top_set_rat ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( ( bNF_re1865807574169326223at_o_o
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re1865807574169326223at_o_o
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ Ya
% 0.14/0.43 @ Xa2 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_cong
% 0.14/0.43 thf(fact_1003_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: $o > $o > $o,X2: char > $o,Y3: char > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ( bNF_re1692451286490762625ar_o_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re1692451286490762625ar_o_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1004_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: $o > nat > $o,X2: char > $o,Y3: char > nat,Ra: $o > nat > $o] :
% 0.14/0.43 ( ( bNF_re4782998131235581479_o_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: nat] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re4782998131235581479_o_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1005_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: $o > int > $o,X2: char > $o,Y3: char > int,Ra: $o > int > $o] :
% 0.14/0.43 ( ( bNF_re4780507660726531203_o_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: int] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re4780507660726531203_o_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1006_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: nat > $o > $o,X2: char > nat,Y3: char > $o,Ra: nat > $o > $o] :
% 0.14/0.43 ( ( bNF_re7885669492343766789_nat_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: $o] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re7885669492343766789_nat_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1007_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,X2: char > nat,Y3: char > nat,Ra: nat > nat > $o] :
% 0.14/0.43 ( ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1008_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: nat > int > $o,X2: char > nat,Y3: char > int,Ra: nat > int > $o] :
% 0.14/0.43 ( ( bNF_re3731845416926587903at_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: nat,Yb: int] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re3731845416926587903at_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1009_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: int > $o > $o,X2: char > int,Y3: char > $o,Ra: int > $o > $o] :
% 0.14/0.43 ( ( bNF_re6064627146911078825_int_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: int,Yb: $o] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re6064627146911078825_int_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1010_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: int > nat > $o,X2: char > int,Y3: char > nat,Ra: int > nat > $o] :
% 0.14/0.43 ( ( bNF_re4733689599336692735nt_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: int,Yb: nat] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re4733689599336692735nt_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1011_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: int > int > $o,X2: char > int,Y3: char > int,Ra: int > int > $o] :
% 0.14/0.43 ( ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: int,Yb: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1012_fun_Orel__mono__strong,axiom,
% 0.14/0.43 ! [R3: $o > $o > $o,X2: rat > $o,Y3: rat > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ( bNF_re1865807574169326223at_o_o
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 )
% 0.14/0.43 => ( ! [Z3: $o,Yb: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_rat_o @ X2 @ top_top_set_rat ) )
% 0.14/0.43 => ( ( member_o @ Yb @ ( image_rat_o @ Y3 @ top_top_set_rat ) )
% 0.14/0.43 => ( ( R3 @ Z3 @ Yb )
% 0.14/0.43 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.14/0.43 => ( bNF_re1865807574169326223at_o_o
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_mono_strong
% 0.14/0.43 thf(fact_1013_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: char > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ! [Z3: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re1692451286490762625ar_o_o
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1014_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: char > nat,Ra: nat > nat > $o] :
% 0.14/0.43 ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1015_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: char > int,Ra: int > int > $o] :
% 0.14/0.43 ( ! [Z3: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1016_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: rat > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ! [Z3: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_rat_o @ X2 @ top_top_set_rat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re1865807574169326223at_o_o
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1017_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: rat > nat,Ra: nat > nat > $o] :
% 0.14/0.43 ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_rat_nat @ X2 @ top_top_set_rat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re6557955094579809201at_nat
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1018_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: rat > int,Ra: int > int > $o] :
% 0.14/0.43 ( ! [Z3: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_rat_int @ X2 @ top_top_set_rat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re7554818335971813481nt_int
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1019_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: nat > rat,Ra: rat > rat > $o] :
% 0.14/0.43 ( ! [Z3: rat] :
% 0.14/0.43 ( ( member_rat @ Z3 @ ( image_nat_rat @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re4702136315717946289at_rat
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1020_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: nat > $o,Ra: $o > $o > $o] :
% 0.14/0.43 ( ! [Z3: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re4705727531993890431at_o_o
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1021_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: nat > nat,Ra: nat > nat > $o] :
% 0.14/0.43 ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re5653821019739307937at_nat
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1022_fun_Orel__refl__strong,axiom,
% 0.14/0.43 ! [X2: nat > int,Ra: int > int > $o] :
% 0.14/0.43 ( ! [Z3: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_nat_int @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( Ra @ Z3 @ Z3 ) )
% 0.14/0.43 => ( bNF_re6650684261131312217nt_int
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ Ra
% 0.14/0.43 @ X2
% 0.14/0.43 @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_refl_strong
% 0.14/0.43 thf(fact_1023_range__subsetD,axiom,
% 0.14/0.43 ! [F: char > $o,B5: set_o,I: char] :
% 0.14/0.43 ( ( ord_less_eq_set_o @ ( image_char_o @ F @ top_top_set_char ) @ B5 )
% 0.14/0.43 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1024_range__subsetD,axiom,
% 0.14/0.43 ! [F: char > nat,B5: set_nat,I: char] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ ( image_char_nat @ F @ top_top_set_char ) @ B5 )
% 0.14/0.43 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1025_range__subsetD,axiom,
% 0.14/0.43 ! [F: char > int,B5: set_int,I: char] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ ( image_char_int @ F @ top_top_set_char ) @ B5 )
% 0.14/0.43 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1026_range__subsetD,axiom,
% 0.14/0.43 ! [F: rat > $o,B5: set_o,I: rat] :
% 0.14/0.43 ( ( ord_less_eq_set_o @ ( image_rat_o @ F @ top_top_set_rat ) @ B5 )
% 0.14/0.43 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1027_range__subsetD,axiom,
% 0.14/0.43 ! [F: rat > nat,B5: set_nat,I: rat] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ ( image_rat_nat @ F @ top_top_set_rat ) @ B5 )
% 0.14/0.43 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1028_range__subsetD,axiom,
% 0.14/0.43 ! [F: rat > int,B5: set_int,I: rat] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ ( image_rat_int @ F @ top_top_set_rat ) @ B5 )
% 0.14/0.43 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1029_range__subsetD,axiom,
% 0.14/0.43 ! [F: nat > rat,B5: set_rat,I: nat] :
% 0.14/0.43 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ top_top_set_nat ) @ B5 )
% 0.14/0.43 => ( member_rat @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1030_range__subsetD,axiom,
% 0.14/0.43 ! [F: nat > $o,B5: set_o,I: nat] :
% 0.14/0.43 ( ( ord_less_eq_set_o @ ( image_nat_o @ F @ top_top_set_nat ) @ B5 )
% 0.14/0.43 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1031_range__subsetD,axiom,
% 0.14/0.43 ! [F: nat > nat,B5: set_nat,I: nat] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ top_top_set_nat ) @ B5 )
% 0.14/0.43 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1032_range__subsetD,axiom,
% 0.14/0.43 ! [F: nat > int,B5: set_int,I: nat] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ top_top_set_nat ) @ B5 )
% 0.14/0.43 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_subsetD
% 0.14/0.43 thf(fact_1033_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > rat,V: char > nat] :
% 0.14/0.43 ( ( image_char_rat @ ( comp_nat_rat_char @ F @ V ) @ top_top_set_char )
% 0.14/0.43 = ( image_nat_rat @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1034_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > nat,V: char > nat] :
% 0.14/0.43 ( ( image_char_nat @ ( comp_nat_nat_char @ F @ V ) @ top_top_set_char )
% 0.14/0.43 = ( image_nat_nat @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1035_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > int,V: char > nat] :
% 0.14/0.43 ( ( image_char_int @ ( comp_nat_int_char @ F @ V ) @ top_top_set_char )
% 0.14/0.43 = ( image_nat_int @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1036_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: int > nat,V: char > int] :
% 0.14/0.43 ( ( image_char_nat @ ( comp_int_nat_char @ F @ V ) @ top_top_set_char )
% 0.14/0.43 = ( image_int_nat @ F @ ( image_char_int @ V @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1037_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: int > int,V: char > int] :
% 0.14/0.43 ( ( image_char_int @ ( comp_int_int_char @ F @ V ) @ top_top_set_char )
% 0.14/0.43 = ( image_int_int @ F @ ( image_char_int @ V @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1038_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > rat,V: rat > nat] :
% 0.14/0.43 ( ( image_rat_rat @ ( comp_nat_rat_rat @ F @ V ) @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_rat @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1039_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > nat,V: rat > nat] :
% 0.14/0.43 ( ( image_rat_nat @ ( comp_nat_nat_rat @ F @ V ) @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_nat @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1040_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: nat > int,V: rat > nat] :
% 0.14/0.43 ( ( image_rat_int @ ( comp_nat_int_rat @ F @ V ) @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_int @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1041_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: int > nat,V: rat > int] :
% 0.14/0.43 ( ( image_rat_nat @ ( comp_int_nat_rat @ F @ V ) @ top_top_set_rat )
% 0.14/0.43 = ( image_int_nat @ F @ ( image_rat_int @ V @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1042_fun_Oset__map,axiom,
% 0.14/0.43 ! [F: int > int,V: rat > int] :
% 0.14/0.43 ( ( image_rat_int @ ( comp_int_int_rat @ F @ V ) @ top_top_set_rat )
% 0.14/0.43 = ( image_int_int @ F @ ( image_rat_int @ V @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.set_map
% 0.14/0.43 thf(fact_1043_fun_Omap__cong,axiom,
% 0.14/0.43 ! [X2: code_integer > code_integer > code_integer,Ya: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ! [Z3: code_integer > code_integer] :
% 0.14/0.43 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ Ya @ top_to4645266643341252675nteger ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 0.14/0.43 = ( comp_C8797469213163452608nteger @ G @ Ya ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong
% 0.14/0.43 thf(fact_1044_fun_Omap__cong,axiom,
% 0.14/0.43 ! [X2: nat > $o,Ya: nat > $o,F: $o > $o,G: $o > $o] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ! [Z3: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_nat_o @ Ya @ top_top_set_nat ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_o_o_nat @ F @ X2 )
% 0.14/0.43 = ( comp_o_o_nat @ G @ Ya ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong
% 0.14/0.43 thf(fact_1045_fun_Omap__cong,axiom,
% 0.14/0.43 ! [X2: nat > nat,Ya: nat > nat,F: nat > nat,G: nat > nat] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_nat_nat @ Ya @ top_top_set_nat ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_nat_nat_nat @ F @ X2 )
% 0.14/0.43 = ( comp_nat_nat_nat @ G @ Ya ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong
% 0.14/0.43 thf(fact_1046_fun_Omap__cong,axiom,
% 0.14/0.43 ! [X2: int > nat,Ya: int > nat,F: nat > num,G: nat > num] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_int_nat @ Ya @ top_top_set_int ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_nat_num_int @ F @ X2 )
% 0.14/0.43 = ( comp_nat_num_int @ G @ Ya ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong
% 0.14/0.43 thf(fact_1047_fun_Omap__cong,axiom,
% 0.14/0.43 ! [X2: int > int,Ya: int > int,F: int > nat,G: int > nat] :
% 0.14/0.43 ( ( X2 = Ya )
% 0.14/0.43 => ( ! [Z3: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_int_int @ Ya @ top_top_set_int ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_int_nat_int @ F @ X2 )
% 0.14/0.43 = ( comp_int_nat_int @ G @ Ya ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong
% 0.14/0.43 thf(fact_1048_fun_Omap__cong0,axiom,
% 0.14/0.43 ! [X2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.43 ( ! [Z3: code_integer > code_integer] :
% 0.14/0.43 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X2 @ top_to4645266643341252675nteger ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 0.14/0.43 = ( comp_C8797469213163452608nteger @ G @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong0
% 0.14/0.43 thf(fact_1049_fun_Omap__cong0,axiom,
% 0.14/0.43 ! [X2: nat > $o,F: $o > $o,G: $o > $o] :
% 0.14/0.43 ( ! [Z3: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_o_o_nat @ F @ X2 )
% 0.14/0.43 = ( comp_o_o_nat @ G @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong0
% 0.14/0.43 thf(fact_1050_fun_Omap__cong0,axiom,
% 0.14/0.43 ! [X2: nat > nat,F: nat > nat,G: nat > nat] :
% 0.14/0.43 ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_nat_nat_nat @ F @ X2 )
% 0.14/0.43 = ( comp_nat_nat_nat @ G @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong0
% 0.14/0.43 thf(fact_1051_fun_Omap__cong0,axiom,
% 0.14/0.43 ! [X2: int > nat,F: nat > num,G: nat > num] :
% 0.14/0.43 ( ! [Z3: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_int_nat @ X2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_nat_num_int @ F @ X2 )
% 0.14/0.43 = ( comp_nat_num_int @ G @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong0
% 0.14/0.43 thf(fact_1052_fun_Omap__cong0,axiom,
% 0.14/0.43 ! [X2: int > int,F: int > nat,G: int > nat] :
% 0.14/0.43 ( ! [Z3: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_int_int @ X2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( F @ Z3 )
% 0.14/0.43 = ( G @ Z3 ) ) )
% 0.14/0.43 => ( ( comp_int_nat_int @ F @ X2 )
% 0.14/0.43 = ( comp_int_nat_int @ G @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_cong0
% 0.14/0.43 thf(fact_1053_fun_Oinj__map__strong,axiom,
% 0.14/0.43 ! [X2: code_integer > code_integer > code_integer,Xa2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.43 ( ! [Z3: code_integer > code_integer,Za: code_integer > code_integer] :
% 0.14/0.43 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X2 @ top_to4645266643341252675nteger ) )
% 0.14/0.43 => ( ( member2790140394383616496nteger @ Za @ ( image_2177946750938214461nteger @ Xa2 @ top_to4645266643341252675nteger ) )
% 0.14/0.43 => ( ( ( F @ Z3 )
% 0.14/0.43 = ( Fa @ Za ) )
% 0.14/0.43 => ( Z3 = Za ) ) ) )
% 0.14/0.43 => ( ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 0.14/0.43 = ( comp_C8797469213163452608nteger @ Fa @ Xa2 ) )
% 0.14/0.43 => ( X2 = Xa2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.inj_map_strong
% 0.14/0.43 thf(fact_1054_fun_Oinj__map__strong,axiom,
% 0.14/0.43 ! [X2: nat > $o,Xa2: nat > $o,F: $o > $o,Fa: $o > $o] :
% 0.14/0.43 ( ! [Z3: $o,Za: $o] :
% 0.14/0.43 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( member_o @ Za @ ( image_nat_o @ Xa2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( ( F @ Z3 )
% 0.14/0.43 = ( Fa @ Za ) )
% 0.14/0.43 => ( Z3 = Za ) ) ) )
% 0.14/0.43 => ( ( ( comp_o_o_nat @ F @ X2 )
% 0.14/0.43 = ( comp_o_o_nat @ Fa @ Xa2 ) )
% 0.14/0.43 => ( X2 = Xa2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.inj_map_strong
% 0.14/0.43 thf(fact_1055_fun_Oinj__map__strong,axiom,
% 0.14/0.43 ! [X2: nat > nat,Xa2: nat > nat,F: nat > nat,Fa: nat > nat] :
% 0.14/0.43 ( ! [Z3: nat,Za: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( member_nat @ Za @ ( image_nat_nat @ Xa2 @ top_top_set_nat ) )
% 0.14/0.43 => ( ( ( F @ Z3 )
% 0.14/0.43 = ( Fa @ Za ) )
% 0.14/0.43 => ( Z3 = Za ) ) ) )
% 0.14/0.43 => ( ( ( comp_nat_nat_nat @ F @ X2 )
% 0.14/0.43 = ( comp_nat_nat_nat @ Fa @ Xa2 ) )
% 0.14/0.43 => ( X2 = Xa2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.inj_map_strong
% 0.14/0.43 thf(fact_1056_fun_Oinj__map__strong,axiom,
% 0.14/0.43 ! [X2: int > nat,Xa2: int > nat,F: nat > num,Fa: nat > num] :
% 0.14/0.43 ( ! [Z3: nat,Za: nat] :
% 0.14/0.43 ( ( member_nat @ Z3 @ ( image_int_nat @ X2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( member_nat @ Za @ ( image_int_nat @ Xa2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( ( F @ Z3 )
% 0.14/0.43 = ( Fa @ Za ) )
% 0.14/0.43 => ( Z3 = Za ) ) ) )
% 0.14/0.43 => ( ( ( comp_nat_num_int @ F @ X2 )
% 0.14/0.43 = ( comp_nat_num_int @ Fa @ Xa2 ) )
% 0.14/0.43 => ( X2 = Xa2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.inj_map_strong
% 0.14/0.43 thf(fact_1057_fun_Oinj__map__strong,axiom,
% 0.14/0.43 ! [X2: int > int,Xa2: int > int,F: int > nat,Fa: int > nat] :
% 0.14/0.43 ( ! [Z3: int,Za: int] :
% 0.14/0.43 ( ( member_int @ Z3 @ ( image_int_int @ X2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( member_int @ Za @ ( image_int_int @ Xa2 @ top_top_set_int ) )
% 0.14/0.43 => ( ( ( F @ Z3 )
% 0.14/0.43 = ( Fa @ Za ) )
% 0.14/0.43 => ( Z3 = Za ) ) ) )
% 0.14/0.43 => ( ( ( comp_int_nat_int @ F @ X2 )
% 0.14/0.43 = ( comp_int_nat_int @ Fa @ Xa2 ) )
% 0.14/0.43 => ( X2 = Xa2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.inj_map_strong
% 0.14/0.43 thf(fact_1058_surj__fun__eq,axiom,
% 0.14/0.43 ! [F: nat > $o,X5: set_nat,G1: $o > $o,G22: $o > $o] :
% 0.14/0.43 ( ( ( image_nat_o @ F @ X5 )
% 0.14/0.43 = top_top_set_o )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( member_nat @ X @ X5 )
% 0.14/0.43 => ( ( comp_o_o_nat @ G1 @ F @ X )
% 0.14/0.43 = ( comp_o_o_nat @ G22 @ F @ X ) ) )
% 0.14/0.43 => ( G1 = G22 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_fun_eq
% 0.14/0.43 thf(fact_1059_surj__fun__eq,axiom,
% 0.14/0.43 ! [F: code_integer > code_integer > code_integer,X5: set_Code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.43 ( ( ( image_2177946750938214461nteger @ F @ X5 )
% 0.14/0.43 = top_to3804862627464599871nteger )
% 0.14/0.43 => ( ! [X: code_integer] :
% 0.14/0.43 ( ( member_Code_integer @ X @ X5 )
% 0.14/0.43 => ( ( comp_C8797469213163452608nteger @ G1 @ F @ X )
% 0.14/0.43 = ( comp_C8797469213163452608nteger @ G22 @ F @ X ) ) )
% 0.14/0.43 => ( G1 = G22 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_fun_eq
% 0.14/0.43 thf(fact_1060_surj__fun__eq,axiom,
% 0.14/0.43 ! [F: nat > nat,X5: set_nat,G1: nat > nat,G22: nat > nat] :
% 0.14/0.43 ( ( ( image_nat_nat @ F @ X5 )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( member_nat @ X @ X5 )
% 0.14/0.43 => ( ( comp_nat_nat_nat @ G1 @ F @ X )
% 0.14/0.43 = ( comp_nat_nat_nat @ G22 @ F @ X ) ) )
% 0.14/0.43 => ( G1 = G22 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_fun_eq
% 0.14/0.43 thf(fact_1061_surj__fun__eq,axiom,
% 0.14/0.43 ! [F: int > nat,X5: set_int,G1: nat > num,G22: nat > num] :
% 0.14/0.43 ( ( ( image_int_nat @ F @ X5 )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( member_int @ X @ X5 )
% 0.14/0.43 => ( ( comp_nat_num_int @ G1 @ F @ X )
% 0.14/0.43 = ( comp_nat_num_int @ G22 @ F @ X ) ) )
% 0.14/0.43 => ( G1 = G22 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_fun_eq
% 0.14/0.43 thf(fact_1062_surj__fun__eq,axiom,
% 0.14/0.43 ! [F: int > int,X5: set_int,G1: int > nat,G22: int > nat] :
% 0.14/0.43 ( ( ( image_int_int @ F @ X5 )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( member_int @ X @ X5 )
% 0.14/0.43 => ( ( comp_int_nat_int @ G1 @ F @ X )
% 0.14/0.43 = ( comp_int_nat_int @ G22 @ F @ X ) ) )
% 0.14/0.43 => ( G1 = G22 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % surj_fun_eq
% 0.14/0.43 thf(fact_1063_comp__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > char] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_char @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_char_char @ ( comp_char_char_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1064_comp__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > rat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_rat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_char_rat @ ( comp_char_rat_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1065_comp__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > nat] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_nat @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( image_char_nat @ ( comp_char_nat_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1066_comp__surj,axiom,
% 0.14/0.43 ! [F: char > char,G: char > int] :
% 0.14/0.43 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( ( image_char_int @ G @ top_top_set_char )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ( image_char_int @ ( comp_char_int_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_int ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1067_comp__surj,axiom,
% 0.14/0.43 ! [F: char > rat,G: rat > char] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( ( image_rat_char @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_char_char @ ( comp_rat_char_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1068_comp__surj,axiom,
% 0.14/0.43 ! [F: char > rat,G: rat > rat] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( ( image_rat_rat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_char_rat @ ( comp_rat_rat_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1069_comp__surj,axiom,
% 0.14/0.43 ! [F: char > rat,G: rat > nat] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( ( image_rat_nat @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( image_char_nat @ ( comp_rat_nat_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1070_comp__surj,axiom,
% 0.14/0.43 ! [F: char > rat,G: rat > int] :
% 0.14/0.43 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( ( image_rat_int @ G @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ( image_char_int @ ( comp_rat_int_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_int ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1071_comp__surj,axiom,
% 0.14/0.43 ! [F: char > nat,G: nat > char] :
% 0.14/0.43 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( ( image_nat_char @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_char )
% 0.14/0.43 => ( ( image_char_char @ ( comp_nat_char_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1072_comp__surj,axiom,
% 0.14/0.43 ! [F: char > nat,G: nat > rat] :
% 0.14/0.43 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ( ( image_nat_rat @ G @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ( image_char_rat @ ( comp_nat_rat_char @ G @ F ) @ top_top_set_char )
% 0.14/0.43 = top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_surj
% 0.14/0.43 thf(fact_1073_apsnd__def,axiom,
% 0.14/0.43 ( produc6499014454317279255nteger
% 0.14/0.43 = ( produc1802105962441033582nteger @ id_Code_integer ) ) ).
% 0.14/0.43
% 0.14/0.43 % apsnd_def
% 0.14/0.43 thf(fact_1074_rel__fun__image2p,axiom,
% 0.14/0.43 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > nat,G: int > nat] : ( bNF_re4555766996558763186at_nat @ R3 @ ( bNF_Gr6955563364113978072nt_nat @ F @ G @ R3 ) @ F @ G ) ).
% 0.14/0.43
% 0.14/0.43 % rel_fun_image2p
% 0.14/0.43 thf(fact_1075_rel__fun__image2p,axiom,
% 0.14/0.43 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] : ( bNF_re7408651293131936558nt_int @ R3 @ ( bNF_Gr1354378531936274772nt_int @ F @ G @ R3 ) @ F @ G ) ).
% 0.14/0.43
% 0.14/0.43 % rel_fun_image2p
% 0.14/0.43 thf(fact_1076_rel__fun__image2p,axiom,
% 0.14/0.43 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] : ( bNF_re717283939379294677_int_o @ R3 @ ( bNF_Gr364077372107685167_int_o @ F @ G @ R3 ) @ F @ G ) ).
% 0.14/0.43
% 0.14/0.43 % rel_fun_image2p
% 0.14/0.43 thf(fact_1077_rel__fun__image2p,axiom,
% 0.14/0.43 ! [R3: int > code_integer > $o,F: int > num,G: code_integer > num] : ( bNF_re6718328864250387230um_num @ R3 @ ( bNF_Gr166583433173494904er_num @ F @ G @ R3 ) @ F @ G ) ).
% 0.14/0.43
% 0.14/0.43 % rel_fun_image2p
% 0.14/0.43 thf(fact_1078_rel__fun__image2p,axiom,
% 0.14/0.43 ! [R3: int > int > $o,F: int > num,G: int > num] : ( bNF_re7626690874201225453um_num @ R3 @ ( bNF_Gr7020624548710275655nt_num @ F @ G @ R3 ) @ F @ G ) ).
% 0.14/0.43
% 0.14/0.43 % rel_fun_image2p
% 0.14/0.43 thf(fact_1079_comp__fun__idem__on_Ocomp__comp__fun__idem__on,axiom,
% 0.14/0.43 ! [S5: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,R3: set_Code_integer] :
% 0.14/0.43 ( ( finite954763878425697269nteger @ S5 @ F )
% 0.14/0.43 => ( ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ G @ top_to4645266643341252675nteger ) @ S5 )
% 0.14/0.43 => ( finite917065715488314481nteger @ R3 @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_fun_idem_on.comp_comp_fun_idem_on
% 0.14/0.43 thf(fact_1080_comp__fun__commute__on_Ocomp__comp__fun__commute__on,axiom,
% 0.14/0.43 ! [S5: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,R3: set_Code_integer] :
% 0.14/0.43 ( ( finite6756937295472016048nteger @ S5 @ F )
% 0.14/0.43 => ( ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ G @ top_to4645266643341252675nteger ) @ S5 )
% 0.14/0.43 => ( finite366418920864469932nteger @ R3 @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % comp_fun_commute_on.comp_comp_fun_commute_on
% 0.14/0.43 thf(fact_1081_image__Pow__mono,axiom,
% 0.14/0.43 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.14/0.43 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.14/0.43 => ( ord_le513522071413781156et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_rat @ B5 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Pow_mono
% 0.14/0.43 thf(fact_1082_image__Pow__mono,axiom,
% 0.14/0.43 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.14/0.43 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_nat @ B5 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Pow_mono
% 0.14/0.43 thf(fact_1083_image__Pow__mono,axiom,
% 0.14/0.43 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.14/0.43 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_int @ B5 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Pow_mono
% 0.14/0.43 thf(fact_1084_image__Pow__mono,axiom,
% 0.14/0.43 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.14/0.43 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) ) @ ( pow_nat @ B5 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Pow_mono
% 0.14/0.43 thf(fact_1085_image__Pow__mono,axiom,
% 0.14/0.43 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.14/0.43 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) ) @ ( pow_int @ B5 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Pow_mono
% 0.14/0.43 thf(fact_1086_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi7262943168399475603_int_o
% 0.14/0.43 = ( ^ [F2: char > int,G3: code_integer > int,P4: int > int > $o] : ( relcom5819909836510906509nteger @ ( bNF_Grp_char_int @ top_top_set_char @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1087_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi508398028314858188_int_o
% 0.14/0.43 = ( ^ [F2: rat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom3409376902655092628nteger @ ( bNF_Grp_rat_int @ top_top_set_rat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1088_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi7331807916455492308_int_o
% 0.14/0.43 = ( ^ [F2: nat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom3277315637376110988nteger @ ( bNF_Grp_nat_int @ top_top_set_nat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1089_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi2125572119366604152_int_o
% 0.14/0.43 = ( ^ [F2: int > int,G3: code_integer > int,P4: int > int > $o] : ( relcom967497705283160040nteger @ ( bNF_Grp_int_int @ top_top_set_int @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1090_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi467646977814820164_int_o
% 0.14/0.43 = ( ^ [F2: list_nat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom7887202796854296604nteger @ ( bNF_Grp_list_nat_int @ top_top_set_list_nat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1091_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi728936465572800120_nat_o
% 0.14/0.43 = ( ^ [F2: char > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom7879471502873553579at_int @ ( bNF_Gr8982933507515605408at_nat @ top_top_set_char @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1092_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi2997284877290766385_nat_o
% 0.14/0.43 = ( ^ [F2: rat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom1211213461163567844at_int @ ( bNF_Gr6883301533820405721at_nat @ top_top_set_rat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1093_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi190728152058600505_nat_o
% 0.14/0.43 = ( ^ [F2: nat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom8569543703982574316at_int @ ( bNF_Gr3553472063123884001at_nat @ top_top_set_nat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1094_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi1204582724742824157_nat_o
% 0.14/0.43 = ( ^ [F2: int > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom1106208330880909712at_int @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1095_vimage2p__Grp,axiom,
% 0.14/0.43 ( bNF_vi5202502398764838569_nat_o
% 0.14/0.43 = ( ^ [F2: list_nat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom170568170053003356at_int @ ( bNF_Gr4119388860389678161at_nat @ top_top_set_list_nat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % vimage2p_Grp
% 0.14/0.43 thf(fact_1096_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,A: char > nat,B: char > nat] :
% 0.14/0.43 ( ( bNF_re3734335887435638179at_nat
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: char > product_prod_nat_nat] :
% 0.14/0.43 ( ( member3295615932019376976at_nat @ Z4
% 0.14/0.43 @ ( collec1683818095804863890at_nat
% 0.14/0.43 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P1491501995297412481t_char @ product_fst_nat_nat @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P1491501995297412481t_char @ product_snd_nat_nat @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1097_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,A: rat > nat,B: rat > nat] :
% 0.14/0.43 ( ( bNF_re6557955094579809201at_nat
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: rat > product_prod_nat_nat] :
% 0.14/0.43 ( ( member849810989832120969at_nat @ Z4
% 0.14/0.43 @ ( collec2824469931397938891at_nat
% 0.14/0.43 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P1320480151300532104at_rat @ product_fst_nat_nat @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P1320480151300532104at_rat @ product_snd_nat_nat @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1098_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,A: nat > nat,B: nat > nat] :
% 0.14/0.43 ( ( bNF_re5653821019739307937at_nat
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: nat > product_prod_nat_nat] :
% 0.14/0.43 ( ( member6743353555990375057at_nat @ Z4
% 0.14/0.43 @ ( collec8718012497556192979at_nat
% 0.14/0.43 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1099_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,A: int > nat,B: int > nat] :
% 0.14/0.43 ( ( bNF_re3715656647883201625at_nat
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: int > product_prod_nat_nat] :
% 0.14/0.43 ( ( member557823603599733045at_nat @ Z4
% 0.14/0.43 @ ( collec2532482545165550967at_nat
% 0.14/0.43 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P1953119740877977564at_int @ product_fst_nat_nat @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P1953119740877977564at_int @ product_snd_nat_nat @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1100_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: num > num > $o,A: int > num,B: int > num] :
% 0.14/0.43 ( ( bNF_re7626690874201225453um_num
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: int > product_prod_num_num] :
% 0.14/0.43 ( ( member7514810323860029129um_num @ Z4
% 0.14/0.43 @ ( collec266097228571071243um_num
% 0.14/0.43 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P4305060815297604026um_int @ product_fst_num_num @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P4305060815297604026um_int @ product_snd_num_num @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1101_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: int > int > $o,A: char > int,B: char > int] :
% 0.14/0.43 ( ( bNF_re4731199128827642459nt_int
% 0.14/0.43 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: char > product_prod_int_int] :
% 0.14/0.43 ( ( member2992454361780672008nt_int @ Z4
% 0.14/0.43 @ ( collec1380656525566158922nt_int
% 0.14/0.43 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P4161745170962941589t_char @ product_fst_int_int @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P4161745170962941589t_char @ product_snd_int_int @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1102_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: int > int > $o,A: rat > int,B: rat > int] :
% 0.14/0.43 ( ( bNF_re7554818335971813481nt_int
% 0.14/0.43 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: rat > product_prod_int_int] :
% 0.14/0.43 ( ( member546649419593416001nt_int @ Z4
% 0.14/0.43 @ ( collec2521308361159233923nt_int
% 0.14/0.43 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P6018825582104210588nt_rat @ product_fst_int_int @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P6018825582104210588nt_rat @ product_snd_int_int @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1103_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: int > int > $o,A: nat > int,B: nat > int] :
% 0.14/0.43 ( ( bNF_re6650684261131312217nt_int
% 0.14/0.43 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: nat > product_prod_int_int] :
% 0.14/0.43 ( ( member6440191985751670089nt_int @ Z4
% 0.14/0.43 @ ( collec8414850927317488011nt_int
% 0.14/0.43 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1104_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: int > int > $o,A: int > int,B: int > int] :
% 0.14/0.43 ( ( bNF_re4712519889275205905nt_int
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: int > product_prod_int_int] :
% 0.14/0.43 ( ( member254662033361028077nt_int @ Z4
% 0.14/0.43 @ ( collec2229320974926845999nt_int
% 0.14/0.43 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P6651465171681656048nt_int @ product_fst_int_int @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P6651465171681656048nt_int @ product_snd_int_int @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1105_fun_Oin__rel,axiom,
% 0.14/0.43 ! [R3: nat > nat > $o,A: list_nat > nat,B: list_nat > nat] :
% 0.14/0.43 ( ( bNF_re4629543205785817921at_nat
% 0.14/0.43 @ ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z )
% 0.14/0.43 @ R3
% 0.14/0.43 @ A
% 0.14/0.43 @ B )
% 0.14/0.43 = ( ? [Z4: list_nat > product_prod_nat_nat] :
% 0.14/0.43 ( ( member3963856813518191233at_nat @ Z4
% 0.14/0.43 @ ( collec3092956710985254339at_nat
% 0.14/0.43 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 0.14/0.43 & ( ( comp_P5292260908303971472st_nat @ product_fst_nat_nat @ Z4 )
% 0.14/0.43 = A )
% 0.14/0.43 & ( ( comp_P5292260908303971472st_nat @ product_snd_nat_nat @ Z4 )
% 0.14/0.43 = B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.in_rel
% 0.14/0.43 thf(fact_1106_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: $o > $o] :
% 0.14/0.43 ( ( F = id_o )
% 0.14/0.43 => ( ( relcompp_o_o_o @ ( conversep_o_o @ ( bNF_Grp_o_o @ top_top_set_o @ F ) ) @ ( bNF_Grp_o_o @ top_top_set_o @ F ) )
% 0.14/0.43 = ( bNF_Grp_o_o @ top_top_set_o @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1107_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: num > num] :
% 0.14/0.43 ( ( F = id_num )
% 0.14/0.43 => ( ( relcompp_num_num_num @ ( conversep_num_num @ ( bNF_Grp_num_num @ top_top_set_num @ F ) ) @ ( bNF_Grp_num_num @ top_top_set_num @ F ) )
% 0.14/0.43 = ( bNF_Grp_num_num @ top_top_set_num @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1108_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: char > char] :
% 0.14/0.43 ( ( F = id_char )
% 0.14/0.43 => ( ( relcom5872928454965100966r_char @ ( conversep_char_char @ ( bNF_Grp_char_char @ top_top_set_char @ F ) ) @ ( bNF_Grp_char_char @ top_top_set_char @ F ) )
% 0.14/0.43 = ( bNF_Grp_char_char @ top_top_set_char @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1109_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: list_nat > list_nat] :
% 0.14/0.43 ( ( F = id_list_nat )
% 0.14/0.43 => ( ( relcom8030397737370142931st_nat @ ( conver909888920752868663st_nat @ ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) ) @ ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) )
% 0.14/0.43 = ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1110_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: rat > rat] :
% 0.14/0.43 ( ( F = id_rat )
% 0.14/0.43 => ( ( relcompp_rat_rat_rat @ ( conversep_rat_rat @ ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) ) @ ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) )
% 0.14/0.43 = ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1111_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: nat > nat] :
% 0.14/0.43 ( ( F = id_nat )
% 0.14/0.43 => ( ( relcompp_nat_nat_nat @ ( conversep_nat_nat @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) )
% 0.14/0.43 = ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1112_Grp__UNIV__id,axiom,
% 0.14/0.43 ! [F: int > int] :
% 0.14/0.43 ( ( F = id_int )
% 0.14/0.43 => ( ( relcompp_int_int_int @ ( conversep_int_int @ ( bNF_Grp_int_int @ top_top_set_int @ F ) ) @ ( bNF_Grp_int_int @ top_top_set_int @ F ) )
% 0.14/0.43 = ( bNF_Grp_int_int @ top_top_set_int @ F ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Grp_UNIV_id
% 0.14/0.43 thf(fact_1113_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: rat > rat,G: rat > rat] :
% 0.14/0.43 ( ( order_4774338944571509483at_rat @ F )
% 0.14/0.43 => ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_4774338944571509483at_rat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1114_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: rat > nat,G: nat > rat] :
% 0.14/0.43 ( ( order_5409469004658005219at_nat @ F )
% 0.14/0.43 => ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_5090893588506375395at_rat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1115_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: rat > int,G: int > rat] :
% 0.14/0.43 ( ( order_5406978534148954943at_int @ F )
% 0.14/0.43 => ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ! [X: rat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_6090247300407429951nt_rat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1116_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: nat > rat,G: rat > nat] :
% 0.14/0.43 ( ( order_5090893588506375395at_rat @ F )
% 0.14/0.43 => ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_5409469004658005219at_nat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1117_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: nat > nat,G: nat > nat] :
% 0.14/0.43 ( ( order_5726023648592871131at_nat @ F )
% 0.14/0.43 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_5726023648592871131at_nat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1118_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: nat > int,G: int > nat] :
% 0.14/0.43 ( ( order_5723533178083820855at_int @ F )
% 0.14/0.43 => ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_6725377360493925687nt_nat @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1119_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: int > rat,G: rat > int] :
% 0.14/0.43 ( ( order_6090247300407429951nt_rat @ F )
% 0.14/0.43 => ( ( ( image_int_rat @ F @ top_top_set_int )
% 0.14/0.43 = top_top_set_rat )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_5406978534148954943at_int @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1120_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: int > nat,G: nat > int] :
% 0.14/0.43 ( ( order_6725377360493925687nt_nat @ F )
% 0.14/0.43 => ( ( ( image_int_nat @ F @ top_top_set_int )
% 0.14/0.43 = top_top_set_nat )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_5723533178083820855at_int @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1121_strict__mono__inv,axiom,
% 0.14/0.43 ! [F: int > int,G: int > int] :
% 0.14/0.43 ( ( order_6722886889984875411nt_int @ F )
% 0.14/0.43 => ( ( ( image_int_int @ F @ top_top_set_int )
% 0.14/0.43 = top_top_set_int )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( G @ ( F @ X ) )
% 0.14/0.43 = X )
% 0.14/0.43 => ( order_6722886889984875411nt_int @ G ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % strict_mono_inv
% 0.14/0.43 thf(fact_1122_Id__on__Gr,axiom,
% 0.14/0.43 ( id_on_nat
% 0.14/0.43 = ( ^ [A6: set_nat] : ( bNF_Gr_nat_nat @ A6 @ id_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_Gr
% 0.14/0.43 thf(fact_1123_Id__on__Gr,axiom,
% 0.14/0.43 ( id_on_o
% 0.14/0.43 = ( ^ [A6: set_o] : ( bNF_Gr_o_o @ A6 @ id_o ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_Gr
% 0.14/0.43 thf(fact_1124_Id__on__Gr,axiom,
% 0.14/0.43 ( id_on_num
% 0.14/0.43 = ( ^ [A6: set_num] : ( bNF_Gr_num_num @ A6 @ id_num ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_Gr
% 0.14/0.43 thf(fact_1125_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: nat > $o,Abs: $o > nat,M: $o > $o] :
% 0.14/0.43 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.43 => ( ( M = id_o )
% 0.14/0.43 => ( ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1126_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: $o > $o,Abs: $o > $o,M: $o > $o] :
% 0.14/0.43 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.43 => ( ( M = id_o )
% 0.14/0.43 => ( ( comp_o_o_o @ ( comp_o_o_o @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_o ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1127_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: num > $o,Abs: $o > num,M: $o > $o] :
% 0.14/0.43 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.43 => ( ( M = id_o )
% 0.14/0.43 => ( ( comp_o_num_num @ ( comp_o_num_o @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_num ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1128_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: nat > num,Abs: num > nat,M: num > num] :
% 0.14/0.43 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.43 => ( ( M = id_num )
% 0.14/0.43 => ( ( comp_num_nat_nat @ ( comp_num_nat_num @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1129_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: $o > num,Abs: num > $o,M: num > num] :
% 0.14/0.43 ( ( type_d3678713432601627782_o_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.43 => ( ( M = id_num )
% 0.14/0.43 => ( ( comp_num_o_o @ ( comp_num_o_num @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_o ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1130_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: num > num,Abs: num > num,M: num > num] :
% 0.14/0.43 ( ( type_d938156138240996706um_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.43 => ( ( M = id_num )
% 0.14/0.43 => ( ( comp_num_num_num @ ( comp_num_num_num @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_num ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1131_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: nat > char,Abs: char > nat,M: char > char] :
% 0.14/0.43 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( M = id_char )
% 0.14/0.43 => ( ( comp_char_nat_nat @ ( comp_char_nat_char @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1132_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: $o > char,Abs: char > $o,M: char > char] :
% 0.14/0.43 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( M = id_char )
% 0.14/0.43 => ( ( comp_char_o_o @ ( comp_char_o_char @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_o ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1133_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: num > char,Abs: char > num,M: char > char] :
% 0.14/0.43 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( M = id_char )
% 0.14/0.43 => ( ( comp_char_num_num @ ( comp_char_num_char @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_num ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1134_type__copy__map__id0,axiom,
% 0.14/0.43 ! [Rep: nat > rat,Abs: rat > nat,M: rat > rat] :
% 0.14/0.43 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.43 => ( ( M = id_rat )
% 0.14/0.43 => ( ( comp_rat_nat_nat @ ( comp_rat_nat_rat @ Abs @ M ) @ Rep )
% 0.14/0.43 = id_nat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_map_id0
% 0.14/0.43 thf(fact_1135_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: nat > char,Abs: char > nat] :
% 0.14/0.43 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( comp_char_nat_nat @ Abs @ Rep )
% 0.14/0.43 = id_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1136_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: $o > char,Abs: char > $o] :
% 0.14/0.43 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( comp_char_o_o @ Abs @ Rep )
% 0.14/0.43 = id_o ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1137_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: num > char,Abs: char > num] :
% 0.14/0.43 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.43 => ( ( comp_char_num_num @ Abs @ Rep )
% 0.14/0.43 = id_num ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1138_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: nat > rat,Abs: rat > nat] :
% 0.14/0.43 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.43 => ( ( comp_rat_nat_nat @ Abs @ Rep )
% 0.14/0.43 = id_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1139_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: $o > rat,Abs: rat > $o] :
% 0.14/0.43 ( ( type_d6486251586359353412_o_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.43 => ( ( comp_rat_o_o @ Abs @ Rep )
% 0.14/0.43 = id_o ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1140_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: num > rat,Abs: rat > num] :
% 0.14/0.43 ( ( type_d3745694291998722336um_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.43 => ( ( comp_rat_num_num @ Abs @ Rep )
% 0.14/0.43 = id_num ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1141_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: $o > nat,Abs: nat > $o] :
% 0.14/0.43 ( ( type_d7121381646445849148_o_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.43 => ( ( comp_nat_o_o @ Abs @ Rep )
% 0.14/0.43 = id_o ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1142_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: num > nat,Abs: nat > num] :
% 0.14/0.43 ( ( type_d4380824352085218072um_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.43 => ( ( comp_nat_num_num @ Abs @ Rep )
% 0.14/0.43 = id_num ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1143_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: nat > nat,Abs: nat > nat] :
% 0.14/0.43 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.43 => ( ( comp_nat_nat_nat @ Abs @ Rep )
% 0.14/0.43 = id_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1144_type__copy__Abs__o__Rep,axiom,
% 0.14/0.43 ! [Rep: nat > int,Abs: int > nat] :
% 0.14/0.43 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ top_top_set_int )
% 0.14/0.43 => ( ( comp_int_nat_nat @ Abs @ Rep )
% 0.14/0.43 = id_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Abs_o_Rep
% 0.14/0.43 thf(fact_1145_type__copy__Rep__o__Abs,axiom,
% 0.14/0.43 ! [Rep: nat > nat,Abs: nat > nat] :
% 0.14/0.43 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.43 => ( ( comp_nat_nat_nat @ Rep @ Abs )
% 0.14/0.43 = id_nat ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Rep_o_Abs
% 0.14/0.43 thf(fact_1146_type__copy__Rep__o__Abs,axiom,
% 0.14/0.43 ! [Rep: product_unit > $o,Abs: $o > product_unit] :
% 0.14/0.43 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.43 => ( ( comp_P5156358013004227690it_o_o @ Rep @ Abs )
% 0.14/0.43 = id_o ) ) ).
% 0.14/0.43
% 0.14/0.43 % type_copy_Rep_o_Abs
% 0.14/0.43 thf(fact_1147_case__prodI2_H,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 0.14/0.43 ( ! [A3: nat,B3: nat] :
% 0.14/0.43 ( ( ( product_Pair_nat_nat @ A3 @ B3 )
% 0.14/0.43 = P )
% 0.14/0.43 => ( C @ A3 @ B3 @ X2 ) )
% 0.14/0.43 => ( produc8739625826339149834_nat_o @ C @ P @ X2 ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2'
% 0.14/0.43 thf(fact_1148_image__ident,axiom,
% 0.14/0.43 ! [Y4: set_nat] :
% 0.14/0.43 ( ( image_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : X4
% 0.14/0.43 @ Y4 )
% 0.14/0.43 = Y4 ) ).
% 0.14/0.43
% 0.14/0.43 % image_ident
% 0.14/0.43 thf(fact_1149_image__ident,axiom,
% 0.14/0.43 ! [Y4: set_int] :
% 0.14/0.43 ( ( image_int_int
% 0.14/0.43 @ ^ [X4: int] : X4
% 0.14/0.43 @ Y4 )
% 0.14/0.43 = Y4 ) ).
% 0.14/0.43
% 0.14/0.43 % image_ident
% 0.14/0.43 thf(fact_1150_split__part,axiom,
% 0.14/0.43 ! [P2: $o,Q2: int > int > $o] :
% 0.14/0.43 ( ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [A5: int,B4: int] :
% 0.14/0.43 ( P2
% 0.14/0.43 & ( Q2 @ A5 @ B4 ) ) )
% 0.14/0.43 = ( ^ [Ab: product_prod_int_int] :
% 0.14/0.43 ( P2
% 0.14/0.43 & ( produc4947309494688390418_int_o @ Q2 @ Ab ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % split_part
% 0.14/0.43 thf(fact_1151_Id__onI,axiom,
% 0.14/0.43 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.43 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ ( id_on_7869290023980668164at_nat @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1152_Id__onI,axiom,
% 0.14/0.43 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.43 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ ( id_on_2554058798563519774at_nat @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1153_Id__onI,axiom,
% 0.14/0.43 ! [A: $o,A4: set_o] :
% 0.14/0.43 ( ( member_o @ A @ A4 )
% 0.14/0.43 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ ( id_on_o @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1154_Id__onI,axiom,
% 0.14/0.43 ! [A: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 0.14/0.43 ( ( member6273874620674182256at_nat @ A @ A4 )
% 0.14/0.43 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ ( id_on_3275838214495744996at_nat @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1155_Id__onI,axiom,
% 0.14/0.43 ! [A: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 0.14/0.43 ( ( member2643936169264416010at_nat @ A @ A4 )
% 0.14/0.43 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ ( id_on_6713504163309144702at_nat @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1156_Id__onI,axiom,
% 0.14/0.43 ! [A: nat,A4: set_nat] :
% 0.14/0.43 ( ( member_nat @ A @ A4 )
% 0.14/0.43 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1157_Id__onI,axiom,
% 0.14/0.43 ! [A: int,A4: set_int] :
% 0.14/0.43 ( ( member_int @ A @ A4 )
% 0.14/0.43 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_onI
% 0.14/0.43 thf(fact_1158_case__prod__conv,axiom,
% 0.14/0.43 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 0.14/0.43 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.14/0.43 = ( F @ A @ B ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_conv
% 0.14/0.43 thf(fact_1159_case__prod__conv,axiom,
% 0.14/0.43 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.14/0.43 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.14/0.43 = ( F @ A @ B ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_conv
% 0.14/0.43 thf(fact_1160_case__prod__conv,axiom,
% 0.14/0.43 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 0.14/0.43 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.14/0.43 = ( F @ A @ B ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_conv
% 0.14/0.43 thf(fact_1161_case__prod__conv,axiom,
% 0.14/0.43 ! [F: int > int > $o,A: int,B: int] :
% 0.14/0.43 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.14/0.43 = ( F @ A @ B ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_conv
% 0.14/0.43 thf(fact_1162_case__prod__conv,axiom,
% 0.14/0.43 ! [F: int > int > int,A: int,B: int] :
% 0.14/0.43 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.14/0.43 = ( F @ A @ B ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_conv
% 0.14/0.43 thf(fact_1163_case__prodI,axiom,
% 0.14/0.43 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( F @ A @ B )
% 0.14/0.43 => ( produc9020218426428501292_nat_o @ F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI
% 0.14/0.43 thf(fact_1164_case__prodI,axiom,
% 0.14/0.43 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( F @ A @ B )
% 0.14/0.43 => ( produc410239310623530412_nat_o @ F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI
% 0.14/0.43 thf(fact_1165_case__prodI,axiom,
% 0.14/0.43 ! [F: nat > num > $o,A: nat,B: num] :
% 0.14/0.43 ( ( F @ A @ B )
% 0.14/0.43 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI
% 0.14/0.43 thf(fact_1166_case__prodI,axiom,
% 0.14/0.43 ! [F: nat > nat > $o,A: nat,B: nat] :
% 0.14/0.43 ( ( F @ A @ B )
% 0.14/0.43 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI
% 0.14/0.43 thf(fact_1167_case__prodI,axiom,
% 0.14/0.43 ! [F: int > int > $o,A: int,B: int] :
% 0.14/0.43 ( ( F @ A @ B )
% 0.14/0.43 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI
% 0.14/0.43 thf(fact_1168_case__prodI2,axiom,
% 0.14/0.43 ! [P: produc1319942482725812455at_nat,C: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o] :
% 0.14/0.43 ( ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( produc9060074326276436823at_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( C @ A3 @ B3 ) )
% 0.14/0.43 => ( produc9020218426428501292_nat_o @ C @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2
% 0.14/0.43 thf(fact_1169_case__prodI2,axiom,
% 0.14/0.43 ! [P: produc3843707927480180839at_nat,C: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.43 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( C @ A3 @ B3 ) )
% 0.14/0.43 => ( produc410239310623530412_nat_o @ C @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2
% 0.14/0.43 thf(fact_1170_case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num,C: nat > num > $o] :
% 0.14/0.43 ( ! [A3: nat,B3: num] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.14/0.43 => ( C @ A3 @ B3 ) )
% 0.14/0.43 => ( produc4927758841916487424_num_o @ C @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2
% 0.14/0.43 thf(fact_1171_case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat,C: nat > nat > $o] :
% 0.14/0.43 ( ! [A3: nat,B3: nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( C @ A3 @ B3 ) )
% 0.14/0.43 => ( produc6081775807080527818_nat_o @ C @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2
% 0.14/0.43 thf(fact_1172_case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_int_int,C: int > int > $o] :
% 0.14/0.43 ( ! [A3: int,B3: int] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_int_int @ A3 @ B3 ) )
% 0.14/0.43 => ( C @ A3 @ B3 ) )
% 0.14/0.43 => ( produc4947309494688390418_int_o @ C @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodI2
% 0.14/0.43 thf(fact_1173_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: $o,C: nat > num > set_o,A: nat,B: num] :
% 0.14/0.43 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1174_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: nat,C: nat > num > set_nat,A: nat,B: num] :
% 0.14/0.43 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1175_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: int,C: nat > num > set_int,A: nat,B: num] :
% 0.14/0.43 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1176_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: $o,C: nat > nat > set_o,A: nat,B: nat] :
% 0.14/0.43 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1177_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: nat,C: nat > nat > set_nat,A: nat,B: nat] :
% 0.14/0.43 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1178_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: int,C: nat > nat > set_int,A: nat,B: nat] :
% 0.14/0.43 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1179_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: $o,C: int > int > set_o,A: int,B: int] :
% 0.14/0.43 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1180_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: nat,C: int > int > set_nat,A: int,B: int] :
% 0.14/0.43 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1181_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: int,C: int > int > set_int,A: int,B: int] :
% 0.14/0.43 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1182_mem__case__prodI,axiom,
% 0.14/0.43 ! [Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat,A: nat,B: num] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ Z2 @ ( C @ A @ B ) )
% 0.14/0.43 => ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI
% 0.14/0.43 thf(fact_1183_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num,Z2: $o,C: nat > num > set_o] :
% 0.14/0.43 ( ! [A3: nat,B3: num] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1184_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num,Z2: nat,C: nat > num > set_nat] :
% 0.14/0.43 ( ! [A3: nat,B3: num] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1185_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num,Z2: int,C: nat > num > set_int] :
% 0.14/0.43 ( ! [A3: nat,B3: num] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1186_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat,Z2: $o,C: nat > nat > set_o] :
% 0.14/0.43 ( ! [A3: nat,B3: nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1187_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat,Z2: nat,C: nat > nat > set_nat] :
% 0.14/0.43 ( ! [A3: nat,B3: nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1188_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat,Z2: int,C: nat > nat > set_int] :
% 0.14/0.43 ( ! [A3: nat,B3: nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1189_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_int_int,Z2: $o,C: int > int > set_o] :
% 0.14/0.43 ( ! [A3: int,B3: int] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_int_int @ A3 @ B3 ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1190_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_int_int,Z2: nat,C: int > int > set_nat] :
% 0.14/0.43 ( ! [A3: int,B3: int] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_int_int @ A3 @ B3 ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1191_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_int_int,Z2: int,C: int > int > set_int] :
% 0.14/0.43 ( ! [A3: int,B3: int] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_int_int @ A3 @ B3 ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1192_mem__case__prodI2,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num,Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ! [A3: nat,B3: num] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 0.14/0.43 => ( member8440522571783428010at_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 0.14/0.43 => ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ P ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % mem_case_prodI2
% 0.14/0.43 thf(fact_1193_case__swap,axiom,
% 0.14/0.43 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P: product_prod_nat_nat] :
% 0.14/0.43 ( ( produc27273713700761075at_nat
% 0.14/0.43 @ ^ [Y5: nat,X4: nat] : ( F @ X4 @ Y5 )
% 0.14/0.43 @ ( product_swap_nat_nat @ P ) )
% 0.14/0.43 = ( produc27273713700761075at_nat @ F @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_swap
% 0.14/0.43 thf(fact_1194_case__swap,axiom,
% 0.14/0.43 ! [F: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 0.14/0.43 ( ( produc8739625826339149834_nat_o
% 0.14/0.43 @ ^ [Y5: nat,X4: nat] : ( F @ X4 @ Y5 )
% 0.14/0.43 @ ( product_swap_nat_nat @ P ) )
% 0.14/0.43 = ( produc8739625826339149834_nat_o @ F @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_swap
% 0.14/0.43 thf(fact_1195_case__swap,axiom,
% 0.14/0.43 ! [F: int > int > product_prod_int_int,P: product_prod_int_int] :
% 0.14/0.43 ( ( produc4245557441103728435nt_int
% 0.14/0.43 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 0.14/0.43 @ ( product_swap_int_int @ P ) )
% 0.14/0.43 = ( produc4245557441103728435nt_int @ F @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_swap
% 0.14/0.43 thf(fact_1196_case__swap,axiom,
% 0.14/0.43 ! [F: int > int > $o,P: product_prod_int_int] :
% 0.14/0.43 ( ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 0.14/0.43 @ ( product_swap_int_int @ P ) )
% 0.14/0.43 = ( produc4947309494688390418_int_o @ F @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_swap
% 0.14/0.43 thf(fact_1197_case__swap,axiom,
% 0.14/0.43 ! [F: int > int > int,P: product_prod_int_int] :
% 0.14/0.43 ( ( produc8211389475949308722nt_int
% 0.14/0.43 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 0.14/0.43 @ ( product_swap_int_int @ P ) )
% 0.14/0.43 = ( produc8211389475949308722nt_int @ F @ P ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_swap
% 0.14/0.43 thf(fact_1198_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > $o] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_o @ ( F @ A @ B ) @ ( image_4451812852358507538_num_o @ ( produc4927758841916487424_num_o @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1199_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > nat] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_nat @ ( F @ A @ B ) @ ( image_4504471508743443926um_nat @ ( produc4973203077627929192um_nat @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1200_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > int] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_int @ ( F @ A @ B ) @ ( image_4501981038234393650um_int @ ( produc4970712607118878916um_int @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1201_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > $o] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_o @ ( F @ A @ B ) @ ( image_3693632289388996572_nat_o @ ( produc6081775807080527818_nat_o @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1202_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_nat @ ( F @ A @ B ) @ ( image_2486076414777270412at_nat @ ( produc6842872674320459806at_nat @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1203_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > int] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_int @ ( F @ A @ B ) @ ( image_2483585944268220136at_int @ ( produc6840382203811409530at_int @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1204_pair__imageI,axiom,
% 0.14/0.43 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > nat] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_nat @ ( F @ A @ B ) @ ( image_5044651549707136836nt_nat @ ( produc8213879946458358998nt_nat @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1205_pair__imageI,axiom,
% 0.14/0.43 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > $o] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_o @ ( F @ A @ B ) @ ( image_2135063354759101220_int_o @ ( produc4947309494688390418_int_o @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1206_pair__imageI,axiom,
% 0.14/0.43 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 0.14/0.43 => ( member_int @ ( F @ A @ B ) @ ( image_5042161079198086560nt_int @ ( produc8211389475949308722nt_int @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1207_pair__imageI,axiom,
% 0.14/0.43 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > product_prod_nat_nat] :
% 0.14/0.43 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 0.14/0.43 => ( member8440522571783428010at_nat @ ( F @ A @ B ) @ ( image_4217639968629731195at_nat @ ( produc8564434177180591209at_nat @ F ) @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % pair_imageI
% 0.14/0.43 thf(fact_1208_Inf_OINF__identity__eq,axiom,
% 0.14/0.43 ! [Inf: set_nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( Inf
% 0.14/0.43 @ ( image_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : X4
% 0.14/0.43 @ A4 ) )
% 0.14/0.43 = ( Inf @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % Inf.INF_identity_eq
% 0.14/0.43 thf(fact_1209_Inf_OINF__identity__eq,axiom,
% 0.14/0.43 ! [Inf: set_int > int,A4: set_int] :
% 0.14/0.43 ( ( Inf
% 0.14/0.43 @ ( image_int_int
% 0.14/0.43 @ ^ [X4: int] : X4
% 0.14/0.43 @ A4 ) )
% 0.14/0.43 = ( Inf @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % Inf.INF_identity_eq
% 0.14/0.43 thf(fact_1210_Sup_OSUP__identity__eq,axiom,
% 0.14/0.43 ! [Sup: set_nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( Sup
% 0.14/0.43 @ ( image_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : X4
% 0.14/0.43 @ A4 ) )
% 0.14/0.43 = ( Sup @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % Sup.SUP_identity_eq
% 0.14/0.43 thf(fact_1211_Sup_OSUP__identity__eq,axiom,
% 0.14/0.43 ! [Sup: set_int > int,A4: set_int] :
% 0.14/0.43 ( ( Sup
% 0.14/0.43 @ ( image_int_int
% 0.14/0.43 @ ^ [X4: int] : X4
% 0.14/0.43 @ A4 ) )
% 0.14/0.43 = ( Sup @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % Sup.SUP_identity_eq
% 0.14/0.43 thf(fact_1212_imageE,axiom,
% 0.14/0.43 ! [B: rat,F: nat > rat,A4: set_nat] :
% 0.14/0.43 ( ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1213_imageE,axiom,
% 0.14/0.43 ! [B: $o,F: $o > $o,A4: set_o] :
% 0.14/0.43 ( ( member_o @ B @ ( image_o_o @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: $o] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_o @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1214_imageE,axiom,
% 0.14/0.43 ! [B: $o,F: nat > $o,A4: set_nat] :
% 0.14/0.43 ( ( member_o @ B @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1215_imageE,axiom,
% 0.14/0.43 ! [B: $o,F: int > $o,A4: set_int] :
% 0.14/0.43 ( ( member_o @ B @ ( image_int_o @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: int] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_int @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1216_imageE,axiom,
% 0.14/0.43 ! [B: nat,F: $o > nat,A4: set_o] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: $o] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_o @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1217_imageE,axiom,
% 0.14/0.43 ! [B: nat,F: nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1218_imageE,axiom,
% 0.14/0.43 ! [B: nat,F: int > nat,A4: set_int] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: int] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_int @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1219_imageE,axiom,
% 0.14/0.43 ! [B: int,F: $o > int,A4: set_o] :
% 0.14/0.43 ( ( member_int @ B @ ( image_o_int @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: $o] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_o @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1220_imageE,axiom,
% 0.14/0.43 ! [B: int,F: nat > int,A4: set_nat] :
% 0.14/0.43 ( ( member_int @ B @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1221_imageE,axiom,
% 0.14/0.43 ! [B: int,F: int > int,A4: set_int] :
% 0.14/0.43 ( ( member_int @ B @ ( image_int_int @ F @ A4 ) )
% 0.14/0.43 => ~ ! [X: int] :
% 0.14/0.43 ( ( B
% 0.14/0.43 = ( F @ X ) )
% 0.14/0.43 => ~ ( member_int @ X @ A4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % imageE
% 0.14/0.43 thf(fact_1222_image__image,axiom,
% 0.14/0.43 ! [F: rat > rat,G: nat > rat,A4: set_nat] :
% 0.14/0.43 ( ( image_rat_rat @ F @ ( image_nat_rat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_rat
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1223_image__image,axiom,
% 0.14/0.43 ! [F: rat > nat,G: nat > rat,A4: set_nat] :
% 0.14/0.43 ( ( image_rat_nat @ F @ ( image_nat_rat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1224_image__image,axiom,
% 0.14/0.43 ! [F: rat > int,G: nat > rat,A4: set_nat] :
% 0.14/0.43 ( ( image_rat_int @ F @ ( image_nat_rat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_int
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1225_image__image,axiom,
% 0.14/0.43 ! [F: int > rat,G: nat > int,A4: set_nat] :
% 0.14/0.43 ( ( image_int_rat @ F @ ( image_nat_int @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_rat
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1226_image__image,axiom,
% 0.14/0.43 ! [F: nat > rat,G: nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( image_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_rat
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1227_image__image,axiom,
% 0.14/0.43 ! [F: nat > rat,G: int > nat,A4: set_int] :
% 0.14/0.43 ( ( image_nat_rat @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_int_rat
% 0.14/0.43 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1228_image__image,axiom,
% 0.14/0.43 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1229_image__image,axiom,
% 0.14/0.43 ! [F: nat > nat,G: int > nat,A4: set_int] :
% 0.14/0.43 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_int_nat
% 0.14/0.43 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1230_image__image,axiom,
% 0.14/0.43 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 0.14/0.43 ( ( image_nat_int @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_nat_int
% 0.14/0.43 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1231_image__image,axiom,
% 0.14/0.43 ! [F: nat > int,G: int > nat,A4: set_int] :
% 0.14/0.43 ( ( image_nat_int @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.43 = ( image_int_int
% 0.14/0.43 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ A4 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_image
% 0.14/0.43 thf(fact_1232_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: $o > $o,A4: set_o,P2: $o > $o] :
% 0.14/0.43 ( ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ ( image_o_o @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_o_o @ F
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1233_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: int > $o,A4: set_int,P2: $o > $o] :
% 0.14/0.43 ( ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ ( image_int_o @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_int_o @ F
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1234_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: $o > int,A4: set_o,P2: int > $o] :
% 0.14/0.43 ( ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ ( image_o_int @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_o_int @ F
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1235_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: int > int,A4: set_int,P2: int > $o] :
% 0.14/0.43 ( ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_int_int @ F
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1236_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 0.14/0.43 ( ( collect_rat
% 0.14/0.43 @ ^ [X4: rat] :
% 0.14/0.43 ( ( member_rat @ X4 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_nat_rat @ F
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1237_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: nat > $o,A4: set_nat,P2: $o > $o] :
% 0.14/0.43 ( ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_nat_o @ F
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1238_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 0.14/0.43 ( ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_nat_int @ F
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1239_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: $o > nat,A4: set_o,P2: nat > $o] :
% 0.14/0.43 ( ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_o_nat @ F
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1240_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 0.14/0.43 ( ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_int_nat @ F
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1241_Compr__image__eq,axiom,
% 0.14/0.43 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 0.14/0.43 ( ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 = ( image_nat_nat @ F
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Compr_image_eq
% 0.14/0.43 thf(fact_1242_Id__on__def_H,axiom,
% 0.14/0.43 ! [A4: product_prod_nat_nat > $o] :
% 0.14/0.43 ( ( id_on_2554058798563519774at_nat @ ( collec3392354462482085612at_nat @ A4 ) )
% 0.14/0.43 = ( collec7088162979684241874at_nat
% 0.14/0.43 @ ( produc6590410687421337004_nat_o
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.14/0.43 ( ( X4 = Y5 )
% 0.14/0.43 & ( A4 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_def'
% 0.14/0.43 thf(fact_1243_Id__on__def_H,axiom,
% 0.14/0.43 ! [A4: nat > $o] :
% 0.14/0.43 ( ( id_on_nat @ ( collect_nat @ A4 ) )
% 0.14/0.43 = ( collec3392354462482085612at_nat
% 0.14/0.43 @ ( produc6081775807080527818_nat_o
% 0.14/0.43 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.43 ( ( X4 = Y5 )
% 0.14/0.43 & ( A4 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_def'
% 0.14/0.43 thf(fact_1244_Id__on__def_H,axiom,
% 0.14/0.43 ! [A4: product_prod_int_int > $o] :
% 0.14/0.43 ( ( id_on_8598933527810153430nt_int @ ( collec213857154873943460nt_int @ A4 ) )
% 0.14/0.43 = ( collec7447955092554649554nt_int
% 0.14/0.43 @ ( produc1676490119946744748_int_o
% 0.14/0.43 @ ^ [X4: product_prod_int_int,Y5: product_prod_int_int] :
% 0.14/0.43 ( ( X4 = Y5 )
% 0.14/0.43 & ( A4 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_def'
% 0.14/0.43 thf(fact_1245_Id__on__def_H,axiom,
% 0.14/0.43 ! [A4: int > $o] :
% 0.14/0.43 ( ( id_on_int @ ( collect_int @ A4 ) )
% 0.14/0.43 = ( collec213857154873943460nt_int
% 0.14/0.43 @ ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [X4: int,Y5: int] :
% 0.14/0.43 ( ( X4 = Y5 )
% 0.14/0.43 & ( A4 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % Id_on_def'
% 0.14/0.43 thf(fact_1246_pred__equals__eq2,axiom,
% 0.14/0.43 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 0.14/0.43 ( ( ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 ) )
% 0.14/0.43 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) ) )
% 0.14/0.43 = ( R3 = S5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pred_equals_eq2
% 0.14/0.43 thf(fact_1247_pred__equals__eq2,axiom,
% 0.14/0.43 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 0.14/0.43 ( ( ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 ) )
% 0.14/0.43 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) ) )
% 0.14/0.43 = ( R3 = S5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pred_equals_eq2
% 0.14/0.43 thf(fact_1248_pred__equals__eq2,axiom,
% 0.14/0.43 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 0.14/0.43 ( ( ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 ) )
% 0.14/0.43 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) ) )
% 0.14/0.43 = ( R3 = S5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pred_equals_eq2
% 0.14/0.43 thf(fact_1249_pred__equals__eq2,axiom,
% 0.14/0.43 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ( ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 ) )
% 0.14/0.43 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) ) )
% 0.14/0.43 = ( R3 = S5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pred_equals_eq2
% 0.14/0.43 thf(fact_1250_pred__equals__eq2,axiom,
% 0.14/0.43 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.43 ( ( ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 ) )
% 0.14/0.43 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) ) )
% 0.14/0.43 = ( R3 = S5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % pred_equals_eq2
% 0.14/0.43 thf(fact_1251_case__prodE_H,axiom,
% 0.14/0.43 ! [C: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 0.14/0.43 ( ( produc8739625826339149834_nat_o @ C @ P @ Z2 )
% 0.14/0.43 => ~ ! [X: nat,Y: nat] :
% 0.14/0.43 ( ( P
% 0.14/0.43 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.14/0.43 => ~ ( C @ X @ Y @ Z2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodE'
% 0.14/0.43 thf(fact_1252_case__prodD_H,axiom,
% 0.14/0.43 ! [R3: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 0.14/0.43 ( ( produc8739625826339149834_nat_o @ R3 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 0.14/0.43 => ( R3 @ A @ B @ C ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prodD'
% 0.14/0.43 thf(fact_1253_case__prod__Pair__iden,axiom,
% 0.14/0.43 ! [P: produc1319942482725812455at_nat] :
% 0.14/0.43 ( ( produc5456455677105495163at_nat @ produc9060074326276436823at_nat @ P )
% 0.14/0.43 = P ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_Pair_iden
% 0.14/0.43 thf(fact_1254_case__prod__Pair__iden,axiom,
% 0.14/0.43 ! [P: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( produc7548845685434208379at_nat @ produc2922128104949294807at_nat @ P )
% 0.14/0.43 = P ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_Pair_iden
% 0.14/0.43 thf(fact_1255_case__prod__Pair__iden,axiom,
% 0.14/0.43 ! [P: product_prod_nat_num] :
% 0.14/0.43 ( ( produc49306077274653107at_num @ product_Pair_nat_num @ P )
% 0.14/0.43 = P ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_Pair_iden
% 0.14/0.43 thf(fact_1256_case__prod__Pair__iden,axiom,
% 0.14/0.43 ! [P: product_prod_nat_nat] :
% 0.14/0.43 ( ( produc2626176000494625587at_nat @ product_Pair_nat_nat @ P )
% 0.14/0.43 = P ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_Pair_iden
% 0.14/0.43 thf(fact_1257_case__prod__Pair__iden,axiom,
% 0.14/0.43 ! [P: product_prod_int_int] :
% 0.14/0.43 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P )
% 0.14/0.43 = P ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_Pair_iden
% 0.14/0.43 thf(fact_1258_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,Q2: produc3843707927480180839at_nat > $o,P2: produc3843707927480180839at_nat > $o] :
% 0.14/0.43 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_le1268244103169919719at_nat
% 0.14/0.43 @ ( collec6321179662152712658at_nat
% 0.14/0.43 @ ^ [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collec6321179662152712658at_nat
% 0.14/0.43 @ ^ [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1259_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_o,A4: set_o,Q2: $o > $o,P2: $o > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: $o] :
% 0.14/0.43 ( ( member_o @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_less_eq_set_o
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1260_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_int,A4: set_int,Q2: int > $o,P2: int > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: int] :
% 0.14/0.43 ( ( member_int @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_less_eq_set_int
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1261_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,Q2: product_prod_nat_nat > $o,P2: product_prod_nat_nat > $o] :
% 0.14/0.43 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_le3146513528884898305at_nat
% 0.14/0.43 @ ( collec3392354462482085612at_nat
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collec3392354462482085612at_nat
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1262_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_nat,A4: set_nat,Q2: nat > $o,P2: nat > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: nat] :
% 0.14/0.43 ( ( member_nat @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_less_eq_set_nat
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1263_subset__CollectI,axiom,
% 0.14/0.43 ! [B5: set_Pr958786334691620121nt_int,A4: set_Pr958786334691620121nt_int,Q2: product_prod_int_int > $o,P2: product_prod_int_int > $o] :
% 0.14/0.43 ( ( ord_le2843351958646193337nt_int @ B5 @ A4 )
% 0.14/0.43 => ( ! [X: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X @ B5 )
% 0.14/0.43 => ( ( Q2 @ X )
% 0.14/0.43 => ( P2 @ X ) ) )
% 0.14/0.43 => ( ord_le2843351958646193337nt_int
% 0.14/0.43 @ ( collec213857154873943460nt_int
% 0.14/0.43 @ ^ [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ B5 )
% 0.14/0.43 & ( Q2 @ X4 ) ) )
% 0.14/0.43 @ ( collec213857154873943460nt_int
% 0.14/0.43 @ ^ [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_CollectI
% 0.14/0.43 thf(fact_1264_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 0.14/0.43 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_le1268244103169919719at_nat @ B5
% 0.14/0.43 @ ( collec6321179662152712658at_nat
% 0.14/0.43 @ ^ [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1265_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_o,A4: set_o,P2: $o > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_less_eq_set_o @ B5
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1266_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_int,A4: set_int,P2: int > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_less_eq_set_int @ B5
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1267_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 0.14/0.43 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_le3146513528884898305at_nat @ B5
% 0.14/0.43 @ ( collec3392354462482085612at_nat
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1268_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_nat,A4: set_nat,P2: nat > $o] :
% 0.14/0.43 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_less_eq_set_nat @ B5
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1269_subset__Collect__iff,axiom,
% 0.14/0.43 ! [B5: set_Pr958786334691620121nt_int,A4: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 0.14/0.43 ( ( ord_le2843351958646193337nt_int @ B5 @ A4 )
% 0.14/0.43 => ( ( ord_le2843351958646193337nt_int @ B5
% 0.14/0.43 @ ( collec213857154873943460nt_int
% 0.14/0.43 @ ^ [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ A4 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 = ( ! [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ B5 )
% 0.14/0.43 => ( P2 @ X4 ) ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % subset_Collect_iff
% 0.14/0.43 thf(fact_1270_prop__restrict,axiom,
% 0.14/0.43 ! [X2: produc3843707927480180839at_nat,Z5: set_Pr4329608150637261639at_nat,X5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_le1268244103169919719at_nat @ Z5
% 0.14/0.43 @ ( collec6321179662152712658at_nat
% 0.14/0.43 @ ^ [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1271_prop__restrict,axiom,
% 0.14/0.43 ! [X2: $o,Z5: set_o,X5: set_o,P2: $o > $o] :
% 0.14/0.43 ( ( member_o @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_less_eq_set_o @ Z5
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1272_prop__restrict,axiom,
% 0.14/0.43 ! [X2: int,Z5: set_int,X5: set_int,P2: int > $o] :
% 0.14/0.43 ( ( member_int @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_less_eq_set_int @ Z5
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1273_prop__restrict,axiom,
% 0.14/0.43 ! [X2: product_prod_nat_nat,Z5: set_Pr1261947904930325089at_nat,X5: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_le3146513528884898305at_nat @ Z5
% 0.14/0.43 @ ( collec3392354462482085612at_nat
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1274_prop__restrict,axiom,
% 0.14/0.43 ! [X2: nat,Z5: set_nat,X5: set_nat,P2: nat > $o] :
% 0.14/0.43 ( ( member_nat @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_less_eq_set_nat @ Z5
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1275_prop__restrict,axiom,
% 0.14/0.43 ! [X2: product_prod_int_int,Z5: set_Pr958786334691620121nt_int,X5: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X2 @ Z5 )
% 0.14/0.43 => ( ( ord_le2843351958646193337nt_int @ Z5
% 0.14/0.43 @ ( collec213857154873943460nt_int
% 0.14/0.43 @ ^ [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) ) )
% 0.14/0.43 => ( P2 @ X2 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % prop_restrict
% 0.14/0.43 thf(fact_1276_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 0.14/0.43 ( ord_le1268244103169919719at_nat
% 0.14/0.43 @ ( collec6321179662152712658at_nat
% 0.14/0.43 @ ^ [X4: produc3843707927480180839at_nat] :
% 0.14/0.43 ( ( member8757157785044589968at_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1277_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_o,P2: $o > $o] :
% 0.14/0.43 ( ord_less_eq_set_o
% 0.14/0.43 @ ( collect_o
% 0.14/0.43 @ ^ [X4: $o] :
% 0.14/0.43 ( ( member_o @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1278_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_int,P2: int > $o] :
% 0.14/0.43 ( ord_less_eq_set_int
% 0.14/0.43 @ ( collect_int
% 0.14/0.43 @ ^ [X4: int] :
% 0.14/0.43 ( ( member_int @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1279_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 0.14/0.43 ( ord_le3146513528884898305at_nat
% 0.14/0.43 @ ( collec3392354462482085612at_nat
% 0.14/0.43 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.43 ( ( member8440522571783428010at_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1280_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_nat,P2: nat > $o] :
% 0.14/0.43 ( ord_less_eq_set_nat
% 0.14/0.43 @ ( collect_nat
% 0.14/0.43 @ ^ [X4: nat] :
% 0.14/0.43 ( ( member_nat @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1281_Collect__restrict,axiom,
% 0.14/0.43 ! [X5: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 0.14/0.43 ( ord_le2843351958646193337nt_int
% 0.14/0.43 @ ( collec213857154873943460nt_int
% 0.14/0.43 @ ^ [X4: product_prod_int_int] :
% 0.14/0.43 ( ( member5262025264175285858nt_int @ X4 @ X5 )
% 0.14/0.43 & ( P2 @ X4 ) ) )
% 0.14/0.43 @ X5 ) ).
% 0.14/0.43
% 0.14/0.43 % Collect_restrict
% 0.14/0.43 thf(fact_1282_fun_Omap__ident,axiom,
% 0.14/0.43 ! [T2: nat > $o] :
% 0.14/0.43 ( ( comp_o_o_nat
% 0.14/0.43 @ ^ [X4: $o] : X4
% 0.14/0.43 @ T2 )
% 0.14/0.43 = T2 ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_ident
% 0.14/0.43 thf(fact_1283_fun_Omap__ident,axiom,
% 0.14/0.43 ! [T2: nat > nat] :
% 0.14/0.43 ( ( comp_nat_nat_nat
% 0.14/0.43 @ ^ [X4: nat] : X4
% 0.14/0.43 @ T2 )
% 0.14/0.43 = T2 ) ).
% 0.14/0.43
% 0.14/0.43 % fun.map_ident
% 0.14/0.43 thf(fact_1284_case__prod__app,axiom,
% 0.14/0.43 ( produc27273713700761075at_nat
% 0.14/0.43 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.14/0.43 ( produc2626176000494625587at_nat
% 0.14/0.43 @ ^ [L3: nat,R5: nat] : ( F2 @ L3 @ R5 @ Y5 )
% 0.14/0.43 @ X4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_app
% 0.14/0.43 thf(fact_1285_case__prod__app,axiom,
% 0.14/0.43 ( produc8739625826339149834_nat_o
% 0.14/0.43 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.14/0.43 ( produc6081775807080527818_nat_o
% 0.14/0.43 @ ^ [L3: nat,R5: nat] : ( F2 @ L3 @ R5 @ Y5 )
% 0.14/0.43 @ X4 ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % case_prod_app
% 0.14/0.43 thf(fact_1286_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 0.14/0.43 = ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1287_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 0.14/0.43 = ( produc8211389475949308722nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1288_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1289_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc8211389475949308722nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1290_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1291_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc8211389475949308722nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1292_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 0.14/0.43 = ( produc4245557441103728435nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1293_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc4245557441103728435nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1294_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.14/0.43 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 0.14/0.43 = ( produc4245557441103728435nt_int
% 0.14/0.43 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1295_prod_Ocase__distrib,axiom,
% 0.14/0.43 ! [H: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.14/0.43 ( ( H @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 0.14/0.43 = ( produc8739625826339149834_nat_o
% 0.14/0.43 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 0.14/0.43 @ Prod ) ) ).
% 0.14/0.43
% 0.14/0.43 % prod.case_distrib
% 0.14/0.43 thf(fact_1296_prod_Odisc__eq__case,axiom,
% 0.14/0.43 ! [Prod: product_prod_int_int] :
% 0.14/0.43 ( produc4947309494688390418_int_o
% 0.14/0.43 @ ^ [Uu: int,Uv: int] : $true
% 0.14/0.43 @ Prod ) ).
% 0.14/0.43
% 0.14/0.43 % prod.disc_eq_case
% 0.14/0.43 thf(fact_1297_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: int > $o,F: int > nat,B5: set_nat] :
% 0.14/0.43 ( ! [X: int] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( collect_int @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1298_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: int > $o,F: int > int,B5: set_int] :
% 0.14/0.43 ( ! [X: int] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_int @ ( image_int_int @ F @ ( collect_int @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1299_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: nat > $o,F: nat > rat,B5: set_rat] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_rat @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1300_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: nat > $o,F: nat > $o,B5: set_o] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_o @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1301_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: nat > $o,F: nat > nat,B5: set_nat] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1302_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: nat > $o,F: nat > int,B5: set_int] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1303_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > $o,B5: set_o] :
% 0.14/0.43 ( ! [X: product_prod_nat_nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_o @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_o @ ( image_3693632289388996572_nat_o @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1304_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > nat,B5: set_nat] :
% 0.14/0.43 ( ! [X: product_prod_nat_nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_nat @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1305_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > int,B5: set_int] :
% 0.14/0.43 ( ! [X: product_prod_nat_nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member_int @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_less_eq_set_int @ ( image_2483585944268220136at_int @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1306_image__Collect__subsetI,axiom,
% 0.14/0.43 ! [P2: nat > $o,F: nat > product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.43 ( ! [X: nat] :
% 0.14/0.43 ( ( P2 @ X )
% 0.14/0.43 => ( member8440522571783428010at_nat @ ( F @ X ) @ B5 ) )
% 0.14/0.43 => ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 0.14/0.43
% 0.14/0.43 % image_Collect_subsetI
% 0.14/0.43 thf(fact_1307_range__composition,axiom,
% 0.14/0.43 ! [F: nat > rat,G: char > nat] :
% 0.14/0.43 ( ( image_char_rat
% 0.14/0.43 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_char )
% 0.14/0.43 = ( image_nat_rat @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1308_range__composition,axiom,
% 0.14/0.43 ! [F: nat > nat,G: char > nat] :
% 0.14/0.43 ( ( image_char_nat
% 0.14/0.43 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_char )
% 0.14/0.43 = ( image_nat_nat @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1309_range__composition,axiom,
% 0.14/0.43 ! [F: nat > int,G: char > nat] :
% 0.14/0.43 ( ( image_char_int
% 0.14/0.43 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_char )
% 0.14/0.43 = ( image_nat_int @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1310_range__composition,axiom,
% 0.14/0.43 ! [F: int > nat,G: char > int] :
% 0.14/0.43 ( ( image_char_nat
% 0.14/0.43 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_char )
% 0.14/0.43 = ( image_int_nat @ F @ ( image_char_int @ G @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1311_range__composition,axiom,
% 0.14/0.43 ! [F: int > int,G: char > int] :
% 0.14/0.43 ( ( image_char_int
% 0.14/0.43 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_char )
% 0.14/0.43 = ( image_int_int @ F @ ( image_char_int @ G @ top_top_set_char ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1312_range__composition,axiom,
% 0.14/0.43 ! [F: nat > rat,G: rat > nat] :
% 0.14/0.43 ( ( image_rat_rat
% 0.14/0.43 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_rat @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1313_range__composition,axiom,
% 0.14/0.43 ! [F: nat > nat,G: rat > nat] :
% 0.14/0.43 ( ( image_rat_nat
% 0.14/0.43 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_nat @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1314_range__composition,axiom,
% 0.14/0.43 ! [F: nat > int,G: rat > nat] :
% 0.14/0.43 ( ( image_rat_int
% 0.14/0.43 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_rat )
% 0.14/0.43 = ( image_nat_int @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1315_range__composition,axiom,
% 0.14/0.43 ! [F: int > nat,G: rat > int] :
% 0.14/0.43 ( ( image_rat_nat
% 0.14/0.43 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_rat )
% 0.14/0.43 = ( image_int_nat @ F @ ( image_rat_int @ G @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1316_range__composition,axiom,
% 0.14/0.43 ! [F: int > int,G: rat > int] :
% 0.14/0.43 ( ( image_rat_int
% 0.14/0.43 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.43 @ top_top_set_rat )
% 0.14/0.43 = ( image_int_int @ F @ ( image_rat_int @ G @ top_top_set_rat ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % range_composition
% 0.14/0.43 thf(fact_1317_rangeE,axiom,
% 0.14/0.43 ! [B: $o,F: char > $o] :
% 0.14/0.43 ( ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( B
% 0.14/0.43 = ( ~ ( F @ X ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1318_rangeE,axiom,
% 0.14/0.43 ! [B: nat,F: char > nat] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1319_rangeE,axiom,
% 0.14/0.43 ! [B: int,F: char > int] :
% 0.14/0.43 ( ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) )
% 0.14/0.43 => ~ ! [X: char] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1320_rangeE,axiom,
% 0.14/0.43 ! [B: $o,F: rat > $o] :
% 0.14/0.43 ( ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( B
% 0.14/0.43 = ( ~ ( F @ X ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1321_rangeE,axiom,
% 0.14/0.43 ! [B: nat,F: rat > nat] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1322_rangeE,axiom,
% 0.14/0.43 ! [B: int,F: rat > int] :
% 0.14/0.43 ( ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) )
% 0.14/0.43 => ~ ! [X: rat] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1323_rangeE,axiom,
% 0.14/0.43 ! [B: rat,F: nat > rat] :
% 0.14/0.43 ( ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1324_rangeE,axiom,
% 0.14/0.43 ! [B: $o,F: nat > $o] :
% 0.14/0.43 ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( B
% 0.14/0.43 = ( ~ ( F @ X ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1325_rangeE,axiom,
% 0.14/0.43 ! [B: nat,F: nat > nat] :
% 0.14/0.43 ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1326_rangeE,axiom,
% 0.14/0.43 ! [B: int,F: nat > int] :
% 0.14/0.43 ( ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) )
% 0.14/0.43 => ~ ! [X: nat] :
% 0.14/0.43 ( B
% 0.14/0.43 != ( F @ X ) ) ) ).
% 0.14/0.43
% 0.14/0.43 % rangeE
% 0.14/0.43 thf(fact_1327_fun_Orel__map_I1_J,axiom,
% 0.14/0.43 ! [Sb: num > num > $o,I: nat > num,X2: int > nat,Y3: int > num] :
% 0.14/0.43 ( ( bNF_re7626690874201225453um_num
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ Sb
% 0.14/0.43 @ ( comp_nat_num_int @ I @ X2 )
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re272988434038980259at_num
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ ^ [X4: nat] : ( Sb @ ( I @ X4 ) )
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_map(1)
% 0.14/0.43 thf(fact_1328_fun_Orel__map_I1_J,axiom,
% 0.14/0.43 ! [Sb: num > num > $o,I: num > num,X2: int > num,Y3: int > num] :
% 0.14/0.43 ( ( bNF_re7626690874201225453um_num
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ Sb
% 0.14/0.43 @ ( comp_num_num_int @ I @ X2 )
% 0.14/0.43 @ Y3 )
% 0.14/0.43 = ( bNF_re7626690874201225453um_num
% 0.14/0.43 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.43 @ ^ [X4: num] : ( Sb @ ( I @ X4 ) )
% 0.14/0.43 @ X2
% 0.14/0.43 @ Y3 ) ) ).
% 0.14/0.43
% 0.14/0.43 % fun.rel_map(1)
% 0.14/0.43 thf(fact_1329_fun_Orel__map_I2_J,axiom,
% 0.14/0.43 ! [Sa: num > num > $o,X2: int > num,G: nat > num,Y3: int > nat] :
% 0.14/0.43 ( ( bNF_re7626690874201225453um_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ Sa
% 0.14/0.44 @ X2
% 0.14/0.44 @ ( comp_nat_num_int @ G @ Y3 ) )
% 0.14/0.44 = ( bNF_re1845987051190671011um_nat
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ^ [X4: num,Y5: nat] : ( Sa @ X4 @ ( G @ Y5 ) )
% 0.14/0.44 @ X2
% 0.14/0.44 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_map(2)
% 0.14/0.44 thf(fact_1330_fun_Orel__map_I2_J,axiom,
% 0.14/0.44 ! [Sa: num > num > $o,X2: int > num,G: num > num,Y3: int > num] :
% 0.14/0.44 ( ( bNF_re7626690874201225453um_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ Sa
% 0.14/0.44 @ X2
% 0.14/0.44 @ ( comp_num_num_int @ G @ Y3 ) )
% 0.14/0.44 = ( bNF_re7626690874201225453um_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ^ [X4: num,Y5: num] : ( Sa @ X4 @ ( G @ Y5 ) )
% 0.14/0.44 @ X2
% 0.14/0.44 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_map(2)
% 0.14/0.44 thf(fact_1331_case__prodE2,axiom,
% 0.14/0.44 ! [Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 0.14/0.44 ( ( Q2 @ ( produc27273713700761075at_nat @ P2 @ Z2 ) )
% 0.14/0.44 => ~ ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( Z2
% 0.14/0.44 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.14/0.44 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE2
% 0.14/0.44 thf(fact_1332_case__prodE2,axiom,
% 0.14/0.44 ! [Q2: ( product_prod_nat_nat > $o ) > $o,P2: nat > nat > product_prod_nat_nat > $o,Z2: product_prod_nat_nat] :
% 0.14/0.44 ( ( Q2 @ ( produc8739625826339149834_nat_o @ P2 @ Z2 ) )
% 0.14/0.44 => ~ ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( Z2
% 0.14/0.44 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.14/0.44 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE2
% 0.14/0.44 thf(fact_1333_case__prodE2,axiom,
% 0.14/0.44 ! [Q2: product_prod_int_int > $o,P2: int > int > product_prod_int_int,Z2: product_prod_int_int] :
% 0.14/0.44 ( ( Q2 @ ( produc4245557441103728435nt_int @ P2 @ Z2 ) )
% 0.14/0.44 => ~ ! [X: int,Y: int] :
% 0.14/0.44 ( ( Z2
% 0.14/0.44 = ( product_Pair_int_int @ X @ Y ) )
% 0.14/0.44 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE2
% 0.14/0.44 thf(fact_1334_case__prodE2,axiom,
% 0.14/0.44 ! [Q2: $o > $o,P2: int > int > $o,Z2: product_prod_int_int] :
% 0.14/0.44 ( ( Q2 @ ( produc4947309494688390418_int_o @ P2 @ Z2 ) )
% 0.14/0.44 => ~ ! [X: int,Y: int] :
% 0.14/0.44 ( ( Z2
% 0.14/0.44 = ( product_Pair_int_int @ X @ Y ) )
% 0.14/0.44 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE2
% 0.14/0.44 thf(fact_1335_case__prodE2,axiom,
% 0.14/0.44 ! [Q2: int > $o,P2: int > int > int,Z2: product_prod_int_int] :
% 0.14/0.44 ( ( Q2 @ ( produc8211389475949308722nt_int @ P2 @ Z2 ) )
% 0.14/0.44 => ~ ! [X: int,Y: int] :
% 0.14/0.44 ( ( Z2
% 0.14/0.44 = ( product_Pair_int_int @ X @ Y ) )
% 0.14/0.44 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE2
% 0.14/0.44 thf(fact_1336_case__prod__eta,axiom,
% 0.14/0.44 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.44 ( ( produc27273713700761075at_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 0.14/0.44 = F ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_eta
% 0.14/0.44 thf(fact_1337_case__prod__eta,axiom,
% 0.14/0.44 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( produc8739625826339149834_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 0.14/0.44 = F ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_eta
% 0.14/0.44 thf(fact_1338_case__prod__eta,axiom,
% 0.14/0.44 ! [F: product_prod_int_int > product_prod_int_int] :
% 0.14/0.44 ( ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 0.14/0.44 = F ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_eta
% 0.14/0.44 thf(fact_1339_case__prod__eta,axiom,
% 0.14/0.44 ! [F: product_prod_int_int > $o] :
% 0.14/0.44 ( ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 0.14/0.44 = F ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_eta
% 0.14/0.44 thf(fact_1340_case__prod__eta,axiom,
% 0.14/0.44 ! [F: product_prod_int_int > int] :
% 0.14/0.44 ( ( produc8211389475949308722nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 0.14/0.44 = F ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_eta
% 0.14/0.44 thf(fact_1341_cond__case__prod__eta,axiom,
% 0.14/0.44 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.44 ( ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( F @ X @ Y )
% 0.14/0.44 = ( G @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 0.14/0.44 => ( ( produc27273713700761075at_nat @ F )
% 0.14/0.44 = G ) ) ).
% 0.14/0.44
% 0.14/0.44 % cond_case_prod_eta
% 0.14/0.44 thf(fact_1342_cond__case__prod__eta,axiom,
% 0.14/0.44 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( F @ X @ Y )
% 0.14/0.44 = ( G @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 0.14/0.44 => ( ( produc8739625826339149834_nat_o @ F )
% 0.14/0.44 = G ) ) ).
% 0.14/0.44
% 0.14/0.44 % cond_case_prod_eta
% 0.14/0.44 thf(fact_1343_cond__case__prod__eta,axiom,
% 0.14/0.44 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 0.14/0.44 ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( F @ X @ Y )
% 0.14/0.44 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 0.14/0.44 => ( ( produc4245557441103728435nt_int @ F )
% 0.14/0.44 = G ) ) ).
% 0.14/0.44
% 0.14/0.44 % cond_case_prod_eta
% 0.14/0.44 thf(fact_1344_cond__case__prod__eta,axiom,
% 0.14/0.44 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 0.14/0.44 ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( F @ X @ Y )
% 0.14/0.44 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 0.14/0.44 => ( ( produc4947309494688390418_int_o @ F )
% 0.14/0.44 = G ) ) ).
% 0.14/0.44
% 0.14/0.44 % cond_case_prod_eta
% 0.14/0.44 thf(fact_1345_cond__case__prod__eta,axiom,
% 0.14/0.44 ! [F: int > int > int,G: product_prod_int_int > int] :
% 0.14/0.44 ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( F @ X @ Y )
% 0.14/0.44 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 0.14/0.44 => ( ( produc8211389475949308722nt_int @ F )
% 0.14/0.44 = G ) ) ).
% 0.14/0.44
% 0.14/0.44 % cond_case_prod_eta
% 0.14/0.44 thf(fact_1346_case__prodD,axiom,
% 0.14/0.44 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( produc9020218426428501292_nat_o @ F @ ( produc9060074326276436823at_nat @ A @ B ) )
% 0.14/0.44 => ( F @ A @ B ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodD
% 0.14/0.44 thf(fact_1347_case__prodD,axiom,
% 0.14/0.44 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( produc410239310623530412_nat_o @ F @ ( produc2922128104949294807at_nat @ A @ B ) )
% 0.14/0.44 => ( F @ A @ B ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodD
% 0.14/0.44 thf(fact_1348_case__prodD,axiom,
% 0.14/0.44 ! [F: nat > num > $o,A: nat,B: num] :
% 0.14/0.44 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 0.14/0.44 => ( F @ A @ B ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodD
% 0.14/0.44 thf(fact_1349_case__prodD,axiom,
% 0.14/0.44 ! [F: nat > nat > $o,A: nat,B: nat] :
% 0.14/0.44 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.14/0.44 => ( F @ A @ B ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodD
% 0.14/0.44 thf(fact_1350_case__prodD,axiom,
% 0.14/0.44 ! [F: int > int > $o,A: int,B: int] :
% 0.14/0.44 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.14/0.44 => ( F @ A @ B ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodD
% 0.14/0.44 thf(fact_1351_case__prodE,axiom,
% 0.14/0.44 ! [C: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,P: produc1319942482725812455at_nat] :
% 0.14/0.44 ( ( produc9020218426428501292_nat_o @ C @ P )
% 0.14/0.44 => ~ ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( P
% 0.14/0.44 = ( produc9060074326276436823at_nat @ X @ Y ) )
% 0.14/0.44 => ~ ( C @ X @ Y ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE
% 0.14/0.44 thf(fact_1352_case__prodE,axiom,
% 0.14/0.44 ! [C: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,P: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( produc410239310623530412_nat_o @ C @ P )
% 0.14/0.44 => ~ ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( P
% 0.14/0.44 = ( produc2922128104949294807at_nat @ X @ Y ) )
% 0.14/0.44 => ~ ( C @ X @ Y ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE
% 0.14/0.44 thf(fact_1353_case__prodE,axiom,
% 0.14/0.44 ! [C: nat > num > $o,P: product_prod_nat_num] :
% 0.14/0.44 ( ( produc4927758841916487424_num_o @ C @ P )
% 0.14/0.44 => ~ ! [X: nat,Y: num] :
% 0.14/0.44 ( ( P
% 0.14/0.44 = ( product_Pair_nat_num @ X @ Y ) )
% 0.14/0.44 => ~ ( C @ X @ Y ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE
% 0.14/0.44 thf(fact_1354_case__prodE,axiom,
% 0.14/0.44 ! [C: nat > nat > $o,P: product_prod_nat_nat] :
% 0.14/0.44 ( ( produc6081775807080527818_nat_o @ C @ P )
% 0.14/0.44 => ~ ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( P
% 0.14/0.44 = ( product_Pair_nat_nat @ X @ Y ) )
% 0.14/0.44 => ~ ( C @ X @ Y ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE
% 0.14/0.44 thf(fact_1355_case__prodE,axiom,
% 0.14/0.44 ! [C: int > int > $o,P: product_prod_int_int] :
% 0.14/0.44 ( ( produc4947309494688390418_int_o @ C @ P )
% 0.14/0.44 => ~ ! [X: int,Y: int] :
% 0.14/0.44 ( ( P
% 0.14/0.44 = ( product_Pair_int_int @ X @ Y ) )
% 0.14/0.44 => ~ ( C @ X @ Y ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prodE
% 0.14/0.44 thf(fact_1356_fst__def,axiom,
% 0.14/0.44 ( produc473321116828791851t_unit
% 0.14/0.44 = ( produc4846201513286513633_ref_a
% 0.14/0.44 @ ^ [X12: ref_a,X23: heap_e7401611519738050253t_unit] : X12 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_def
% 0.14/0.44 thf(fact_1357_fst__def,axiom,
% 0.14/0.44 ( product_fst_int_int
% 0.14/0.44 = ( produc8211389475949308722nt_int
% 0.14/0.44 @ ^ [X12: int,X23: int] : X12 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_def
% 0.14/0.44 thf(fact_1358_snd__def,axiom,
% 0.14/0.44 ( produc1126150082675451753t_unit
% 0.14/0.44 = ( produc2552614499379209865t_unit
% 0.14/0.44 @ ^ [X12: ref_a,X23: heap_e7401611519738050253t_unit] : X23 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_def
% 0.14/0.44 thf(fact_1359_snd__def,axiom,
% 0.14/0.44 ( product_snd_int_int
% 0.14/0.44 = ( produc8211389475949308722nt_int
% 0.14/0.44 @ ^ [X12: int,X23: int] : X23 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_def
% 0.14/0.44 thf(fact_1360_map__prod__def,axiom,
% 0.14/0.44 ( produc6036585564866528938nt_int
% 0.14/0.44 = ( ^ [F2: int > int,G3: int > int] :
% 0.14/0.44 ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ ( F2 @ X4 ) @ ( G3 @ Y5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_def
% 0.14/0.44 thf(fact_1361_case__prod__map__prod,axiom,
% 0.14/0.44 ! [H: nat > nat > product_prod_nat_nat > product_prod_nat_nat,F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
% 0.14/0.44 ( ( produc27273713700761075at_nat @ H @ ( produc6977886695330630970at_nat @ F @ G @ X2 ) )
% 0.14/0.44 = ( produc27273713700761075at_nat
% 0.14/0.44 @ ^ [L3: nat,R5: nat] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 0.14/0.44 @ X2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_map_prod
% 0.14/0.44 thf(fact_1362_case__prod__map__prod,axiom,
% 0.14/0.44 ! [H: nat > nat > product_prod_nat_nat > $o,F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
% 0.14/0.44 ( ( produc8739625826339149834_nat_o @ H @ ( produc6977886695330630970at_nat @ F @ G @ X2 ) )
% 0.14/0.44 = ( produc8739625826339149834_nat_o
% 0.14/0.44 @ ^ [L3: nat,R5: nat] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 0.14/0.44 @ X2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_map_prod
% 0.14/0.44 thf(fact_1363_case__prod__map__prod,axiom,
% 0.14/0.44 ! [H: int > int > product_prod_int_int,F: int > int,G: int > int,X2: product_prod_int_int] :
% 0.14/0.44 ( ( produc4245557441103728435nt_int @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 0.14/0.44 = ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 0.14/0.44 @ X2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_map_prod
% 0.14/0.44 thf(fact_1364_case__prod__map__prod,axiom,
% 0.14/0.44 ! [H: int > int > $o,F: int > int,G: int > int,X2: product_prod_int_int] :
% 0.14/0.44 ( ( produc4947309494688390418_int_o @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 0.14/0.44 = ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 0.14/0.44 @ X2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_map_prod
% 0.14/0.44 thf(fact_1365_case__prod__map__prod,axiom,
% 0.14/0.44 ! [H: int > int > int,F: int > int,G: int > int,X2: product_prod_int_int] :
% 0.14/0.44 ( ( produc8211389475949308722nt_int @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 0.14/0.44 = ( produc8211389475949308722nt_int
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 0.14/0.44 @ X2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_map_prod
% 0.14/0.44 thf(fact_1366_converse__relcompp,axiom,
% 0.14/0.44 ! [R: int > product_prod_nat_nat > $o,S2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( conver1866313717161370910at_nat @ ( relcom716700242784427165at_nat @ R @ S2 ) )
% 0.14/0.44 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ S2 ) @ ( conver1866313717161370910at_nat @ R ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % converse_relcompp
% 0.14/0.44 thf(fact_1367_converse__relcompp,axiom,
% 0.14/0.44 ! [R: code_integer > int > $o,S2: int > int > $o] :
% 0.14/0.44 ( ( conver1462408618118490240er_int @ ( relcom3789353511612409832nt_int @ R @ S2 ) )
% 0.14/0.44 = ( relcom967497705283160040nteger @ ( conversep_int_int @ S2 ) @ ( conver1462408618118490240er_int @ R ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % converse_relcompp
% 0.14/0.44 thf(fact_1368_converse__relcompp,axiom,
% 0.14/0.44 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o] :
% 0.14/0.44 ( ( conver4689305806000247544at_int @ ( relcom8911704206367525917at_int @ R @ S2 ) )
% 0.14/0.44 = ( relcom716700242784427165at_nat @ ( conver4689305806000247544at_int @ S2 ) @ ( conver6965824823119931701at_nat @ R ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % converse_relcompp
% 0.14/0.44 thf(fact_1369_converse__relcompp,axiom,
% 0.14/0.44 ! [R: int > int > $o,S2: int > code_integer > $o] :
% 0.14/0.44 ( ( conver2101108097643427968nteger @ ( relcom967497705283160040nteger @ R @ S2 ) )
% 0.14/0.44 = ( relcom3789353511612409832nt_int @ ( conver2101108097643427968nteger @ S2 ) @ ( conversep_int_int @ R ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % converse_relcompp
% 0.14/0.44 thf(fact_1370_flip__pred,axiom,
% 0.14/0.44 ! [A4: set_Pr7459493094073627847at_nat,R3: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o] :
% 0.14/0.44 ( ( ord_le5997549366648089703at_nat @ A4 @ ( collec7872792499061297490at_nat @ ( produc9020218426428501292_nat_o @ ( conver9095369822871743413at_nat @ R3 ) ) ) )
% 0.14/0.44 => ( ord_le5997549366648089703at_nat
% 0.14/0.44 @ ( image_3313167189156628421at_nat
% 0.14/0.44 @ ( produc5456455677105495163at_nat
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) )
% 0.14/0.44 @ A4 )
% 0.14/0.44 @ ( collec7872792499061297490at_nat @ ( produc9020218426428501292_nat_o @ R3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % flip_pred
% 0.14/0.44 thf(fact_1371_flip__pred,axiom,
% 0.14/0.44 ! [A4: set_Pr4329608150637261639at_nat,R3: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.44 ( ( ord_le1268244103169919719at_nat @ A4 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( conver5243090411617913141at_nat @ R3 ) ) ) )
% 0.14/0.44 => ( ord_le1268244103169919719at_nat
% 0.14/0.44 @ ( image_960689587819713477at_nat
% 0.14/0.44 @ ( produc7548845685434208379at_nat
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) )
% 0.14/0.44 @ A4 )
% 0.14/0.44 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ R3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % flip_pred
% 0.14/0.44 thf(fact_1372_flip__pred,axiom,
% 0.14/0.44 ! [A4: set_Pr3280342998896498603um_nat,R3: nat > num > $o] :
% 0.14/0.44 ( ( ord_le5164908622851071819um_nat @ A4 @ ( collec1522684865789554998um_nat @ ( produc6857965554392702720_nat_o @ ( conversep_nat_num @ R3 ) ) ) )
% 0.14/0.44 => ( ord_le8085105155179020875at_num
% 0.14/0.44 @ ( image_7762062833379733445at_num
% 0.14/0.44 @ ( produc5219324331026901427at_num
% 0.14/0.44 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) )
% 0.14/0.44 @ A4 )
% 0.14/0.44 @ ( collec4100598399430923318at_num @ ( produc4927758841916487424_num_o @ R3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % flip_pred
% 0.14/0.44 thf(fact_1373_flip__pred,axiom,
% 0.14/0.44 ! [A4: set_Pr1261947904930325089at_nat,R3: nat > nat > $o] :
% 0.14/0.44 ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( conversep_nat_nat @ R3 ) ) ) )
% 0.14/0.44 => ( ord_le3146513528884898305at_nat
% 0.14/0.44 @ ( image_5168914502847457605at_nat
% 0.14/0.44 @ ( produc2626176000494625587at_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 0.14/0.44 @ A4 )
% 0.14/0.44 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % flip_pred
% 0.14/0.44 thf(fact_1374_flip__pred,axiom,
% 0.14/0.44 ! [A4: set_Pr958786334691620121nt_int,R3: int > int > $o] :
% 0.14/0.44 ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( conversep_int_int @ R3 ) ) ) )
% 0.14/0.44 => ( ord_le2843351958646193337nt_int
% 0.14/0.44 @ ( image_2653370878348428101nt_int
% 0.14/0.44 @ ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) )
% 0.14/0.44 @ A4 )
% 0.14/0.44 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % flip_pred
% 0.14/0.44 thf(fact_1375_type__copy__wit,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: produc3843707927480180839at_nat,S5: $o > set_Pr4329608150637261639at_nat,Y3: $o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ X2 @ ( comp_o4913564575355137019t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 0.14/0.44 => ( member8757157785044589968at_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_wit
% 0.14/0.44 thf(fact_1376_type__copy__wit,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: product_prod_nat_nat,S5: $o > set_Pr1261947904930325089at_nat,Y3: $o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ X2 @ ( comp_o2254869825208929t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 0.14/0.44 => ( member8440522571783428010at_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_wit
% 0.14/0.44 thf(fact_1377_type__copy__wit,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: $o,S5: $o > set_o,Y3: $o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( member_o @ X2 @ ( comp_o6895741221744486154t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 0.14/0.44 => ( member_o @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_wit
% 0.14/0.44 thf(fact_1378_type__copy__wit,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: nat,S5: $o > set_nat,Y3: $o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( member_nat @ X2 @ ( comp_o9190160103024335696t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 0.14/0.44 => ( member_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_wit
% 0.14/0.44 thf(fact_1379_type__copy__wit,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: int,S5: $o > set_int,Y3: $o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( member_int @ X2 @ ( comp_o1521574261646630388t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 0.14/0.44 => ( member_int @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_wit
% 0.14/0.44 thf(fact_1380_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,F: nat > nat,P2: nat > $o,H: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( bNF_vi6818137723729380987_o_o_o @ F @ Rep @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1381_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,F: int > int,P2: int > $o,H: int > char] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( bNF_vi9149698133064535136char_o @ F @ Rep @ ( bNF_Grp_int_char @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_nat
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1382_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: $o > char,Abs: char > $o,F: nat > $o,P2: $o > $o,H: $o > char] :
% 0.14/0.44 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( bNF_vi8816436626763797690char_o @ F @ Rep @ ( bNF_Grp_o_char @ ( collect_o @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1383_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: num > char,Abs: char > num,F: int > nat,P2: nat > $o,H: nat > char] :
% 0.14/0.44 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( bNF_vi1300075849944819442char_o @ F @ Rep @ ( bNF_Grp_nat_char @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_num
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1384_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,F: nat > nat,P2: nat > $o,H: nat > char] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( bNF_vi8943400373106913048char_o @ F @ Rep @ ( bNF_Grp_nat_char @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_nat
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1385_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: nat > rat,Abs: rat > nat,F: int > int,P2: int > $o,H: int > rat] :
% 0.14/0.44 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.44 => ( ( bNF_vi1281217848275042457_rat_o @ F @ Rep @ ( bNF_Grp_int_rat @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_nat
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_nat_int @ ( comp_rat_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1386_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: $o > rat,Abs: rat > $o,F: nat > $o,P2: $o > $o,H: $o > rat] :
% 0.14/0.44 ( ( type_d6486251586359353412_o_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.44 => ( ( bNF_vi3868162310295888627_rat_o @ F @ Rep @ ( bNF_Grp_o_rat @ ( collect_o @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_o_o_nat @ ( comp_rat_o_o @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1387_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: num > rat,Abs: rat > num,F: int > nat,P2: nat > $o,H: nat > rat] :
% 0.14/0.44 ( ( type_d3745694291998722336um_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.44 => ( ( bNF_vi7769575839906753835_rat_o @ F @ Rep @ ( bNF_Grp_nat_rat @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_num
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_num_int @ ( comp_rat_num_nat @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1388_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: nat > rat,Abs: rat > nat,F: nat > nat,P2: nat > $o,H: nat > rat] :
% 0.14/0.44 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 0.14/0.44 => ( ( bNF_vi2930123780028963665_rat_o @ F @ Rep @ ( bNF_Grp_nat_rat @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_nat
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_nat_nat @ ( comp_rat_nat_nat @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1389_type__copy__vimage2p__Grp__Rep,axiom,
% 0.14/0.44 ! [Rep: nat > nat,Abs: nat > nat,F: int > int,P2: int > $o,H: int > nat] :
% 0.14/0.44 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.44 => ( ( bNF_vi5018550775591610529_nat_o @ F @ Rep @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_nat
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_nat_int @ ( comp_nat_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Rep
% 0.14/0.44 thf(fact_1390_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: nat > num,Abs: num > nat,G: nat > int,P2: int > $o,H: int > nat] :
% 0.14/0.44 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.44 => ( ( bNF_vi1731478210338170163_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_num
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_num_nat @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1391_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,G: nat > nat,P2: nat > $o,H: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( bNF_vi6818137723729380987_o_o_o @ G @ Abs @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1392_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: int > nat,Abs: nat > int,G: int > int,P2: int > $o,H: int > int] :
% 0.14/0.44 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.44 => ( ( bNF_vi3197508430158922565_int_o @ G @ Abs @ ( bNF_Grp_int_int @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_int_nat
% 0.14/0.44 @ ( collect_int
% 0.14/0.44 @ ^ [X4: int] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_nat_int @ ( comp_int_nat_int @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1393_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: int > nat,Abs: nat > int,G: nat > int,P2: int > $o,H: int > int] :
% 0.14/0.44 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.44 => ( ( bNF_vi8357618154448083105_int_o @ G @ Abs @ ( bNF_Grp_int_int @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_nat
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_int_nat_nat @ ( comp_int_nat_int @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1394_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: nat > nat,Abs: nat > nat,G: nat > nat,P2: nat > $o,H: nat > nat] :
% 0.14/0.44 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 0.14/0.44 => ( ( bNF_vi6667456707345531737_nat_o @ G @ Abs @ ( bNF_Grp_nat_nat @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_nat
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1395_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,G: nat > $o,P2: $o > $o,H: $o > product_unit] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( bNF_vi5856767400800367702unit_o @ G @ Abs @ ( bNF_Gr395642070819736771t_unit @ ( collect_o @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_o_o_nat @ ( comp_P5156358013004227690it_o_o @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1396_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,G: nat > nat,P2: nat > $o,H: nat > product_unit] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( bNF_vi1443435967014148806unit_o @ G @ Abs @ ( bNF_Gr1993012052113314029t_unit @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Grp_nat_o
% 0.14/0.44 @ ( collect_nat
% 0.14/0.44 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_nat_o_nat @ ( comp_P4985893458130756478_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1397_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: nat > num,Abs: num > nat,G: product_prod_nat_nat > int,P2: int > $o,H: int > nat] :
% 0.14/0.44 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.44 => ( ( bNF_vi9094538908245281400_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Gr5974128493091723341at_num
% 0.14/0.44 @ ( collec3392354462482085612at_nat
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_i1186163378102392086at_nat @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1398_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: nat > num,Abs: num > nat,G: product_prod_int_int > int,P2: int > $o,H: int > nat] :
% 0.14/0.44 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 0.14/0.44 => ( ( bNF_vi1633389952966819264_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Gr8532703628021589765nt_num
% 0.14/0.44 @ ( collec213857154873943460nt_int
% 0.14/0.44 @ ^ [X4: product_prod_int_int] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_i7231038107349025742nt_int @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1399_type__copy__vimage2p__Grp__Abs,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,G: product_prod_nat_nat > nat,P2: nat > $o,H: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( bNF_vi9025507403824386624_o_o_o @ G @ Abs @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 0.14/0.44 = ( bNF_Gr8859634586176591525_nat_o
% 0.14/0.44 @ ( collec3392354462482085612at_nat
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat] : ( P2 @ ( G @ X4 ) ) )
% 0.14/0.44 @ ( comp_n1662990198670838940at_nat @ ( comp_o_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_vimage2p_Grp_Abs
% 0.14/0.44 thf(fact_1400_exE__realizer,axiom,
% 0.14/0.44 ! [P2: nat > nat > $o,P: product_prod_nat_nat,Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ ( product_snd_nat_nat @ P ) @ ( product_fst_nat_nat @ P ) )
% 0.14/0.44 => ( ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( P2 @ Y @ X )
% 0.14/0.44 => ( Q2 @ ( F @ X @ Y ) ) )
% 0.14/0.44 => ( Q2 @ ( produc27273713700761075at_nat @ F @ P ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % exE_realizer
% 0.14/0.44 thf(fact_1401_exE__realizer,axiom,
% 0.14/0.44 ! [P2: nat > nat > $o,P: product_prod_nat_nat,Q2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( P2 @ ( product_snd_nat_nat @ P ) @ ( product_fst_nat_nat @ P ) )
% 0.14/0.44 => ( ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( P2 @ Y @ X )
% 0.14/0.44 => ( Q2 @ ( F @ X @ Y ) ) )
% 0.14/0.44 => ( Q2 @ ( produc8739625826339149834_nat_o @ F @ P ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % exE_realizer
% 0.14/0.44 thf(fact_1402_exE__realizer,axiom,
% 0.14/0.44 ! [P2: int > int > $o,P: product_prod_int_int,Q2: product_prod_int_int > $o,F: int > int > product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 0.14/0.44 => ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( P2 @ Y @ X )
% 0.14/0.44 => ( Q2 @ ( F @ X @ Y ) ) )
% 0.14/0.44 => ( Q2 @ ( produc4245557441103728435nt_int @ F @ P ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % exE_realizer
% 0.14/0.44 thf(fact_1403_exE__realizer,axiom,
% 0.14/0.44 ! [P2: int > int > $o,P: product_prod_int_int,Q2: $o > $o,F: int > int > $o] :
% 0.14/0.44 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 0.14/0.44 => ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( P2 @ Y @ X )
% 0.14/0.44 => ( Q2 @ ( F @ X @ Y ) ) )
% 0.14/0.44 => ( Q2 @ ( produc4947309494688390418_int_o @ F @ P ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % exE_realizer
% 0.14/0.44 thf(fact_1404_exE__realizer,axiom,
% 0.14/0.44 ! [P2: int > int > $o,P: product_prod_int_int,Q2: int > $o,F: int > int > int] :
% 0.14/0.44 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 0.14/0.44 => ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( P2 @ Y @ X )
% 0.14/0.44 => ( Q2 @ ( F @ X @ Y ) ) )
% 0.14/0.44 => ( Q2 @ ( produc8211389475949308722nt_int @ F @ P ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % exE_realizer
% 0.14/0.44 thf(fact_1405_case__prod__beta_H,axiom,
% 0.14/0.44 ( produc27273713700761075at_nat
% 0.14/0.44 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X4 ) @ ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_beta'
% 0.14/0.44 thf(fact_1406_case__prod__beta_H,axiom,
% 0.14/0.44 ( produc8739625826339149834_nat_o
% 0.14/0.44 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X4 ) @ ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_beta'
% 0.14/0.44 thf(fact_1407_case__prod__beta_H,axiom,
% 0.14/0.44 ( produc4245557441103728435nt_int
% 0.14/0.44 = ( ^ [F2: int > int > product_prod_int_int,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_beta'
% 0.14/0.44 thf(fact_1408_case__prod__beta_H,axiom,
% 0.14/0.44 ( produc4947309494688390418_int_o
% 0.14/0.44 = ( ^ [F2: int > int > $o,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_beta'
% 0.14/0.44 thf(fact_1409_case__prod__beta_H,axiom,
% 0.14/0.44 ( produc8211389475949308722nt_int
% 0.14/0.44 = ( ^ [F2: int > int > int,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_beta'
% 0.14/0.44 thf(fact_1410_case__prod__unfold,axiom,
% 0.14/0.44 ( produc27273713700761075at_nat
% 0.14/0.44 = ( ^ [C4: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P3: product_prod_nat_nat] : ( C4 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_unfold
% 0.14/0.44 thf(fact_1411_case__prod__unfold,axiom,
% 0.14/0.44 ( produc8739625826339149834_nat_o
% 0.14/0.44 = ( ^ [C4: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat] : ( C4 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_unfold
% 0.14/0.44 thf(fact_1412_case__prod__unfold,axiom,
% 0.14/0.44 ( produc4245557441103728435nt_int
% 0.14/0.44 = ( ^ [C4: int > int > product_prod_int_int,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_unfold
% 0.14/0.44 thf(fact_1413_case__prod__unfold,axiom,
% 0.14/0.44 ( produc4947309494688390418_int_o
% 0.14/0.44 = ( ^ [C4: int > int > $o,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_unfold
% 0.14/0.44 thf(fact_1414_case__prod__unfold,axiom,
% 0.14/0.44 ( produc8211389475949308722nt_int
% 0.14/0.44 = ( ^ [C4: int > int > int,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_unfold
% 0.14/0.44 thf(fact_1415_pred__subset__eq2,axiom,
% 0.14/0.44 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 0.14/0.44 ( ( ord_le3072208448688395470_nat_o
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.44 = ( ord_le5997549366648089703at_nat @ R3 @ S5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % pred_subset_eq2
% 0.14/0.44 thf(fact_1416_pred__subset__eq2,axiom,
% 0.14/0.44 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( ord_le3935385432712749774_nat_o
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.44 = ( ord_le1268244103169919719at_nat @ R3 @ S5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % pred_subset_eq2
% 0.14/0.44 thf(fact_1417_pred__subset__eq2,axiom,
% 0.14/0.44 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 0.14/0.44 ( ( ord_le3404735783095501756_num_o
% 0.14/0.44 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 0.14/0.44 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.44 = ( ord_le8085105155179020875at_num @ R3 @ S5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % pred_subset_eq2
% 0.14/0.44 thf(fact_1418_pred__subset__eq2,axiom,
% 0.14/0.44 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( ord_le2646555220125990790_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.44 = ( ord_le3146513528884898305at_nat @ R3 @ S5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % pred_subset_eq2
% 0.14/0.44 thf(fact_1419_pred__subset__eq2,axiom,
% 0.14/0.44 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.44 ( ( ord_le6741204236512500942_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.44 = ( ord_le2843351958646193337nt_int @ R3 @ S5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % pred_subset_eq2
% 0.14/0.44 thf(fact_1420_comp__fun__commute__on__def,axiom,
% 0.14/0.44 ( finite8619596206551965927at_nat
% 0.14/0.44 = ( ^ [S4: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat > nat] :
% 0.14/0.44 ! [X4: produc3843707927480180839at_nat,Y5: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ X4 @ S4 )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ Y5 @ S4 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on_def
% 0.14/0.44 thf(fact_1421_comp__fun__commute__on__def,axiom,
% 0.14/0.44 ( finite2110315540964234241at_nat
% 0.14/0.44 = ( ^ [S4: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat > nat] :
% 0.14/0.44 ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ X4 @ S4 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ Y5 @ S4 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on_def
% 0.14/0.44 thf(fact_1422_comp__fun__commute__on__def,axiom,
% 0.14/0.44 ( finite4703585013658510744_o_nat
% 0.14/0.44 = ( ^ [S4: set_o,F2: $o > nat > nat] :
% 0.14/0.44 ! [X4: $o,Y5: $o] :
% 0.14/0.44 ( ( member_o @ X4 @ S4 )
% 0.14/0.44 => ( ( member_o @ Y5 @ S4 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on_def
% 0.14/0.44 thf(fact_1423_comp__fun__commute__on__def,axiom,
% 0.14/0.44 ( finite3582905537739598962at_nat
% 0.14/0.44 = ( ^ [S4: set_nat,F2: nat > nat > nat] :
% 0.14/0.44 ! [X4: nat,Y5: nat] :
% 0.14/0.44 ( ( member_nat @ X4 @ S4 )
% 0.14/0.44 => ( ( member_nat @ Y5 @ S4 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on_def
% 0.14/0.44 thf(fact_1424_comp__fun__commute__on__def,axiom,
% 0.14/0.44 ( finite4582259249640653518nt_nat
% 0.14/0.44 = ( ^ [S4: set_int,F2: int > nat > nat] :
% 0.14/0.44 ! [X4: int,Y5: int] :
% 0.14/0.44 ( ( member_int @ X4 @ S4 )
% 0.14/0.44 => ( ( member_int @ Y5 @ S4 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on_def
% 0.14/0.44 thf(fact_1425_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 0.14/0.44 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( finite8619596206551965927at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.comp_fun_commute_on
% 0.14/0.44 thf(fact_1426_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 0.14/0.44 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.14/0.44 ( ( finite2110315540964234241at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.comp_fun_commute_on
% 0.14/0.44 thf(fact_1427_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 0.14/0.44 ! [S5: set_o,F: $o > nat > nat,X2: $o,Y3: $o] :
% 0.14/0.44 ( ( finite4703585013658510744_o_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_o @ X2 @ S5 )
% 0.14/0.44 => ( ( member_o @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.comp_fun_commute_on
% 0.14/0.44 thf(fact_1428_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 0.14/0.44 ! [S5: set_nat,F: nat > nat > nat,X2: nat,Y3: nat] :
% 0.14/0.44 ( ( finite3582905537739598962at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.comp_fun_commute_on
% 0.14/0.44 thf(fact_1429_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 0.14/0.44 ! [S5: set_int,F: int > nat > nat,X2: int,Y3: int] :
% 0.14/0.44 ( ( finite4582259249640653518nt_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_int @ X2 @ S5 )
% 0.14/0.44 => ( ( member_int @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.comp_fun_commute_on
% 0.14/0.44 thf(fact_1430_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > $o > $o,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,G: nat > $o] :
% 0.14/0.44 ( ( finite2818816984019561153_nat_o @ S5 @ F )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1431_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,G: nat > nat] :
% 0.14/0.44 ( ( finite8619596206551965927at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1432_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > $o > $o,X2: product_prod_nat_nat,Y3: product_prod_nat_nat,G: nat > $o] :
% 0.14/0.44 ( ( finite1496024664758132007_nat_o @ S5 @ F )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1433_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat,G: nat > nat] :
% 0.14/0.44 ( ( finite2110315540964234241at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1434_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_o,F: $o > $o > $o,X2: $o,Y3: $o,G: nat > $o] :
% 0.14/0.44 ( ( finite7905178416053733328on_o_o @ S5 @ F )
% 0.14/0.44 => ( ( member_o @ X2 @ S5 )
% 0.14/0.44 => ( ( member_o @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1435_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_o,F: $o > nat > nat,X2: $o,Y3: $o,G: nat > nat] :
% 0.14/0.44 ( ( finite4703585013658510744_o_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_o @ X2 @ S5 )
% 0.14/0.44 => ( ( member_o @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1436_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_nat,F: nat > $o > $o,X2: nat,Y3: nat,G: nat > $o] :
% 0.14/0.44 ( ( finite7806256374766696054_nat_o @ S5 @ F )
% 0.14/0.44 => ( ( member_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1437_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_nat,F: nat > nat > nat,X2: nat,Y3: nat,G: nat > nat] :
% 0.14/0.44 ( ( finite3582905537739598962at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( member_nat @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1438_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_int,F: int > $o > $o,X2: int,Y3: int,G: nat > $o] :
% 0.14/0.44 ( ( finite5985214029334008090_int_o @ S5 @ F )
% 0.14/0.44 => ( ( member_int @ X2 @ S5 )
% 0.14/0.44 => ( ( member_int @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1439_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 0.14/0.44 ! [S5: set_int,F: int > nat > nat,X2: int,Y3: int,G: nat > nat] :
% 0.14/0.44 ( ( finite4582259249640653518nt_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_int @ X2 @ S5 )
% 0.14/0.44 => ( ( member_int @ Y3 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.commute_left_comp
% 0.14/0.44 thf(fact_1440_comp__fun__commute__on_Ointro,axiom,
% 0.14/0.44 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat] :
% 0.14/0.44 ( ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ X @ S5 )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ Y @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 0.14/0.44 => ( finite8619596206551965927at_nat @ S5 @ F ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.intro
% 0.14/0.44 thf(fact_1441_comp__fun__commute__on_Ointro,axiom,
% 0.14/0.44 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat] :
% 0.14/0.44 ( ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ X @ S5 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ Y @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 0.14/0.44 => ( finite2110315540964234241at_nat @ S5 @ F ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.intro
% 0.14/0.44 thf(fact_1442_comp__fun__commute__on_Ointro,axiom,
% 0.14/0.44 ! [S5: set_o,F: $o > nat > nat] :
% 0.14/0.44 ( ! [X: $o,Y: $o] :
% 0.14/0.44 ( ( member_o @ X @ S5 )
% 0.14/0.44 => ( ( member_o @ Y @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 0.14/0.44 => ( finite4703585013658510744_o_nat @ S5 @ F ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.intro
% 0.14/0.44 thf(fact_1443_comp__fun__commute__on_Ointro,axiom,
% 0.14/0.44 ! [S5: set_nat,F: nat > nat > nat] :
% 0.14/0.44 ( ! [X: nat,Y: nat] :
% 0.14/0.44 ( ( member_nat @ X @ S5 )
% 0.14/0.44 => ( ( member_nat @ Y @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 0.14/0.44 => ( finite3582905537739598962at_nat @ S5 @ F ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.intro
% 0.14/0.44 thf(fact_1444_comp__fun__commute__on_Ointro,axiom,
% 0.14/0.44 ! [S5: set_int,F: int > nat > nat] :
% 0.14/0.44 ( ! [X: int,Y: int] :
% 0.14/0.44 ( ( member_int @ X @ S5 )
% 0.14/0.44 => ( ( member_int @ Y @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 0.14/0.44 => ( finite4582259249640653518nt_nat @ S5 @ F ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_commute_on.intro
% 0.14/0.44 thf(fact_1445_case__prod__o__map__prod,axiom,
% 0.14/0.44 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G1: nat > nat,G22: nat > nat] :
% 0.14/0.44 ( ( comp_P3913276677246710332at_nat @ ( produc27273713700761075at_nat @ F ) @ ( produc6977886695330630970at_nat @ G1 @ G22 ) )
% 0.14/0.44 = ( produc27273713700761075at_nat
% 0.14/0.44 @ ^ [L3: nat,R5: nat] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_o_map_prod
% 0.14/0.44 thf(fact_1446_case__prod__o__map__prod,axiom,
% 0.14/0.44 ! [F: nat > nat > product_prod_nat_nat > $o,G1: nat > nat,G22: nat > nat] :
% 0.14/0.44 ( ( comp_P2002127591014248037at_nat @ ( produc8739625826339149834_nat_o @ F ) @ ( produc6977886695330630970at_nat @ G1 @ G22 ) )
% 0.14/0.44 = ( produc8739625826339149834_nat_o
% 0.14/0.44 @ ^ [L3: nat,R5: nat] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_o_map_prod
% 0.14/0.44 thf(fact_1447_case__prod__o__map__prod,axiom,
% 0.14/0.44 ! [F: int > int > product_prod_int_int,G1: int > int,G22: int > int] :
% 0.14/0.44 ( ( comp_P2788356708182965334nt_int @ ( produc4245557441103728435nt_int @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 0.14/0.44 = ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_o_map_prod
% 0.14/0.44 thf(fact_1448_case__prod__o__map__prod,axiom,
% 0.14/0.44 ! [F: int > int > $o,G1: int > int,G22: int > int] :
% 0.14/0.44 ( ( comp_P9034173210191959223nt_int @ ( produc4947309494688390418_int_o @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 0.14/0.44 = ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_o_map_prod
% 0.14/0.44 thf(fact_1449_case__prod__o__map__prod,axiom,
% 0.14/0.44 ! [F: int > int > int,G1: int > int,G22: int > int] :
% 0.14/0.44 ( ( comp_P5356232565778667509nt_int @ ( produc8211389475949308722nt_int @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 0.14/0.44 = ( produc8211389475949308722nt_int
% 0.14/0.44 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_o_map_prod
% 0.14/0.44 thf(fact_1450_vimage2p__relcompp__converse,axiom,
% 0.14/0.44 ! [Rep: product_prod_nat_nat > product_prod_nat_nat,Abs: product_prod_nat_nat > product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: int > int,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 0.14/0.44 ( ( type_d281131942595027436at_nat @ Rep @ Abs @ top_to4669805908274784177at_nat )
% 0.14/0.44 => ( ( bNF_vi5426221348228882691_int_o @ F @ G @ ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ R3 ) @ S5 ) )
% 0.14/0.44 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_vi763171854521451549_nat_o @ Rep @ F @ R3 ) ) @ ( bNF_vi5426221348228882691_int_o @ Rep @ G @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % vimage2p_relcompp_converse
% 0.14/0.44 thf(fact_1451_vimage2p__relcompp__converse,axiom,
% 0.14/0.44 ! [Rep: int > product_prod_nat_nat,Abs: product_prod_nat_nat > int,F: int > product_prod_nat_nat,G: code_integer > int,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 0.14/0.44 ( ( type_d7732240953928457511at_nat @ Rep @ Abs @ top_to4669805908274784177at_nat )
% 0.14/0.44 => ( ( bNF_vi2881549544236934259_int_o @ F @ G @ ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ R3 ) @ S5 ) )
% 0.14/0.44 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_vi1204582724742824157_nat_o @ Rep @ F @ R3 ) ) @ ( bNF_vi2881549544236934259_int_o @ Rep @ G @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % vimage2p_relcompp_converse
% 0.14/0.44 thf(fact_1452_vimage2p__relcompp__converse,axiom,
% 0.14/0.44 ! [Rep: product_prod_nat_nat > int,Abs: int > product_prod_nat_nat,F: product_prod_nat_nat > int,G: int > code_integer,R3: int > int > $o,S5: int > code_integer > $o] :
% 0.14/0.44 ( ( type_d1331861005912558337at_int @ Rep @ Abs @ top_top_set_int )
% 0.14/0.44 => ( ( bNF_vi33923956287962137eger_o @ F @ G @ ( relcom967497705283160040nteger @ ( conversep_int_int @ R3 ) @ S5 ) )
% 0.14/0.44 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_vi2682369418337388893_int_o @ Rep @ F @ R3 ) ) @ ( bNF_vi33923956287962137eger_o @ Rep @ G @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % vimage2p_relcompp_converse
% 0.14/0.44 thf(fact_1453_vimage2p__relcompp__converse,axiom,
% 0.14/0.44 ! [Rep: int > int,Abs: int > int,F: int > int,G: code_integer > code_integer,R3: int > int > $o,S5: int > code_integer > $o] :
% 0.14/0.44 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ top_top_set_int )
% 0.14/0.44 => ( ( bNF_vi699694178825965831eger_o @ F @ G @ ( relcom967497705283160040nteger @ ( conversep_int_int @ R3 ) @ S5 ) )
% 0.14/0.44 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_vi3884084463199473129_int_o @ Rep @ F @ R3 ) ) @ ( bNF_vi699694178825965831eger_o @ Rep @ G @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % vimage2p_relcompp_converse
% 0.14/0.44 thf(fact_1454_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ ( id_on_7869290023980668164at_nat @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member8757157785044589968at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1455_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ ( id_on_2554058798563519774at_nat @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member8440522571783428010at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1456_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: $o,Y3: $o,A4: set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ ( id_on_o @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member_o @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1457_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ ( id_on_3275838214495744996at_nat @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member6273874620674182256at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1458_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( id_on_6713504163309144702at_nat @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member2643936169264416010at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1459_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: nat,Y3: nat,A4: set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( id_on_nat @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1460_Id__on__iff,axiom,
% 0.14/0.44 ! [X2: int,Y3: int,A4: set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( id_on_int @ A4 ) )
% 0.14/0.44 = ( ( X2 = Y3 )
% 0.14/0.44 & ( member_int @ X2 @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_iff
% 0.14/0.44 thf(fact_1461_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.44 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ ( id_on_7869290023980668164at_nat @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1462_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.44 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( id_on_2554058798563519774at_nat @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1463_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: $o,B: $o,A4: set_o] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member_o @ A @ A4 )
% 0.14/0.44 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( id_on_o @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1464_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 0.14/0.44 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( id_on_3275838214495744996at_nat @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1465_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 0.14/0.44 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( id_on_6713504163309144702at_nat @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1466_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: nat,B: nat,A4: set_nat] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1467_Id__on__eqI,axiom,
% 0.14/0.44 ! [A: int,B: int,A4: set_int] :
% 0.14/0.44 ( ( A = B )
% 0.14/0.44 => ( ( member_int @ A @ A4 )
% 0.14/0.44 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_on_eqI
% 0.14/0.44 thf(fact_1468_Id__onE,axiom,
% 0.14/0.44 ! [C: produc1906917888121415911at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( member6009668390874684176at_nat @ C @ ( id_on_7869290023980668164at_nat @ A4 ) )
% 0.14/0.44 => ~ ! [X: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( produc2335810615602371415at_nat @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1469_Id__onE,axiom,
% 0.14/0.44 ! [C: produc859450856879609959at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member8206827879206165904at_nat @ C @ ( id_on_2554058798563519774at_nat @ A4 ) )
% 0.14/0.44 => ~ ! [X: product_prod_nat_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( produc6161850002892822231at_nat @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1470_Id__onE,axiom,
% 0.14/0.44 ! [C: product_prod_o_o,A4: set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ C @ ( id_on_o @ A4 ) )
% 0.14/0.44 => ~ ! [X: $o] :
% 0.14/0.44 ( ( member_o @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_o_o @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1471_Id__onE,axiom,
% 0.14/0.44 ! [C: produc1319942482725812455at_nat,A4: set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( member1466754251312161552at_nat @ C @ ( id_on_3275838214495744996at_nat @ A4 ) )
% 0.14/0.44 => ~ ! [X: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( member6273874620674182256at_nat @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( produc9060074326276436823at_nat @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1472_Id__onE,axiom,
% 0.14/0.44 ! [C: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ C @ ( id_on_6713504163309144702at_nat @ A4 ) )
% 0.14/0.44 => ~ ! [X: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member2643936169264416010at_nat @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( produc2922128104949294807at_nat @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1473_Id__onE,axiom,
% 0.14/0.44 ! [C: product_prod_nat_nat,A4: set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A4 ) )
% 0.14/0.44 => ~ ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_nat_nat @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1474_Id__onE,axiom,
% 0.14/0.44 ! [C: product_prod_int_int,A4: set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A4 ) )
% 0.14/0.44 => ~ ! [X: int] :
% 0.14/0.44 ( ( member_int @ X @ A4 )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_int_int @ X @ X ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Id_onE
% 0.14/0.44 thf(fact_1475_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,R22: nat > nat > $o,P2: nat > nat > $o,Q2: nat > nat > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( bNF_re578469030762574527_nat_o @ R1
% 0.14/0.44 @ ( bNF_re4705727531993890431at_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_fst_nat_nat @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1476_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,R22: int > int > $o,P2: nat > int > $o,Q2: nat > int > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 0.14/0.44 ( ( bNF_re605504016728627135_int_o @ R1
% 0.14/0.44 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_fst_int_int @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1477_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: int > int > $o,R22: nat > nat > $o,P2: int > nat > $o,Q2: int > nat > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( bNF_re3376528473927230327_nat_o @ R1
% 0.14/0.44 @ ( bNF_re4705727531993890431at_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( product_fst_nat_nat @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_int_int @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1478_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: int > int > $o,R22: int > int > $o,P2: int > int > $o,Q2: int > int > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 0.14/0.44 ( ( bNF_re3403563459893282935_int_o @ R1
% 0.14/0.44 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( product_fst_int_int @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_int_int @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1479_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: nat > ref_a > $o,Q2: nat > heap_e7401611519738050253t_unit > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 0.14/0.44 ( ( bNF_re5655699643857186083unit_o @ R1
% 0.14/0.44 @ ( bNF_re1850668159662942673it_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1480_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: nat > nat > $o,P2: ref_a > nat > $o,Q2: heap_e7401611519738050253t_unit > nat > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( bNF_re9202112420002600977_nat_o @ R1
% 0.14/0.44 @ ( bNF_re4705727531993890431at_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( product_fst_nat_nat @ B ) )
% 0.14/0.44 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1481_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: int > int > $o,P2: ref_a > int > $o,Q2: heap_e7401611519738050253t_unit > int > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 0.14/0.44 ( ( bNF_re5775369113877777_int_o @ R1
% 0.14/0.44 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( product_fst_int_int @ B ) )
% 0.14/0.44 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1482_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: int > int > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: int > ref_a > $o,Q2: int > heap_e7401611519738050253t_unit > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 0.14/0.44 ( ( bNF_re5404797796594736747unit_o @ R1
% 0.14/0.44 @ ( bNF_re1850668159662942673it_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 0.14/0.44 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 0.14/0.44 = ( Q2 @ ( product_snd_int_int @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1483_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: product_prod_nat_nat > int > $o,R22: product_prod_nat_nat > int > $o,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: int > int > $o,A: produc4196048018000912732at_int,A4: set_Pr49084382684228242at_int,B: produc4196048018000912732at_int,B5: set_Pr49084382684228242at_int] :
% 0.14/0.44 ( ( bNF_re717283939379294677_int_o @ R1
% 0.14/0.44 @ ( bNF_re6644619430987730960nt_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member8394280151737582451at_int @ A @ A4 )
% 0.14/0.44 => ( ( member8394280151737582451at_int @ B @ B5 )
% 0.14/0.44 => ( ( ord_le4604737605482584818at_int @ A4 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le4604737605482584818at_int @ B5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( produc4619704898428564714at_int @ A ) @ ( produc4619704898428564714at_int @ B ) )
% 0.14/0.44 = ( Q2 @ ( produc3064508320661873192at_int @ A ) @ ( produc3064508320661873192at_int @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1484_predicate2__transferD,axiom,
% 0.14/0.44 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: ref_a > ref_a > $o,Q2: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 0.14/0.44 ( ( bNF_re1366391616432607057unit_o @ R1
% 0.14/0.44 @ ( bNF_re1850668159662942673it_o_o @ R22
% 0.14/0.44 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.44 @ P2
% 0.14/0.44 @ Q2 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 0.14/0.44 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 0.14/0.44 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 0.14/0.44 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 0.14/0.44 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % predicate2_transferD
% 0.14/0.44 thf(fact_1485_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: $o] :
% 0.14/0.44 ( ( comp_P2137996956111167876_o_o_o @ product_fst_o_o
% 0.14/0.44 @ ^ [X4: $o] : ( product_Pair_o_o @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_o @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1486_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: num] :
% 0.14/0.44 ( ( comp_P864883071962432936um_num @ product_fst_num_num
% 0.14/0.44 @ ^ [X4: num] : ( product_Pair_num_num @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_num @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1487_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( comp_P8235817900121468292at_nat @ produc4486455499028916547at_nat
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_set7849613212452405432at_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1488_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( comp_P4528037747288561284at_nat @ produc6011863565407846595at_nat
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_set2334057505560298834at_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1489_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: nat] :
% 0.14/0.44 ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat
% 0.14/0.44 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1490_fst__diag__id,axiom,
% 0.14/0.44 ! [Z2: int] :
% 0.14/0.44 ( ( comp_P6651465171681656048nt_int @ product_fst_int_int
% 0.14/0.44 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_int @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_id
% 0.14/0.44 thf(fact_1491_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: $o] :
% 0.14/0.44 ( ( comp_P2137996956111167876_o_o_o @ product_snd_o_o
% 0.14/0.44 @ ^ [X4: $o] : ( product_Pair_o_o @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_o @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1492_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: num] :
% 0.14/0.44 ( ( comp_P864883071962432936um_num @ product_snd_num_num
% 0.14/0.44 @ ^ [X4: num] : ( product_Pair_num_num @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_num @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1493_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( comp_P8235817900121468292at_nat @ produc826222791318859909at_nat
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_set7849613212452405432at_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1494_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( comp_P4528037747288561284at_nat @ produc2937545259423399429at_nat
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_set2334057505560298834at_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1495_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: nat] :
% 0.14/0.44 ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat
% 0.14/0.44 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_nat @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1496_snd__diag__id,axiom,
% 0.14/0.44 ! [Z2: int] :
% 0.14/0.44 ( ( comp_P6651465171681656048nt_int @ product_snd_int_int
% 0.14/0.44 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ X4 )
% 0.14/0.44 @ Z2 )
% 0.14/0.44 = ( id_int @ Z2 ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_id
% 0.14/0.44 thf(fact_1497_case__prod__comp,axiom,
% 0.14/0.44 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: produc3346328345660746739nteger] :
% 0.14/0.44 ( ( produc4281629032016041417nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X2 )
% 0.14/0.44 = ( F @ ( G @ ( produc1861665112190112313nteger @ X2 ) ) @ ( produc7955729907432593271nteger @ X2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % case_prod_comp
% 0.14/0.44 thf(fact_1498_lookup__def,axiom,
% 0.14/0.44 ( lookup_a
% 0.14/0.44 = ( ^ [R5: ref_a] :
% 0.14/0.44 ( heap_tap_a
% 0.14/0.44 @ ^ [H5: heap_e7401611519738050253t_unit] : ( get_a @ H5 @ R5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % lookup_def
% 0.14/0.44 thf(fact_1499_fst__snd__flip,axiom,
% 0.14/0.44 ( produc4486455499028916547at_nat
% 0.14/0.44 = ( comp_P3728553842126764068at_nat @ produc826222791318859909at_nat
% 0.14/0.44 @ ( produc5456455677105495163at_nat
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1500_fst__snd__flip,axiom,
% 0.14/0.44 ( produc6011863565407846595at_nat
% 0.14/0.44 = ( comp_P4974406650942564362at_nat @ produc2937545259423399429at_nat
% 0.14/0.44 @ ( produc7548845685434208379at_nat
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1501_fst__snd__flip,axiom,
% 0.14/0.44 ( product_fst_num_nat
% 0.14/0.44 = ( comp_P5051845089628979463um_nat @ product_snd_nat_num
% 0.14/0.44 @ ( produc5219324331026901427at_num
% 0.14/0.44 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1502_fst__snd__flip,axiom,
% 0.14/0.44 ( product_fst_nat_nat
% 0.14/0.44 = ( comp_P1567445206330693457at_nat @ product_snd_nat_nat
% 0.14/0.44 @ ( produc2626176000494625587at_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1503_fst__snd__flip,axiom,
% 0.14/0.44 ( produc473321116828791851t_unit
% 0.14/0.44 = ( comp_P1287623958910499840t_unit @ produc6369869760173755749_ref_a
% 0.14/0.44 @ ( produc2058451029528183389_ref_a
% 0.14/0.44 @ ^ [X4: ref_a,Y5: heap_e7401611519738050253t_unit] : ( produc2564672488694626579_ref_a @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1504_fst__snd__flip,axiom,
% 0.14/0.44 ( produc5717040794327095847_ref_a
% 0.14/0.44 = ( comp_P2006160480335490974_ref_a @ produc1126150082675451753t_unit
% 0.14/0.44 @ ( produc4426278547552487717t_unit
% 0.14/0.44 @ ^ [X4: heap_e7401611519738050253t_unit,Y5: ref_a] : ( produc6544324848051098391t_unit @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1505_fst__snd__flip,axiom,
% 0.14/0.44 ( product_fst_int_int
% 0.14/0.44 = ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 0.14/0.44 @ ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fst_snd_flip
% 0.14/0.44 thf(fact_1506_snd__fst__flip,axiom,
% 0.14/0.44 ( produc826222791318859909at_nat
% 0.14/0.44 = ( comp_P3728553842126764068at_nat @ produc4486455499028916547at_nat
% 0.14/0.44 @ ( produc5456455677105495163at_nat
% 0.14/0.44 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1507_snd__fst__flip,axiom,
% 0.14/0.44 ( produc2937545259423399429at_nat
% 0.14/0.44 = ( comp_P4974406650942564362at_nat @ produc6011863565407846595at_nat
% 0.14/0.44 @ ( produc7548845685434208379at_nat
% 0.14/0.44 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1508_snd__fst__flip,axiom,
% 0.14/0.44 ( product_snd_num_nat
% 0.14/0.44 = ( comp_P8336958949797789649um_nat @ product_fst_nat_num
% 0.14/0.44 @ ( produc5219324331026901427at_num
% 0.14/0.44 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1509_snd__fst__flip,axiom,
% 0.14/0.44 ( product_snd_nat_nat
% 0.14/0.44 = ( comp_P1567445206330693457at_nat @ product_fst_nat_nat
% 0.14/0.44 @ ( produc2626176000494625587at_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1510_snd__fst__flip,axiom,
% 0.14/0.44 ( produc6369869760173755749_ref_a
% 0.14/0.44 = ( comp_P7254561687666694144_ref_a @ produc473321116828791851t_unit
% 0.14/0.44 @ ( produc4426278547552487717t_unit
% 0.14/0.44 @ ^ [X4: heap_e7401611519738050253t_unit,Y5: ref_a] : ( produc6544324848051098391t_unit @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1511_snd__fst__flip,axiom,
% 0.14/0.44 ( produc1126150082675451753t_unit
% 0.14/0.44 = ( comp_P3239167524078694454t_unit @ produc5717040794327095847_ref_a
% 0.14/0.44 @ ( produc2058451029528183389_ref_a
% 0.14/0.44 @ ^ [X4: ref_a,Y5: heap_e7401611519738050253t_unit] : ( produc2564672488694626579_ref_a @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1512_snd__fst__flip,axiom,
% 0.14/0.44 ( product_snd_int_int
% 0.14/0.44 = ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 0.14/0.44 @ ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % snd_fst_flip
% 0.14/0.44 thf(fact_1513_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 0.14/0.44 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat] :
% 0.14/0.44 ( ( finite352855791390415404at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( F @ X2 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_idem_on.comp_fun_idem_on
% 0.14/0.44 thf(fact_1514_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 0.14/0.44 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat] :
% 0.14/0.44 ( ( finite5150387867909132486at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( F @ X2 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_idem_on.comp_fun_idem_on
% 0.14/0.44 thf(fact_1515_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 0.14/0.44 ! [S5: set_o,F: $o > nat > nat,X2: $o] :
% 0.14/0.44 ( ( finite2426395113773319005_o_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_o @ X2 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( F @ X2 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_idem_on.comp_fun_idem_on
% 0.14/0.44 thf(fact_1516_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 0.14/0.44 ! [S5: set_nat,F: nat > nat > nat,X2: nat] :
% 0.14/0.44 ( ( finite7982400111564556781at_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_nat @ X2 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( F @ X2 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_idem_on.comp_fun_idem_on
% 0.14/0.44 thf(fact_1517_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 0.14/0.44 ! [S5: set_int,F: int > nat > nat,X2: int] :
% 0.14/0.44 ( ( finite8981753823465611337nt_nat @ S5 @ F )
% 0.14/0.44 => ( ( member_int @ X2 @ S5 )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 0.14/0.44 = ( F @ X2 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % comp_fun_idem_on.comp_fun_idem_on
% 0.14/0.44 thf(fact_1518_OO__Grp__cong,axiom,
% 0.14/0.44 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > int] :
% 0.14/0.44 ( ( A4 = B5 )
% 0.14/0.44 => ( ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_Gr7275288873855648526at_nat @ A4 @ F ) ) @ ( bNF_Gr190934199572118623at_int @ A4 @ G ) )
% 0.14/0.44 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_Gr7275288873855648526at_nat @ B5 @ F ) ) @ ( bNF_Gr190934199572118623at_int @ B5 @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % OO_Grp_cong
% 0.14/0.44 thf(fact_1519_OO__Grp__cong,axiom,
% 0.14/0.44 ! [A4: set_int,B5: set_int,F: int > int,G: int > code_integer] :
% 0.14/0.44 ( ( A4 = B5 )
% 0.14/0.44 => ( ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_Grp_int_int @ A4 @ F ) ) @ ( bNF_Gr6684649993275963353nteger @ A4 @ G ) )
% 0.14/0.44 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_Grp_int_int @ B5 @ F ) ) @ ( bNF_Gr6684649993275963353nteger @ B5 @ G ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % OO_Grp_cong
% 0.14/0.44 thf(fact_1520_fst__diag__fst,axiom,
% 0.14/0.44 ( ( comp_P9134237804721252988t_unit @ produc6942380573175061695_ref_a
% 0.14/0.44 @ ( comp_r6154141770783548544t_unit
% 0.14/0.44 @ ^ [X4: ref_a] : ( produc1340070678782110931_ref_a @ X4 @ X4 )
% 0.14/0.44 @ produc473321116828791851t_unit ) )
% 0.14/0.44 = produc473321116828791851t_unit ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_fst
% 0.14/0.44 thf(fact_1521_snd__diag__snd,axiom,
% 0.14/0.44 ( ( comp_P8237986404257982958t_unit @ produc1692618790031806469t_unit
% 0.14/0.44 @ ( comp_h5940001671827863714t_unit
% 0.14/0.44 @ ^ [X4: heap_e7401611519738050253t_unit] : ( produc8256076736985659095t_unit @ X4 @ X4 )
% 0.14/0.44 @ produc1126150082675451753t_unit ) )
% 0.14/0.44 = produc1126150082675451753t_unit ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_snd
% 0.14/0.44 thf(fact_1522_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,M: nat > nat,M1: $o > nat,M2: nat > $o,F: nat > nat,G: nat > nat] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_nat_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_nat_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1523_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: int > $o,Abs: $o > int,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: int > nat] :
% 0.14/0.44 ( ( type_d8403010662121346494_int_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_nat_int @ ( comp_o_nat_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_int_nat_int @ ( comp_o_nat_int @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_int_int @ ( comp_o_int_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1524_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: num > $o,Abs: $o > num,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: int > nat] :
% 0.14/0.44 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_o_int @ ( comp_o_o_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_num_o_int @ ( comp_o_o_num @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1525_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: nat > nat] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1526_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: nat > nat] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_o_o_nat @ ( comp_o_o_o @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1527_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_o_num_int @ ( comp_o_num_o @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_int @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1528_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: num > $o,Abs: $o > num,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 0.14/0.44 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_num_num_int @ ( comp_o_num_num @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1529_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_nat_num_int @ ( comp_o_num_nat @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1530_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: nat > nat] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1531_type__copy__map__comp0,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: nat > nat] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( M
% 0.14/0.44 = ( comp_o_o_nat @ M1 @ M2 ) )
% 0.14/0.44 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ M ) @ G )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( comp_o_nat_nat @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0
% 0.14/0.44 thf(fact_1532_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: int > $o,Abs: $o > int,Rep2: nat > $o,Abs2: $o > nat,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d8403010662121346494_int_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_int_nat_int @ ( comp_o_nat_int @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_int_int @ ( comp_o_int_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1533_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: num > $o,Abs: $o > num,Rep2: $o > $o,Abs2: $o > $o,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_o_int @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_num_o_int @ ( comp_o_o_num @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1534_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,Rep2: $o > $o,Abs2: $o > $o,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1535_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,Rep2: $o > $o,Abs2: $o > $o,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_o_o_nat @ ( comp_o_o_o @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1536_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_o_num_int @ ( comp_o_num_o @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_int @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1537_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: num > $o,Abs: $o > num,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_num_num_int @ ( comp_o_num_num @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1538_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_nat_num_int @ ( comp_o_num_nat @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1539_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: $o > $o,Abs: $o > $o,Rep2: nat > $o,Abs2: $o > nat,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1540_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,Rep2: nat > $o,Abs2: $o > nat,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 0.14/0.44 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 0.14/0.44 => ( ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_nat_nat_nat @ ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_o_nat @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1541_type__copy__map__comp0__undo,axiom,
% 0.14/0.44 ! [Rep: nat > $o,Abs: $o > nat,Rep2: $o > char,Abs2: char > $o,Rep3: nat > $o,Abs3: $o > nat,M: $o > char,M1: $o > char,M2: $o > $o] :
% 0.14/0.44 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 0.14/0.44 => ( ( type_d9076672964931703357o_char @ Rep2 @ Abs2 @ top_top_set_char )
% 0.14/0.44 => ( ( type_d1000680970699258650_nat_o @ Rep3 @ Abs3 @ top_top_set_o )
% 0.14/0.44 => ( ( ( comp_o_o_nat @ ( comp_char_o_o @ Abs2 @ M ) @ Rep3 )
% 0.14/0.44 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs @ M2 ) @ Rep3 ) ) )
% 0.14/0.44 => ( ( comp_o_char_o @ M1 @ M2 )
% 0.14/0.44 = M ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_map_comp0_undo
% 0.14/0.44 thf(fact_1542_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( bNF_re3734335887435638179at_nat
% 0.14/0.44 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom8141925468094106422ar_nat
% 0.14/0.44 @ ( conver5210974729819302706ar_nat
% 0.14/0.44 @ ( bNF_Gr1779741795384719769ar_nat
% 0.14/0.44 @ ( collec1683818095804863890at_nat
% 0.14/0.44 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1491501995297412481t_char @ product_fst_nat_nat ) ) )
% 0.14/0.44 @ ( bNF_Gr1779741795384719769ar_nat
% 0.14/0.44 @ ( collec1683818095804863890at_nat
% 0.14/0.44 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1491501995297412481t_char @ product_snd_nat_nat ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1543_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( bNF_re6557955094579809201at_nat
% 0.14/0.44 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom7707146719550107439at_nat
% 0.14/0.44 @ ( conver7478146827351332082at_nat
% 0.14/0.44 @ ( bNF_Gr7368557922277781849at_nat
% 0.14/0.44 @ ( collec2824469931397938891at_nat
% 0.14/0.44 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1320480151300532104at_rat @ product_fst_nat_nat ) ) )
% 0.14/0.44 @ ( bNF_Gr7368557922277781849at_nat
% 0.14/0.44 @ ( collec2824469931397938891at_nat
% 0.14/0.44 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1320480151300532104at_rat @ product_snd_nat_nat ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1544_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( bNF_re5653821019739307937at_nat
% 0.14/0.44 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom8186637903969514807at_nat
% 0.14/0.44 @ ( conver3498139987538047730at_nat
% 0.14/0.44 @ ( bNF_Gr3388551082464497497at_nat
% 0.14/0.44 @ ( collec8718012497556192979at_nat
% 0.14/0.44 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat ) ) )
% 0.14/0.44 @ ( bNF_Gr3388551082464497497at_nat
% 0.14/0.44 @ ( collec8718012497556192979at_nat
% 0.14/0.44 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1545_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( bNF_re3715656647883201625at_nat
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom2406850561174050523nt_nat
% 0.14/0.44 @ ( conver1572571282669976050nt_nat
% 0.14/0.44 @ ( bNF_Gr1462982377596425817nt_nat
% 0.14/0.44 @ ( collec2532482545165550967at_nat
% 0.14/0.44 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1953119740877977564at_int @ product_fst_nat_nat ) ) )
% 0.14/0.44 @ ( bNF_Gr1462982377596425817nt_nat
% 0.14/0.44 @ ( collec2532482545165550967at_nat
% 0.14/0.44 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P1953119740877977564at_int @ product_snd_nat_nat ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1546_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: num > num > $o] :
% 0.14/0.44 ( ( bNF_re7626690874201225453um_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom1697847500783689711nt_num
% 0.14/0.44 @ ( conver5699786650113435344nt_num
% 0.14/0.44 @ ( bNF_Gr5590197745039885111nt_num
% 0.14/0.44 @ ( collec266097228571071243um_num
% 0.14/0.44 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P4305060815297604026um_int @ product_fst_num_num ) ) )
% 0.14/0.44 @ ( bNF_Gr5590197745039885111nt_num
% 0.14/0.44 @ ( collec266097228571071243um_num
% 0.14/0.44 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P4305060815297604026um_int @ product_snd_num_num ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1547_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: int > int > $o] :
% 0.14/0.44 ( ( bNF_re4731199128827642459nt_int
% 0.14/0.44 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom4417706183330134766ar_int
% 0.14/0.44 @ ( conver1155128050257070662ar_int
% 0.14/0.44 @ ( bNF_Gr6947267152677263533ar_int
% 0.14/0.44 @ ( collec1380656525566158922nt_int
% 0.14/0.44 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P4161745170962941589t_char @ product_fst_int_int ) ) )
% 0.14/0.44 @ ( bNF_Gr6947267152677263533ar_int
% 0.14/0.44 @ ( collec1380656525566158922nt_int
% 0.14/0.44 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P4161745170962941589t_char @ product_snd_int_int ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1548_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: int > int > $o] :
% 0.14/0.44 ( ( bNF_re7554818335971813481nt_int
% 0.14/0.44 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom2810802720173317863at_int
% 0.14/0.44 @ ( conver6967689361887734790at_int
% 0.14/0.44 @ ( bNF_Gr6858100456814184557at_int
% 0.14/0.44 @ ( collec2521308361159233923nt_int
% 0.14/0.44 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6018825582104210588nt_rat @ product_fst_int_int ) ) )
% 0.14/0.44 @ ( bNF_Gr6858100456814184557at_int
% 0.14/0.44 @ ( collec2521308361159233923nt_int
% 0.14/0.44 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6018825582104210588nt_rat @ product_snd_int_int ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1549_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: int > int > $o] :
% 0.14/0.44 ( ( bNF_re6650684261131312217nt_int
% 0.14/0.44 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom3290293904592725231at_int
% 0.14/0.44 @ ( conver2987682522074450438at_int
% 0.14/0.44 @ ( bNF_Gr2878093617000900205at_int
% 0.14/0.44 @ ( collec8414850927317488011nt_int
% 0.14/0.44 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int ) ) )
% 0.14/0.44 @ ( bNF_Gr2878093617000900205at_int
% 0.14/0.44 @ ( collec8414850927317488011nt_int
% 0.14/0.44 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1550_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: int > int > $o] :
% 0.14/0.44 ( ( bNF_re4712519889275205905nt_int
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom6733878598652036755nt_int
% 0.14/0.44 @ ( conver1062113817206378758nt_int
% 0.14/0.44 @ ( bNF_Gr952524912132828525nt_int
% 0.14/0.44 @ ( collec2229320974926845999nt_int
% 0.14/0.44 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6651465171681656048nt_int @ product_fst_int_int ) ) )
% 0.14/0.44 @ ( bNF_Gr952524912132828525nt_int
% 0.14/0.44 @ ( collec2229320974926845999nt_int
% 0.14/0.44 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P6651465171681656048nt_int @ product_snd_int_int ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1551_fun_Orel__compp__Grp,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( bNF_re4629543205785817921at_nat
% 0.14/0.44 @ ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 = ( relcom5920149085449455271at_nat
% 0.14/0.44 @ ( conver6066198818478722162at_nat
% 0.14/0.44 @ ( bNF_Gr1532745923208276441at_nat
% 0.14/0.44 @ ( collec3092956710985254339at_nat
% 0.14/0.44 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P5292260908303971472st_nat @ product_fst_nat_nat ) ) )
% 0.14/0.44 @ ( bNF_Gr1532745923208276441at_nat
% 0.14/0.44 @ ( collec3092956710985254339at_nat
% 0.14/0.44 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 0.14/0.44 @ ( comp_P5292260908303971472st_nat @ product_snd_nat_nat ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_compp_Grp
% 0.14/0.44 thf(fact_1552_image__Pow__surj,axiom,
% 0.14/0.44 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.14/0.44 ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.44 = B5 )
% 0.14/0.44 => ( ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) )
% 0.14/0.44 = ( pow_rat @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_Pow_surj
% 0.14/0.44 thf(fact_1553_image__Pow__surj,axiom,
% 0.14/0.44 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( ( image_nat_nat @ F @ A4 )
% 0.14/0.44 = B5 )
% 0.14/0.44 => ( ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) )
% 0.14/0.44 = ( pow_nat @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_Pow_surj
% 0.14/0.44 thf(fact_1554_image__Pow__surj,axiom,
% 0.14/0.44 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.44 = B5 )
% 0.14/0.44 => ( ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) )
% 0.14/0.44 = ( pow_int @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_Pow_surj
% 0.14/0.44 thf(fact_1555_image__Pow__surj,axiom,
% 0.14/0.44 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.44 = B5 )
% 0.14/0.44 => ( ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) )
% 0.14/0.44 = ( pow_nat @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_Pow_surj
% 0.14/0.44 thf(fact_1556_image__Pow__surj,axiom,
% 0.14/0.44 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.44 ( ( ( image_int_int @ F @ A4 )
% 0.14/0.44 = B5 )
% 0.14/0.44 => ( ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) )
% 0.14/0.44 = ( pow_int @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_Pow_surj
% 0.14/0.44 thf(fact_1557_fst__diag__snd,axiom,
% 0.14/0.44 ( ( comp_P8237986404257982958t_unit @ produc2762368996035445955t_unit
% 0.14/0.44 @ ( comp_h5940001671827863714t_unit
% 0.14/0.44 @ ^ [X4: heap_e7401611519738050253t_unit] : ( produc8256076736985659095t_unit @ X4 @ X4 )
% 0.14/0.44 @ produc1126150082675451753t_unit ) )
% 0.14/0.44 = produc1126150082675451753t_unit ) ).
% 0.14/0.44
% 0.14/0.44 % fst_diag_snd
% 0.14/0.44 thf(fact_1558_snd__diag__fst,axiom,
% 0.14/0.44 ( ( comp_P9134237804721252988t_unit @ produc8185483580310833921_ref_a
% 0.14/0.44 @ ( comp_r6154141770783548544t_unit
% 0.14/0.44 @ ^ [X4: ref_a] : ( produc1340070678782110931_ref_a @ X4 @ X4 )
% 0.14/0.44 @ produc473321116828791851t_unit ) )
% 0.14/0.44 = produc473321116828791851t_unit ) ).
% 0.14/0.44
% 0.14/0.44 % snd_diag_fst
% 0.14/0.44 thf(fact_1559_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.44 ( ( bNF_re1181178334029315097nteger
% 0.14/0.44 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Gr4092539093814444494nteger @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Gr1453458339979195462nteger
% 0.14/0.44 @ ( collec5651646645946169514nteger
% 0.14/0.44 @ ^ [X4: code_integer > code_integer > code_integer] : ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ X4 @ top_to4645266643341252675nteger ) @ A4 ) )
% 0.14/0.44 @ ( comp_C8797469213163452608nteger @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1560_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_o,F: $o > $o] :
% 0.14/0.44 ( ( bNF_re4705727531993890431at_o_o
% 0.14/0.44 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Grp_o_o @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Grp_nat_o_nat_o
% 0.14/0.44 @ ( collect_nat_o
% 0.14/0.44 @ ^ [X4: nat > $o] : ( ord_less_eq_set_o @ ( image_nat_o @ X4 @ top_top_set_nat ) @ A4 ) )
% 0.14/0.44 @ ( comp_o_o_nat @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1561_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.44 ( ( bNF_re5653821019739307937at_nat
% 0.14/0.44 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Grp_nat_nat @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Gr3847987472475283150at_nat
% 0.14/0.44 @ ( collect_nat_nat
% 0.14/0.44 @ ^ [X4: nat > nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ X4 @ top_top_set_nat ) @ A4 ) )
% 0.14/0.44 @ ( comp_nat_nat_nat @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1562_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_nat,F: nat > num] :
% 0.14/0.44 ( ( bNF_re272988434038980259at_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Grp_nat_num @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Gr6763702254253555408nt_num
% 0.14/0.44 @ ( collect_int_nat
% 0.14/0.44 @ ^ [X4: int > nat] : ( ord_less_eq_set_nat @ ( image_int_nat @ X4 @ top_top_set_int ) @ A4 ) )
% 0.14/0.44 @ ( comp_nat_num_int @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1563_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_int,F: int > nat] :
% 0.14/0.44 ( ( bNF_re4715010359784256181nt_nat
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Grp_int_nat @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Gr2243168462153404386nt_nat
% 0.14/0.44 @ ( collect_int_int
% 0.14/0.44 @ ^ [X4: int > int] : ( ord_less_eq_set_int @ ( image_int_int @ X4 @ top_top_set_int ) @ A4 ) )
% 0.14/0.44 @ ( comp_int_nat_int @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1564_fun_Orel__Grp,axiom,
% 0.14/0.44 ! [A4: set_num,F: num > num] :
% 0.14/0.44 ( ( bNF_re7626690874201225453um_num
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ( bNF_Grp_num_num @ A4 @ F ) )
% 0.14/0.44 = ( bNF_Gr318824752125099290nt_num
% 0.14/0.44 @ ( collect_int_num
% 0.14/0.44 @ ^ [X4: int > num] : ( ord_less_eq_set_num @ ( image_int_num @ X4 @ top_top_set_int ) @ A4 ) )
% 0.14/0.44 @ ( comp_num_num_int @ F ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % fun.rel_Grp
% 0.14/0.44 thf(fact_1565_Grp__fst__snd,axiom,
% 0.14/0.44 ! [R3: nat > nat > $o] :
% 0.14/0.44 ( ( relcom8572034174491624592at_nat @ ( conver4691796276509297820at_nat @ ( bNF_Gr193424670081168899at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) @ product_fst_nat_nat ) ) @ ( bNF_Gr193424670081168899at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) @ product_snd_nat_nat ) )
% 0.14/0.44 = R3 ) ).
% 0.14/0.44
% 0.14/0.44 % Grp_fst_snd
% 0.14/0.44 thf(fact_1566_Grp__fst__snd,axiom,
% 0.14/0.44 ! [R3: ref_a > heap_e7401611519738050253t_unit > $o] :
% 0.14/0.44 ( ( relcom3136146828236442456t_unit @ ( conver4368408235330554745_ref_a @ ( bNF_Gr5964920315653434322_ref_a @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R3 ) ) @ produc473321116828791851t_unit ) ) @ ( bNF_Gr5237703264515865432t_unit @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R3 ) ) @ produc1126150082675451753t_unit ) )
% 0.14/0.44 = R3 ) ).
% 0.14/0.44
% 0.14/0.44 % Grp_fst_snd
% 0.14/0.44 thf(fact_1567_Grp__fst__snd,axiom,
% 0.14/0.44 ! [R3: int > int > $o] :
% 0.14/0.44 ( ( relcom3664783465810776136nt_int @ ( conver7247880940930113968nt_int @ ( bNF_Gr2749509334501985047nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) @ product_fst_int_int ) ) @ ( bNF_Gr2749509334501985047nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) @ product_snd_int_int ) )
% 0.14/0.44 = R3 ) ).
% 0.14/0.44
% 0.14/0.44 % Grp_fst_snd
% 0.14/0.44 thf(fact_1568_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: $o > char,Abs: char > $o,S5: char > set_rat,M: $o > char,F: nat > rat,S6: $o > set_nat,G: nat > $o] :
% 0.14/0.44 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_char_set_rat_o @ S5 @ M )
% 0.14/0.44 = ( comp_s8507027185284273247_rat_o @ ( image_nat_rat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_o_set_rat_nat @ ( comp_char_set_rat_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1569_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: num > char,Abs: char > num,S5: char > set_rat,M: nat > char,F: nat > rat,S6: nat > set_nat,G: int > nat] :
% 0.14/0.44 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c5738158305436223508at_nat @ S5 @ M )
% 0.14/0.44 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_num_set_rat_int @ ( comp_c2295490091592002142at_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1570_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,S5: char > set_rat,M: nat > char,F: nat > rat,S6: nat > set_nat,G: nat > nat] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c5738158305436223508at_nat @ S5 @ M )
% 0.14/0.44 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_nat_set_rat_nat @ ( comp_c5738158305436223508at_nat @ S5 @ Rep ) @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ ( comp_nat_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1571_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,S5: char > set_rat,M: int > char,F: nat > rat,S6: int > set_nat,G: int > int] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c5735667834927173232at_int @ S5 @ M )
% 0.14/0.44 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_nat_set_rat_int @ ( comp_c5738158305436223508at_nat @ S5 @ Rep ) @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ ( comp_int_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1572_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: $o > char,Abs: char > $o,S5: char > set_nat,M: $o > char,F: nat > nat,S6: $o > set_nat,G: nat > $o] :
% 0.14/0.44 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_char_set_nat_o @ S5 @ M )
% 0.14/0.44 = ( comp_s33089643564333159_nat_o @ ( image_nat_nat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_o_set_nat_nat @ ( comp_char_set_nat_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1573_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: num > char,Abs: char > num,S5: char > set_nat,M: nat > char,F: nat > nat,S6: nat > set_nat,G: int > nat] :
% 0.14/0.44 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c915470459090449932at_nat @ S5 @ M )
% 0.14/0.44 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_num_set_nat_int @ ( comp_c6696174282101004374at_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1574_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,S5: char > set_nat,M: nat > char,F: nat > nat,S6: nat > set_nat,G: nat > nat] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c915470459090449932at_nat @ S5 @ M )
% 0.14/0.44 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_nat_set_nat_nat @ ( comp_c915470459090449932at_nat @ S5 @ Rep ) @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ ( comp_nat_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1575_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: nat > char,Abs: char > nat,S5: char > set_nat,M: int > char,F: nat > nat,S6: int > set_nat,G: int > int] :
% 0.14/0.44 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c912979988581399656at_int @ S5 @ M )
% 0.14/0.44 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_nat_set_nat_int @ ( comp_c915470459090449932at_nat @ S5 @ Rep ) @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ ( comp_int_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1576_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: $o > char,Abs: char > $o,S5: char > set_int,M: $o > char,F: nat > int,S6: $o > set_nat,G: nat > $o] :
% 0.14/0.44 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_char_set_int_o @ S5 @ M )
% 0.14/0.44 = ( comp_s7011316712748663051_int_o @ ( image_nat_int @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_o_set_int_nat @ ( comp_char_set_int_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s5620162763104547101nt_nat @ ( image_nat_int @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1577_type__copy__set__map0,axiom,
% 0.14/0.44 ! [Rep: num > char,Abs: char > num,S5: char > set_int,M: nat > char,F: nat > int,S6: nat > set_nat,G: int > nat] :
% 0.14/0.44 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 0.14/0.44 => ( ( ( comp_c3102392033783471720nt_nat @ S5 @ M )
% 0.14/0.44 = ( comp_s5620162763104547101nt_nat @ ( image_nat_int @ F ) @ S6 ) )
% 0.14/0.44 => ( ( comp_num_set_int_int @ ( comp_c8883095856794026162nt_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 0.14/0.44 = ( comp_s5617672292595496825nt_int @ ( image_nat_int @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_copy_set_map0
% 0.14/0.44 thf(fact_1578_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: nat > rat,Abs: rat > nat,A4: set_rat] :
% 0.14/0.44 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_rat @ Rep @ top_top_set_nat )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1579_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: nat > nat,Abs: nat > nat,A4: set_nat] :
% 0.14/0.44 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_nat @ Rep @ top_top_set_nat )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1580_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: nat > int,Abs: int > nat,A4: set_int] :
% 0.14/0.44 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_int @ Rep @ top_top_set_nat )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1581_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: int > nat,Abs: nat > int,A4: set_nat] :
% 0.14/0.44 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_int_nat @ Rep @ top_top_set_int )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1582_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: int > int,Abs: int > int,A4: set_int] :
% 0.14/0.44 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_int_int @ Rep @ top_top_set_int )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1583_type__definition_ORep__range,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,A4: set_o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_Product_unit_o @ Rep @ top_to1996260823553986621t_unit )
% 0.14/0.44 = A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Rep_range
% 0.14/0.44 thf(fact_1584_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: rat > nat,Abs: nat > rat,A4: set_nat] :
% 0.14/0.44 ( ( type_d5933939304842882774at_nat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_rat @ Abs @ A4 )
% 0.14/0.44 = top_top_set_rat ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1585_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: nat > nat,Abs: nat > nat,A4: set_nat] :
% 0.14/0.44 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_nat @ Abs @ A4 )
% 0.14/0.44 = top_top_set_nat ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1586_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: nat > int,Abs: int > nat,A4: set_int] :
% 0.14/0.44 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_int_nat @ Abs @ A4 )
% 0.14/0.44 = top_top_set_nat ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1587_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: int > nat,Abs: nat > int,A4: set_nat] :
% 0.14/0.44 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_nat_int @ Abs @ A4 )
% 0.14/0.44 = top_top_set_int ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1588_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: int > int,Abs: int > int,A4: set_int] :
% 0.14/0.44 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_int_int @ Abs @ A4 )
% 0.14/0.44 = top_top_set_int ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1589_type__definition_OAbs__image,axiom,
% 0.14/0.44 ! [Rep: product_unit > $o,Abs: $o > product_unit,A4: set_o] :
% 0.14/0.44 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A4 )
% 0.14/0.44 => ( ( image_o_Product_unit @ Abs @ A4 )
% 0.14/0.44 = top_to1996260823553986621t_unit ) ) ).
% 0.14/0.44
% 0.14/0.44 % type_definition.Abs_image
% 0.14/0.44 thf(fact_1590_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_char_char
% 0.14/0.44 = ( ^ [R6: char > char > $o,Abs4: char > char,Rep4: char > char,T4: char > char > $o] :
% 0.14/0.44 ( ( ord_le2540245887939449860char_o @ T4 @ ( bNF_Grp_char_char @ top_top_set_char @ Abs4 ) )
% 0.14/0.44 & ( ord_le2540245887939449860char_o @ ( bNF_Grp_char_char @ top_top_set_char @ Rep4 ) @ ( conversep_char_char @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom5872928454965100966r_char @ T4 @ ( conversep_char_char @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1591_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_char_rat
% 0.14/0.44 = ( ^ [R6: char > char > $o,Abs4: char > rat,Rep4: rat > char,T4: char > rat > $o] :
% 0.14/0.44 ( ( ord_le4891902658761385405_rat_o @ T4 @ ( bNF_Grp_char_rat @ top_top_set_char @ Abs4 ) )
% 0.14/0.44 & ( ord_le6546876390139131069char_o @ ( bNF_Grp_rat_char @ top_top_set_rat @ Rep4 ) @ ( conversep_char_rat @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom3428143170894750637t_char @ T4 @ ( conversep_char_rat @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1592_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_char_nat
% 0.14/0.44 = ( ^ [R6: char > char > $o,Abs4: char > nat,Rep4: nat > char,T4: char > nat > $o] :
% 0.14/0.44 ( ( ord_le5641337153896221125_nat_o @ T4 @ ( bNF_Grp_char_nat @ top_top_set_char @ Abs4 ) )
% 0.14/0.44 & ( ord_le4878496333587278021char_o @ ( bNF_Grp_nat_char @ top_top_set_nat @ Rep4 ) @ ( conversep_char_nat @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom6755291642603558309t_char @ T4 @ ( conversep_char_nat @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1593_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_char_int
% 0.14/0.44 = ( ^ [R6: char > char > $o,Abs4: char > int,Rep4: int > char,T4: char > int > $o] :
% 0.14/0.44 ( ( ord_le3396192186225775209_int_o @ T4 @ ( bNF_Grp_char_int @ top_top_set_char @ Abs4 ) )
% 0.14/0.44 & ( ord_le7608100903186094441char_o @ ( bNF_Grp_int_char @ top_top_set_int @ Rep4 ) @ ( conversep_char_int @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom750623199913152513t_char @ T4 @ ( conversep_char_int @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1594_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_rat_char
% 0.14/0.44 = ( ^ [R6: rat > rat > $o,Abs4: rat > char,Rep4: char > rat,T4: rat > char > $o] :
% 0.14/0.44 ( ( ord_le6546876390139131069char_o @ T4 @ ( bNF_Grp_rat_char @ top_top_set_rat @ Abs4 ) )
% 0.14/0.44 & ( ord_le4891902658761385405_rat_o @ ( bNF_Grp_char_rat @ top_top_set_char @ Rep4 ) @ ( conversep_rat_char @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom1505247221262953652ar_rat @ T4 @ ( conversep_rat_char @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1595_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_rat_rat
% 0.14/0.44 = ( ^ [R6: rat > rat > $o,Abs4: rat > rat,Rep4: rat > rat,T4: rat > rat > $o] :
% 0.14/0.44 ( ( ord_le4717968354871517046_rat_o @ T4 @ ( bNF_Grp_rat_rat @ top_top_set_rat @ Abs4 ) )
% 0.14/0.44 & ( ord_le4717968354871517046_rat_o @ ( bNF_Grp_rat_rat @ top_top_set_rat @ Rep4 ) @ ( conversep_rat_rat @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcompp_rat_rat_rat @ T4 @ ( conversep_rat_rat @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1596_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_rat_nat
% 0.14/0.44 = ( ^ [R6: rat > rat > $o,Abs4: rat > nat,Rep4: nat > rat,T4: rat > nat > $o] :
% 0.14/0.44 ( ( ord_le5467402850006352766_nat_o @ T4 @ ( bNF_Grp_rat_nat @ top_top_set_rat @ Abs4 ) )
% 0.14/0.44 & ( ord_le1897120724991155070_rat_o @ ( bNF_Grp_nat_rat @ top_top_set_nat @ Rep4 ) @ ( conversep_rat_nat @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcompp_rat_nat_rat @ T4 @ ( conversep_rat_nat @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1597_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_rat_int
% 0.14/0.44 = ( ^ [R6: rat > rat > $o,Abs4: rat > int,Rep4: int > rat,T4: rat > int > $o] :
% 0.14/0.44 ( ( ord_le3222257882335906850_int_o @ T4 @ ( bNF_Grp_rat_int @ top_top_set_rat @ Abs4 ) )
% 0.14/0.44 & ( ord_le8236914709048111138_rat_o @ ( bNF_Grp_int_rat @ top_top_set_int @ Rep4 ) @ ( conversep_rat_int @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcompp_rat_int_rat @ T4 @ ( conversep_rat_int @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1598_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_nat_char
% 0.14/0.44 = ( ^ [R6: nat > nat > $o,Abs4: nat > char,Rep4: char > nat,T4: nat > char > $o] :
% 0.14/0.44 ( ( ord_le4878496333587278021char_o @ T4 @ ( bNF_Grp_nat_char @ top_top_set_nat @ Abs4 ) )
% 0.14/0.44 & ( ord_le5641337153896221125_nat_o @ ( bNF_Grp_char_nat @ top_top_set_char @ Rep4 ) @ ( conversep_nat_char @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcom8112501251453913252ar_nat @ T4 @ ( conversep_nat_char @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1599_Quotient__alt__def5,axiom,
% 0.14/0.44 ( quotient_nat_rat
% 0.14/0.44 = ( ^ [R6: nat > nat > $o,Abs4: nat > rat,Rep4: rat > nat,T4: nat > rat > $o] :
% 0.14/0.44 ( ( ord_le1897120724991155070_rat_o @ T4 @ ( bNF_Grp_nat_rat @ top_top_set_nat @ Abs4 ) )
% 0.14/0.44 & ( ord_le5467402850006352766_nat_o @ ( bNF_Grp_rat_nat @ top_top_set_rat @ Rep4 ) @ ( conversep_nat_rat @ T4 ) )
% 0.14/0.44 & ( R6
% 0.14/0.44 = ( relcompp_nat_rat_nat @ T4 @ ( conversep_nat_rat @ T4 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_alt_def5
% 0.14/0.44 thf(fact_1600_K__record__comp,axiom,
% 0.14/0.44 ! [C: $o,F: nat > $o] :
% 0.14/0.44 ( ( comp_o_o_nat
% 0.14/0.44 @ ^ [X4: $o] : C
% 0.14/0.44 @ F )
% 0.14/0.44 = ( ^ [X4: nat] : C ) ) ).
% 0.14/0.44
% 0.14/0.44 % K_record_comp
% 0.14/0.44 thf(fact_1601_K__record__comp,axiom,
% 0.14/0.44 ! [C: num,F: int > nat] :
% 0.14/0.44 ( ( comp_nat_num_int
% 0.14/0.44 @ ^ [X4: nat] : C
% 0.14/0.44 @ F )
% 0.14/0.44 = ( ^ [X4: int] : C ) ) ).
% 0.14/0.44
% 0.14/0.44 % K_record_comp
% 0.14/0.44 thf(fact_1602_K__record__comp,axiom,
% 0.14/0.44 ! [C: nat,F: nat > nat] :
% 0.14/0.44 ( ( comp_nat_nat_nat
% 0.14/0.44 @ ^ [X4: nat] : C
% 0.14/0.44 @ F )
% 0.14/0.44 = ( ^ [X4: nat] : C ) ) ).
% 0.14/0.44
% 0.14/0.44 % K_record_comp
% 0.14/0.44 thf(fact_1603_K__record__comp,axiom,
% 0.14/0.44 ! [C: nat,F: int > int] :
% 0.14/0.44 ( ( comp_int_nat_int
% 0.14/0.44 @ ^ [X4: int] : C
% 0.14/0.44 @ F )
% 0.14/0.44 = ( ^ [X4: int] : C ) ) ).
% 0.14/0.44
% 0.14/0.44 % K_record_comp
% 0.14/0.44 thf(fact_1604_K__record__comp,axiom,
% 0.14/0.44 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 0.14/0.44 ( ( comp_C8797469213163452608nteger
% 0.14/0.44 @ ^ [X4: code_integer > code_integer] : C
% 0.14/0.44 @ F )
% 0.14/0.44 = ( ^ [X4: code_integer] : C ) ) ).
% 0.14/0.44
% 0.14/0.44 % K_record_comp
% 0.14/0.44 thf(fact_1605_image__paired__Times,axiom,
% 0.14/0.44 ! [F: nat > rat,G: int > nat,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( image_3755276878268593137at_nat
% 0.14/0.44 @ ( produc5347463441023893471at_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: int] : ( product_Pair_rat_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc140472662868866674at_nat @ ( image_nat_rat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: rat] : ( image_int_nat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1606_image__paired__Times,axiom,
% 0.14/0.44 ! [F: nat > rat,G: int > int,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( image_8800797895614172237at_int
% 0.14/0.44 @ ( produc1169612421514696763at_int
% 0.14/0.44 @ ^ [X4: nat,Y5: int] : ( product_Pair_rat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc137982192359816398at_int @ ( image_nat_rat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: rat] : ( image_int_int @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1607_image__paired__Times,axiom,
% 0.14/0.44 ! [F: nat > nat,G: int > int,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( image_9117352539549038149at_int
% 0.14/0.44 @ ( produc1486167065449562675at_int
% 0.14/0.44 @ ^ [X4: nat,Y5: int] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1608_image__paired__Times,axiom,
% 0.14/0.44 ! [F: nat > int,G: int > nat,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( image_5071185234104513605nt_nat
% 0.14/0.44 @ ( produc6663371796859813939nt_nat
% 0.14/0.44 @ ^ [X4: nat,Y5: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: int] : ( image_int_nat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1609_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > nat,G: nat > rat,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( image_3420722608207172081at_rat
% 0.14/0.44 @ ( produc877984105854340063at_rat
% 0.14/0.44 @ ^ [X4: int,Y5: nat] : ( product_Pair_nat_rat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc9045269283572012658at_rat @ ( image_int_nat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: nat] : ( image_nat_rat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1610_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > nat,G: nat > int,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( image_2751100147091372101at_int
% 0.14/0.44 @ ( produc208361644738540083at_int
% 0.14/0.44 @ ^ [X4: int,Y5: nat] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ ( image_int_nat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: nat] : ( image_nat_int @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1611_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > nat,G: int > int,A4: set_int,B5: set_int] :
% 0.14/0.44 ( ( image_1654017166447373545at_int
% 0.14/0.44 @ ( produc3246203729202673879at_int
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ ( image_int_nat @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1612_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > int,G: nat > rat,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( image_4420076320108226637nt_rat
% 0.14/0.44 @ ( produc1877337817755394619nt_rat
% 0.14/0.44 @ ^ [X4: int,Y5: nat] : ( product_Pair_int_rat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc821250958618291406nt_rat @ ( image_int_int @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: int] : ( image_nat_rat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1613_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > int,G: nat > nat,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( image_7928304878501623365nt_nat
% 0.14/0.44 @ ( produc5385566376148791347nt_nat
% 0.14/0.44 @ ^ [X4: int,Y5: nat] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: int] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1614_image__paired__Times,axiom,
% 0.14/0.44 ! [F: int > int,G: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.44 ( ( image_6831221897857624809nt_nat
% 0.14/0.44 @ ( produc8423408460612925143nt_nat
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 0.14/0.44 @ ^ [Uu: int] : ( image_int_nat @ G @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % image_paired_Times
% 0.14/0.44 thf(fact_1615_Gr__incl,axiom,
% 0.14/0.44 ! [A4: set_nat,F: nat > rat,B5: set_rat] :
% 0.14/0.44 ( ( ord_le5989899228261996553at_rat @ ( bNF_Gr_nat_rat @ A4 @ F )
% 0.14/0.44 @ ( produc9045269283572012658at_rat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % Gr_incl
% 0.14/0.44 thf(fact_1616_Gr__incl,axiom,
% 0.14/0.44 ! [A4: set_nat,F: nat > int,B5: set_int] :
% 0.14/0.44 ( ( ord_le656430383953171549at_int @ ( bNF_Gr_nat_int @ A4 @ F )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % Gr_incl
% 0.14/0.44 thf(fact_1617_Gr__incl,axiom,
% 0.14/0.44 ! [A4: set_int,F: int > nat,B5: set_nat] :
% 0.14/0.44 ( ( ord_le5333435103577920093nt_nat @ ( bNF_Gr_int_nat @ A4 @ F )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % Gr_incl
% 0.14/0.44 thf(fact_1618_Gr__incl,axiom,
% 0.14/0.44 ! [A4: set_int,F: int > int,B5: set_int] :
% 0.14/0.44 ( ( ord_le2843351958646193337nt_int @ ( bNF_Gr_int_int @ A4 @ F )
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % Gr_incl
% 0.14/0.44 thf(fact_1619_Gr__incl,axiom,
% 0.14/0.44 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 0.14/0.44 ( ( ord_le3146513528884898305at_nat @ ( bNF_Gr_nat_nat @ A4 @ F )
% 0.14/0.44 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 ) ) ).
% 0.14/0.44
% 0.14/0.44 % Gr_incl
% 0.14/0.44 thf(fact_1620_subset__fst__snd,axiom,
% 0.14/0.44 ! [A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ord_le3146513528884898305at_nat @ A4
% 0.14/0.44 @ ( produc457027306803732586at_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A4 )
% 0.14/0.44 @ ^ [Uu: nat] : ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % subset_fst_snd
% 0.14/0.44 thf(fact_1621_subset__fst__snd,axiom,
% 0.14/0.44 ! [A4: set_Pr1133966238863718811t_unit] :
% 0.14/0.44 ( ord_le5525191956872776187t_unit @ A4
% 0.14/0.44 @ ( produc3946373962484743846t_unit @ ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ A4 )
% 0.14/0.44 @ ^ [Uu: ref_a] : ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ A4 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % subset_fst_snd
% 0.14/0.44 thf(fact_1622_inv__image__def,axiom,
% 0.14/0.44 ( inv_im2903009620893676101at_nat
% 0.14/0.44 = ( ^ [R5: set_Pr7459493094073627847at_nat,F2: nat > set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1623_inv__image__def,axiom,
% 0.14/0.44 ( inv_im4437241714082187487at_nat
% 0.14/0.44 = ( ^ [R5: set_Pr4329608150637261639at_nat,F2: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1624_inv__image__def,axiom,
% 0.14/0.44 ( inv_image_nat_nat
% 0.14/0.44 = ( ^ [R5: set_Pr1261947904930325089at_nat,F2: nat > nat] :
% 0.14/0.44 ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1625_inv__image__def,axiom,
% 0.14/0.44 ( inv_image_int_nat
% 0.14/0.44 = ( ^ [R5: set_Pr958786334691620121nt_int,F2: nat > int] :
% 0.14/0.44 ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1626_inv__image__def,axiom,
% 0.14/0.44 ( inv_im2900519150384625825at_int
% 0.14/0.44 = ( ^ [R5: set_Pr7459493094073627847at_nat,F2: int > set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1627_inv__image__def,axiom,
% 0.14/0.44 ( inv_im4434751243573137211at_int
% 0.14/0.44 = ( ^ [R5: set_Pr4329608150637261639at_nat,F2: int > set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1628_inv__image__def,axiom,
% 0.14/0.44 ( inv_image_nat_int
% 0.14/0.44 = ( ^ [R5: set_Pr1261947904930325089at_nat,F2: int > nat] :
% 0.14/0.44 ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1629_inv__image__def,axiom,
% 0.14/0.44 ( inv_image_int_int
% 0.14/0.44 = ( ^ [R5: set_Pr958786334691620121nt_int,F2: int > int] :
% 0.14/0.44 ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % inv_image_def
% 0.14/0.44 thf(fact_1630_The__case__prod,axiom,
% 0.14/0.44 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 0.14/0.44 ( ( the_Pr5012129486825234846t_unit @ ( produc4924168586796184916unit_o @ P2 ) )
% 0.14/0.44 = ( the_Pr5012129486825234846t_unit
% 0.14/0.44 @ ^ [Xy: produc7812382424243267045t_unit] : ( P2 @ ( produc473321116828791851t_unit @ Xy ) @ ( produc1126150082675451753t_unit @ Xy ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_case_prod
% 0.14/0.44 thf(fact_1631_The__case__prod,axiom,
% 0.14/0.44 ! [P2: int > int > $o] :
% 0.14/0.44 ( ( the_Pr4378521158711661632nt_int @ ( produc4947309494688390418_int_o @ P2 ) )
% 0.14/0.44 = ( the_Pr4378521158711661632nt_int
% 0.14/0.44 @ ^ [Xy: product_prod_int_int] : ( P2 @ ( product_fst_int_int @ Xy ) @ ( product_snd_int_int @ Xy ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_case_prod
% 0.14/0.44 thf(fact_1632_Quotient__composition__ge__eq,axiom,
% 0.14/0.44 ! [T3: int > product_prod_nat_nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( left_t8261381459436684205at_nat @ T3 )
% 0.14/0.44 => ( ( ord_le5604493270027003598_nat_o
% 0.14/0.44 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 => ( ord_le6741204236512500942_int_o
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ ( relcom1106208330880909712at_int @ T3 @ ( relcom8911704206367525917at_int @ R3 @ ( conver1866313717161370910at_nat @ T3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_composition_ge_eq
% 0.14/0.44 thf(fact_1633_Quotient__composition__ge__eq,axiom,
% 0.14/0.44 ! [T3: code_integer > int > $o,R3: int > int > $o] :
% 0.14/0.44 ( ( left_t1735413524555719857er_int @ T3 )
% 0.14/0.44 => ( ( ord_le6741204236512500942_int_o
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.44 @ R3 )
% 0.14/0.44 => ( ord_le3602516367967493612eger_o
% 0.14/0.44 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z )
% 0.14/0.44 @ ( relcom692387321444912665nteger @ T3 @ ( relcom967497705283160040nteger @ R3 @ ( conver1462408618118490240er_int @ T3 ) ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_composition_ge_eq
% 0.14/0.44 thf(fact_1634_Quotient__composition__le__eq,axiom,
% 0.14/0.44 ! [T3: int > product_prod_nat_nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( left_u1182257597767569412at_nat @ T3 )
% 0.14/0.44 => ( ( ord_le5604493270027003598_nat_o @ R3
% 0.14/0.44 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z ) )
% 0.14/0.44 => ( ord_le6741204236512500942_int_o @ ( relcom1106208330880909712at_int @ T3 @ ( relcom8911704206367525917at_int @ R3 @ ( conver1866313717161370910at_nat @ T3 ) ) )
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_composition_le_eq
% 0.14/0.44 thf(fact_1635_Quotient__composition__le__eq,axiom,
% 0.14/0.44 ! [T3: code_integer > int > $o,R3: int > int > $o] :
% 0.14/0.44 ( ( left_u6156896403773009178er_int @ T3 )
% 0.14/0.44 => ( ( ord_le6741204236512500942_int_o @ R3
% 0.14/0.44 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 0.14/0.44 => ( ord_le3602516367967493612eger_o @ ( relcom692387321444912665nteger @ T3 @ ( relcom967497705283160040nteger @ R3 @ ( conver1462408618118490240er_int @ T3 ) ) )
% 0.14/0.44 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_composition_le_eq
% 0.14/0.44 thf(fact_1636_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_o @ A @ A4 )
% 0.14/0.44 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1637_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: $o,B: nat,A4: set_o,B5: $o > set_nat] :
% 0.14/0.44 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_o @ A @ A4 )
% 0.14/0.44 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1638_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: $o,B: int,A4: set_o,B5: $o > set_int] :
% 0.14/0.44 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_o @ A @ A4 )
% 0.14/0.44 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1639_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: nat,B: $o,A4: set_nat,B5: nat > set_o] :
% 0.14/0.44 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_nat @ A @ A4 )
% 0.14/0.44 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1640_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: nat,B: int,A4: set_nat,B5: nat > set_int] :
% 0.14/0.44 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_nat @ A @ A4 )
% 0.14/0.44 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1641_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: int,B: $o,A4: set_int,B5: int > set_o] :
% 0.14/0.44 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_int @ A @ A4 )
% 0.14/0.44 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1642_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: int,B: nat,A4: set_int,B5: int > set_nat] :
% 0.14/0.44 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_int @ A @ A4 )
% 0.14/0.44 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1643_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 0.14/0.44 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_nat @ A @ A4 )
% 0.14/0.44 & ( member_num @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1644_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_int @ A @ A4 )
% 0.14/0.44 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1645_mem__Sigma__iff,axiom,
% 0.14/0.44 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.44 = ( ( member_nat @ A @ A4 )
% 0.14/0.44 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Sigma_iff
% 0.14/0.44 thf(fact_1646_SigmaI,axiom,
% 0.14/0.44 ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
% 0.14/0.44 ( ( member_o @ A @ A4 )
% 0.14/0.44 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1647_SigmaI,axiom,
% 0.14/0.44 ! [A: $o,A4: set_o,B: nat,B5: $o > set_nat] :
% 0.14/0.44 ( ( member_o @ A @ A4 )
% 0.14/0.44 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1648_SigmaI,axiom,
% 0.14/0.44 ! [A: $o,A4: set_o,B: int,B5: $o > set_int] :
% 0.14/0.44 ( ( member_o @ A @ A4 )
% 0.14/0.44 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1649_SigmaI,axiom,
% 0.14/0.44 ! [A: nat,A4: set_nat,B: $o,B5: nat > set_o] :
% 0.14/0.44 ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1650_SigmaI,axiom,
% 0.14/0.44 ! [A: nat,A4: set_nat,B: int,B5: nat > set_int] :
% 0.14/0.44 ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1651_SigmaI,axiom,
% 0.14/0.44 ! [A: int,A4: set_int,B: $o,B5: int > set_o] :
% 0.14/0.44 ( ( member_int @ A @ A4 )
% 0.14/0.44 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1652_SigmaI,axiom,
% 0.14/0.44 ! [A: int,A4: set_int,B: nat,B5: int > set_nat] :
% 0.14/0.44 ( ( member_int @ A @ A4 )
% 0.14/0.44 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1653_SigmaI,axiom,
% 0.14/0.44 ! [A: nat,A4: set_nat,B: num,B5: nat > set_num] :
% 0.14/0.44 ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ( ( member_num @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1654_SigmaI,axiom,
% 0.14/0.44 ! [A: int,A4: set_int,B: int,B5: int > set_int] :
% 0.14/0.44 ( ( member_int @ A @ A4 )
% 0.14/0.44 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1655_SigmaI,axiom,
% 0.14/0.44 ! [A: nat,A4: set_nat,B: nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.44 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaI
% 0.14/0.44 thf(fact_1656_in__inv__image,axiom,
% 0.14/0.44 ! [X2: nat,Y3: nat,R: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_image_nat_nat @ R @ F ) )
% 0.14/0.44 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1657_in__inv__image,axiom,
% 0.14/0.44 ! [X2: nat,Y3: nat,R: set_Pr958786334691620121nt_int,F: nat > int] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_image_int_nat @ R @ F ) )
% 0.14/0.44 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1658_in__inv__image,axiom,
% 0.14/0.44 ! [X2: int,Y3: int,R: set_Pr1261947904930325089at_nat,F: int > nat] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_image_nat_int @ R @ F ) )
% 0.14/0.44 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1659_in__inv__image,axiom,
% 0.14/0.44 ! [X2: int,Y3: int,R: set_Pr958786334691620121nt_int,F: int > int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_image_int_int @ R @ F ) )
% 0.14/0.44 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1660_in__inv__image,axiom,
% 0.14/0.44 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im6750873321330482877at_nat @ R @ F ) )
% 0.14/0.44 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1661_in__inv__image,axiom,
% 0.14/0.44 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr958786334691620121nt_int,F: set_Pr1261947904930325089at_nat > int] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im8510909985083594081at_nat @ R @ F ) )
% 0.14/0.44 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1662_in__inv__image,axiom,
% 0.14/0.44 ! [X2: nat,Y3: nat,R: set_Pr4329608150637261639at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_im4437241714082187487at_nat @ R @ F ) )
% 0.14/0.44 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1663_in__inv__image,axiom,
% 0.14/0.44 ! [X2: int,Y3: int,R: set_Pr4329608150637261639at_nat,F: int > set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_im4434751243573137211at_int @ R @ F ) )
% 0.14/0.44 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1664_in__inv__image,axiom,
% 0.14/0.44 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im7023619800666061458at_nat @ R @ F ) )
% 0.14/0.44 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1665_in__inv__image,axiom,
% 0.14/0.44 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,R: set_Pr1261947904930325089at_nat,F: set_Pr4329608150637261639at_nat > nat] :
% 0.14/0.44 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ ( inv_im2354225701593503139at_nat @ R @ F ) )
% 0.14/0.44 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 0.14/0.44
% 0.14/0.44 % in_inv_image
% 0.14/0.44 thf(fact_1666_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec7088162979684241874at_nat
% 0.14/0.44 @ ( produc6590410687421337004_nat_o
% 0.14/0.44 @ ^ [A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc2761391749766926216at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_nat_nat] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1667_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: nat > $o] :
% 0.14/0.44 ( ( collec7029190964493513045at_nat
% 0.14/0.44 @ ( produc8758269395934548017_nat_o
% 0.14/0.44 @ ^ [A5: product_prod_nat_nat,B4: nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc7672662199629908489at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_nat_nat] : ( collect_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1668_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec6785001409445536906nt_int
% 0.14/0.44 @ ( produc5031841752791441652_int_o
% 0.14/0.44 @ ^ [A5: product_prod_nat_nat,B4: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc8806266479013559872nt_int @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_nat_nat] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1669_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec5903703980526211963at_nat
% 0.14/0.44 @ ( produc5864757623865647827_nat_o
% 0.14/0.44 @ ^ [A5: nat,B4: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc1809337555817847783at_nat @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: nat] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1670_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec5600542410287506995nt_int
% 0.14/0.44 @ ( produc4306188689235752475_int_o
% 0.14/0.44 @ ^ [A5: nat,B4: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc7854212285064481439nt_int @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: nat] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1671_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec7751116662793354522at_nat
% 0.14/0.44 @ ( produc3235059054576640100_nat_o
% 0.14/0.44 @ ^ [A5: product_prod_int_int,B4: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc3424345432876038864at_nat @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_int_int] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1672_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: nat > $o] :
% 0.14/0.44 ( ( collec364394062568603661nt_nat
% 0.14/0.44 @ ( produc5441891513209881465_nat_o
% 0.14/0.44 @ ^ [A5: product_prod_int_int,B4: nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc1007865297704999105nt_nat @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_int_int] : ( collect_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1673_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec7447955092554649554nt_int
% 0.14/0.44 @ ( produc1676490119946744748_int_o
% 0.14/0.44 @ ^ [A5: product_prod_int_int,B4: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc245848125267896712nt_int @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [Uu: product_prod_int_int] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1674_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: nat > $o] :
% 0.14/0.44 ( ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [A5: nat,B4: nat] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc457027306803732586at_nat @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [Uu: nat] : ( collect_nat @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1675_Collect__case__prod,axiom,
% 0.14/0.44 ! [P2: int > $o,Q2: int > $o] :
% 0.14/0.44 ( ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [A5: int,B4: int] :
% 0.14/0.44 ( ( P2 @ A5 )
% 0.14/0.44 & ( Q2 @ B4 ) ) ) )
% 0.14/0.44 = ( produc1453890548195736866nt_int @ ( collect_int @ P2 )
% 0.14/0.44 @ ^ [Uu: int] : ( collect_int @ Q2 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod
% 0.14/0.44 thf(fact_1676_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc2936396906406871148r_char @ top_top_set_char
% 0.14/0.44 @ ^ [Uu: char] : top_top_set_char )
% 0.14/0.44 = top_to1235241553633177651r_char ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1677_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc1204236661673008499ar_rat @ top_top_set_char
% 0.14/0.44 @ ^ [Uu: char] : top_top_set_rat )
% 0.14/0.44 = top_to8437673547576850234ar_rat ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1678_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc1839366721759504235ar_nat @ top_top_set_char
% 0.14/0.44 @ ^ [Uu: char] : top_top_set_nat )
% 0.14/0.44 = top_to5594287848199751986ar_nat ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1679_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc1836876251250453959ar_int @ top_top_set_char
% 0.14/0.44 @ ^ [Uu: char] : top_top_set_int )
% 0.14/0.44 = top_to3104204703268025230ar_int ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1680_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc1427039474575272051t_char @ top_top_set_rat
% 0.14/0.44 @ ^ [Uu: rat] : top_top_set_char )
% 0.14/0.44 = top_to3221206985699244474t_char ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1681_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc8728714639637146746at_rat @ top_top_set_rat
% 0.14/0.44 @ ^ [Uu: rat] : top_top_set_rat )
% 0.14/0.44 = top_to3112507417142880193at_rat ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1682_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc140472662868866674at_nat @ top_top_set_rat
% 0.14/0.44 @ ^ [Uu: rat] : top_top_set_nat )
% 0.14/0.44 = top_to269121717765781945at_nat ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1683_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc137982192359816398at_int @ top_top_set_rat
% 0.14/0.44 @ ^ [Uu: rat] : top_top_set_int )
% 0.14/0.44 = top_to7002410609688830997at_int ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1684_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc4754187946284079723t_char @ top_top_set_nat
% 0.14/0.44 @ ^ [Uu: nat] : top_top_set_char )
% 0.14/0.44 = top_to7107842681480589234t_char ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1685_UNIV__Times__UNIV,axiom,
% 0.14/0.44 ( ( produc9045269283572012658at_rat @ top_top_set_nat
% 0.14/0.44 @ ^ [Uu: nat] : top_top_set_rat )
% 0.14/0.44 = top_to7513191607651882425at_rat ) ).
% 0.14/0.44
% 0.14/0.44 % UNIV_Times_UNIV
% 0.14/0.44 thf(fact_1686_The__split__eq,axiom,
% 0.14/0.44 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( the_Pr4877703158196064750at_nat
% 0.14/0.44 @ ( produc9020218426428501292_nat_o
% 0.14/0.44 @ ^ [X7: set_Pr4329608150637261639at_nat,Y6: set_Pr4329608150637261639at_nat] :
% 0.14/0.44 ( ( X2 = X7 )
% 0.14/0.44 & ( Y3 = Y6 ) ) ) )
% 0.14/0.44 = ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_split_eq
% 0.14/0.44 thf(fact_1687_The__split__eq,axiom,
% 0.14/0.44 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( the_Pr4604535484834969198at_nat
% 0.14/0.44 @ ( produc410239310623530412_nat_o
% 0.14/0.44 @ ^ [X7: set_Pr1261947904930325089at_nat,Y6: set_Pr1261947904930325089at_nat] :
% 0.14/0.44 ( ( X2 = X7 )
% 0.14/0.44 & ( Y3 = Y6 ) ) ) )
% 0.14/0.44 = ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_split_eq
% 0.14/0.44 thf(fact_1688_The__split__eq,axiom,
% 0.14/0.44 ! [X2: nat,Y3: num] :
% 0.14/0.44 ( ( the_Pr8265262403268641490at_num
% 0.14/0.44 @ ( produc4927758841916487424_num_o
% 0.14/0.44 @ ^ [X7: nat,Y6: num] :
% 0.14/0.44 ( ( X2 = X7 )
% 0.14/0.44 & ( Y3 = Y6 ) ) ) )
% 0.14/0.44 = ( product_Pair_nat_num @ X2 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_split_eq
% 0.14/0.44 thf(fact_1689_The__split__eq,axiom,
% 0.14/0.44 ! [X2: nat,Y3: nat] :
% 0.14/0.44 ( ( the_Pr7557018466319803784at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X7: nat,Y6: nat] :
% 0.14/0.44 ( ( X2 = X7 )
% 0.14/0.44 & ( Y3 = Y6 ) ) ) )
% 0.14/0.44 = ( product_Pair_nat_nat @ X2 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_split_eq
% 0.14/0.44 thf(fact_1690_The__split__eq,axiom,
% 0.14/0.44 ! [X2: int,Y3: int] :
% 0.14/0.44 ( ( the_Pr4378521158711661632nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X7: int,Y6: int] :
% 0.14/0.44 ( ( X2 = X7 )
% 0.14/0.44 & ( Y3 = Y6 ) ) ) )
% 0.14/0.44 = ( product_Pair_int_int @ X2 @ Y3 ) ) ).
% 0.14/0.44
% 0.14/0.44 % The_split_eq
% 0.14/0.44 thf(fact_1691_Times__eq__cancel2,axiom,
% 0.14/0.44 ! [X2: nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( member_nat @ X2 @ C3 )
% 0.14/0.44 => ( ( ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : C3 )
% 0.14/0.44 = ( produc457027306803732586at_nat @ B5
% 0.14/0.44 @ ^ [Uu: nat] : C3 ) )
% 0.14/0.44 = ( A4 = B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Times_eq_cancel2
% 0.14/0.44 thf(fact_1692_Sigma__cong,axiom,
% 0.14/0.44 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 0.14/0.44 ( ( A4 = B5 )
% 0.14/0.44 => ( ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ B5 )
% 0.14/0.44 => ( ( C3 @ X )
% 0.14/0.44 = ( D @ X ) ) )
% 0.14/0.44 => ( ( produc457027306803732586at_nat @ A4 @ C3 )
% 0.14/0.44 = ( produc457027306803732586at_nat @ B5 @ D ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Sigma_cong
% 0.14/0.44 thf(fact_1693_SigmaE2,axiom,
% 0.14/0.44 ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_o @ A @ A4 )
% 0.14/0.44 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1694_SigmaE2,axiom,
% 0.14/0.44 ! [A: $o,B: nat,A4: set_o,B5: $o > set_nat] :
% 0.14/0.44 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_o @ A @ A4 )
% 0.14/0.44 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1695_SigmaE2,axiom,
% 0.14/0.44 ! [A: $o,B: int,A4: set_o,B5: $o > set_int] :
% 0.14/0.44 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_o @ A @ A4 )
% 0.14/0.44 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1696_SigmaE2,axiom,
% 0.14/0.44 ! [A: nat,B: $o,A4: set_nat,B5: nat > set_o] :
% 0.14/0.44 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1697_SigmaE2,axiom,
% 0.14/0.44 ! [A: nat,B: int,A4: set_nat,B5: nat > set_int] :
% 0.14/0.44 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1698_SigmaE2,axiom,
% 0.14/0.44 ! [A: int,B: $o,A4: set_int,B5: int > set_o] :
% 0.14/0.44 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_int @ A @ A4 )
% 0.14/0.44 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1699_SigmaE2,axiom,
% 0.14/0.44 ! [A: int,B: nat,A4: set_int,B5: int > set_nat] :
% 0.14/0.44 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_int @ A @ A4 )
% 0.14/0.44 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1700_SigmaE2,axiom,
% 0.14/0.44 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 0.14/0.44 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ~ ( member_num @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1701_SigmaE2,axiom,
% 0.14/0.44 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_int @ A @ A4 )
% 0.14/0.44 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1702_SigmaE2,axiom,
% 0.14/0.44 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ( ( member_nat @ A @ A4 )
% 0.14/0.44 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE2
% 0.14/0.44 thf(fact_1703_SigmaD2,axiom,
% 0.14/0.44 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,B5: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( produc6258361011560675592at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member6273874620674182256at_nat @ B @ ( B5 @ A ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD2
% 0.14/0.44 thf(fact_1704_SigmaD2,axiom,
% 0.14/0.44 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member2643936169264416010at_nat @ B @ ( B5 @ A ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD2
% 0.14/0.44 thf(fact_1705_SigmaD2,axiom,
% 0.14/0.44 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 0.14/0.44 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 0.14/0.44 => ( member_num @ B @ ( B5 @ A ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD2
% 0.14/0.44 thf(fact_1706_SigmaD2,axiom,
% 0.14/0.44 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 0.14/0.44 => ( member_int @ B @ ( B5 @ A ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD2
% 0.14/0.44 thf(fact_1707_SigmaD2,axiom,
% 0.14/0.44 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member_nat @ B @ ( B5 @ A ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD2
% 0.14/0.44 thf(fact_1708_SigmaD1,axiom,
% 0.14/0.44 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,B5: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( produc6258361011560675592at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member6273874620674182256at_nat @ A @ A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD1
% 0.14/0.44 thf(fact_1709_SigmaD1,axiom,
% 0.14/0.44 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member2643936169264416010at_nat @ A @ A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD1
% 0.14/0.44 thf(fact_1710_SigmaD1,axiom,
% 0.14/0.44 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 0.14/0.44 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 0.14/0.44 => ( member_nat @ A @ A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD1
% 0.14/0.44 thf(fact_1711_SigmaD1,axiom,
% 0.14/0.44 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 0.14/0.44 => ( member_int @ A @ A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD1
% 0.14/0.44 thf(fact_1712_SigmaD1,axiom,
% 0.14/0.44 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ( member_nat @ A @ A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaD1
% 0.14/0.44 thf(fact_1713_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_o_o,A4: set_o,B5: $o > set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ C @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: $o] :
% 0.14/0.44 ( ( member_o @ X @ A4 )
% 0.14/0.44 => ! [Y: $o] :
% 0.14/0.44 ( ( member_o @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_o_o @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1714_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_o_nat,A4: set_o,B5: $o > set_nat] :
% 0.14/0.44 ( ( member2802428098988154798_o_nat @ C @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: $o] :
% 0.14/0.44 ( ( member_o @ X @ A4 )
% 0.14/0.44 => ! [Y: nat] :
% 0.14/0.44 ( ( member_nat @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_o_nat @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1715_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_o_int,A4: set_o,B5: $o > set_int] :
% 0.14/0.44 ( ( member7847949116333733898_o_int @ C @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: $o] :
% 0.14/0.44 ( ( member_o @ X @ A4 )
% 0.14/0.44 => ! [Y: int] :
% 0.14/0.44 ( ( member_int @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_o_int @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1716_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_nat_o,A4: set_nat,B5: nat > set_o] :
% 0.14/0.44 ( ( member6310962623043647828_nat_o @ C @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ! [Y: $o] :
% 0.14/0.44 ( ( member_o @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_nat_o @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1717_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_nat_int,A4: set_nat,B5: nat > set_int] :
% 0.14/0.44 ( ( member4262671552274231302at_int @ C @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ! [Y: int] :
% 0.14/0.44 ( ( member_int @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_nat_int @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1718_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_int_o,A4: set_int,B5: int > set_o] :
% 0.14/0.44 ( ( member4489920277610959864_int_o @ C @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: int] :
% 0.14/0.44 ( ( member_int @ X @ A4 )
% 0.14/0.44 => ! [Y: $o] :
% 0.14/0.44 ( ( member_o @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_int_o @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1719_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_int_nat,A4: set_int,B5: int > set_nat] :
% 0.14/0.44 ( ( member216504246829706758nt_nat @ C @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: int] :
% 0.14/0.44 ( ( member_int @ X @ A4 )
% 0.14/0.44 => ! [Y: nat] :
% 0.14/0.44 ( ( member_nat @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_int_nat @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1720_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_nat_num,A4: set_nat,B5: nat > set_num] :
% 0.14/0.44 ( ( member9148766508732265716at_num @ C @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ! [Y: num] :
% 0.14/0.44 ( ( member_num @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_nat_num @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1721_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_int_int,A4: set_int,B5: int > set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ C @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: int] :
% 0.14/0.44 ( ( member_int @ X @ A4 )
% 0.14/0.44 => ! [Y: int] :
% 0.14/0.44 ( ( member_int @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_int_int @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1722_SigmaE,axiom,
% 0.14/0.44 ! [C: product_prod_nat_nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ C @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.44 => ~ ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ! [Y: nat] :
% 0.14/0.44 ( ( member_nat @ Y @ ( B5 @ X ) )
% 0.14/0.44 => ( C
% 0.14/0.44 != ( product_Pair_nat_nat @ X @ Y ) ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % SigmaE
% 0.14/0.44 thf(fact_1723_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec7088162979684241874at_nat
% 0.14/0.44 @ ( produc6590410687421337004_nat_o
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc2761391749766926216at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1724_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > nat > $o] :
% 0.14/0.44 ( ( collec7029190964493513045at_nat
% 0.14/0.44 @ ( produc8758269395934548017_nat_o
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat,Y5: nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc7672662199629908489at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1725_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec6785001409445536906nt_int
% 0.14/0.44 @ ( produc5031841752791441652_int_o
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc8806266479013559872nt_int @ ( collec3392354462482085612at_nat @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_nat_nat] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1726_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: nat > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec5903703980526211963at_nat
% 0.14/0.44 @ ( produc5864757623865647827_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc1809337555817847783at_nat @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [X4: nat] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1727_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: nat > product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec5600542410287506995nt_int
% 0.14/0.44 @ ( produc4306188689235752475_int_o
% 0.14/0.44 @ ^ [X4: nat,Y5: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc7854212285064481439nt_int @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [X4: nat] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1728_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > product_prod_nat_nat > $o] :
% 0.14/0.44 ( ( collec7751116662793354522at_nat
% 0.14/0.44 @ ( produc3235059054576640100_nat_o
% 0.14/0.44 @ ^ [X4: product_prod_int_int,Y5: product_prod_nat_nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc3424345432876038864at_nat @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_int_int] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1729_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > nat > $o] :
% 0.14/0.44 ( ( collec364394062568603661nt_nat
% 0.14/0.44 @ ( produc5441891513209881465_nat_o
% 0.14/0.44 @ ^ [X4: product_prod_int_int,Y5: nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc1007865297704999105nt_nat @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_int_int] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1730_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > product_prod_int_int > $o] :
% 0.14/0.44 ( ( collec7447955092554649554nt_int
% 0.14/0.44 @ ( produc1676490119946744748_int_o
% 0.14/0.44 @ ^ [X4: product_prod_int_int,Y5: product_prod_int_int] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc245848125267896712nt_int @ ( collec213857154873943460nt_int @ P2 )
% 0.14/0.44 @ ^ [X4: product_prod_int_int] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1731_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: nat > $o,Q2: nat > nat > $o] :
% 0.14/0.44 ( ( collec3392354462482085612at_nat
% 0.14/0.44 @ ( produc6081775807080527818_nat_o
% 0.14/0.44 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc457027306803732586at_nat @ ( collect_nat @ P2 )
% 0.14/0.44 @ ^ [X4: nat] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1732_Collect__case__prod__Sigma,axiom,
% 0.14/0.44 ! [P2: int > $o,Q2: int > int > $o] :
% 0.14/0.44 ( ( collec213857154873943460nt_int
% 0.14/0.44 @ ( produc4947309494688390418_int_o
% 0.14/0.44 @ ^ [X4: int,Y5: int] :
% 0.14/0.44 ( ( P2 @ X4 )
% 0.14/0.44 & ( Q2 @ X4 @ Y5 ) ) ) )
% 0.14/0.44 = ( produc1453890548195736866nt_int @ ( collect_int @ P2 )
% 0.14/0.44 @ ^ [X4: int] : ( collect_int @ ( Q2 @ X4 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Collect_case_prod_Sigma
% 0.14/0.44 thf(fact_1733_Sigma__mono,axiom,
% 0.14/0.44 ! [A4: set_nat,C3: set_nat,B5: nat > set_nat,D: nat > set_nat] :
% 0.14/0.44 ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.44 => ( ! [X: nat] :
% 0.14/0.44 ( ( member_nat @ X @ A4 )
% 0.14/0.44 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ ( D @ X ) ) )
% 0.14/0.44 => ( ord_le3146513528884898305at_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) @ ( produc457027306803732586at_nat @ C3 @ D ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Sigma_mono
% 0.14/0.44 thf(fact_1734_Times__subset__cancel2,axiom,
% 0.14/0.44 ! [X2: nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( member_nat @ X2 @ C3 )
% 0.14/0.44 => ( ( ord_le3146513528884898305at_nat
% 0.14/0.44 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : C3 )
% 0.14/0.44 @ ( produc457027306803732586at_nat @ B5
% 0.14/0.44 @ ^ [Uu: nat] : C3 ) )
% 0.14/0.44 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Times_subset_cancel2
% 0.14/0.44 thf(fact_1735_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_o_o,A4: set_o,B5: set_o] :
% 0.14/0.44 ( ( member7466972457876170832od_o_o @ X2
% 0.14/0.44 @ ( product_Sigma_o_o @ A4
% 0.14/0.44 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.44 = ( ( member_o @ ( product_fst_o_o @ X2 ) @ A4 )
% 0.14/0.44 & ( member_o @ ( product_snd_o_o @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1736_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_o_nat,A4: set_o,B5: set_nat] :
% 0.14/0.44 ( ( member2802428098988154798_o_nat @ X2
% 0.14/0.44 @ ( product_Sigma_o_nat @ A4
% 0.14/0.44 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.44 = ( ( member_o @ ( product_fst_o_nat @ X2 ) @ A4 )
% 0.14/0.44 & ( member_nat @ ( product_snd_o_nat @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1737_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_o_int,A4: set_o,B5: set_int] :
% 0.14/0.44 ( ( member7847949116333733898_o_int @ X2
% 0.14/0.44 @ ( product_Sigma_o_int @ A4
% 0.14/0.44 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.44 = ( ( member_o @ ( product_fst_o_int @ X2 ) @ A4 )
% 0.14/0.44 & ( member_int @ ( product_snd_o_int @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1738_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_nat_o,A4: set_nat,B5: set_o] :
% 0.14/0.44 ( ( member6310962623043647828_nat_o @ X2
% 0.14/0.44 @ ( product_Sigma_nat_o @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ( member_nat @ ( product_fst_nat_o @ X2 ) @ A4 )
% 0.14/0.44 & ( member_o @ ( product_snd_nat_o @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1739_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_nat_int,A4: set_nat,B5: set_int] :
% 0.14/0.44 ( ( member4262671552274231302at_int @ X2
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ( member_nat @ ( product_fst_nat_int @ X2 ) @ A4 )
% 0.14/0.44 & ( member_int @ ( product_snd_nat_int @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1740_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_int_o,A4: set_int,B5: set_o] :
% 0.14/0.44 ( ( member4489920277610959864_int_o @ X2
% 0.14/0.44 @ ( product_Sigma_int_o @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( ( member_int @ ( product_fst_int_o @ X2 ) @ A4 )
% 0.14/0.44 & ( member_o @ ( product_snd_int_o @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1741_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_int_nat,A4: set_int,B5: set_nat] :
% 0.14/0.44 ( ( member216504246829706758nt_nat @ X2
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( ( member_int @ ( product_fst_int_nat @ X2 ) @ A4 )
% 0.14/0.44 & ( member_nat @ ( product_snd_int_nat @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1742_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_int_int,A4: set_int,B5: set_int] :
% 0.14/0.44 ( ( member5262025264175285858nt_int @ X2
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( ( member_int @ ( product_fst_int_int @ X2 ) @ A4 )
% 0.14/0.44 & ( member_int @ ( product_snd_int_int @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1743_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( member8440522571783428010at_nat @ X2
% 0.14/0.44 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( ( member_nat @ ( product_fst_nat_nat @ X2 ) @ A4 )
% 0.14/0.44 & ( member_nat @ ( product_snd_nat_nat @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1744_mem__Times__iff,axiom,
% 0.14/0.44 ! [X2: produc652263959640188542_nat_o,A4: set_Pr1261947904930325089at_nat,B5: set_o] :
% 0.14/0.44 ( ( member2200362271989506215_nat_o @ X2
% 0.14/0.44 @ ( produc203973861852599583_nat_o @ A4
% 0.14/0.44 @ ^ [Uu: product_prod_nat_nat] : B5 ) )
% 0.14/0.44 = ( ( member8440522571783428010at_nat @ ( produc6435950281062462810_nat_o @ X2 ) @ A4 )
% 0.14/0.44 & ( member_o @ ( produc668916169454083228_nat_o @ X2 ) @ B5 ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % mem_Times_iff
% 0.14/0.44 thf(fact_1745_product__swap,axiom,
% 0.14/0.44 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( image_5168914502847457605at_nat @ product_swap_nat_nat
% 0.14/0.44 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc457027306803732586at_nat @ B5
% 0.14/0.44 @ ^ [Uu: nat] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % product_swap
% 0.14/0.44 thf(fact_1746_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: $o > $o > $o,Abs1: $o > $o,Rep1: $o > $o,T1: $o > $o > $o,R22: $o > $o > $o,Abs22: $o > nat,Rep22: nat > $o,T22: $o > nat > $o] :
% 0.14/0.44 ( ( quotient_o_o @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_o_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_o_nat @ ( relcompp_o_o_o @ T1 @ ( relcompp_o_o_o @ R22 @ ( conversep_o_o @ T1 ) ) ) @ ( comp_o_nat_o @ Abs22 @ Abs1 ) @ ( comp_o_o_nat @ Rep1 @ Rep22 ) @ ( relcompp_o_o_nat @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1747_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: num > num > $o,Abs1: num > nat,Rep1: nat > num,T1: num > nat > $o,R22: nat > nat > $o,Abs22: nat > int,Rep22: int > nat,T22: nat > int > $o] :
% 0.14/0.44 ( ( quotient_num_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_nat_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_num_int @ ( relcompp_num_nat_num @ T1 @ ( relcompp_nat_nat_num @ R22 @ ( conversep_num_nat @ T1 ) ) ) @ ( comp_nat_int_num @ Abs22 @ Abs1 ) @ ( comp_nat_num_int @ Rep1 @ Rep22 ) @ ( relcompp_num_nat_int @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1748_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,Abs1: nat > int,Rep1: int > nat,T1: nat > int > $o,R22: int > int > $o,Abs22: int > int,Rep22: int > int,T22: int > int > $o] :
% 0.14/0.44 ( ( quotient_nat_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_int_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_nat_int @ ( relcompp_nat_int_nat @ T1 @ ( relcompp_int_int_nat @ R22 @ ( conversep_nat_int @ T1 ) ) ) @ ( comp_int_int_nat @ Abs22 @ Abs1 ) @ ( comp_int_nat_int @ Rep1 @ Rep22 ) @ ( relcompp_nat_int_int @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1749_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,Abs1: nat > $o,Rep1: $o > nat,T1: nat > $o > $o,R22: $o > $o > $o,Abs22: $o > $o,Rep22: $o > $o,T22: $o > $o > $o] :
% 0.14/0.44 ( ( quotient_nat_o @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_o_o @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_nat_o @ ( relcompp_nat_o_nat @ T1 @ ( relcompp_o_o_nat @ R22 @ ( conversep_nat_o @ T1 ) ) ) @ ( comp_o_o_nat @ Abs22 @ Abs1 ) @ ( comp_o_nat_o @ Rep1 @ Rep22 ) @ ( relcompp_nat_o_o @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1750_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: int > int > $o,Abs1: int > nat,Rep1: nat > int,T1: int > nat > $o,R22: nat > nat > $o,Abs22: nat > num,Rep22: num > nat,T22: nat > num > $o] :
% 0.14/0.44 ( ( quotient_int_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_nat_num @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_int_num @ ( relcompp_int_nat_int @ T1 @ ( relcompp_nat_nat_int @ R22 @ ( conversep_int_nat @ T1 ) ) ) @ ( comp_nat_num_int @ Abs22 @ Abs1 ) @ ( comp_nat_int_num @ Rep1 @ Rep22 ) @ ( relcompp_int_nat_num @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1751_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: nat > nat > $o,Abs1: nat > nat,Rep1: nat > nat,T1: nat > nat > $o,R22: nat > nat > $o,Abs22: nat > nat,Rep22: nat > nat,T22: nat > nat > $o] :
% 0.14/0.44 ( ( quotient_nat_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_nat_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_nat_nat @ ( relcompp_nat_nat_nat @ T1 @ ( relcompp_nat_nat_nat @ R22 @ ( conversep_nat_nat @ T1 ) ) ) @ ( comp_nat_nat_nat @ Abs22 @ Abs1 ) @ ( comp_nat_nat_nat @ Rep1 @ Rep22 ) @ ( relcompp_nat_nat_nat @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1752_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: int > int > $o,Abs1: int > int,Rep1: int > int,T1: int > int > $o,R22: int > int > $o,Abs22: int > nat,Rep22: nat > int,T22: int > nat > $o] :
% 0.14/0.44 ( ( quotient_int_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotient_int_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotient_int_nat @ ( relcompp_int_int_int @ T1 @ ( relcompp_int_int_int @ R22 @ ( conversep_int_int @ T1 ) ) ) @ ( comp_int_nat_int @ Abs22 @ Abs1 ) @ ( comp_int_int_nat @ Rep1 @ Rep22 ) @ ( relcompp_int_int_nat @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1753_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: int > int > $o,Abs1: int > int,Rep1: int > int,T1: int > int > $o,R22: int > int > $o,Abs22: int > code_integer,Rep22: code_integer > int,T22: int > code_integer > $o] :
% 0.14/0.44 ( ( quotient_int_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotie2291698863146621601nteger @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotie2291698863146621601nteger @ ( relcompp_int_int_int @ T1 @ ( relcompp_int_int_int @ R22 @ ( conversep_int_int @ T1 ) ) ) @ ( comp_i1585864551200866970er_int @ Abs22 @ Abs1 ) @ ( comp_i2224564030725804698nteger @ Rep1 @ Rep22 ) @ ( relcom967497705283160040nteger @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1754_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,Abs1: product_prod_nat_nat > product_prod_nat_nat,Rep1: product_prod_nat_nat > product_prod_nat_nat,T1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o,Abs22: product_prod_nat_nat > int,Rep22: int > product_prod_nat_nat,T22: product_prod_nat_nat > int > $o] :
% 0.14/0.44 ( ( quotie4166942682936818134at_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotie1194848508323700631at_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotie1194848508323700631at_int @ ( relcom282571730187242960at_nat @ T1 @ ( relcom282571730187242960at_nat @ R22 @ ( conver6965824823119931701at_nat @ T1 ) ) ) @ ( comp_P4605287290794827253at_nat @ Abs22 @ Abs1 ) @ ( comp_P7428279379633703887at_int @ Rep1 @ Rep22 ) @ ( relcom8911704206367525917at_int @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1755_Quotient__compose,axiom,
% 0.14/0.44 ! [R1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,Abs1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer,Rep1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,T1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o,R22: ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o,Abs22: ( code_integer > code_integer ) > code_integer,Rep22: code_integer > code_integer > code_integer,T22: ( code_integer > code_integer ) > code_integer > $o] :
% 0.14/0.44 ( ( quotie8207154290130328982nteger @ R1 @ Abs1 @ Rep1 @ T1 )
% 0.14/0.44 => ( ( quotie9062115205763428814nteger @ R22 @ Abs22 @ Rep22 @ T22 )
% 0.14/0.44 => ( quotie8803226531959296410nteger @ ( relcom458776940982682326nteger @ T1 @ ( relcom1820845089908643850nteger @ R22 @ ( conver3229387634306789365nteger @ T1 ) ) ) @ ( comp_C7826480081638475456nteger @ Abs22 @ Abs1 ) @ ( comp_C8797469213163452608nteger @ Rep1 @ Rep22 ) @ ( relcom4829277440228594702nteger @ T1 @ T22 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % Quotient_compose
% 0.14/0.44 thf(fact_1756_swap__product,axiom,
% 0.14/0.44 ! [A4: set_se5479201105039950375at_nat,B5: set_se5479201105039950375at_nat] :
% 0.14/0.44 ( ( image_3313167189156628421at_nat
% 0.14/0.44 @ ( produc5456455677105495163at_nat
% 0.14/0.44 @ ^ [I2: set_Pr4329608150637261639at_nat,J: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ J @ I2 ) )
% 0.14/0.44 @ ( produc6258361011560675592at_nat @ A4
% 0.14/0.44 @ ^ [Uu: set_Pr4329608150637261639at_nat] : B5 ) )
% 0.14/0.44 = ( produc6258361011560675592at_nat @ B5
% 0.14/0.44 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % swap_product
% 0.14/0.44 thf(fact_1757_swap__product,axiom,
% 0.14/0.44 ! [A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat] :
% 0.14/0.44 ( ( image_960689587819713477at_nat
% 0.14/0.44 @ ( produc7548845685434208379at_nat
% 0.14/0.44 @ ^ [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ J @ I2 ) )
% 0.14/0.44 @ ( produc7726050920695093128at_nat @ A4
% 0.14/0.44 @ ^ [Uu: set_Pr1261947904930325089at_nat] : B5 ) )
% 0.14/0.44 = ( produc7726050920695093128at_nat @ B5
% 0.14/0.44 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % swap_product
% 0.14/0.44 thf(fact_1758_swap__product,axiom,
% 0.14/0.44 ! [A4: set_num,B5: set_nat] :
% 0.14/0.44 ( ( image_7762062833379733445at_num
% 0.14/0.44 @ ( produc5219324331026901427at_num
% 0.14/0.44 @ ^ [I2: num,J: nat] : ( product_Pair_nat_num @ J @ I2 ) )
% 0.14/0.44 @ ( produc7810729746965977780um_nat @ A4
% 0.14/0.44 @ ^ [Uu: num] : B5 ) )
% 0.14/0.44 = ( produc6237731129814287028at_num @ B5
% 0.14/0.44 @ ^ [Uu: nat] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % swap_product
% 0.14/0.44 thf(fact_1759_swap__product,axiom,
% 0.14/0.44 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.44 ( ( image_5168914502847457605at_nat
% 0.14/0.44 @ ( produc2626176000494625587at_nat
% 0.14/0.44 @ ^ [I2: nat,J: nat] : ( product_Pair_nat_nat @ J @ I2 ) )
% 0.14/0.44 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc457027306803732586at_nat @ B5
% 0.14/0.44 @ ^ [Uu: nat] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % swap_product
% 0.14/0.44 thf(fact_1760_swap__product,axiom,
% 0.14/0.44 ! [A4: set_int,B5: set_int] :
% 0.14/0.44 ( ( image_2653370878348428101nt_int
% 0.14/0.44 @ ( produc4245557441103728435nt_int
% 0.14/0.44 @ ^ [I2: int,J: int] : ( product_Pair_int_int @ J @ I2 ) )
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc1453890548195736866nt_int @ B5
% 0.14/0.44 @ ^ [Uu: int] : A4 ) ) ).
% 0.14/0.44
% 0.14/0.44 % swap_product
% 0.14/0.44 thf(fact_1761_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: nat > rat,A4: set_nat,A7: set_rat,G: int > nat,B5: set_int,B7: set_nat] :
% 0.14/0.44 ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_nat @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_3755276878268593137at_nat @ ( produc8749313216793205150nt_nat @ F @ G )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc140472662868866674at_nat @ A7
% 0.14/0.44 @ ^ [Uu: rat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1762_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: nat > rat,A4: set_nat,A7: set_rat,G: int > int,B5: set_int,B7: set_int] :
% 0.14/0.44 ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_int @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_8800797895614172237at_int @ ( produc8746822746284154874nt_int @ F @ G )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc137982192359816398at_int @ A7
% 0.14/0.44 @ ^ [Uu: rat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1763_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: nat > nat,A4: set_nat,A7: set_nat,G: int > int,B5: set_int,B7: set_int] :
% 0.14/0.44 ( ( ( image_nat_nat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_int @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_9117352539549038149at_int @ ( produc7974749936722635250nt_int @ F @ G )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ A7
% 0.14/0.44 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1764_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: nat > int,A4: set_nat,A7: set_int,G: int > nat,B5: set_int,B7: set_nat] :
% 0.14/0.44 ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_nat @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_5071185234104513605nt_nat @ ( produc8348893967468530162nt_nat @ F @ G )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc1456381018704787142nt_nat @ A7
% 0.14/0.44 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1765_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: nat > int,A4: set_nat,A7: set_int,G: int > int,B5: set_int,B7: set_int] :
% 0.14/0.44 ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_int @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_893334214595316897nt_int @ ( produc8346403496959479886nt_int @ F @ G )
% 0.14/0.44 @ ( produc454536836294682310at_int @ A4
% 0.14/0.44 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.44 = ( produc1453890548195736866nt_int @ A7
% 0.14/0.44 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1766_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: int > nat,A4: set_int,A7: set_nat,G: nat > rat,B5: set_nat,B7: set_rat] :
% 0.14/0.44 ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_nat_rat @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_3420722608207172081at_rat @ ( produc4032938703151184286at_rat @ F @ G )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc9045269283572012658at_rat @ A7
% 0.14/0.44 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1767_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: int > nat,A4: set_int,A7: set_nat,G: nat > int,B5: set_nat,B7: set_int] :
% 0.14/0.44 ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_nat_int @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_2751100147091372101at_int @ ( produc4665578292728629746at_int @ F @ G )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ A7
% 0.14/0.44 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1768_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: int > nat,A4: set_int,A7: set_nat,G: int > int,B5: set_int,B7: set_int] :
% 0.14/0.44 ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_int_int @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_1654017166447373545at_int @ ( produc5664932004629684302nt_int @ F @ G )
% 0.14/0.44 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc454536836294682310at_int @ A7
% 0.14/0.44 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1769_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: int > int,A4: set_int,A7: set_int,G: nat > rat,B5: set_nat,B7: set_rat] :
% 0.14/0.44 ( ( ( image_int_int @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_nat_rat @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_4420076320108226637nt_rat @ ( produc4404592263388028922at_rat @ F @ G )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc821250958618291406nt_rat @ A7
% 0.14/0.44 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1770_map__prod__surj__on,axiom,
% 0.14/0.44 ! [F: int > int,A4: set_int,A7: set_int,G: nat > nat,B5: set_nat,B7: set_nat] :
% 0.14/0.44 ( ( ( image_int_int @ F @ A4 )
% 0.14/0.44 = A7 )
% 0.14/0.44 => ( ( ( image_nat_nat @ G @ B5 )
% 0.14/0.44 = B7 )
% 0.14/0.44 => ( ( image_7928304878501623365nt_nat @ ( produc5039722323474524658at_nat @ F @ G )
% 0.14/0.44 @ ( produc1456381018704787142nt_nat @ A4
% 0.14/0.44 @ ^ [Uu: int] : B5 ) )
% 0.14/0.44 = ( produc1456381018704787142nt_nat @ A7
% 0.14/0.44 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % map_prod_surj_on
% 0.14/0.44 thf(fact_1771_left__total__OO,axiom,
% 0.14/0.44 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 0.14/0.44 ( ( left_t5646938096895998950at_nat @ R3 )
% 0.14/0.44 => ( ( left_t1861001511420785031at_int @ S5 )
% 0.14/0.44 => ( left_t1861001511420785031at_int @ ( relcom8911704206367525917at_int @ R3 @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % left_total_OO
% 0.14/0.44 thf(fact_1772_left__total__OO,axiom,
% 0.14/0.44 ! [R3: int > int > $o,S5: int > code_integer > $o] :
% 0.14/0.44 ( ( left_total_int_int @ R3 )
% 0.14/0.44 => ( ( left_t2374113004080657585nteger @ S5 )
% 0.14/0.44 => ( left_t2374113004080657585nteger @ ( relcom967497705283160040nteger @ R3 @ S5 ) ) ) ) ).
% 0.14/0.44
% 0.14/0.44 % left_total_OO
% 0.14/0.44 thf(fact_1773_left__unique__OO,axiom,
% 0.14/0.44 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 0.14/0.45 ( ( left_u7296345956935681743at_nat @ R3 )
% 0.14/0.45 => ( ( left_u4005249686606446046at_int @ S5 )
% 0.14/0.45 => ( left_u4005249686606446046at_int @ ( relcom8911704206367525917at_int @ R3 @ S5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % left_unique_OO
% 0.14/0.45 thf(fact_1774_left__unique__OO,axiom,
% 0.14/0.45 ! [R3: int > int > $o,S5: int > code_integer > $o] :
% 0.14/0.45 ( ( left_unique_int_int @ R3 )
% 0.14/0.45 => ( ( left_u6795595883297946906nteger @ S5 )
% 0.14/0.45 => ( left_u6795595883297946906nteger @ ( relcom967497705283160040nteger @ R3 @ S5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % left_unique_OO
% 0.14/0.45 thf(fact_1775_Product__Type_Oproduct__def,axiom,
% 0.14/0.45 ( produc929334515565554804at_nat
% 0.14/0.45 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.14/0.45 ( produc457027306803732586at_nat @ A6
% 0.14/0.45 @ ^ [Uu: nat] : B6 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Product_Type.product_def
% 0.14/0.45 thf(fact_1776_member__product,axiom,
% 0.14/0.45 ! [X2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat] :
% 0.14/0.45 ( ( member8757157785044589968at_nat @ X2 @ ( produc3241716407206042770at_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( member8757157785044589968at_nat @ X2
% 0.14/0.45 @ ( produc7726050920695093128at_nat @ A4
% 0.14/0.45 @ ^ [Uu: set_Pr1261947904930325089at_nat] : B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % member_product
% 0.14/0.45 thf(fact_1777_member__product,axiom,
% 0.14/0.45 ! [X2: product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ X2 @ ( produc929334515565554804at_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( member8440522571783428010at_nat @ X2
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % member_product
% 0.14/0.45 thf(fact_1778_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_262127665112854123t_unit @ produc6786084904866402309t_unit
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_262127665112854123t_unit @ produc6786084904866402309t_unit
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1779_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_1801747192096393899it_o_o @ produc7461459235754980752unit_o
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_1801747192096393899it_o_o @ produc7461459235754980752unit_o
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1780_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_6725568594985674851at_nat @ produc996414825743149016it_nat
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_6725568594985674851at_nat @ produc996414825743149016it_nat
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1781_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_4419268941131634678t_unit @ produc2875488738488844090t_unit
% 0.14/0.45 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_4419268941131634678t_unit @ produc2875488738488844090t_unit
% 0.14/0.45 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1782_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1783_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 0.14/0.45 @ ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 0.14/0.45 @ ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1784_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_5511522805742971924t_unit @ produc8850949007409916470t_unit
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_5511522805742971924t_unit @ produc8850949007409916470t_unit
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1785_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 0.14/0.45 @ ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 0.14/0.45 @ ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1786_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1787_snd__image__times,axiom,
% 0.14/0.45 ! [A4: set_ref_a,B5: set_he8644174446132254637t_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_ref_a )
% 0.14/0.45 => ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit
% 0.14/0.45 @ ( produc3946373962484743846t_unit @ A4
% 0.14/0.45 @ ^ [Uu: ref_a] : B5 ) )
% 0.14/0.45 = bot_bo3686245532977126937t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_ref_a )
% 0.14/0.45 => ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit
% 0.14/0.45 @ ( produc3946373962484743846t_unit @ A4
% 0.14/0.45 @ ^ [Uu: ref_a] : B5 ) )
% 0.14/0.45 = B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_times
% 0.14/0.45 thf(fact_1788_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_Product_unit,A4: set_Product_unit] :
% 0.14/0.45 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_262127665112854123t_unit @ produc6963936691090040003t_unit
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_262127665112854123t_unit @ produc6963936691090040003t_unit
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1789_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_Product_unit,A4: set_o] :
% 0.14/0.45 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit
% 0.14/0.45 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit
% 0.14/0.45 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1790_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_Product_unit,A4: set_nat] :
% 0.14/0.45 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1791_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_o,A4: set_Product_unit] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_4246157487713968288t_unit @ produc582253812616888142unit_o
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_4246157487713968288t_unit @ produc582253812616888142unit_o
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1792_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_o,A4: set_o] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1793_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_o,A4: set_nat] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_o )
% 0.14/0.45 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 0.14/0.45 @ ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_o )
% 0.14/0.45 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 0.14/0.45 @ ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1794_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_nat,A4: set_Product_unit] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_7474191388529947450t_unit @ produc5169466786534984090it_nat
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_7474191388529947450t_unit @ produc5169466786534984090it_nat
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1795_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_nat,A4: set_o] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 0.14/0.45 @ ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 0.14/0.45 @ ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1796_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_nat,A4: set_nat] :
% 0.14/0.45 ( ( ( B5 = bot_bot_set_nat )
% 0.14/0.45 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( B5 != bot_bot_set_nat )
% 0.14/0.45 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1797_fst__image__times,axiom,
% 0.14/0.45 ! [B5: set_he8644174446132254637t_unit,A4: set_ref_a] :
% 0.14/0.45 ( ( ( B5 = bot_bo3686245532977126937t_unit )
% 0.14/0.45 => ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit
% 0.14/0.45 @ ( produc3946373962484743846t_unit @ A4
% 0.14/0.45 @ ^ [Uu: ref_a] : B5 ) )
% 0.14/0.45 = bot_bot_set_ref_a ) )
% 0.14/0.45 & ( ( B5 != bot_bo3686245532977126937t_unit )
% 0.14/0.45 => ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit
% 0.14/0.45 @ ( produc3946373962484743846t_unit @ A4
% 0.14/0.45 @ ^ [Uu: ref_a] : B5 ) )
% 0.14/0.45 = A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_times
% 0.14/0.45 thf(fact_1798_image__is__empty,axiom,
% 0.14/0.45 ! [F: int > int,A4: set_int] :
% 0.14/0.45 ( ( ( image_int_int @ F @ A4 )
% 0.14/0.45 = bot_bot_set_int )
% 0.14/0.45 = ( A4 = bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1799_image__is__empty,axiom,
% 0.14/0.45 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.45 ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.45 = bot_bot_set_rat )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1800_image__is__empty,axiom,
% 0.14/0.45 ! [F: nat > int,A4: set_nat] :
% 0.14/0.45 ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.45 = bot_bot_set_int )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1801_image__is__empty,axiom,
% 0.14/0.45 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 0.14/0.45 ( ( ( image_405062704495631173t_unit @ F @ A4 )
% 0.14/0.45 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1802_image__is__empty,axiom,
% 0.14/0.45 ! [F: $o > product_unit,A4: set_o] :
% 0.14/0.45 ( ( ( image_o_Product_unit @ F @ A4 )
% 0.14/0.45 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 = ( A4 = bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1803_image__is__empty,axiom,
% 0.14/0.45 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.45 ( ( ( image_8730104196221521654t_unit @ F @ A4 )
% 0.14/0.45 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1804_image__is__empty,axiom,
% 0.14/0.45 ! [F: product_unit > $o,A4: set_Product_unit] :
% 0.14/0.45 ( ( ( image_Product_unit_o @ F @ A4 )
% 0.14/0.45 = bot_bot_set_o )
% 0.14/0.45 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1805_image__is__empty,axiom,
% 0.14/0.45 ! [F: $o > $o,A4: set_o] :
% 0.14/0.45 ( ( ( image_o_o @ F @ A4 )
% 0.14/0.45 = bot_bot_set_o )
% 0.14/0.45 = ( A4 = bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1806_image__is__empty,axiom,
% 0.14/0.45 ! [F: nat > $o,A4: set_nat] :
% 0.14/0.45 ( ( ( image_nat_o @ F @ A4 )
% 0.14/0.45 = bot_bot_set_o )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1807_image__is__empty,axiom,
% 0.14/0.45 ! [F: int > nat,A4: set_int] :
% 0.14/0.45 ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.45 = bot_bot_set_nat )
% 0.14/0.45 = ( A4 = bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_is_empty
% 0.14/0.45 thf(fact_1808_empty__is__image,axiom,
% 0.14/0.45 ! [F: int > int,A4: set_int] :
% 0.14/0.45 ( ( bot_bot_set_int
% 0.14/0.45 = ( image_int_int @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1809_empty__is__image,axiom,
% 0.14/0.45 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.45 ( ( bot_bot_set_rat
% 0.14/0.45 = ( image_nat_rat @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1810_empty__is__image,axiom,
% 0.14/0.45 ! [F: nat > int,A4: set_nat] :
% 0.14/0.45 ( ( bot_bot_set_int
% 0.14/0.45 = ( image_nat_int @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1811_empty__is__image,axiom,
% 0.14/0.45 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 0.14/0.45 ( ( bot_bo3957492148770167129t_unit
% 0.14/0.45 = ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1812_empty__is__image,axiom,
% 0.14/0.45 ! [F: $o > product_unit,A4: set_o] :
% 0.14/0.45 ( ( bot_bo3957492148770167129t_unit
% 0.14/0.45 = ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1813_empty__is__image,axiom,
% 0.14/0.45 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.45 ( ( bot_bo3957492148770167129t_unit
% 0.14/0.45 = ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1814_empty__is__image,axiom,
% 0.14/0.45 ! [F: product_unit > $o,A4: set_Product_unit] :
% 0.14/0.45 ( ( bot_bot_set_o
% 0.14/0.45 = ( image_Product_unit_o @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1815_empty__is__image,axiom,
% 0.14/0.45 ! [F: $o > $o,A4: set_o] :
% 0.14/0.45 ( ( bot_bot_set_o
% 0.14/0.45 = ( image_o_o @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1816_empty__is__image,axiom,
% 0.14/0.45 ! [F: nat > $o,A4: set_nat] :
% 0.14/0.45 ( ( bot_bot_set_o
% 0.14/0.45 = ( image_nat_o @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1817_empty__is__image,axiom,
% 0.14/0.45 ! [F: int > nat,A4: set_int] :
% 0.14/0.45 ( ( bot_bot_set_nat
% 0.14/0.45 = ( image_int_nat @ F @ A4 ) )
% 0.14/0.45 = ( A4 = bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % empty_is_image
% 0.14/0.45 thf(fact_1818_image__empty,axiom,
% 0.14/0.45 ! [F: int > int] :
% 0.14/0.45 ( ( image_int_int @ F @ bot_bot_set_int )
% 0.14/0.45 = bot_bot_set_int ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1819_image__empty,axiom,
% 0.14/0.45 ! [F: int > nat] :
% 0.14/0.45 ( ( image_int_nat @ F @ bot_bot_set_int )
% 0.14/0.45 = bot_bot_set_nat ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1820_image__empty,axiom,
% 0.14/0.45 ! [F: product_unit > product_unit] :
% 0.14/0.45 ( ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1821_image__empty,axiom,
% 0.14/0.45 ! [F: product_unit > $o] :
% 0.14/0.45 ( ( image_Product_unit_o @ F @ bot_bo3957492148770167129t_unit )
% 0.14/0.45 = bot_bot_set_o ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1822_image__empty,axiom,
% 0.14/0.45 ! [F: product_unit > nat] :
% 0.14/0.45 ( ( image_875570014554754200it_nat @ F @ bot_bo3957492148770167129t_unit )
% 0.14/0.45 = bot_bot_set_nat ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1823_image__empty,axiom,
% 0.14/0.45 ! [F: $o > product_unit] :
% 0.14/0.45 ( ( image_o_Product_unit @ F @ bot_bot_set_o )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1824_image__empty,axiom,
% 0.14/0.45 ! [F: $o > $o] :
% 0.14/0.45 ( ( image_o_o @ F @ bot_bot_set_o )
% 0.14/0.45 = bot_bot_set_o ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1825_image__empty,axiom,
% 0.14/0.45 ! [F: $o > nat] :
% 0.14/0.45 ( ( image_o_nat @ F @ bot_bot_set_o )
% 0.14/0.45 = bot_bot_set_nat ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1826_image__empty,axiom,
% 0.14/0.45 ! [F: nat > rat] :
% 0.14/0.45 ( ( image_nat_rat @ F @ bot_bot_set_nat )
% 0.14/0.45 = bot_bot_set_rat ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1827_image__empty,axiom,
% 0.14/0.45 ! [F: nat > int] :
% 0.14/0.45 ( ( image_nat_int @ F @ bot_bot_set_nat )
% 0.14/0.45 = bot_bot_set_int ) ).
% 0.14/0.45
% 0.14/0.45 % image_empty
% 0.14/0.45 thf(fact_1828_Sigma__empty1,axiom,
% 0.14/0.45 ! [B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.45 ( ( produc7726050920695093128at_nat @ bot_bo3083307316010499117at_nat @ B5 )
% 0.14/0.45 = bot_bo228742789529271731at_nat ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty1
% 0.14/0.45 thf(fact_1829_Sigma__empty1,axiom,
% 0.14/0.45 ! [B5: nat > set_nat] :
% 0.14/0.45 ( ( produc457027306803732586at_nat @ bot_bot_set_nat @ B5 )
% 0.14/0.45 = bot_bo2099793752762293965at_nat ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty1
% 0.14/0.45 thf(fact_1830_Sigma__empty2,axiom,
% 0.14/0.45 ! [A4: set_se7855581050983116737at_nat] :
% 0.14/0.45 ( ( produc7726050920695093128at_nat @ A4
% 0.14/0.45 @ ^ [Uu: set_Pr1261947904930325089at_nat] : bot_bo3083307316010499117at_nat )
% 0.14/0.45 = bot_bo228742789529271731at_nat ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty2
% 0.14/0.45 thf(fact_1831_Sigma__empty2,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : bot_bot_set_nat )
% 0.14/0.45 = bot_bo2099793752762293965at_nat ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty2
% 0.14/0.45 thf(fact_1832_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = bot_bo1654022762305692595t_unit )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1833_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_o] :
% 0.14/0.45 ( ( ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = bot_bo3195362268743713342unit_o )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1834_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_nat] :
% 0.14/0.45 ( ( ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = bot_bo2472676621365177558it_nat )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1835_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = bot_bo4402188677660116584t_unit )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1836_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o] :
% 0.14/0.45 ( ( ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = bot_bo7073875226086086771od_o_o )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1837_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_nat] :
% 0.14/0.45 ( ( ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = bot_bo66526543525301729_o_nat )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1838_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_Product_unit] :
% 0.14/0.45 ( ( ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = bot_bo5043309098482578556t_unit )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1839_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_o] :
% 0.14/0.45 ( ( ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = bot_bo1114129665703605383_nat_o )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1840_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.45 ( ( ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = bot_bo2099793752762293965at_nat )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1841_Times__empty,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ( produc3904733337175673596at_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = bot_bo6659885642593197735at_nat )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Times_empty
% 0.14/0.45 thf(fact_1842_Collect__const__case__prod,axiom,
% 0.14/0.45 ! [P2: $o] :
% 0.14/0.45 ( ( P2
% 0.14/0.45 => ( ( collec6321179662152712658at_nat
% 0.14/0.45 @ ( produc410239310623530412_nat_o
% 0.14/0.45 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P2 ) )
% 0.14/0.45 = top_to6833984726390702231at_nat ) )
% 0.14/0.45 & ( ~ P2
% 0.14/0.45 => ( ( collec6321179662152712658at_nat
% 0.14/0.45 @ ( produc410239310623530412_nat_o
% 0.14/0.45 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P2 ) )
% 0.14/0.45 = bot_bo228742789529271731at_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Collect_const_case_prod
% 0.14/0.45 thf(fact_1843_Collect__const__case__prod,axiom,
% 0.14/0.45 ! [P2: $o] :
% 0.14/0.45 ( ( P2
% 0.14/0.45 => ( ( collec3392354462482085612at_nat
% 0.14/0.45 @ ( produc6081775807080527818_nat_o
% 0.14/0.45 @ ^ [A5: nat,B4: nat] : P2 ) )
% 0.14/0.45 = top_to4669805908274784177at_nat ) )
% 0.14/0.45 & ( ~ P2
% 0.14/0.45 => ( ( collec3392354462482085612at_nat
% 0.14/0.45 @ ( produc6081775807080527818_nat_o
% 0.14/0.45 @ ^ [A5: nat,B4: nat] : P2 ) )
% 0.14/0.45 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Collect_const_case_prod
% 0.14/0.45 thf(fact_1844_Collect__const__case__prod,axiom,
% 0.14/0.45 ! [P2: $o] :
% 0.14/0.45 ( ( P2
% 0.14/0.45 => ( ( collec213857154873943460nt_int
% 0.14/0.45 @ ( produc4947309494688390418_int_o
% 0.14/0.45 @ ^ [A5: int,B4: int] : P2 ) )
% 0.14/0.45 = top_to4366644338036079209nt_int ) )
% 0.14/0.45 & ( ~ P2
% 0.14/0.45 => ( ( collec213857154873943460nt_int
% 0.14/0.45 @ ( produc4947309494688390418_int_o
% 0.14/0.45 @ ^ [A5: int,B4: int] : P2 ) )
% 0.14/0.45 = bot_bo1796632182523588997nt_int ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Collect_const_case_prod
% 0.14/0.45 thf(fact_1845_Sigma__empty__iff,axiom,
% 0.14/0.45 ! [I3: set_se7855581050983116737at_nat,X5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.45 ( ( ( produc7726050920695093128at_nat @ I3 @ X5 )
% 0.14/0.45 = bot_bo228742789529271731at_nat )
% 0.14/0.45 = ( ! [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( member2643936169264416010at_nat @ X4 @ I3 )
% 0.14/0.45 => ( ( X5 @ X4 )
% 0.14/0.45 = bot_bo3083307316010499117at_nat ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty_iff
% 0.14/0.45 thf(fact_1846_Sigma__empty__iff,axiom,
% 0.14/0.45 ! [I3: set_nat,X5: nat > set_nat] :
% 0.14/0.45 ( ( ( produc457027306803732586at_nat @ I3 @ X5 )
% 0.14/0.45 = bot_bo2099793752762293965at_nat )
% 0.14/0.45 = ( ! [X4: nat] :
% 0.14/0.45 ( ( member_nat @ X4 @ I3 )
% 0.14/0.45 => ( ( X5 @ X4 )
% 0.14/0.45 = bot_bot_set_nat ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_empty_iff
% 0.14/0.45 thf(fact_1847_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_int] :
% 0.14/0.45 ( ! [X: int] :
% 0.14/0.45 ~ ( member_int @ X @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_int @ A4 @ bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1848_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ! [X: product_unit] :
% 0.14/0.45 ~ ( member_Product_unit @ X @ A4 )
% 0.14/0.45 => ( ord_le3507040750410214029t_unit @ A4 @ bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1849_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.45 ~ ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.45 => ( ord_le1268244103169919719at_nat @ A4 @ bot_bo228742789529271731at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1850_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ! [X: product_prod_nat_nat] :
% 0.14/0.45 ~ ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.45 => ( ord_le3146513528884898305at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1851_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_o] :
% 0.14/0.45 ( ! [X: $o] :
% 0.14/0.45 ~ ( member_o @ X @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1852_subset__emptyI,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ! [X: nat] :
% 0.14/0.45 ~ ( member_nat @ X @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % subset_emptyI
% 0.14/0.45 thf(fact_1853_less__by__empty,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( A4 = bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ).
% 0.14/0.45
% 0.14/0.45 % less_by_empty
% 0.14/0.45 thf(fact_1854_less__by__empty,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( A4 = bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ).
% 0.14/0.45
% 0.14/0.45 % less_by_empty
% 0.14/0.45 thf(fact_1855_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_Product_unit,C3: set_Product_unit,D: set_Product_unit] :
% 0.14/0.45 ( ( ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = ( produc6121607364029222536t_unit @ C3
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1856_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_o,C3: set_Product_unit,D: set_o] :
% 0.14/0.45 ( ( ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = ( produc4996980317674386579unit_o @ C3
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1857_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_nat,C3: set_Product_unit,D: set_nat] :
% 0.14/0.45 ( ( ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = ( produc6875377002296012693it_nat @ C3
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1858_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_Product_unit,C3: set_o,D: set_Product_unit] :
% 0.14/0.45 ( ( ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = ( produc411009820408249917t_unit @ C3
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1859_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: set_o,D: set_o] :
% 0.14/0.45 ( ( ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = ( product_Sigma_o_o @ C3
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1860_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_nat,C3: set_o,D: set_nat] :
% 0.14/0.45 ( ( ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : B5 )
% 0.14/0.45 = ( product_Sigma_o_nat @ C3
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1861_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_Product_unit,C3: set_nat,D: set_Product_unit] :
% 0.14/0.45 ( ( ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = ( produc5506539147108004339t_unit @ C3
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1862_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_o,C3: set_nat,D: set_o] :
% 0.14/0.45 ( ( ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = ( product_Sigma_nat_o @ C3
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1863_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: set_nat,D: set_nat] :
% 0.14/0.45 ( ( ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 )
% 0.14/0.45 = ( produc457027306803732586at_nat @ C3
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( B5 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1864_times__eq__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,B5: set_Pr1261947904930325089at_nat,C3: set_Product_unit,D: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ( produc3904733337175673596at_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : B5 )
% 0.14/0.45 = ( produc3904733337175673596at_nat @ C3
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( ( A4 = C3 )
% 0.14/0.45 & ( B5 = D ) )
% 0.14/0.45 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( B5 = bot_bo2099793752762293965at_nat ) )
% 0.14/0.45 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( D = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_eq_iff
% 0.14/0.45 thf(fact_1865_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C3: set_Product_unit,B5: set_Product_unit,D: set_Product_unit] :
% 0.14/0.45 ( ( ord_le930853871177014503t_unit
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : C3 )
% 0.14/0.45 @ ( produc6121607364029222536t_unit @ B5
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.45 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1866_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C3: set_o,B5: set_Product_unit,D: set_o] :
% 0.14/0.45 ( ( ord_le8534741403851954546unit_o
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : C3 )
% 0.14/0.45 @ ( produc4996980317674386579unit_o @ B5
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1867_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C3: set_nat,B5: set_Product_unit,D: set_nat] :
% 0.14/0.45 ( ( ord_le8121013740822022818it_nat
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : C3 )
% 0.14/0.45 @ ( produc6875377002296012693it_nat @ B5
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1868_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_o,C3: set_Product_unit,B5: set_o,D: set_Product_unit] :
% 0.14/0.45 ( ( ord_le518195775913581980t_unit
% 0.14/0.45 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.45 @ ^ [Uu: $o] : C3 )
% 0.14/0.45 @ ( produc411009820408249917t_unit @ B5
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.45 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1869_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_o,C3: set_o,B5: set_o,D: set_o] :
% 0.14/0.45 ( ( ord_le192195778054999463od_o_o
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : C3 )
% 0.14/0.45 @ ( product_Sigma_o_o @ B5
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1870_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_o,C3: set_nat,B5: set_o,D: set_nat] :
% 0.14/0.45 ( ( ord_le6472378536984071597_o_nat
% 0.14/0.45 @ ( product_Sigma_o_nat @ A4
% 0.14/0.45 @ ^ [Uu: $o] : C3 )
% 0.14/0.45 @ ( product_Sigma_o_nat @ B5
% 0.14/0.45 @ ^ [Uu: $o] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_o )
% 0.14/0.45 | ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1871_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,C3: set_Product_unit,B5: set_nat,D: set_Product_unit] :
% 0.14/0.45 ( ( ord_le1468274181084648008t_unit
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.45 @ ^ [Uu: nat] : C3 )
% 0.14/0.45 @ ( produc5506539147108004339t_unit @ B5
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.45 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1872_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,C3: set_o,B5: set_nat,D: set_o] :
% 0.14/0.45 ( ( ord_le7519981659162375251_nat_o
% 0.14/0.45 @ ( product_Sigma_nat_o @ A4
% 0.14/0.45 @ ^ [Uu: nat] : C3 )
% 0.14/0.45 @ ( product_Sigma_nat_o @ B5
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( C3 = bot_bot_set_o )
% 0.14/0.45 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1873_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_nat,C3: set_nat,B5: set_nat,D: set_nat] :
% 0.14/0.45 ( ( ord_le3146513528884898305at_nat
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : C3 )
% 0.14/0.45 @ ( produc457027306803732586at_nat @ B5
% 0.14/0.45 @ ^ [Uu: nat] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 | ( C3 = bot_bot_set_nat )
% 0.14/0.45 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.45 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1874_times__subset__iff,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C3: set_Pr1261947904930325089at_nat,B5: set_Product_unit,D: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ord_le8681960759543468507at_nat
% 0.14/0.45 @ ( produc3904733337175673596at_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_unit] : C3 )
% 0.14/0.45 @ ( produc3904733337175673596at_nat @ B5
% 0.14/0.45 @ ^ [Uu: product_unit] : D ) )
% 0.14/0.45 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 | ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.45 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.45 & ( ord_le3146513528884898305at_nat @ C3 @ D ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % times_subset_iff
% 0.14/0.45 thf(fact_1875_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_o,B5: $o > set_Product_unit] :
% 0.14/0.45 ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit @ ( produc411009820408249917t_unit @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_o
% 0.14/0.45 @ ^ [X4: $o] :
% 0.14/0.45 ( ( member_o @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1876_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_int,B5: int > set_Product_unit] :
% 0.14/0.45 ( ( image_7716461468295075337it_int @ produc917050878549155996t_unit @ ( produc2622961094310184599t_unit @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_int
% 0.14/0.45 @ ^ [X4: int] :
% 0.14/0.45 ( ( member_int @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1877_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: nat > set_Product_unit] :
% 0.14/0.45 ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit @ ( produc5506539147108004339t_unit @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_nat
% 0.14/0.45 @ ^ [X4: nat] :
% 0.14/0.45 ( ( member_nat @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1878_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_o,B5: $o > set_o] :
% 0.14/0.45 ( ( image_7896445794123959606_o_o_o @ product_fst_o_o @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_o
% 0.14/0.45 @ ^ [X4: $o] :
% 0.14/0.45 ( ( member_o @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_o ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1879_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_int,B5: int > set_o] :
% 0.14/0.45 ( ( image_90517134139374612_o_int @ product_fst_int_o @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_int
% 0.14/0.45 @ ^ [X4: int] :
% 0.14/0.45 ( ( member_int @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_o ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1880_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: nat > set_o] :
% 0.14/0.45 ( ( image_8629803608462650132_o_nat @ product_fst_nat_o @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_nat
% 0.14/0.45 @ ^ [X4: nat] :
% 0.14/0.45 ( ( member_nat @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_o ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1881_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_o,B5: $o > set_nat] :
% 0.14/0.45 ( ( image_8105710389281276538_nat_o @ product_fst_o_nat @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_o
% 0.14/0.45 @ ^ [X4: $o] :
% 0.14/0.45 ( ( member_o @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_nat ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1882_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_int,B5: int > set_nat] :
% 0.14/0.45 ( ( image_2855239504505064772at_int @ product_fst_int_nat @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_int
% 0.14/0.45 @ ^ [X4: int] :
% 0.14/0.45 ( ( member_int @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_nat ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1883_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( image_2486076414777270412at_nat @ product_fst_nat_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_nat
% 0.14/0.45 @ ^ [X4: nat] :
% 0.14/0.45 ( ( member_nat @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bot_set_nat ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1884_fst__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_ref_a,B5: ref_a > set_he8644174446132254637t_unit] :
% 0.14/0.45 ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ ( produc3946373962484743846t_unit @ A4 @ B5 ) )
% 0.14/0.45 = ( collect_ref_a
% 0.14/0.45 @ ^ [X4: ref_a] :
% 0.14/0.45 ( ( member_ref_a @ X4 @ A4 )
% 0.14/0.45 & ( ( B5 @ X4 )
% 0.14/0.45 != bot_bo3686245532977126937t_unit ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % fst_image_Sigma
% 0.14/0.45 thf(fact_1885_rp__inv__image__rp,axiom,
% 0.14/0.45 ! [P2: produc1319942482725812455at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( fun_re2478310338295953701at_nat @ P2 )
% 0.14/0.45 => ( fun_re2478310338295953701at_nat @ ( fun_rp8445993449185644698at_nat @ P2 @ F ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % rp_inv_image_rp
% 0.14/0.45 thf(fact_1886_the__elem__image__unique,axiom,
% 0.14/0.45 ! [A4: set_int,F: int > nat,X2: int] :
% 0.14/0.45 ( ( A4 != bot_bot_set_int )
% 0.14/0.45 => ( ! [Y: int] :
% 0.14/0.45 ( ( member_int @ Y @ A4 )
% 0.14/0.45 => ( ( F @ Y )
% 0.14/0.45 = ( F @ X2 ) ) )
% 0.14/0.45 => ( ( the_elem_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.45 = ( F @ X2 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % the_elem_image_unique
% 0.14/0.45 thf(fact_1887_the__elem__image__unique,axiom,
% 0.14/0.45 ! [A4: set_int,F: int > int,X2: int] :
% 0.14/0.45 ( ( A4 != bot_bot_set_int )
% 0.14/0.45 => ( ! [Y: int] :
% 0.14/0.45 ( ( member_int @ Y @ A4 )
% 0.14/0.45 => ( ( F @ Y )
% 0.14/0.45 = ( F @ X2 ) ) )
% 0.14/0.45 => ( ( the_elem_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.45 = ( F @ X2 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % the_elem_image_unique
% 0.14/0.45 thf(fact_1888_the__elem__image__unique,axiom,
% 0.14/0.45 ! [A4: set_nat,F: nat > rat,X2: nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ! [Y: nat] :
% 0.14/0.45 ( ( member_nat @ Y @ A4 )
% 0.14/0.45 => ( ( F @ Y )
% 0.14/0.45 = ( F @ X2 ) ) )
% 0.14/0.45 => ( ( the_elem_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.45 = ( F @ X2 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % the_elem_image_unique
% 0.14/0.45 thf(fact_1889_the__elem__image__unique,axiom,
% 0.14/0.45 ! [A4: set_nat,F: nat > nat,X2: nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ! [Y: nat] :
% 0.14/0.45 ( ( member_nat @ Y @ A4 )
% 0.14/0.45 => ( ( F @ Y )
% 0.14/0.45 = ( F @ X2 ) ) )
% 0.14/0.45 => ( ( the_elem_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.45 = ( F @ X2 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % the_elem_image_unique
% 0.14/0.45 thf(fact_1890_the__elem__image__unique,axiom,
% 0.14/0.45 ! [A4: set_nat,F: nat > int,X2: nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ! [Y: nat] :
% 0.14/0.45 ( ( member_nat @ Y @ A4 )
% 0.14/0.45 => ( ( F @ Y )
% 0.14/0.45 = ( F @ X2 ) ) )
% 0.14/0.45 => ( ( the_elem_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.45 = ( F @ X2 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % the_elem_image_unique
% 0.14/0.45 thf(fact_1891_snd__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_ref_a,B5: ref_a > set_he8644174446132254637t_unit] :
% 0.14/0.45 ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ ( produc3946373962484743846t_unit @ A4 @ B5 ) )
% 0.14/0.45 = ( comple6989579708249578522t_unit @ ( image_5570573867351727369t_unit @ B5 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_Sigma
% 0.14/0.45 thf(fact_1892_snd__image__Sigma,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( image_2486076414777270412at_nat @ product_snd_nat_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % snd_image_Sigma
% 0.14/0.45 thf(fact_1893_range__constant,axiom,
% 0.14/0.45 ! [X2: product_unit] :
% 0.14/0.45 ( ( image_4337914935673063477t_unit
% 0.14/0.45 @ ^ [Uu: char] : X2
% 0.14/0.45 @ top_top_set_char )
% 0.14/0.45 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1894_range__constant,axiom,
% 0.14/0.45 ! [X2: $o] :
% 0.14/0.45 ( ( image_char_o
% 0.14/0.45 @ ^ [Uu: char] : X2
% 0.14/0.45 @ top_top_set_char )
% 0.14/0.45 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1895_range__constant,axiom,
% 0.14/0.45 ! [X2: nat] :
% 0.14/0.45 ( ( image_char_nat
% 0.14/0.45 @ ^ [Uu: char] : X2
% 0.14/0.45 @ top_top_set_char )
% 0.14/0.45 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1896_range__constant,axiom,
% 0.14/0.45 ! [X2: product_unit] :
% 0.14/0.45 ( ( image_2327579789247107822t_unit
% 0.14/0.45 @ ^ [Uu: rat] : X2
% 0.14/0.45 @ top_top_set_rat )
% 0.14/0.45 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1897_range__constant,axiom,
% 0.14/0.45 ! [X2: $o] :
% 0.14/0.45 ( ( image_rat_o
% 0.14/0.45 @ ^ [Uu: rat] : X2
% 0.14/0.45 @ top_top_set_rat )
% 0.14/0.45 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1898_range__constant,axiom,
% 0.14/0.45 ! [X2: nat] :
% 0.14/0.45 ( ( image_rat_nat
% 0.14/0.45 @ ^ [Uu: rat] : X2
% 0.14/0.45 @ top_top_set_rat )
% 0.14/0.45 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1899_range__constant,axiom,
% 0.14/0.45 ! [X2: rat] :
% 0.14/0.45 ( ( image_nat_rat
% 0.14/0.45 @ ^ [Uu: nat] : X2
% 0.14/0.45 @ top_top_set_nat )
% 0.14/0.45 = ( insert_rat @ X2 @ bot_bot_set_rat ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1900_range__constant,axiom,
% 0.14/0.45 ! [X2: int] :
% 0.14/0.45 ( ( image_nat_int
% 0.14/0.45 @ ^ [Uu: nat] : X2
% 0.14/0.45 @ top_top_set_nat )
% 0.14/0.45 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1901_range__constant,axiom,
% 0.14/0.45 ! [X2: product_unit] :
% 0.14/0.45 ( ( image_8730104196221521654t_unit
% 0.14/0.45 @ ^ [Uu: nat] : X2
% 0.14/0.45 @ top_top_set_nat )
% 0.14/0.45 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1902_range__constant,axiom,
% 0.14/0.45 ! [X2: $o] :
% 0.14/0.45 ( ( image_nat_o
% 0.14/0.45 @ ^ [Uu: nat] : X2
% 0.14/0.45 @ top_top_set_nat )
% 0.14/0.45 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % range_constant
% 0.14/0.45 thf(fact_1903_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_char] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_5325685772115642575t_char
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_char ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_5325685772115642575t_char
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1904_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_char] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_o_set_char
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_char ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_o_set_char
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1905_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_char] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_nat_set_char
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_char ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7965528767983648192t_char
% 0.14/0.45 @ ( image_nat_set_char
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1906_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_rat] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_4665621433434589782et_rat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_rat ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_4665621433434589782et_rat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1907_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_rat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_o_set_rat
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_rat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_o_set_rat
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1908_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_rat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_nat_set_rat
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_rat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple4298007329820168263et_rat
% 0.14/0.45 @ ( image_nat_set_rat
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1909_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_int] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_3995998972318789802et_int
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_int ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_3995998972318789802et_int
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1910_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_int] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_o_set_int
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_int ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_o_set_int
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1911_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_int] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_nat_set_int
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_int ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3628384868704368283et_int
% 0.14/0.45 @ ( image_nat_set_int
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1912_INT__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = top_top_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_constant
% 0.14/0.45 thf(fact_1913_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > code_integer > $o,R7: code_integer > code_integer > $o,S5: num > num > $o,S6: num > num > $o] :
% 0.14/0.45 ( ( left_u6795595883297946906nteger @ R3 )
% 0.14/0.45 => ( ( right_7281159819619925802nteger @ R3 )
% 0.14/0.45 => ( ( right_5866438497372881682nteger @ R7 )
% 0.14/0.45 => ( ( left_t2884206969071330nteger @ R7 )
% 0.14/0.45 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1914_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > code_integer > $o,R7: code_integer > int > $o,S5: num > num > $o,S6: num > num > $o] :
% 0.14/0.45 ( ( left_u6795595883297946906nteger @ R3 )
% 0.14/0.45 => ( ( right_7281159819619925802nteger @ R3 )
% 0.14/0.45 => ( ( right_7836862732553076961er_int @ R7 )
% 0.14/0.45 => ( ( left_t1735413524555719857er_int @ R7 )
% 0.14/0.45 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1915_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > int > $o,R7: int > int > $o,S5: num > num > $o,S6: num > num > $o] :
% 0.14/0.45 ( ( left_unique_int_int @ R3 )
% 0.14/0.45 => ( ( right_total_int_int @ R3 )
% 0.14/0.45 => ( ( right_unique_int_int @ R7 )
% 0.14/0.45 => ( ( left_total_int_int @ R7 )
% 0.14/0.45 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1916_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: num > num > $o,S6: num > num > $o] :
% 0.14/0.45 ( ( left_unique_int_int @ R3 )
% 0.14/0.45 => ( ( right_total_int_int @ R3 )
% 0.14/0.45 => ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1917_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: int > int > $o,S6: int > code_integer > $o] :
% 0.14/0.45 ( ( left_unique_int_int @ R3 )
% 0.14/0.45 => ( ( right_total_int_int @ R3 )
% 0.14/0.45 => ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ord_le7522433683449569238eger_o @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1918_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: product_prod_nat_nat > int > $o,R7: int > int > $o,S5: nat > nat > $o,S6: nat > nat > $o] :
% 0.14/0.45 ( ( left_u4005249686606446046at_int @ R3 )
% 0.14/0.45 => ( ( right_1157779049177982926at_int @ R3 )
% 0.14/0.45 => ( ( right_unique_int_int @ R7 )
% 0.14/0.45 => ( ( left_total_int_int @ R7 )
% 0.14/0.45 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1919_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: nat > nat > $o,S6: nat > nat > $o] :
% 0.14/0.45 ( ( left_u7296345956935681743at_nat @ R3 )
% 0.14/0.45 => ( ( right_4094035864313884895at_nat @ R3 )
% 0.14/0.45 => ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1920_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: int > int > $o,S6: int > code_integer > $o] :
% 0.14/0.45 ( ( left_u7296345956935681743at_nat @ R3 )
% 0.14/0.45 => ( ( right_4094035864313884895at_nat @ R3 )
% 0.14/0.45 => ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ord_le6141271677531915726eger_o @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1921_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,S6: product_prod_nat_nat > int > $o] :
% 0.14/0.45 ( ( left_unique_int_int @ R3 )
% 0.14/0.45 => ( ( right_total_int_int @ R3 )
% 0.14/0.45 => ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ord_le8615040745438789472_int_o @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1922_neg__fun__distr1,axiom,
% 0.14/0.45 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,S6: product_prod_nat_nat > int > $o] :
% 0.14/0.45 ( ( left_u7296345956935681743at_nat @ R3 )
% 0.14/0.45 => ( ( right_4094035864313884895at_nat @ R3 )
% 0.14/0.45 => ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ord_le2484784447047653514_int_o @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr1
% 0.14/0.45 thf(fact_1923_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: code_integer > code_integer > $o,S6: num > num > $o,R3: int > code_integer > $o,S5: num > num > $o] :
% 0.14/0.45 ( ( right_5866438497372881682nteger @ R7 )
% 0.14/0.45 => ( ( left_t2884206969071330nteger @ R7 )
% 0.14/0.45 => ( ( left_unique_num_num @ S6 )
% 0.14/0.45 => ( ( right_total_num_num @ S6 )
% 0.14/0.45 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1924_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: code_integer > int > $o,S6: num > num > $o,R3: int > code_integer > $o,S5: num > num > $o] :
% 0.14/0.45 ( ( right_7836862732553076961er_int @ R7 )
% 0.14/0.45 => ( ( left_t1735413524555719857er_int @ R7 )
% 0.14/0.45 => ( ( left_unique_num_num @ S6 )
% 0.14/0.45 => ( ( right_total_num_num @ S6 )
% 0.14/0.45 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1925_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: int > int > $o,S6: num > num > $o,R3: int > int > $o,S5: num > num > $o] :
% 0.14/0.45 ( ( right_unique_int_int @ R7 )
% 0.14/0.45 => ( ( left_total_int_int @ R7 )
% 0.14/0.45 => ( ( left_unique_num_num @ S6 )
% 0.14/0.45 => ( ( right_total_num_num @ S6 )
% 0.14/0.45 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1926_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: int > code_integer > $o,S6: num > num > $o,R3: int > int > $o,S5: num > num > $o] :
% 0.14/0.45 ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ( left_unique_num_num @ S6 )
% 0.14/0.45 => ( ( right_total_num_num @ S6 )
% 0.14/0.45 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1927_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: int > code_integer > $o,S6: int > code_integer > $o,R3: int > int > $o,S5: int > int > $o] :
% 0.14/0.45 ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ( left_u6795595883297946906nteger @ S6 )
% 0.14/0.45 => ( ( right_7281159819619925802nteger @ S6 )
% 0.14/0.45 => ( ord_le7522433683449569238eger_o @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1928_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: int > int > $o,S6: nat > nat > $o,R3: product_prod_nat_nat > int > $o,S5: nat > nat > $o] :
% 0.14/0.45 ( ( right_unique_int_int @ R7 )
% 0.14/0.45 => ( ( left_total_int_int @ R7 )
% 0.14/0.45 => ( ( left_unique_nat_nat @ S6 )
% 0.14/0.45 => ( ( right_total_nat_nat @ S6 )
% 0.14/0.45 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1929_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: product_prod_nat_nat > int > $o,S6: nat > nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: nat > nat > $o] :
% 0.14/0.45 ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ( left_unique_nat_nat @ S6 )
% 0.14/0.45 => ( ( right_total_nat_nat @ S6 )
% 0.14/0.45 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1930_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: product_prod_nat_nat > int > $o,S6: int > code_integer > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: int > int > $o] :
% 0.14/0.45 ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ( left_u6795595883297946906nteger @ S6 )
% 0.14/0.45 => ( ( right_7281159819619925802nteger @ S6 )
% 0.14/0.45 => ( ord_le6141271677531915726eger_o @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1931_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: int > code_integer > $o,S6: product_prod_nat_nat > int > $o,R3: int > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.45 ( ( right_8475562212078014689nteger @ R7 )
% 0.14/0.45 => ( ( left_t2374113004080657585nteger @ R7 )
% 0.14/0.45 => ( ( left_u4005249686606446046at_int @ S6 )
% 0.14/0.45 => ( ( right_1157779049177982926at_int @ S6 )
% 0.14/0.45 => ( ord_le8615040745438789472_int_o @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1932_neg__fun__distr2,axiom,
% 0.14/0.45 ! [R7: product_prod_nat_nat > int > $o,S6: product_prod_nat_nat > int > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.45 ( ( right_8621877368619751767at_int @ R7 )
% 0.14/0.45 => ( ( left_t1861001511420785031at_int @ R7 )
% 0.14/0.45 => ( ( left_u4005249686606446046at_int @ S6 )
% 0.14/0.45 => ( ( right_1157779049177982926at_int @ S6 )
% 0.14/0.45 => ( ord_le2484784447047653514_int_o @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % neg_fun_distr2
% 0.14/0.45 thf(fact_1933_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr5564308138774400199at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( ord_le3091953645718357095at_nat @ R
% 0.14/0.45 @ ( produc4441300235185154312at_nat @ A4
% 0.14/0.45 @ ^ [Uu: produc3843707927480180839at_nat] : A4 ) )
% 0.14/0.45 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.45 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.45 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_o7446464703481863270at_nat @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1934_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr8693737435421807431at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ord_le3000389064537975527at_nat @ R
% 0.14/0.45 @ ( produc2761391749766926216at_nat @ A4
% 0.14/0.45 @ ^ [Uu: product_prod_nat_nat] : A4 ) )
% 0.14/0.45 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.45 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_o7122697186039111552at_nat @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1935_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Product_prod_o_o,A4: set_o] :
% 0.14/0.45 ( ( ord_le192195778054999463od_o_o @ R
% 0.14/0.45 @ ( product_Sigma_o_o @ A4
% 0.14/0.45 @ ^ [Uu: $o] : A4 ) )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_on_o @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1936_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr7459493094073627847at_nat,A4: set_se5479201105039950375at_nat] :
% 0.14/0.45 ( ( ord_le5997549366648089703at_nat @ R
% 0.14/0.45 @ ( produc6258361011560675592at_nat @ A4
% 0.14/0.45 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A4 ) )
% 0.14/0.45 => ( ! [X: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( member6273874620674182256at_nat @ X @ A4 )
% 0.14/0.45 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_o6272981002401706822at_nat @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1937_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr4329608150637261639at_nat,A4: set_se7855581050983116737at_nat] :
% 0.14/0.45 ( ( ord_le1268244103169919719at_nat @ R
% 0.14/0.45 @ ( produc7726050920695093128at_nat @ A4
% 0.14/0.45 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A4 ) )
% 0.14/0.45 => ( ! [X: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( member2643936169264416010at_nat @ X @ A4 )
% 0.14/0.45 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_o6955724340487615712at_nat @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1938_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr958786334691620121nt_int,A4: set_int] :
% 0.14/0.45 ( ( ord_le2843351958646193337nt_int @ R
% 0.14/0.45 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.45 @ ^ [Uu: int] : A4 ) )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_on_int @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1939_refl__onI,axiom,
% 0.14/0.45 ! [R: set_Pr1261947904930325089at_nat,A4: set_nat] :
% 0.14/0.45 ( ( ord_le3146513528884898305at_nat @ R
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : A4 ) )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R ) )
% 0.14/0.45 => ( refl_on_nat @ A4 @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onI
% 0.14/0.45 thf(fact_1940_refl__on__def,axiom,
% 0.14/0.45 ( refl_o6272981002401706822at_nat
% 0.14/0.45 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 0.14/0.45 ( ( ord_le5997549366648089703at_nat @ R5
% 0.14/0.45 @ ( produc6258361011560675592at_nat @ A6
% 0.14/0.45 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A6 ) )
% 0.14/0.45 & ! [X4: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 0.14/0.45 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_def
% 0.14/0.45 thf(fact_1941_refl__on__def,axiom,
% 0.14/0.45 ( refl_o6955724340487615712at_nat
% 0.14/0.45 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( ord_le1268244103169919719at_nat @ R5
% 0.14/0.45 @ ( produc7726050920695093128at_nat @ A6
% 0.14/0.45 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A6 ) )
% 0.14/0.45 & ! [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 0.14/0.45 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_def
% 0.14/0.45 thf(fact_1942_refl__on__def,axiom,
% 0.14/0.45 ( refl_on_int
% 0.14/0.45 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 0.14/0.45 ( ( ord_le2843351958646193337nt_int @ R5
% 0.14/0.45 @ ( produc1453890548195736866nt_int @ A6
% 0.14/0.45 @ ^ [Uu: int] : A6 ) )
% 0.14/0.45 & ! [X4: int] :
% 0.14/0.45 ( ( member_int @ X4 @ A6 )
% 0.14/0.45 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_def
% 0.14/0.45 thf(fact_1943_refl__on__def,axiom,
% 0.14/0.45 ( refl_on_nat
% 0.14/0.45 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ord_le3146513528884898305at_nat @ R5
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A6
% 0.14/0.45 @ ^ [Uu: nat] : A6 ) )
% 0.14/0.45 & ! [X4: nat] :
% 0.14/0.45 ( ( member_nat @ X4 @ A6 )
% 0.14/0.45 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_def
% 0.14/0.45 thf(fact_1944_image__insert,axiom,
% 0.14/0.45 ! [F: int > int,A: int,B5: set_int] :
% 0.14/0.45 ( ( image_int_int @ F @ ( insert_int @ A @ B5 ) )
% 0.14/0.45 = ( insert_int @ ( F @ A ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1945_image__insert,axiom,
% 0.14/0.45 ! [F: int > nat,A: int,B5: set_int] :
% 0.14/0.45 ( ( image_int_nat @ F @ ( insert_int @ A @ B5 ) )
% 0.14/0.45 = ( insert_nat @ ( F @ A ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1946_image__insert,axiom,
% 0.14/0.45 ! [F: nat > rat,A: nat,B5: set_nat] :
% 0.14/0.45 ( ( image_nat_rat @ F @ ( insert_nat @ A @ B5 ) )
% 0.14/0.45 = ( insert_rat @ ( F @ A ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1947_image__insert,axiom,
% 0.14/0.45 ! [F: nat > int,A: nat,B5: set_nat] :
% 0.14/0.45 ( ( image_nat_int @ F @ ( insert_nat @ A @ B5 ) )
% 0.14/0.45 = ( insert_int @ ( F @ A ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1948_image__insert,axiom,
% 0.14/0.45 ! [F: nat > nat,A: nat,B5: set_nat] :
% 0.14/0.45 ( ( image_nat_nat @ F @ ( insert_nat @ A @ B5 ) )
% 0.14/0.45 = ( insert_nat @ ( F @ A ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1949_image__insert,axiom,
% 0.14/0.45 ! [F: nat > product_unit,A: nat,B5: set_nat] :
% 0.14/0.45 ( ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ B5 ) )
% 0.14/0.45 = ( insert_Product_unit @ ( F @ A ) @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1950_image__insert,axiom,
% 0.14/0.45 ! [F: nat > $o,A: nat,B5: set_nat] :
% 0.14/0.45 ( ( image_nat_o @ F @ ( insert_nat @ A @ B5 ) )
% 0.14/0.45 = ( insert_o @ ( F @ A ) @ ( image_nat_o @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1951_image__insert,axiom,
% 0.14/0.45 ! [F: product_unit > nat,A: product_unit,B5: set_Product_unit] :
% 0.14/0.45 ( ( image_875570014554754200it_nat @ F @ ( insert_Product_unit @ A @ B5 ) )
% 0.14/0.45 = ( insert_nat @ ( F @ A ) @ ( image_875570014554754200it_nat @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1952_image__insert,axiom,
% 0.14/0.45 ! [F: product_unit > product_unit,A: product_unit,B5: set_Product_unit] :
% 0.14/0.45 ( ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ B5 ) )
% 0.14/0.45 = ( insert_Product_unit @ ( F @ A ) @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1953_image__insert,axiom,
% 0.14/0.45 ! [F: product_unit > $o,A: product_unit,B5: set_Product_unit] :
% 0.14/0.45 ( ( image_Product_unit_o @ F @ ( insert_Product_unit @ A @ B5 ) )
% 0.14/0.45 = ( insert_o @ ( F @ A ) @ ( image_Product_unit_o @ F @ B5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % image_insert
% 0.14/0.45 thf(fact_1954_insert__image,axiom,
% 0.14/0.45 ! [X2: $o,A4: set_o,F: $o > nat] :
% 0.14/0.45 ( ( member_o @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_nat @ ( F @ X2 ) @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.45 = ( image_o_nat @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1955_insert__image,axiom,
% 0.14/0.45 ! [X2: $o,A4: set_o,F: $o > product_unit] :
% 0.14/0.45 ( ( member_o @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_Product_unit @ ( F @ X2 ) @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.45 = ( image_o_Product_unit @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1956_insert__image,axiom,
% 0.14/0.45 ! [X2: $o,A4: set_o,F: $o > $o] :
% 0.14/0.45 ( ( member_o @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_o @ ( F @ X2 ) @ ( image_o_o @ F @ A4 ) )
% 0.14/0.45 = ( image_o_o @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1957_insert__image,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,F: nat > rat] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.45 = ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1958_insert__image,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,F: nat > int] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_int @ ( F @ X2 ) @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.45 = ( image_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1959_insert__image,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.45 = ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1960_insert__image,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,F: nat > product_unit] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_Product_unit @ ( F @ X2 ) @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.45 = ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1961_insert__image,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,F: nat > $o] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_o @ ( F @ X2 ) @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.45 = ( image_nat_o @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1962_insert__image,axiom,
% 0.14/0.45 ! [X2: int,A4: set_int,F: int > int] :
% 0.14/0.45 ( ( member_int @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_int @ ( F @ X2 ) @ ( image_int_int @ F @ A4 ) )
% 0.14/0.45 = ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1963_insert__image,axiom,
% 0.14/0.45 ! [X2: int,A4: set_int,F: int > nat] :
% 0.14/0.45 ( ( member_int @ X2 @ A4 )
% 0.14/0.45 => ( ( insert_nat @ ( F @ X2 ) @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.45 = ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_image
% 0.14/0.45 thf(fact_1964_SUP__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( complete_Sup_Sup_nat
% 0.14/0.45 @ ( image_nat_nat
% 0.14/0.45 @ ^ [X4: nat] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_identity_eq
% 0.14/0.45 thf(fact_1965_SUP__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_set_nat] :
% 0.14/0.45 ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_7916887816326733075et_nat
% 0.14/0.45 @ ^ [X4: set_nat] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_identity_eq
% 0.14/0.45 thf(fact_1966_SUP__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_int] :
% 0.14/0.45 ( ( complete_Sup_Sup_int
% 0.14/0.45 @ ( image_int_int
% 0.14/0.45 @ ^ [X4: int] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_int @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_identity_eq
% 0.14/0.45 thf(fact_1967_SUP__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_405062704495631173t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( comple4687483117567863418t_unit @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_identity_eq
% 0.14/0.45 thf(fact_1968_INF__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( complete_Inf_Inf_nat
% 0.14/0.45 @ ( image_nat_nat
% 0.14/0.45 @ ^ [X4: nat] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_identity_eq
% 0.14/0.45 thf(fact_1969_INF__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_set_nat] :
% 0.14/0.45 ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_7916887816326733075et_nat
% 0.14/0.45 @ ^ [X4: set_nat] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( comple7806235888213564991et_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_identity_eq
% 0.14/0.45 thf(fact_1970_INF__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_int] :
% 0.14/0.45 ( ( complete_Inf_Inf_int
% 0.14/0.45 @ ( image_int_int
% 0.14/0.45 @ ^ [X4: int] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_int @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_identity_eq
% 0.14/0.45 thf(fact_1971_INF__identity__eq,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_405062704495631173t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : X4
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_identity_eq
% 0.14/0.45 thf(fact_1972_UN__I,axiom,
% 0.14/0.45 ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
% 0.14/0.45 ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1973_UN__I,axiom,
% 0.14/0.45 ! [A: $o,A4: set_o,B: int,B5: $o > set_int] :
% 0.14/0.45 ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1974_UN__I,axiom,
% 0.14/0.45 ! [A: nat,A4: set_nat,B: $o,B5: nat > set_o] :
% 0.14/0.45 ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1975_UN__I,axiom,
% 0.14/0.45 ! [A: nat,A4: set_nat,B: int,B5: nat > set_int] :
% 0.14/0.45 ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1976_UN__I,axiom,
% 0.14/0.45 ! [A: int,A4: set_int,B: $o,B5: int > set_o] :
% 0.14/0.45 ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1977_UN__I,axiom,
% 0.14/0.45 ! [A: int,A4: set_int,B: int,B5: int > set_int] :
% 0.14/0.45 ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1978_UN__I,axiom,
% 0.14/0.45 ! [A: $o,A4: set_o,B: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1979_UN__I,axiom,
% 0.14/0.45 ! [A: nat,A4: set_nat,B: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1980_UN__I,axiom,
% 0.14/0.45 ! [A: int,A4: set_int,B: nat,B5: int > set_nat] :
% 0.14/0.45 ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1981_UN__I,axiom,
% 0.14/0.45 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.45 => ( ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_501298686397505212_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_I
% 0.14/0.45 thf(fact_1982_INT__I,axiom,
% 0.14/0.45 ! [A4: set_o,B: $o,B5: $o > set_o] :
% 0.14/0.45 ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1983_INT__I,axiom,
% 0.14/0.45 ! [A4: set_o,B: int,B5: $o > set_int] :
% 0.14/0.45 ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1984_INT__I,axiom,
% 0.14/0.45 ! [A4: set_nat,B: $o,B5: nat > set_o] :
% 0.14/0.45 ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1985_INT__I,axiom,
% 0.14/0.45 ! [A4: set_nat,B: int,B5: nat > set_int] :
% 0.14/0.45 ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1986_INT__I,axiom,
% 0.14/0.45 ! [A4: set_int,B: $o,B5: int > set_o] :
% 0.14/0.45 ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1987_INT__I,axiom,
% 0.14/0.45 ! [A4: set_int,B: int,B5: int > set_int] :
% 0.14/0.45 ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1988_INT__I,axiom,
% 0.14/0.45 ! [A4: set_o,B: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1989_INT__I,axiom,
% 0.14/0.45 ! [A4: set_nat,B: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1990_INT__I,axiom,
% 0.14/0.45 ! [A4: set_int,B: nat,B5: int > set_nat] :
% 0.14/0.45 ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1991_INT__I,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 0.14/0.45 ( ! [X: product_prod_nat_nat] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ X ) ) )
% 0.14/0.45 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_501298686397505212_set_o @ B5 @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_I
% 0.14/0.45 thf(fact_1992_SUP__id__eq,axiom,
% 0.14/0.45 ! [A4: set_o] :
% 0.14/0.45 ( ( complete_Sup_Sup_o @ ( image_o_o @ id_o @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_o @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_id_eq
% 0.14/0.45 thf(fact_1993_SUP__id__eq,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ id_nat @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_id_eq
% 0.14/0.45 thf(fact_1994_SUP__id__eq,axiom,
% 0.14/0.45 ! [A4: set_set_nat] :
% 0.14/0.45 ( ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ id_set_nat @ A4 ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_id_eq
% 0.14/0.45 thf(fact_1995_SUP__id__eq,axiom,
% 0.14/0.45 ! [A4: set_int] :
% 0.14/0.45 ( ( complete_Sup_Sup_int @ ( image_int_int @ id_int @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_int @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_id_eq
% 0.14/0.45 thf(fact_1996_SUP__id__eq,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ id_Product_unit @ A4 ) )
% 0.14/0.45 = ( comple4687483117567863418t_unit @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_id_eq
% 0.14/0.45 thf(fact_1997_INF__id__eq,axiom,
% 0.14/0.45 ! [A4: set_o] :
% 0.14/0.45 ( ( complete_Inf_Inf_o @ ( image_o_o @ id_o @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_o @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_id_eq
% 0.14/0.45 thf(fact_1998_INF__id__eq,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ id_nat @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_id_eq
% 0.14/0.45 thf(fact_1999_INF__id__eq,axiom,
% 0.14/0.45 ! [A4: set_set_nat] :
% 0.14/0.45 ( ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ id_set_nat @ A4 ) )
% 0.14/0.45 = ( comple7806235888213564991et_nat @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_id_eq
% 0.14/0.45 thf(fact_2000_INF__id__eq,axiom,
% 0.14/0.45 ! [A4: set_int] :
% 0.14/0.45 ( ( complete_Inf_Inf_int @ ( image_int_int @ id_int @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_int @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_id_eq
% 0.14/0.45 thf(fact_2001_INF__id__eq,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ id_Product_unit @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_id_eq
% 0.14/0.45 thf(fact_2002_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [I2: product_unit] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2003_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_3160451284896210088et_nat
% 0.14/0.45 @ ^ [I2: produc3843707927480180839at_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2004_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_15824709712370754et_nat
% 0.14/0.45 @ ^ [I2: product_prod_nat_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2005_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_o,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [I2: $o] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2006_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [I2: nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2007_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_405062704495631173t_unit
% 0.14/0.45 @ ^ [I2: product_unit] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2008_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_7082456443403096939t_unit
% 0.14/0.45 @ ^ [I2: produc3843707927480180839at_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2009_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_6169909464789311569t_unit
% 0.14/0.45 @ ^ [I2: product_prod_nat_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2010_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_o,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_o_Product_unit
% 0.14/0.45 @ ^ [I2: $o] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2011_SUP__const,axiom,
% 0.14/0.45 ! [A4: set_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit
% 0.14/0.45 @ ( image_8730104196221521654t_unit
% 0.14/0.45 @ ^ [I2: nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_const
% 0.14/0.45 thf(fact_2012_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [I2: product_unit] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2013_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_3160451284896210088et_nat
% 0.14/0.45 @ ^ [I2: produc3843707927480180839at_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2014_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_15824709712370754et_nat
% 0.14/0.45 @ ^ [I2: product_prod_nat_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2015_INF__const,axiom,
% 0.14/0.45 ! [A4: set_o,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [I2: $o] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2016_INF__const,axiom,
% 0.14/0.45 ! [A4: set_nat,F: set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [I2: nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2017_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_405062704495631173t_unit
% 0.14/0.45 @ ^ [I2: product_unit] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2018_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_7082456443403096939t_unit
% 0.14/0.45 @ ^ [I2: produc3843707927480180839at_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2019_INF__const,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_6169909464789311569t_unit
% 0.14/0.45 @ ^ [I2: product_prod_nat_nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2020_INF__const,axiom,
% 0.14/0.45 ! [A4: set_o,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_o_Product_unit
% 0.14/0.45 @ ^ [I2: $o] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2021_INF__const,axiom,
% 0.14/0.45 ! [A4: set_nat,F: product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit
% 0.14/0.45 @ ( image_8730104196221521654t_unit
% 0.14/0.45 @ ^ [I2: nat] : F
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = F ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_const
% 0.14/0.45 thf(fact_2022_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2023_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_6930536745178679216_set_o
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_6930536745178679216_set_o
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2024_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2025_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2026_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_Product_unit] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2027_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_o] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2028_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2029_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_o,C: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [Y5: $o] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2030_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_nat,C: set_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [Y5: nat] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2031_UN__constant,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,C: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_3617315916088684441at_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = bot_bo2099793752762293965at_nat ) )
% 0.14/0.45 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_3617315916088684441at_nat
% 0.14/0.45 @ ^ [Y5: product_unit] : C
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = C ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_constant
% 0.14/0.45 thf(fact_2032_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: product_unit,B5: product_unit > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2033_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: $o,B5: product_unit > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_6930536745178679216_set_o
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_6930536745178679216_set_o
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2034_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2035_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: $o,B5: $o > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2036_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2037_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: $o,B5: nat > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_o ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2038_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: nat,B5: product_unit > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2039_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2040_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bot_set_nat ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2041_UN__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: product_prod_nat_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_3617315916088684441at_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = bot_bo2099793752762293965at_nat ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_3617315916088684441at_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) )
% 0.14/0.45 = ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_simps(1)
% 0.14/0.45 thf(fact_2042_UN__singleton,axiom,
% 0.14/0.45 ! [A4: set_Product_unit] :
% 0.14/0.45 ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = A4 ) ).
% 0.14/0.45
% 0.14/0.45 % UN_singleton
% 0.14/0.45 thf(fact_2043_UN__singleton,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( comple4364388969068068532at_nat
% 0.14/0.45 @ ( image_7364710425340685989at_nat
% 0.14/0.45 @ ^ [X4: produc3843707927480180839at_nat] : ( insert9069300056098147895at_nat @ X4 @ bot_bo228742789529271731at_nat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = A4 ) ).
% 0.14/0.45
% 0.14/0.45 % UN_singleton
% 0.14/0.45 thf(fact_2044_UN__singleton,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_5423882813909314213at_nat
% 0.14/0.45 @ ^ [X4: product_prod_nat_nat] : ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = A4 ) ).
% 0.14/0.45
% 0.14/0.45 % UN_singleton
% 0.14/0.45 thf(fact_2045_UN__singleton,axiom,
% 0.14/0.45 ! [A4: set_o] :
% 0.14/0.45 ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ X4 @ bot_bot_set_o )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = A4 ) ).
% 0.14/0.45
% 0.14/0.45 % UN_singleton
% 0.14/0.45 thf(fact_2046_UN__singleton,axiom,
% 0.14/0.45 ! [A4: set_nat] :
% 0.14/0.45 ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ X4 @ bot_bot_set_nat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = A4 ) ).
% 0.14/0.45
% 0.14/0.45 % UN_singleton
% 0.14/0.45 thf(fact_2047_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: set_Pr4329608150637261639at_nat] : ( refl_o6272981002401706822at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2048_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: int] : ( refl_on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2049_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: set_Pr1261947904930325089at_nat] : ( refl_o6955724340487615712at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2050_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: product_unit] : ( refl_on_Product_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2051_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: produc3843707927480180839at_nat] : ( refl_o7446464703481863270at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2052_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: product_prod_nat_nat] : ( refl_o7122697186039111552at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2053_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: $o] : ( refl_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2054_refl__on__singleton,axiom,
% 0.14/0.45 ! [X2: nat] : ( refl_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_on_singleton
% 0.14/0.45 thf(fact_2055_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple7216939928495492468t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2056_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: $o,B5: $o > set_o] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple3063163877087187839_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2057_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple7216939928495492468t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_4824033694279209942t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2058_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: $o,B5: nat > set_o] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple3063163877087187839_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2059_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: product_unit,B5: int > set_Product_unit] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple7216939928495492468t_unit
% 0.14/0.45 @ ( image_8658272795163236474t_unit
% 0.14/0.45 @ ^ [X4: int] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2060_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: $o,B5: int > set_o] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple3063163877087187839_set_o
% 0.14/0.45 @ ( image_int_set_o
% 0.14/0.45 @ ^ [X4: int] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2061_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2062_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2063_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: nat,B5: int > set_nat] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_int_set_nat
% 0.14/0.45 @ ^ [X4: int] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2064_INT__insert__distrib,axiom,
% 0.14/0.45 ! [U: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,A: product_unit,B5: product_prod_nat_nat > set_Product_unit] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple7216939928495492468t_unit
% 0.14/0.45 @ ( image_121980125215734065t_unit
% 0.14/0.45 @ ^ [X4: product_prod_nat_nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_121980125215734065t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_insert_distrib
% 0.14/0.45 thf(fact_2065_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2066_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: $o,B5: $o > set_o] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2067_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2068_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: $o,B5: nat > set_o] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2069_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: product_unit,B5: int > set_Product_unit] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_8658272795163236474t_unit
% 0.14/0.45 @ ^ [X4: int] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2070_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: $o,B5: int > set_o] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_int_set_o
% 0.14/0.45 @ ^ [X4: int] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2071_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: $o,A4: set_o,A: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ( member_o @ U @ A4 )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2072_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: nat,A4: set_nat,A: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( member_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2073_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: int,A4: set_int,A: nat,B5: int > set_nat] :
% 0.14/0.45 ( ( member_int @ U @ A4 )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_int_set_nat
% 0.14/0.45 @ ^ [X4: int] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2074_UN__insert__distrib,axiom,
% 0.14/0.45 ! [U: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,A: product_unit,B5: product_prod_nat_nat > set_Product_unit] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ U @ A4 )
% 0.14/0.45 => ( ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_121980125215734065t_unit
% 0.14/0.45 @ ^ [X4: product_prod_nat_nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_121980125215734065t_unit @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_insert_distrib
% 0.14/0.45 thf(fact_2075_Sigma__Union,axiom,
% 0.14/0.45 ! [X5: set_set_nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ X5 ) @ B5 )
% 0.14/0.45 = ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_6521575952113991828at_nat
% 0.14/0.45 @ ^ [A6: set_nat] : ( produc457027306803732586at_nat @ A6 @ B5 )
% 0.14/0.45 @ X5 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_Union
% 0.14/0.45 thf(fact_2076_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2077_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_nat @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2078_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > int,D: $o > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Inf_Inf_int @ ( image_o_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_int @ ( image_o_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2079_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_int @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2080_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Inf_Inf_int @ ( image_int_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Inf_Inf_int @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2081_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > product_unit,D: $o > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2082_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > product_unit,D: nat > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2083_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > product_unit,D: int > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2084_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > set_nat,D: $o > set_nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2085_INF__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_cong
% 0.14/0.45 thf(fact_2086_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2087_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_nat @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2088_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > int,D: $o > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Sup_Sup_int @ ( image_o_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_int @ ( image_o_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2089_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_int @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2090_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( complete_Sup_Sup_int @ ( image_int_int @ C3 @ A4 ) )
% 0.14/0.45 = ( complete_Sup_Sup_int @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2091_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > product_unit,D: $o > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2092_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > product_unit,D: nat > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2093_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_int,B5: set_int,C3: int > product_unit,D: int > product_unit] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ C3 @ A4 ) )
% 0.14/0.45 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2094_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,C3: $o > set_nat,D: $o > set_nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2095_SUP__cong,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 0.14/0.45 ( ( A4 = B5 )
% 0.14/0.45 => ( ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ B5 )
% 0.14/0.45 => ( ( C3 @ X )
% 0.14/0.45 = ( D @ X ) ) )
% 0.14/0.45 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ C3 @ A4 ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ D @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % SUP_cong
% 0.14/0.45 thf(fact_2096_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: product_unit,A4: set_Product_unit,X5: set_Product_unit] :
% 0.14/0.45 ( ( member_Product_unit @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_le3507040750410214029t_unit @ X5 @ A4 )
% 0.14/0.45 => ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2097_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,X5: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( member8757157785044589968at_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_le1268244103169919719at_nat @ X5 @ A4 )
% 0.14/0.45 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2098_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,X5: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_le3146513528884898305at_nat @ X5 @ A4 )
% 0.14/0.45 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2099_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: $o,A4: set_o,X5: set_o] :
% 0.14/0.45 ( ( member_o @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_less_eq_set_o @ X5 @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_o @ ( insert_o @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2100_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: nat,A4: set_nat,X5: set_nat] :
% 0.14/0.45 ( ( member_nat @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_less_eq_set_nat @ X5 @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2101_insert__subsetI,axiom,
% 0.14/0.45 ! [X2: int,A4: set_int,X5: set_int] :
% 0.14/0.45 ( ( member_int @ X2 @ A4 )
% 0.14/0.45 => ( ( ord_less_eq_set_int @ X5 @ A4 )
% 0.14/0.45 => ( ord_less_eq_set_int @ ( insert_int @ X2 @ X5 ) @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % insert_subsetI
% 0.14/0.45 thf(fact_2102_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: product_unit,B5: product_unit > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_7778121751606633509t_unit
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2103_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: $o,B5: product_unit > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_6930536745178679216_set_o
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2104_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_663195431845683034t_unit
% 0.14/0.45 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2105_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: $o,B5: $o > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_o_set_o
% 0.14/0.45 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2106_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple3349607820504768346t_unit
% 0.14/0.45 @ ( image_4824033694279209942t_unit
% 0.14/0.45 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2107_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: $o,B5: nat > set_o] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple90263536869209701_set_o
% 0.14/0.45 @ ( image_nat_set_o
% 0.14/0.45 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2108_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: nat,B5: product_unit > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_8173849991827986510et_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2109_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_o,A: nat,B5: $o > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_o )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_o_set_nat
% 0.14/0.45 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2110_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_nat,A: nat,B5: nat > set_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.14/0.45 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.45 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2111_UN__extend__simps_I1_J,axiom,
% 0.14/0.45 ! [C3: set_Product_unit,A: product_prod_nat_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.14/0.45 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 0.14/0.45 = ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_3617315916088684441at_nat
% 0.14/0.45 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 0.14/0.45 @ C3 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_extend_simps(1)
% 0.14/0.45 thf(fact_2112_Sigma__def,axiom,
% 0.14/0.45 ( produc6258361011560675592at_nat
% 0.14/0.45 = ( ^ [A6: set_se5479201105039950375at_nat,B6: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 0.14/0.45 ( comple7342073961973170484at_nat
% 0.14/0.45 @ ( image_1124969593608450885at_nat
% 0.14/0.45 @ ^ [X4: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( comple7342073961973170484at_nat
% 0.14/0.45 @ ( image_1124969593608450885at_nat
% 0.14/0.45 @ ^ [Y5: set_Pr4329608150637261639at_nat] : ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ bot_bo4948859079157340979at_nat )
% 0.14/0.45 @ ( B6 @ X4 ) ) )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_def
% 0.14/0.45 thf(fact_2113_Sigma__def,axiom,
% 0.14/0.45 ( produc6237731129814287028at_num
% 0.14/0.45 = ( ^ [A6: set_nat,B6: nat > set_num] :
% 0.14/0.45 ( comple1400524285282149784at_num
% 0.14/0.45 @ ( image_2893549341467670548at_num
% 0.14/0.45 @ ^ [X4: nat] :
% 0.14/0.45 ( comple1400524285282149784at_num
% 0.14/0.45 @ ( image_4778453735051108682at_num
% 0.14/0.45 @ ^ [Y5: num] : ( insert8920054152555992091at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ bot_bo7038385379056416535at_num )
% 0.14/0.45 @ ( B6 @ X4 ) ) )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_def
% 0.14/0.45 thf(fact_2114_Sigma__def,axiom,
% 0.14/0.45 ( produc1453890548195736866nt_int
% 0.14/0.45 = ( ^ [A6: set_int,B6: int > set_int] :
% 0.14/0.45 ( comple5382143125604098054nt_int
% 0.14/0.45 @ ( image_8635204845542730022nt_int
% 0.14/0.45 @ ^ [X4: int] :
% 0.14/0.45 ( comple5382143125604098054nt_int
% 0.14/0.45 @ ( image_8635204845542730022nt_int
% 0.14/0.45 @ ^ [Y5: int] : ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ bot_bo1796632182523588997nt_int )
% 0.14/0.45 @ ( B6 @ X4 ) ) )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_def
% 0.14/0.45 thf(fact_2115_Sigma__def,axiom,
% 0.14/0.45 ( produc7726050920695093128at_nat
% 0.14/0.45 = ( ^ [A6: set_se7855581050983116737at_nat,B6: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.45 ( comple4364388969068068532at_nat
% 0.14/0.45 @ ( image_6898982319499645995at_nat
% 0.14/0.45 @ ^ [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( comple4364388969068068532at_nat
% 0.14/0.45 @ ( image_6898982319499645995at_nat
% 0.14/0.45 @ ^ [Y5: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ bot_bo228742789529271731at_nat )
% 0.14/0.45 @ ( B6 @ X4 ) ) )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_def
% 0.14/0.45 thf(fact_2116_Sigma__def,axiom,
% 0.14/0.45 ( produc457027306803732586at_nat
% 0.14/0.45 = ( ^ [A6: set_nat,B6: nat > set_nat] :
% 0.14/0.45 ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_7178329752028323786at_nat
% 0.14/0.45 @ ^ [X4: nat] :
% 0.14/0.45 ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_7178329752028323786at_nat
% 0.14/0.45 @ ^ [Y5: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ bot_bo2099793752762293965at_nat )
% 0.14/0.45 @ ( B6 @ X4 ) ) )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Sigma_def
% 0.14/0.45 thf(fact_2117_UN__Times__distrib,axiom,
% 0.14/0.45 ! [E2: nat > set_nat,F4: nat > set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.45 ( ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_5423882813909314213at_nat
% 0.14/0.45 @ ( produc8197505143624133779at_nat
% 0.14/0.45 @ ^ [A5: nat,B4: nat] :
% 0.14/0.45 ( produc457027306803732586at_nat @ ( E2 @ A5 )
% 0.14/0.45 @ ^ [Uu: nat] : ( F4 @ B4 ) ) )
% 0.14/0.45 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.45 @ ^ [Uu: nat] : B5 ) ) )
% 0.14/0.45 = ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ E2 @ A4 ) )
% 0.14/0.45 @ ^ [Uu: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F4 @ B5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_Times_distrib
% 0.14/0.45 thf(fact_2118_right__total__OO,axiom,
% 0.14/0.45 ! [A4: product_prod_nat_nat > product_prod_nat_nat > $o,B5: product_prod_nat_nat > int > $o] :
% 0.14/0.45 ( ( right_4094035864313884895at_nat @ A4 )
% 0.14/0.45 => ( ( right_1157779049177982926at_int @ B5 )
% 0.14/0.45 => ( right_1157779049177982926at_int @ ( relcom8911704206367525917at_int @ A4 @ B5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % right_total_OO
% 0.14/0.45 thf(fact_2119_right__total__OO,axiom,
% 0.14/0.45 ! [A4: int > int > $o,B5: int > code_integer > $o] :
% 0.14/0.45 ( ( right_total_int_int @ A4 )
% 0.14/0.45 => ( ( right_7281159819619925802nteger @ B5 )
% 0.14/0.45 => ( right_7281159819619925802nteger @ ( relcom967497705283160040nteger @ A4 @ B5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % right_total_OO
% 0.14/0.45 thf(fact_2120_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat] :
% 0.14/0.45 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.45 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2121_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat] :
% 0.14/0.45 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.45 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2122_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_o,R: set_Product_prod_o_o,A: $o] :
% 0.14/0.45 ( ( refl_on_o @ A4 @ R )
% 0.14/0.45 => ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2123_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 0.14/0.45 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2124_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 0.14/0.45 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2125_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat] :
% 0.14/0.45 ( ( refl_on_nat @ A4 @ R )
% 0.14/0.45 => ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2126_refl__onD,axiom,
% 0.14/0.45 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int] :
% 0.14/0.45 ( ( refl_on_int @ A4 @ R )
% 0.14/0.45 => ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ R ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD
% 0.14/0.45 thf(fact_2127_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 0.14/0.45 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member8757157785044589968at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2128_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.14/0.45 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member8440522571783428010at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2129_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_o,R: set_Product_prod_o_o,X2: $o,Y3: $o] :
% 0.14/0.45 ( ( refl_on_o @ A4 @ R )
% 0.14/0.45 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_o @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2130_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member6273874620674182256at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2131_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member2643936169264416010at_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2132_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,X2: nat,Y3: nat] :
% 0.14/0.45 ( ( refl_on_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_nat @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2133_refl__onD1,axiom,
% 0.14/0.45 ! [A4: set_int,R: set_Pr958786334691620121nt_int,X2: int,Y3: int] :
% 0.14/0.45 ( ( refl_on_int @ A4 @ R )
% 0.14/0.45 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_int @ X2 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD1
% 0.14/0.45 thf(fact_2134_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 0.14/0.45 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member8757157785044589968at_nat @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2135_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.14/0.45 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member8440522571783428010at_nat @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2136_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_o,R: set_Product_prod_o_o,X2: $o,Y3: $o] :
% 0.14/0.45 ( ( refl_on_o @ A4 @ R )
% 0.14/0.45 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_o @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2137_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.45 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member6273874620674182256at_nat @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2138_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.14/0.45 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member2643936169264416010at_nat @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2139_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,X2: nat,Y3: nat] :
% 0.14/0.45 ( ( refl_on_nat @ A4 @ R )
% 0.14/0.45 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_nat @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2140_refl__onD2,axiom,
% 0.14/0.45 ! [A4: set_int,R: set_Pr958786334691620121nt_int,X2: int,Y3: int] :
% 0.14/0.45 ( ( refl_on_int @ A4 @ R )
% 0.14/0.45 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R )
% 0.14/0.45 => ( member_int @ Y3 @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % refl_onD2
% 0.14/0.45 thf(fact_2141_INT__extend__simps_I8_J,axiom,
% 0.14/0.45 ! [B5: nat > set_nat,A4: set_set_nat] :
% 0.14/0.45 ( ( comple7806235888213564991et_nat
% 0.14/0.45 @ ( image_7916887816326733075et_nat
% 0.14/0.45 @ ^ [Y5: set_nat] : ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ Y5 ) )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_extend_simps(8)
% 0.14/0.45 thf(fact_2142_Id__on__def,axiom,
% 0.14/0.45 ( id_on_3275838214495744996at_nat
% 0.14/0.45 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 0.14/0.45 ( comple7342073961973170484at_nat
% 0.14/0.45 @ ( image_1124969593608450885at_nat
% 0.14/0.45 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X4 @ X4 ) @ bot_bo4948859079157340979at_nat )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Id_on_def
% 0.14/0.45 thf(fact_2143_Id__on__def,axiom,
% 0.14/0.45 ( id_on_int
% 0.14/0.45 = ( ^ [A6: set_int] :
% 0.14/0.45 ( comple5382143125604098054nt_int
% 0.14/0.45 @ ( image_8635204845542730022nt_int
% 0.14/0.45 @ ^ [X4: int] : ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X4 @ X4 ) @ bot_bo1796632182523588997nt_int )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Id_on_def
% 0.14/0.45 thf(fact_2144_Id__on__def,axiom,
% 0.14/0.45 ( id_on_6713504163309144702at_nat
% 0.14/0.45 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 0.14/0.45 ( comple4364388969068068532at_nat
% 0.14/0.45 @ ( image_6898982319499645995at_nat
% 0.14/0.45 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X4 @ X4 ) @ bot_bo228742789529271731at_nat )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Id_on_def
% 0.14/0.45 thf(fact_2145_Id__on__def,axiom,
% 0.14/0.45 ( id_on_nat
% 0.14/0.45 = ( ^ [A6: set_nat] :
% 0.14/0.45 ( comple5685304695842803022at_nat
% 0.14/0.45 @ ( image_7178329752028323786at_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X4 @ X4 ) @ bot_bo2099793752762293965at_nat )
% 0.14/0.45 @ A6 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % Id_on_def
% 0.14/0.45 thf(fact_2146_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: product_unit > set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2147_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2148_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2149_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_o,F: $o > set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2150_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_nat,F: nat > set_nat] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2151_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Product_unit,F: product_unit > product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.45 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2152_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo228742789529271731at_nat )
% 0.14/0.45 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2153_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 0.14/0.45 ( ( A4 != bot_bo2099793752762293965at_nat )
% 0.14/0.45 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2154_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_o,F: $o > product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_o )
% 0.14/0.45 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2155_INF__le__SUP,axiom,
% 0.14/0.45 ! [A4: set_nat,F: nat > product_unit] :
% 0.14/0.45 ( ( A4 != bot_bot_set_nat )
% 0.14/0.45 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_le_SUP
% 0.14/0.45 thf(fact_2156_right__unique__OO,axiom,
% 0.14/0.45 ! [A4: product_prod_nat_nat > product_prod_nat_nat > $o,B5: product_prod_nat_nat > int > $o] :
% 0.14/0.45 ( ( right_1383565826979811350at_nat @ A4 )
% 0.14/0.45 => ( ( right_8621877368619751767at_int @ B5 )
% 0.14/0.45 => ( right_8621877368619751767at_int @ ( relcom8911704206367525917at_int @ A4 @ B5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % right_unique_OO
% 0.14/0.45 thf(fact_2157_right__unique__OO,axiom,
% 0.14/0.45 ! [A4: int > int > $o,B5: int > code_integer > $o] :
% 0.14/0.45 ( ( right_unique_int_int @ A4 )
% 0.14/0.45 => ( ( right_8475562212078014689nteger @ B5 )
% 0.14/0.45 => ( right_8475562212078014689nteger @ ( relcom967497705283160040nteger @ A4 @ B5 ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % right_unique_OO
% 0.14/0.45 thf(fact_2158_INT__E,axiom,
% 0.14/0.45 ! [B: $o,B5: $o > set_o,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2159_INT__E,axiom,
% 0.14/0.45 ! [B: $o,B5: nat > set_o,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2160_INT__E,axiom,
% 0.14/0.45 ! [B: $o,B5: int > set_o,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_int @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2161_INT__E,axiom,
% 0.14/0.45 ! [B: int,B5: $o > set_int,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2162_INT__E,axiom,
% 0.14/0.45 ! [B: int,B5: nat > set_int,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2163_INT__E,axiom,
% 0.14/0.45 ! [B: int,B5: int > set_int,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_int @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2164_INT__E,axiom,
% 0.14/0.45 ! [B: nat,B5: $o > set_nat,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2165_INT__E,axiom,
% 0.14/0.45 ! [B: nat,B5: nat > set_nat,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2166_INT__E,axiom,
% 0.14/0.45 ! [B: nat,B5: int > set_nat,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_int @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2167_INT__E,axiom,
% 0.14/0.45 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ B @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ~ ( member8440522571783428010at_nat @ B @ ( B5 @ A ) )
% 0.14/0.45 => ~ ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_E
% 0.14/0.45 thf(fact_2168_INT__D,axiom,
% 0.14/0.45 ! [B: $o,B5: $o > set_o,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2169_INT__D,axiom,
% 0.14/0.45 ! [B: $o,B5: nat > set_o,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2170_INT__D,axiom,
% 0.14/0.45 ! [B: $o,B5: int > set_o,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2171_INT__D,axiom,
% 0.14/0.45 ! [B: int,B5: $o > set_int,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2172_INT__D,axiom,
% 0.14/0.45 ! [B: int,B5: nat > set_int,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2173_INT__D,axiom,
% 0.14/0.45 ! [B: int,B5: int > set_int,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2174_INT__D,axiom,
% 0.14/0.45 ! [B: nat,B5: $o > set_nat,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2175_INT__D,axiom,
% 0.14/0.45 ! [B: nat,B5: nat > set_nat,A4: set_nat,A: nat] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_nat @ A @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2176_INT__D,axiom,
% 0.14/0.45 ! [B: nat,B5: int > set_nat,A4: set_int,A: int] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_int @ A @ A4 )
% 0.14/0.45 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2177_INT__D,axiom,
% 0.14/0.45 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o,A: $o] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ B @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ( ( member_o @ A @ A4 )
% 0.14/0.45 => ( member8440522571783428010at_nat @ B @ ( B5 @ A ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INT_D
% 0.14/0.45 thf(fact_2178_UN__E,axiom,
% 0.14/0.45 ! [B: $o,B5: $o > set_o,A4: set_o] :
% 0.14/0.45 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2179_UN__E,axiom,
% 0.14/0.45 ! [B: $o,B5: nat > set_o,A4: set_nat] :
% 0.14/0.45 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2180_UN__E,axiom,
% 0.14/0.45 ! [B: $o,B5: int > set_o,A4: set_int] :
% 0.14/0.45 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2181_UN__E,axiom,
% 0.14/0.45 ! [B: int,B5: $o > set_int,A4: set_o] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2182_UN__E,axiom,
% 0.14/0.45 ! [B: int,B5: nat > set_int,A4: set_nat] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2183_UN__E,axiom,
% 0.14/0.45 ! [B: int,B5: int > set_int,A4: set_int] :
% 0.14/0.45 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2184_UN__E,axiom,
% 0.14/0.45 ! [B: nat,B5: $o > set_nat,A4: set_o] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2185_UN__E,axiom,
% 0.14/0.45 ! [B: nat,B5: nat > set_nat,A4: set_nat] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: nat] :
% 0.14/0.45 ( ( member_nat @ X @ A4 )
% 0.14/0.45 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2186_UN__E,axiom,
% 0.14/0.45 ! [B: nat,B5: int > set_nat,A4: set_int] :
% 0.14/0.45 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: int] :
% 0.14/0.45 ( ( member_int @ X @ A4 )
% 0.14/0.45 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2187_UN__E,axiom,
% 0.14/0.45 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o] :
% 0.14/0.45 ( ( member8440522571783428010at_nat @ B @ ( comple5685304695842803022at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 0.14/0.45 => ~ ! [X: $o] :
% 0.14/0.45 ( ( member_o @ X @ A4 )
% 0.14/0.45 => ~ ( member8440522571783428010at_nat @ B @ ( B5 @ X ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % UN_E
% 0.14/0.45 thf(fact_2188_UNION__singleton__eq__range,axiom,
% 0.14/0.45 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.45 ( ( comple3890839924845867745et_rat
% 0.14/0.45 @ ( image_nat_set_rat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_rat @ ( F @ X4 ) @ bot_bot_set_rat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( image_nat_rat @ F @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % UNION_singleton_eq_range
% 0.14/0.45 thf(fact_2189_UNION__singleton__eq__range,axiom,
% 0.14/0.45 ! [F: nat > int,A4: set_nat] :
% 0.14/0.45 ( ( comple3221217463730067765et_int
% 0.14/0.45 @ ( image_nat_set_int
% 0.14/0.45 @ ^ [X4: nat] : ( insert_int @ ( F @ X4 ) @ bot_bot_set_int )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( image_nat_int @ F @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % UNION_singleton_eq_range
% 0.14/0.45 thf(fact_2190_UNION__singleton__eq__range,axiom,
% 0.14/0.45 ! [F: int > int,A4: set_int] :
% 0.14/0.45 ( ( comple3221217463730067765et_int
% 0.14/0.45 @ ( image_int_set_int
% 0.14/0.45 @ ^ [X4: int] : ( insert_int @ ( F @ X4 ) @ bot_bot_set_int )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( image_int_int @ F @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % UNION_singleton_eq_range
% 0.14/0.45 thf(fact_2191_UNION__singleton__eq__range,axiom,
% 0.14/0.45 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.45 ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_nat_set_nat
% 0.14/0.45 @ ^ [X4: nat] : ( insert_nat @ ( F @ X4 ) @ bot_bot_set_nat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( image_nat_nat @ F @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % UNION_singleton_eq_range
% 0.14/0.45 thf(fact_2192_UNION__singleton__eq__range,axiom,
% 0.14/0.45 ! [F: int > nat,A4: set_int] :
% 0.14/0.45 ( ( comple7399068483239264473et_nat
% 0.14/0.45 @ ( image_int_set_nat
% 0.14/0.45 @ ^ [X4: int] : ( insert_nat @ ( F @ X4 ) @ bot_bot_set_nat )
% 0.14/0.45 @ A4 ) )
% 0.14/0.45 = ( image_int_nat @ F @ A4 ) ) ).
% 0.14/0.45
% 0.14/0.45 % UNION_singleton_eq_range
% 0.14/0.45 thf(fact_2193_INF__eq,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_o,G: $o > product_unit,F: $o > product_unit] :
% 0.14/0.45 ( ! [I4: $o] :
% 0.14/0.45 ( ( member_o @ I4 @ A4 )
% 0.14/0.45 => ? [X6: $o] :
% 0.14/0.45 ( ( member_o @ X6 @ B5 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.45 => ( ! [J2: $o] :
% 0.14/0.45 ( ( member_o @ J2 @ B5 )
% 0.14/0.45 => ? [X6: $o] :
% 0.14/0.45 ( ( member_o @ X6 @ A4 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_eq
% 0.14/0.45 thf(fact_2194_INF__eq,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_nat,G: nat > product_unit,F: $o > product_unit] :
% 0.14/0.45 ( ! [I4: $o] :
% 0.14/0.45 ( ( member_o @ I4 @ A4 )
% 0.14/0.45 => ? [X6: nat] :
% 0.14/0.45 ( ( member_nat @ X6 @ B5 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.45 => ( ! [J2: nat] :
% 0.14/0.45 ( ( member_nat @ J2 @ B5 )
% 0.14/0.45 => ? [X6: $o] :
% 0.14/0.45 ( ( member_o @ X6 @ A4 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_eq
% 0.14/0.45 thf(fact_2195_INF__eq,axiom,
% 0.14/0.45 ! [A4: set_o,B5: set_int,G: int > product_unit,F: $o > product_unit] :
% 0.14/0.45 ( ! [I4: $o] :
% 0.14/0.45 ( ( member_o @ I4 @ A4 )
% 0.14/0.45 => ? [X6: int] :
% 0.14/0.45 ( ( member_int @ X6 @ B5 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.45 => ( ! [J2: int] :
% 0.14/0.45 ( ( member_int @ J2 @ B5 )
% 0.14/0.45 => ? [X6: $o] :
% 0.14/0.45 ( ( member_o @ X6 @ A4 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.45 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.45 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.45
% 0.14/0.45 % INF_eq
% 0.14/0.45 thf(fact_2196_INF__eq,axiom,
% 0.14/0.45 ! [A4: set_nat,B5: set_o,G: $o > product_unit,F: nat > product_unit] :
% 0.14/0.45 ( ! [I4: nat] :
% 0.14/0.45 ( ( member_nat @ I4 @ A4 )
% 0.14/0.45 => ? [X6: $o] :
% 0.14/0.45 ( ( member_o @ X6 @ B5 )
% 0.14/0.45 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.45 => ( ! [J2: $o] :
% 0.14/0.45 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2197_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,G: nat > product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: nat] :
% 0.14/0.46 ( ( member_nat @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2198_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_int,G: int > product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: int] :
% 0.14/0.46 ( ( member_int @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2199_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_o,G: $o > product_unit,F: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2200_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_nat,G: nat > product_unit,F: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: nat] :
% 0.14/0.46 ( ( member_nat @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2201_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,G: int > product_unit,F: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: int] :
% 0.14/0.46 ( ( member_int @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2202_INF__eq,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,G: $o > set_nat,F: $o > set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_less_eq_set_nat @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ A4 )
% 0.14/0.46 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq
% 0.14/0.46 thf(fact_2203_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > product_unit,G: $o > product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2204_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_nat,F: $o > product_unit,G: nat > product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: nat] :
% 0.14/0.46 ( ( member_nat @ J2 @ B5 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2205_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_int,F: $o > product_unit,G: int > product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: int] :
% 0.14/0.46 ( ( member_int @ J2 @ B5 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2206_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_o,F: nat > product_unit,G: $o > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2207_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: nat] :
% 0.14/0.46 ( ( member_nat @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2208_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_int,F: nat > product_unit,G: int > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: int] :
% 0.14/0.46 ( ( member_int @ J2 @ B5 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2209_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_o,F: int > product_unit,G: $o > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2210_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_nat,F: int > product_unit,G: nat > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: nat] :
% 0.14/0.46 ( ( member_nat @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: nat] :
% 0.14/0.46 ( ( member_nat @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2211_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,F: int > product_unit,G: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ B5 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: int] :
% 0.14/0.46 ( ( member_int @ J2 @ B5 )
% 0.14/0.46 => ? [X6: int] :
% 0.14/0.46 ( ( member_int @ X6 @ A4 )
% 0.14/0.46 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2212_SUP__eq,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ B5 )
% 0.14/0.46 & ( ord_less_eq_set_nat @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 0.14/0.46 => ( ! [J2: $o] :
% 0.14/0.46 ( ( member_o @ J2 @ B5 )
% 0.14/0.46 => ? [X6: $o] :
% 0.14/0.46 ( ( member_o @ X6 @ A4 )
% 0.14/0.46 & ( ord_less_eq_set_nat @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq
% 0.14/0.46 thf(fact_2213_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2214_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2215_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2216_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2217_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2218_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2219_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2220_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2221_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2222_INF__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_const
% 0.14/0.46 thf(fact_2223_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2224_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2225_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2226_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2227_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2228_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2229_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2230_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2231_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2232_SUP__eq__const,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ( F @ I4 )
% 0.14/0.46 = X2 ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_const
% 0.14/0.46 thf(fact_2233_INF__image,axiom,
% 0.14/0.46 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_o @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_o @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2234_INF__image,axiom,
% 0.14/0.46 ! [G: rat > nat,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_nat @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2235_INF__image,axiom,
% 0.14/0.46 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2236_INF__image,axiom,
% 0.14/0.46 ! [G: nat > nat,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_nat @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2237_INF__image,axiom,
% 0.14/0.46 ! [G: int > nat,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2238_INF__image,axiom,
% 0.14/0.46 ! [G: int > nat,F: int > int,A4: set_int] :
% 0.14/0.46 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_int_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_nat @ ( image_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2239_INF__image,axiom,
% 0.14/0.46 ! [G: rat > int,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_int @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2240_INF__image,axiom,
% 0.14/0.46 ! [G: nat > int,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2241_INF__image,axiom,
% 0.14/0.46 ! [G: nat > int,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2242_INF__image,axiom,
% 0.14/0.46 ! [G: int > int,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_image
% 0.14/0.46 thf(fact_2243_SUP__image,axiom,
% 0.14/0.46 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_o @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_o @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2244_SUP__image,axiom,
% 0.14/0.46 ! [G: rat > nat,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_nat @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2245_SUP__image,axiom,
% 0.14/0.46 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2246_SUP__image,axiom,
% 0.14/0.46 ! [G: nat > nat,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_nat @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2247_SUP__image,axiom,
% 0.14/0.46 ! [G: int > nat,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2248_SUP__image,axiom,
% 0.14/0.46 ! [G: int > nat,F: int > int,A4: set_int] :
% 0.14/0.46 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_int_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_nat @ ( image_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2249_SUP__image,axiom,
% 0.14/0.46 ! [G: rat > int,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_int @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2250_SUP__image,axiom,
% 0.14/0.46 ! [G: nat > int,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2251_SUP__image,axiom,
% 0.14/0.46 ! [G: nat > int,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2252_SUP__image,axiom,
% 0.14/0.46 ! [G: int > int,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_image
% 0.14/0.46 thf(fact_2253_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,U: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2254_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,U: set_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2255_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_o,U: set_nat,F: $o > set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2256_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_nat,U: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2257_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,U: set_nat,F: int > set_nat] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2258_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,U: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2259_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,U: product_unit,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2260_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_o,U: product_unit,F: $o > product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2261_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_nat,U: product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2262_INF__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,U: product_unit,F: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_greatest
% 0.14/0.46 thf(fact_2263_INF__lower2,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2264_INF__lower2,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2265_INF__lower2,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > set_nat,U: set_nat] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2266_INF__lower2,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2267_INF__lower2,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > set_nat,U: set_nat] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2268_INF__lower2,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2269_INF__lower2,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2270_INF__lower2,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > product_unit,U: product_unit] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2271_INF__lower2,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2272_INF__lower2,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > product_unit,U: product_unit] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower2
% 0.14/0.46 thf(fact_2273_INF__lower,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2274_INF__lower,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2275_INF__lower,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > set_nat] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2276_INF__lower,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2277_INF__lower,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > set_nat] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2278_INF__lower,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2279_INF__lower,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2280_INF__lower,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > product_unit] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2281_INF__lower,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > product_unit] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2282_INF__lower,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > product_unit] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_lower
% 0.14/0.46 thf(fact_2283_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,X2: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2284_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,X2: set_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2285_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_o,X2: set_nat,F: $o > set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: $o] :
% 0.14/0.46 ( ( member_o @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2286_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_nat,X2: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: nat] :
% 0.14/0.46 ( ( member_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2287_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_int,X2: set_nat,F: int > set_nat] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: int] :
% 0.14/0.46 ( ( member_int @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2288_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,X2: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2289_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,X2: product_unit,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2290_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_o,X2: product_unit,F: $o > product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: $o] :
% 0.14/0.46 ( ( member_o @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2291_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_nat,X2: product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: nat] :
% 0.14/0.46 ( ( member_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2292_INF__eqI,axiom,
% 0.14/0.46 ! [A4: set_int,X2: product_unit,F: int > product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: int] :
% 0.14/0.46 ( ( member_int @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eqI
% 0.14/0.46 thf(fact_2293_SUP__upper2,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,U: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2294_SUP__upper2,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,U: set_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2295_SUP__upper2,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,U: set_nat,F: $o > set_nat] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2296_SUP__upper2,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,U: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2297_SUP__upper2,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,U: set_nat,F: int > set_nat] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2298_SUP__upper2,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,U: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2299_SUP__upper2,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,U: product_unit,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2300_SUP__upper2,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,U: product_unit,F: $o > product_unit] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2301_SUP__upper2,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,U: product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2302_SUP__upper2,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,U: product_unit,F: int > product_unit] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper2
% 0.14/0.46 thf(fact_2303_SUP__upper,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2304_SUP__upper,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2305_SUP__upper,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > set_nat] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2306_SUP__upper,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2307_SUP__upper,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > set_nat] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2308_SUP__upper,axiom,
% 0.14/0.46 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2309_SUP__upper,axiom,
% 0.14/0.46 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2310_SUP__upper,axiom,
% 0.14/0.46 ! [I: $o,A4: set_o,F: $o > product_unit] :
% 0.14/0.46 ( ( member_o @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2311_SUP__upper,axiom,
% 0.14/0.46 ! [I: nat,A4: set_nat,F: nat > product_unit] :
% 0.14/0.46 ( ( member_nat @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2312_SUP__upper,axiom,
% 0.14/0.46 ! [I: int,A4: set_int,F: int > product_unit] :
% 0.14/0.46 ( ( member_int @ I @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_upper
% 0.14/0.46 thf(fact_2313_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2314_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2315_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > set_nat,U: set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2316_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > set_nat,U: set_nat] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2317_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > set_nat,U: set_nat] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2318_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2319_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2320_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2321_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > product_unit,U: product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2322_SUP__least,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > product_unit,U: product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_least
% 0.14/0.46 thf(fact_2323_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2324_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2325_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > set_nat,X2: set_nat] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: $o] :
% 0.14/0.46 ( ( member_o @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2326_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > set_nat,X2: set_nat] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: nat] :
% 0.14/0.46 ( ( member_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2327_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > set_nat,X2: set_nat] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: set_nat] :
% 0.14/0.46 ( ! [I5: int] :
% 0.14/0.46 ( ( member_int @ I5 @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2328_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ! [I4: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2329_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2330_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > product_unit,X2: product_unit] :
% 0.14/0.46 ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: $o] :
% 0.14/0.46 ( ( member_o @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2331_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > product_unit,X2: product_unit] :
% 0.14/0.46 ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: nat] :
% 0.14/0.46 ( ( member_nat @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2332_SUP__eqI,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > product_unit,X2: product_unit] :
% 0.14/0.46 ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 0.14/0.46 => ( ! [Y: product_unit] :
% 0.14/0.46 ( ! [I5: int] :
% 0.14/0.46 ( ( member_int @ I5 @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.46 = X2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eqI
% 0.14/0.46 thf(fact_2333_INT__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: rat > set_nat,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_rat_set_nat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(10)
% 0.14/0.46 thf(fact_2334_INT__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: nat > set_nat,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(10)
% 0.14/0.46 thf(fact_2335_INT__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: int > set_nat,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(10)
% 0.14/0.46 thf(fact_2336_INT__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: nat > set_nat,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_int_set_nat
% 0.14/0.46 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(10)
% 0.14/0.46 thf(fact_2337_INT__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: int > set_nat,F: int > int,A4: set_int] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_int_set_nat
% 0.14/0.46 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(10)
% 0.14/0.46 thf(fact_2338_INT__lower,axiom,
% 0.14/0.46 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_lower
% 0.14/0.46 thf(fact_2339_INT__lower,axiom,
% 0.14/0.46 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_lower
% 0.14/0.46 thf(fact_2340_INT__lower,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,B5: $o > set_nat] :
% 0.14/0.46 ( ( member_o @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_lower
% 0.14/0.46 thf(fact_2341_INT__lower,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.46 ( ( member_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_lower
% 0.14/0.46 thf(fact_2342_INT__lower,axiom,
% 0.14/0.46 ! [A: int,A4: set_int,B5: int > set_nat] :
% 0.14/0.46 ( ( member_int @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_lower
% 0.14/0.46 thf(fact_2343_INT__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,C3: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_greatest
% 0.14/0.46 thf(fact_2344_INT__greatest,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,C3: set_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_greatest
% 0.14/0.46 thf(fact_2345_INT__greatest,axiom,
% 0.14/0.46 ! [A4: set_o,C3: set_nat,B5: $o > set_nat] :
% 0.14/0.46 ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_greatest
% 0.14/0.46 thf(fact_2346_INT__greatest,axiom,
% 0.14/0.46 ! [A4: set_nat,C3: set_nat,B5: nat > set_nat] :
% 0.14/0.46 ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_greatest
% 0.14/0.46 thf(fact_2347_INT__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,C3: set_nat,B5: int > set_nat] :
% 0.14/0.46 ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_greatest
% 0.14/0.46 thf(fact_2348_INT__anti__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ G @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_anti_mono
% 0.14/0.46 thf(fact_2349_INT__anti__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ G @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_anti_mono
% 0.14/0.46 thf(fact_2350_INT__anti__mono,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_anti_mono
% 0.14/0.46 thf(fact_2351_INT__anti__mono,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ G @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_anti_mono
% 0.14/0.46 thf(fact_2352_INT__anti__mono,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ G @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_anti_mono
% 0.14/0.46 thf(fact_2353_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_int,C: int] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_int )
% 0.14/0.46 => ( ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_int ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_int @ C @ bot_bot_set_int ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2354_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_int,C: nat] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_int )
% 0.14/0.46 => ( ( image_int_nat
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_nat ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( image_int_nat
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2355_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2356_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: $o] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_Product_unit_o
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_o ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_Product_unit_o
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_o @ C @ bot_bot_set_o ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2357_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: nat] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_875570014554754200it_nat
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_nat ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( image_875570014554754200it_nat
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2358_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_Product_unit
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_Product_unit
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2359_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_o,C: $o] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_o
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_o ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_o
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_o @ C @ bot_bot_set_o ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2360_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_o,C: nat] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_nat
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_nat ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( image_o_nat
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2361_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_nat,C: rat] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( image_nat_rat
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_rat ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( image_nat_rat
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_rat @ C @ bot_bot_set_rat ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2362_image__constant__conv,axiom,
% 0.14/0.46 ! [A4: set_nat,C: int] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = bot_bot_set_int ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_int @ C @ bot_bot_set_int ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant_conv
% 0.14/0.46 thf(fact_2363_image__constant,axiom,
% 0.14/0.46 ! [X2: nat,A4: set_nat,C: rat] :
% 0.14/0.46 ( ( member_nat @ X2 @ A4 )
% 0.14/0.46 => ( ( image_nat_rat
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_rat @ C @ bot_bot_set_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2364_image__constant,axiom,
% 0.14/0.46 ! [X2: nat,A4: set_nat,C: int] :
% 0.14/0.46 ( ( member_nat @ X2 @ A4 )
% 0.14/0.46 => ( ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_int @ C @ bot_bot_set_int ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2365_image__constant,axiom,
% 0.14/0.46 ! [X2: int,A4: set_int,C: int] :
% 0.14/0.46 ( ( member_int @ X2 @ A4 )
% 0.14/0.46 => ( ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_int @ C @ bot_bot_set_int ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2366_image__constant,axiom,
% 0.14/0.46 ! [X2: $o,A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( member_o @ X2 @ A4 )
% 0.14/0.46 => ( ( image_o_Product_unit
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2367_image__constant,axiom,
% 0.14/0.46 ! [X2: nat,A4: set_nat,C: product_unit] :
% 0.14/0.46 ( ( member_nat @ X2 @ A4 )
% 0.14/0.46 => ( ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2368_image__constant,axiom,
% 0.14/0.46 ! [X2: int,A4: set_int,C: product_unit] :
% 0.14/0.46 ( ( member_int @ X2 @ A4 )
% 0.14/0.46 => ( ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2369_image__constant,axiom,
% 0.14/0.46 ! [X2: $o,A4: set_o,C: $o] :
% 0.14/0.46 ( ( member_o @ X2 @ A4 )
% 0.14/0.46 => ( ( image_o_o
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2370_image__constant,axiom,
% 0.14/0.46 ! [X2: nat,A4: set_nat,C: $o] :
% 0.14/0.46 ( ( member_nat @ X2 @ A4 )
% 0.14/0.46 => ( ( image_nat_o
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2371_image__constant,axiom,
% 0.14/0.46 ! [X2: int,A4: set_int,C: $o] :
% 0.14/0.46 ( ( member_int @ X2 @ A4 )
% 0.14/0.46 => ( ( image_int_o
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2372_image__constant,axiom,
% 0.14/0.46 ! [X2: $o,A4: set_o,C: nat] :
% 0.14/0.46 ( ( member_o @ X2 @ A4 )
% 0.14/0.46 => ( ( image_o_nat
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 )
% 0.14/0.46 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_constant
% 0.14/0.46 thf(fact_2373_UN__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: rat > set_nat,F: nat > rat,A4: set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_rat_set_nat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(10)
% 0.14/0.46 thf(fact_2374_UN__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: nat > set_nat,F: nat > nat,A4: set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(10)
% 0.14/0.46 thf(fact_2375_UN__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: int > set_nat,F: nat > int,A4: set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(10)
% 0.14/0.46 thf(fact_2376_UN__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: nat > set_nat,F: int > nat,A4: set_int] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_int_set_nat
% 0.14/0.46 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(10)
% 0.14/0.46 thf(fact_2377_UN__extend__simps_I10_J,axiom,
% 0.14/0.46 ! [B5: int > set_nat,F: int > int,A4: set_int] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_int_set_nat
% 0.14/0.46 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(10)
% 0.14/0.46 thf(fact_2378_UN__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2379_UN__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2380_UN__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2381_UN__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2382_UN__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2383_UN__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2384_UN__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bot_set_nat ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2385_UN__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bot_set_nat ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2386_UN__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bot_set_nat ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2387_UN__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.46 ( ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bo2099793752762293965at_nat ) ).
% 0.14/0.46
% 0.14/0.46 % UN_empty
% 0.14/0.46 thf(fact_2388_UN__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_mono
% 0.14/0.46 thf(fact_2389_UN__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_mono
% 0.14/0.46 thf(fact_2390_UN__mono,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_mono
% 0.14/0.46 thf(fact_2391_UN__mono,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_mono
% 0.14/0.46 thf(fact_2392_UN__mono,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_mono
% 0.14/0.46 thf(fact_2393_UN__least,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat,C3: set_nat] :
% 0.14/0.46 ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_least
% 0.14/0.46 thf(fact_2394_UN__least,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat,C3: set_nat] :
% 0.14/0.46 ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_least
% 0.14/0.46 thf(fact_2395_UN__least,axiom,
% 0.14/0.46 ! [A4: set_o,B5: $o > set_nat,C3: set_nat] :
% 0.14/0.46 ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_least
% 0.14/0.46 thf(fact_2396_UN__least,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: nat > set_nat,C3: set_nat] :
% 0.14/0.46 ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_least
% 0.14/0.46 thf(fact_2397_UN__least,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_nat,C3: set_nat] :
% 0.14/0.46 ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_least
% 0.14/0.46 thf(fact_2398_UN__upper,axiom,
% 0.14/0.46 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_upper
% 0.14/0.46 thf(fact_2399_UN__upper,axiom,
% 0.14/0.46 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_upper
% 0.14/0.46 thf(fact_2400_UN__upper,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,B5: $o > set_nat] :
% 0.14/0.46 ( ( member_o @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_upper
% 0.14/0.46 thf(fact_2401_UN__upper,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.46 ( ( member_nat @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_upper
% 0.14/0.46 thf(fact_2402_UN__upper,axiom,
% 0.14/0.46 ! [A: int,A4: set_int,B5: int > set_nat] :
% 0.14/0.46 ( ( member_int @ A @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_upper
% 0.14/0.46 thf(fact_2403_Union__natural,axiom,
% 0.14/0.46 ! [F: int > int] :
% 0.14/0.46 ( ( comp_s8709038167382007543et_int @ comple3221217463730067765et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) ) )
% 0.14/0.46 = ( comp_s2487324123861929025et_int @ ( image_int_int @ F ) @ comple3221217463730067765et_int ) ) ).
% 0.14/0.46
% 0.14/0.46 % Union_natural
% 0.14/0.46 thf(fact_2404_Union__natural,axiom,
% 0.14/0.46 ! [F: nat > rat] :
% 0.14/0.46 ( ( comp_s703482200030188019et_nat @ comple3890839924845867745et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) ) )
% 0.14/0.46 = ( comp_s6435139744279249717et_nat @ ( image_nat_rat @ F ) @ comple7399068483239264473et_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % Union_natural
% 0.14/0.46 thf(fact_2405_Union__natural,axiom,
% 0.14/0.46 ! [F: nat > int] :
% 0.14/0.46 ( ( comp_s1975749275458958491et_nat @ comple3221217463730067765et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) ) )
% 0.14/0.46 = ( comp_s3768223441818958217et_nat @ ( image_nat_int @ F ) @ comple7399068483239264473et_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % Union_natural
% 0.14/0.46 thf(fact_2406_Union__natural,axiom,
% 0.14/0.46 ! [F: int > nat] :
% 0.14/0.46 ( ( comp_s6907669228194913343et_int @ comple7399068483239264473et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) ) )
% 0.14/0.46 = ( comp_s5712175470073906149et_int @ ( image_int_nat @ F ) @ comple3221217463730067765et_int ) ) ).
% 0.14/0.46
% 0.14/0.46 % Union_natural
% 0.14/0.46 thf(fact_2407_Union__natural,axiom,
% 0.14/0.46 ! [F: nat > nat] :
% 0.14/0.46 ( ( comp_s174380336271864291et_nat @ comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) ) )
% 0.14/0.46 = ( comp_s6993074788030935341et_nat @ ( image_nat_nat @ F ) @ comple7399068483239264473et_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % Union_natural
% 0.14/0.46 thf(fact_2408_image__Union,axiom,
% 0.14/0.46 ! [F: int > int,S5: set_set_int] :
% 0.14/0.46 ( ( image_int_int @ F @ ( comple3221217463730067765et_int @ S5 ) )
% 0.14/0.46 = ( comple3221217463730067765et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ S5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_Union
% 0.14/0.46 thf(fact_2409_image__Union,axiom,
% 0.14/0.46 ! [F: int > nat,S5: set_set_int] :
% 0.14/0.46 ( ( image_int_nat @ F @ ( comple3221217463730067765et_int @ S5 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ S5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_Union
% 0.14/0.46 thf(fact_2410_image__Union,axiom,
% 0.14/0.46 ! [F: nat > rat,S5: set_set_nat] :
% 0.14/0.46 ( ( image_nat_rat @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 0.14/0.46 = ( comple3890839924845867745et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ S5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_Union
% 0.14/0.46 thf(fact_2411_image__Union,axiom,
% 0.14/0.46 ! [F: nat > int,S5: set_set_nat] :
% 0.14/0.46 ( ( image_nat_int @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 0.14/0.46 = ( comple3221217463730067765et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ S5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_Union
% 0.14/0.46 thf(fact_2412_image__Union,axiom,
% 0.14/0.46 ! [F: nat > nat,S5: set_set_nat] :
% 0.14/0.46 ( ( image_nat_nat @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ S5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_Union
% 0.14/0.46 thf(fact_2413_UN__extend__simps_I8_J,axiom,
% 0.14/0.46 ! [B5: nat > set_nat,A4: set_set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_7916887816326733075et_nat
% 0.14/0.46 @ ^ [Y5: set_nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ Y5 ) )
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_extend_simps(8)
% 0.14/0.46 thf(fact_2414_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > product_unit,C: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: int] :
% 0.14/0.46 ( ( member_int @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2415_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > product_unit,C: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2416_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > product_unit,C: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: $o] :
% 0.14/0.46 ( ( member_o @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2417_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > product_unit,C: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: nat] :
% 0.14/0.46 ( ( member_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2418_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_int,F: int > set_nat,C: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: int] :
% 0.14/0.46 ( ( member_int @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2419_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,F: product_unit > set_nat,C: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2420_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_o,F: $o > set_nat,C: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: $o] :
% 0.14/0.46 ( ( member_o @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2421_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_nat,F: nat > set_nat,C: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: nat] :
% 0.14/0.46 ( ( member_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2422_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,C: product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2423_INF__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,C: set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 0.14/0.46 => ( ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_eq_iff
% 0.14/0.46 thf(fact_2424_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_int,C: product_unit,F: int > product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: int] :
% 0.14/0.46 ( ( member_int @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2425_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,C: product_unit,F: product_unit > product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2426_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_o,C: product_unit,F: $o > product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: $o] :
% 0.14/0.46 ( ( member_o @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2427_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_nat,C: product_unit,F: nat > product_unit] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: nat] :
% 0.14/0.46 ( ( member_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2428_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_int,C: set_nat,F: int > set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_int )
% 0.14/0.46 => ( ! [I4: int] :
% 0.14/0.46 ( ( member_int @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: int] :
% 0.14/0.46 ( ( member_int @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2429_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Product_unit,C: set_nat,F: product_unit > set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [I4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2430_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_o,C: set_nat,F: $o > set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_o )
% 0.14/0.46 => ( ! [I4: $o] :
% 0.14/0.46 ( ( member_o @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: $o] :
% 0.14/0.46 ( ( member_o @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2431_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_nat,C: set_nat,F: nat > set_nat] :
% 0.14/0.46 ( ( I3 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [I4: nat] :
% 0.14/0.46 ( ( member_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: nat] :
% 0.14/0.46 ( ( member_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2432_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,C: product_unit,F: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2433_SUP__eq__iff,axiom,
% 0.14/0.46 ! [I3: set_Pr1261947904930325089at_nat,C: set_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ! [I4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 0.14/0.46 => ( ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 0.14/0.46 = C )
% 0.14/0.46 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.46 => ( ( F @ X4 )
% 0.14/0.46 = C ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_eq_iff
% 0.14/0.46 thf(fact_2434_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: char > product_unit,A: product_unit,X2: char] :
% 0.14/0.46 ( ( ( image_4337914935673063477t_unit @ F @ top_top_set_char )
% 0.14/0.46 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2435_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: char > $o,A: $o,X2: char] :
% 0.14/0.46 ( ( ( image_char_o @ F @ top_top_set_char )
% 0.14/0.46 = ( insert_o @ A @ bot_bot_set_o ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2436_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: char > nat,A: nat,X2: char] :
% 0.14/0.46 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.46 = ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2437_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: rat > product_unit,A: product_unit,X2: rat] :
% 0.14/0.46 ( ( ( image_2327579789247107822t_unit @ F @ top_top_set_rat )
% 0.14/0.46 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2438_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: rat > $o,A: $o,X2: rat] :
% 0.14/0.46 ( ( ( image_rat_o @ F @ top_top_set_rat )
% 0.14/0.46 = ( insert_o @ A @ bot_bot_set_o ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2439_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: rat > nat,A: nat,X2: rat] :
% 0.14/0.46 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.46 = ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2440_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: nat > rat,A: rat,X2: nat] :
% 0.14/0.46 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.46 = ( insert_rat @ A @ bot_bot_set_rat ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2441_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: nat > int,A: int,X2: nat] :
% 0.14/0.46 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 0.14/0.46 = ( insert_int @ A @ bot_bot_set_int ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2442_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: nat > product_unit,A: product_unit,X2: nat] :
% 0.14/0.46 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 0.14/0.46 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2443_range__eq__singletonD,axiom,
% 0.14/0.46 ! [F: nat > $o,A: $o,X2: nat] :
% 0.14/0.46 ( ( ( image_nat_o @ F @ top_top_set_nat )
% 0.14/0.46 = ( insert_o @ A @ bot_bot_set_o ) )
% 0.14/0.46 => ( ( F @ X2 )
% 0.14/0.46 = A ) ) ).
% 0.14/0.46
% 0.14/0.46 % range_eq_singletonD
% 0.14/0.46 thf(fact_2444_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ B5 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2445_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ B5 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2446_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_o,A4: set_o,F: $o > set_nat,G: $o > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ B5 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2447_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_nat,A4: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ B5 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2448_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_int,A4: set_int,F: int > set_nat,G: int > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ B5 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2449_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,G: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ B5 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2450_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,G: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ B5 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2451_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_o,A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ B5 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2452_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_nat,A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ B5 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2453_INF__superset__mono,axiom,
% 0.14/0.46 ! [B5: set_int,A4: set_int,F: int > product_unit,G: int > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ B5 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_superset_mono
% 0.14/0.46 thf(fact_2454_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2455_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2456_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2457_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2458_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2459_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,G: produc3843707927480180839at_nat > product_unit] :
% 0.14/0.46 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2460_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,G: product_prod_nat_nat > product_unit] :
% 0.14/0.46 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2461_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_o,B5: set_o,F: $o > product_unit,G: $o > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2462_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2463_SUP__subset__mono,axiom,
% 0.14/0.46 ! [A4: set_int,B5: set_int,F: int > product_unit,G: int > product_unit] :
% 0.14/0.46 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_subset_mono
% 0.14/0.46 thf(fact_2464_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2465_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2466_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2467_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_char] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2468_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: set_char] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2469_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: set_char] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2470_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_rat] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2471_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: set_rat] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2472_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: set_rat] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2473_INF__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_int] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_constant
% 0.14/0.46 thf(fact_2474_INF__empty,axiom,
% 0.14/0.46 ! [F: product_unit > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2475_INF__empty,axiom,
% 0.14/0.46 ! [F: $o > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2476_INF__empty,axiom,
% 0.14/0.46 ! [F: nat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2477_INF__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2478_INF__empty,axiom,
% 0.14/0.46 ! [F: $o > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_o_set_char @ F @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2479_INF__empty,axiom,
% 0.14/0.46 ! [F: nat > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_nat_set_char @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2480_INF__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2481_INF__empty,axiom,
% 0.14/0.46 ! [F: $o > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_o_set_rat @ F @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2482_INF__empty,axiom,
% 0.14/0.46 ! [F: nat > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2483_INF__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_int] :
% 0.14/0.46 ( ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_int ) ).
% 0.14/0.46
% 0.14/0.46 % INF_empty
% 0.14/0.46 thf(fact_2484_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2485_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2486_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_Product_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2487_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_Product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_7778121751606633509t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_7778121751606633509t_unit
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2488_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_o] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_6930536745178679216_set_o
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_set_o ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_6930536745178679216_set_o
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2489_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: set_Product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_663195431845683034t_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_663195431845683034t_unit
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2490_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_o,C: set_o] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_o_set_o
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_set_o ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_o_set_o
% 0.14/0.46 @ ^ [Y5: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2491_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: set_Product_unit] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_4824033694279209942t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3349607820504768346t_unit
% 0.14/0.46 @ ( image_4824033694279209942t_unit
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2492_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_nat,C: set_o] :
% 0.14/0.46 ( ( ( A4 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_nat_set_o
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_set_o ) )
% 0.14/0.46 & ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple90263536869209701_set_o
% 0.14/0.46 @ ( image_nat_set_o
% 0.14/0.46 @ ^ [Y5: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2493_SUP__constant,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_nat] :
% 0.14/0.46 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = bot_bot_set_nat ) )
% 0.14/0.46 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [Y5: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_constant
% 0.14/0.46 thf(fact_2494_SUP__empty,axiom,
% 0.14/0.46 ! [F: product_unit > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bot_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2495_SUP__empty,axiom,
% 0.14/0.46 ! [F: $o > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bot_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2496_SUP__empty,axiom,
% 0.14/0.46 ! [F: nat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bot_Product_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2497_SUP__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2498_SUP__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2499_SUP__empty,axiom,
% 0.14/0.46 ! [F: $o > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ F @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2500_SUP__empty,axiom,
% 0.14/0.46 ! [F: $o > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ F @ bot_bot_set_o ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2501_SUP__empty,axiom,
% 0.14/0.46 ! [F: nat > set_Product_unit] :
% 0.14/0.46 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bo3957492148770167129t_unit ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2502_SUP__empty,axiom,
% 0.14/0.46 ! [F: nat > set_o] :
% 0.14/0.46 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ F @ bot_bot_set_nat ) )
% 0.14/0.46 = bot_bot_set_o ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2503_SUP__empty,axiom,
% 0.14/0.46 ! [F: product_unit > set_nat] :
% 0.14/0.46 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = bot_bot_set_nat ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_empty
% 0.14/0.46 thf(fact_2504_INT__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2505_INT__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_o_set_char @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2506_INT__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_char] :
% 0.14/0.46 ( ( comple7965528767983648192t_char @ ( image_nat_set_char @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_set_char ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2507_INT__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2508_INT__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_o_set_rat @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2509_INT__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_rat] :
% 0.14/0.46 ( ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2510_INT__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_int] :
% 0.14/0.46 ( ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_int ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2511_INT__empty,axiom,
% 0.14/0.46 ! [B5: $o > set_int] :
% 0.14/0.46 ( ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ bot_bot_set_o ) )
% 0.14/0.46 = top_top_set_int ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2512_INT__empty,axiom,
% 0.14/0.46 ! [B5: nat > set_int] :
% 0.14/0.46 ( ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ bot_bot_set_nat ) )
% 0.14/0.46 = top_top_set_int ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2513_INT__empty,axiom,
% 0.14/0.46 ! [B5: product_unit > set_nat] :
% 0.14/0.46 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 = top_top_set_nat ) ).
% 0.14/0.46
% 0.14/0.46 % INT_empty
% 0.14/0.46 thf(fact_2514_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_int,C: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( complete_Inf_Inf_nat
% 0.14/0.46 @ ( image_int_nat
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2515_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( complete_Inf_Inf_nat
% 0.14/0.46 @ ( image_nat_nat
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2516_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_int,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( complete_Inf_Inf_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2517_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( complete_Inf_Inf_int
% 0.14/0.46 @ ( image_873079544045703924it_int
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2518_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_o,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( complete_Inf_Inf_int
% 0.14/0.46 @ ( image_o_int
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2519_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( complete_Inf_Inf_int
% 0.14/0.46 @ ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2520_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2521_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2522_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2523_cINF__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_nat] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_const
% 0.14/0.46 thf(fact_2524_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_int,C: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( complete_Sup_Sup_nat
% 0.14/0.46 @ ( image_int_nat
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2525_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( complete_Sup_Sup_nat
% 0.14/0.46 @ ( image_nat_nat
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2526_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_int,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2527_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_873079544045703924it_int
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2528_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_o,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_o_int
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2529_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2530_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_405062704495631173t_unit
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2531_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_o,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_o_Product_unit
% 0.14/0.46 @ ^ [X4: $o] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2532_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_nat,C: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2533_cSUP__const,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,C: set_nat] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : C
% 0.14/0.46 @ A4 ) )
% 0.14/0.46 = C ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_const
% 0.14/0.46 thf(fact_2534_SUP__INF,axiom,
% 0.14/0.46 ! [P2: char > char > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8077363282794994245t_unit
% 0.14/0.46 @ ^ [X4: char > char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_to8079350907815874599r_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2535_SUP__INF,axiom,
% 0.14/0.46 ! [P2: char > rat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_6940606515012899070t_unit
% 0.14/0.46 @ ^ [X4: rat > char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2536_SUP__INF,axiom,
% 0.14/0.46 ! [P2: char > nat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4600008085730780422t_unit
% 0.14/0.46 @ ^ [X4: nat > char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_nat_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2537_SUP__INF,axiom,
% 0.14/0.46 ! [P2: char > int > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4409302170498516394t_unit
% 0.14/0.46 @ ^ [X4: int > char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 @ top_top_set_int_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2538_SUP__INF,axiom,
% 0.14/0.46 ! [P2: rat > char > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_7615136836863079294t_unit
% 0.14/0.46 @ ^ [X4: char > rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2539_SUP__INF,axiom,
% 0.14/0.46 ! [P2: rat > rat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_1193274288206594871t_unit
% 0.14/0.46 @ ^ [X4: rat > rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2540_SUP__INF,axiom,
% 0.14/0.46 ! [P2: rat > nat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_340470173791133503t_unit
% 0.14/0.46 @ ^ [X4: nat > rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_nat_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2541_SUP__INF,axiom,
% 0.14/0.46 ! [P2: rat > int > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4174709274675160035t_unit
% 0.14/0.46 @ ^ [X4: int > rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 @ top_top_set_int_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2542_SUP__INF,axiom,
% 0.14/0.46 ! [P2: nat > char > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_108929247839792006t_unit
% 0.14/0.46 @ ^ [X4: char > nat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2543_SUP__INF,axiom,
% 0.14/0.46 ! [P2: nat > rat > product_unit] :
% 0.14/0.46 ( ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2910438736038083391t_unit
% 0.14/0.46 @ ^ [X4: rat > nat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_INF
% 0.14/0.46 thf(fact_2544_INF__SUP,axiom,
% 0.14/0.46 ! [P2: char > char > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8077363282794994245t_unit
% 0.14/0.46 @ ^ [F2: char > char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_to8079350907815874599r_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2545_INF__SUP,axiom,
% 0.14/0.46 ! [P2: char > rat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_6940606515012899070t_unit
% 0.14/0.46 @ ^ [F2: rat > char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2546_INF__SUP,axiom,
% 0.14/0.46 ! [P2: char > nat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4600008085730780422t_unit
% 0.14/0.46 @ ^ [F2: nat > char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_nat_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2547_INF__SUP,axiom,
% 0.14/0.46 ! [P2: char > int > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4409302170498516394t_unit
% 0.14/0.46 @ ^ [F2: int > char] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [X4: int] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 @ top_top_set_int_char ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2548_INF__SUP,axiom,
% 0.14/0.46 ! [P2: rat > char > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_7615136836863079294t_unit
% 0.14/0.46 @ ^ [F2: char > rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2549_INF__SUP,axiom,
% 0.14/0.46 ! [P2: rat > rat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_1193274288206594871t_unit
% 0.14/0.46 @ ^ [F2: rat > rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2550_INF__SUP,axiom,
% 0.14/0.46 ! [P2: rat > nat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [Y5: nat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_340470173791133503t_unit
% 0.14/0.46 @ ^ [F2: nat > rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_nat_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2551_INF__SUP,axiom,
% 0.14/0.46 ! [P2: rat > int > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [Y5: int] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_4174709274675160035t_unit
% 0.14/0.46 @ ^ [F2: int > rat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_5846526143423701914t_unit
% 0.14/0.46 @ ^ [X4: int] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_int ) )
% 0.14/0.46 @ top_top_set_int_rat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2552_INF__SUP,axiom,
% 0.14/0.46 ! [P2: nat > char > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [Y5: char] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_108929247839792006t_unit
% 0.14/0.46 @ ^ [F2: char > nat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_4337914935673063477t_unit
% 0.14/0.46 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_char ) )
% 0.14/0.46 @ top_top_set_char_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2553_INF__SUP,axiom,
% 0.14/0.46 ! [P2: nat > rat > product_unit] :
% 0.14/0.46 ( ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [Y5: rat] :
% 0.14/0.46 ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_8730104196221521654t_unit
% 0.14/0.46 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 0.14/0.46 @ top_top_set_nat ) )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 = ( comple4687483117567863418t_unit
% 0.14/0.46 @ ( image_2910438736038083391t_unit
% 0.14/0.46 @ ^ [F2: rat > nat] :
% 0.14/0.46 ( comple2584293577114468500t_unit
% 0.14/0.46 @ ( image_2327579789247107822t_unit
% 0.14/0.46 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 0.14/0.46 @ top_top_set_rat ) )
% 0.14/0.46 @ top_top_set_rat_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_SUP
% 0.14/0.46 thf(fact_2554_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,M3: nat,F: int > nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2555_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,M3: nat,F: product_unit > nat] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2556_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_o,M3: nat,F: $o > nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2557_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_nat,M3: nat,F: nat > nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2558_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,M3: int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2559_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,M3: int,F: product_unit > int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2560_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_o,M3: int,F: $o > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2561_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_nat,M3: int,F: nat > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2562_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_int,M3: product_unit,F: int > product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ M3 @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2563_cINF__greatest,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,M3: product_unit,F: product_unit > product_unit] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ M3 @ ( F @ X ) ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ M3 @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_greatest
% 0.14/0.46 thf(fact_2564_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > nat,M: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2565_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,F: product_unit > nat,M: nat] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2566_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > nat,M: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2567_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > nat,M: nat] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2568_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > int,M: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2569_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,F: product_unit > int,M: int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2570_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_o,F: $o > int,M: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2571_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_nat,F: nat > int,M: int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2572_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_int,F: int > product_unit,M: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2573_cSUP__least,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,F: product_unit > product_unit,M: product_unit] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ M ) )
% 0.14/0.46 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ M ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_least
% 0.14/0.46 thf(fact_2574_UN__constant__eq,axiom,
% 0.14/0.46 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,C: set_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.46 => ( ! [X: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.46 => ( ( F @ X )
% 0.14/0.46 = C ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_constant_eq
% 0.14/0.46 thf(fact_2575_UN__constant__eq,axiom,
% 0.14/0.46 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,C: set_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.46 => ( ! [X: product_prod_nat_nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.46 => ( ( F @ X )
% 0.14/0.46 = C ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_constant_eq
% 0.14/0.46 thf(fact_2576_UN__constant__eq,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,F: $o > set_nat,C: set_nat] :
% 0.14/0.46 ( ( member_o @ A @ A4 )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ( F @ X )
% 0.14/0.46 = C ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_constant_eq
% 0.14/0.46 thf(fact_2577_UN__constant__eq,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,F: nat > set_nat,C: set_nat] :
% 0.14/0.46 ( ( member_nat @ A @ A4 )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ( F @ X )
% 0.14/0.46 = C ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_constant_eq
% 0.14/0.46 thf(fact_2578_UN__constant__eq,axiom,
% 0.14/0.46 ! [A: int,A4: set_int,F: int > set_nat,C: set_nat] :
% 0.14/0.46 ( ( member_int @ A @ A4 )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( F @ X )
% 0.14/0.46 = C ) )
% 0.14/0.46 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 0.14/0.46 = C ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % UN_constant_eq
% 0.14/0.46 thf(fact_2579_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.14/0.46 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 0.14/0.46 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 0.14/0.46 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.46 & ( member8757157785044589968at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2580_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.14/0.46 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 0.14/0.46 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 0.14/0.46 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.46 & ( member8440522571783428010at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2581_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_o,R: set_Product_prod_o_o,A: $o,B: $o] :
% 0.14/0.46 ( ( refl_on_o @ A4 @ R )
% 0.14/0.46 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 0.14/0.46 => ( ( member_o @ A @ A4 )
% 0.14/0.46 & ( member_o @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2582_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.46 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 0.14/0.46 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 0.14/0.46 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 0.14/0.46 & ( member6273874620674182256at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2583_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.46 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 0.14/0.46 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 0.14/0.46 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 0.14/0.46 & ( member2643936169264416010at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2584_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 0.14/0.46 ( ( refl_on_nat @ A4 @ R )
% 0.14/0.46 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.14/0.46 => ( ( member_nat @ A @ A4 )
% 0.14/0.46 & ( member_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2585_refl__on__domain,axiom,
% 0.14/0.46 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 0.14/0.46 ( ( refl_on_int @ A4 @ R )
% 0.14/0.46 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.14/0.46 => ( ( member_int @ A @ A4 )
% 0.14/0.46 & ( member_int @ B @ A4 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % refl_on_domain
% 0.14/0.46 thf(fact_2586_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_char,B5: product_unit > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_5325685772115642575t_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2587_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_char,B5: $o > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_o_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2588_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_char,B5: nat > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_nat_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2589_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_rat,B5: product_unit > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_4665621433434589782et_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2590_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_rat,B5: $o > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_o_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2591_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_rat,B5: nat > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_nat_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2592_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_int,B5: product_unit > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2593_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_int,B5: $o > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2594_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_int,B5: nat > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2595_INT__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_nat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(4)
% 0.14/0.46 thf(fact_2596_relcompp__bot2,axiom,
% 0.14/0.46 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.14/0.46 ( ( relcom8911704206367525917at_int @ R3 @ bot_bo5438875203632553179_int_o )
% 0.14/0.46 = bot_bo5438875203632553179_int_o ) ).
% 0.14/0.46
% 0.14/0.46 % relcompp_bot2
% 0.14/0.46 thf(fact_2597_relcompp__bot2,axiom,
% 0.14/0.46 ! [R3: int > int > $o] :
% 0.14/0.46 ( ( relcom967497705283160040nteger @ R3 @ bot_bo341146761387662761eger_o )
% 0.14/0.46 = bot_bo341146761387662761eger_o ) ).
% 0.14/0.46
% 0.14/0.46 % relcompp_bot2
% 0.14/0.46 thf(fact_2598_relcompp__bot1,axiom,
% 0.14/0.46 ! [R3: product_prod_nat_nat > int > $o] :
% 0.14/0.46 ( ( relcom8911704206367525917at_int @ bot_bo4898103413517107610_nat_o @ R3 )
% 0.14/0.46 = bot_bo5438875203632553179_int_o ) ).
% 0.14/0.46
% 0.14/0.46 % relcompp_bot1
% 0.14/0.46 thf(fact_2599_relcompp__bot1,axiom,
% 0.14/0.46 ! [R3: int > code_integer > $o] :
% 0.14/0.46 ( ( relcom967497705283160040nteger @ bot_bot_int_int_o @ R3 )
% 0.14/0.46 = bot_bo341146761387662761eger_o ) ).
% 0.14/0.46
% 0.14/0.46 % relcompp_bot1
% 0.14/0.46 thf(fact_2600_surj__diff__right,axiom,
% 0.14/0.46 ! [A: int] :
% 0.14/0.46 ( ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.46 @ top_top_set_int )
% 0.14/0.46 = top_top_set_int ) ).
% 0.14/0.46
% 0.14/0.46 % surj_diff_right
% 0.14/0.46 thf(fact_2601_surj__diff__right,axiom,
% 0.14/0.46 ! [A: rat] :
% 0.14/0.46 ( ( image_rat_rat
% 0.14/0.46 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.46 @ top_top_set_rat )
% 0.14/0.46 = top_top_set_rat ) ).
% 0.14/0.46
% 0.14/0.46 % surj_diff_right
% 0.14/0.46 thf(fact_2602_surj__diff__right,axiom,
% 0.14/0.46 ! [A: code_integer] :
% 0.14/0.46 ( ( image_4470545334726330049nteger
% 0.14/0.46 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.46 @ top_to4645266643341252675nteger )
% 0.14/0.46 = top_to4645266643341252675nteger ) ).
% 0.14/0.46
% 0.14/0.46 % surj_diff_right
% 0.14/0.46 thf(fact_2603_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2604_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2605_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2606_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2607_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2608_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2609_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2610_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2611_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2612_INT__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_nat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(3)
% 0.14/0.46 thf(fact_2613_Sigma__Diff__distrib1,axiom,
% 0.14/0.46 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 0.14/0.46 ( ( produc457027306803732586at_nat @ ( minus_minus_set_nat @ I3 @ J3 ) @ C3 )
% 0.14/0.46 = ( minus_1356011639430497352at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sigma_Diff_distrib1
% 0.14/0.46 thf(fact_2614_translation__subtract__diff,axiom,
% 0.14/0.46 ! [A: int,S2: set_int,T2: set_int] :
% 0.14/0.46 ( ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.46 @ ( minus_minus_set_int @ S2 @ T2 ) )
% 0.14/0.46 = ( minus_minus_set_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.46 @ S2 )
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.46 @ T2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % translation_subtract_diff
% 0.14/0.46 thf(fact_2615_translation__subtract__diff,axiom,
% 0.14/0.46 ! [A: rat,S2: set_rat,T2: set_rat] :
% 0.14/0.46 ( ( image_rat_rat
% 0.14/0.46 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.46 @ ( minus_minus_set_rat @ S2 @ T2 ) )
% 0.14/0.46 = ( minus_minus_set_rat
% 0.14/0.46 @ ( image_rat_rat
% 0.14/0.46 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.46 @ S2 )
% 0.14/0.46 @ ( image_rat_rat
% 0.14/0.46 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.46 @ T2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % translation_subtract_diff
% 0.14/0.46 thf(fact_2616_translation__subtract__diff,axiom,
% 0.14/0.46 ! [A: code_integer,S2: set_Code_integer,T2: set_Code_integer] :
% 0.14/0.46 ( ( image_4470545334726330049nteger
% 0.14/0.46 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.46 @ ( minus_2355218937544613996nteger @ S2 @ T2 ) )
% 0.14/0.46 = ( minus_2355218937544613996nteger
% 0.14/0.46 @ ( image_4470545334726330049nteger
% 0.14/0.46 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.46 @ S2 )
% 0.14/0.46 @ ( image_4470545334726330049nteger
% 0.14/0.46 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.46 @ T2 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % translation_subtract_diff
% 0.14/0.46 thf(fact_2617_Times__Diff__distrib1,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 0.14/0.46 ( ( produc457027306803732586at_nat @ ( minus_minus_set_nat @ A4 @ B5 )
% 0.14/0.46 @ ^ [Uu: nat] : C3 )
% 0.14/0.46 = ( minus_1356011639430497352at_nat
% 0.14/0.46 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.46 @ ^ [Uu: nat] : C3 )
% 0.14/0.46 @ ( produc457027306803732586at_nat @ B5
% 0.14/0.46 @ ^ [Uu: nat] : C3 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Times_Diff_distrib1
% 0.14/0.46 thf(fact_2618_Sigma__Diff__distrib2,axiom,
% 0.14/0.46 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 0.14/0.46 ( ( produc457027306803732586at_nat @ I3
% 0.14/0.46 @ ^ [I2: nat] : ( minus_minus_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 0.14/0.46 = ( minus_1356011639430497352at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sigma_Diff_distrib2
% 0.14/0.46 thf(fact_2619_Sup__SUP__eq,axiom,
% 0.14/0.46 ( comple1177764198577243945_nat_o
% 0.14/0.46 = ( ^ [S4: set_Pr7010166363911110284_nat_o,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2620_Sup__SUP__eq,axiom,
% 0.14/0.46 ( complete_Sup_Sup_o_o
% 0.14/0.46 = ( ^ [S4: set_o_o,X4: $o] : ( member_o @ X4 @ ( comple90263536869209701_set_o @ ( image_o_o_set_o @ collect_o @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2621_Sup__SUP__eq,axiom,
% 0.14/0.46 ( comple6496622788309502864_int_o
% 0.14/0.46 = ( ^ [S4: set_int_o,X4: int] : ( member_int @ X4 @ ( comple3221217463730067765et_int @ ( image_int_o_set_int @ collect_int @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2622_Sup__SUP__eq,axiom,
% 0.14/0.46 ( comple1901448594430626575_nat_o
% 0.14/0.46 = ( ^ [S4: set_Pr5582243495563764594_nat_o,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2623_Sup__SUP__eq,axiom,
% 0.14/0.46 ( comple342879659800731223_int_o
% 0.14/0.46 = ( ^ [S4: set_Pr8049984349381595834_int_o,X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ ( comple5382143125604098054nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2624_Sup__SUP__eq,axiom,
% 0.14/0.46 ( comple8317665133742190828_nat_o
% 0.14/0.46 = ( ^ [S4: set_nat_o,X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ ( image_nat_o_set_nat @ collect_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq
% 0.14/0.46 thf(fact_2625_Inf__INT__eq,axiom,
% 0.14/0.46 ( comple8183010123678664591_nat_o
% 0.14/0.46 = ( ^ [S4: set_Pr7010166363911110284_nat_o,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2626_Inf__INT__eq,axiom,
% 0.14/0.46 ( complete_Inf_Inf_o_o
% 0.14/0.46 = ( ^ [S4: set_o_o,X4: $o] : ( member_o @ X4 @ ( comple3063163877087187839_set_o @ ( image_o_o_set_o @ collect_o @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2627_Inf__INT__eq,axiom,
% 0.14/0.46 ( comple4393433247856107946_int_o
% 0.14/0.46 = ( ^ [S4: set_int_o,X4: int] : ( member_int @ X4 @ ( comple3628384868704368283et_int @ ( image_int_o_set_int @ collect_int @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2628_Inf__INT__eq,axiom,
% 0.14/0.46 ( comple6265855634338933877_nat_o
% 0.14/0.46 = ( ^ [S4: set_Pr5582243495563764594_nat_o,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2629_Inf__INT__eq,axiom,
% 0.14/0.46 ( comple4707286699709038525_int_o
% 0.14/0.46 = ( ^ [S4: set_Pr8049984349381595834_int_o,X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ ( comple1626965760690514720nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2630_Inf__INT__eq,axiom,
% 0.14/0.46 ( comple6214475593288795910_nat_o
% 0.14/0.46 = ( ^ [S4: set_nat_o,X4: nat] : ( member_nat @ X4 @ ( comple7806235888213564991et_nat @ ( image_nat_o_set_nat @ collect_nat @ S4 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq
% 0.14/0.46 thf(fact_2631_INF__Int__eq2,axiom,
% 0.14/0.46 ! [S5: set_se7592288975875140775at_nat] :
% 0.14/0.46 ( ( comple5307621999477653941_nat_o
% 0.14/0.46 @ ( image_5337237954834410540_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple4403251139954110286at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq2
% 0.14/0.46 thf(fact_2632_INF__Int__eq2,axiom,
% 0.14/0.46 ! [S5: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( ( comple8322679762649017525_nat_o
% 0.14/0.46 @ ( image_6595146019508340652_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple6751905152567503566at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq2
% 0.14/0.46 thf(fact_2633_INF__Int__eq2,axiom,
% 0.14/0.46 ! [S5: set_se4826145725398303499at_num] :
% 0.14/0.46 ( ( comple2433913294995299363_num_o
% 0.14/0.46 @ ( image_2055017250723459638_num_o
% 0.14/0.46 @ ^ [I2: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple6868718957223342258at_num @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq2
% 0.14/0.46 thf(fact_2634_INF__Int__eq2,axiom,
% 0.14/0.46 ! [S5: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( ( comple1675732732025788397_nat_o
% 0.14/0.46 @ ( image_6923511907955291850_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple1930127330929219688at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq2
% 0.14/0.46 thf(fact_2635_INF__Int__eq2,axiom,
% 0.14/0.46 ! [S5: set_se6260736226359567993nt_int] :
% 0.14/0.46 ( ( comple5770381748412298549_int_o
% 0.14/0.46 @ ( image_4446226961036766042_int_o
% 0.14/0.46 @ ^ [I2: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple1626965760690514720nt_int @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq2
% 0.14/0.46 thf(fact_2636_SUP__Sup__eq2,axiom,
% 0.14/0.46 ! [S5: set_se7592288975875140775at_nat] :
% 0.14/0.46 ( ( comple4502628867940267931_nat_o
% 0.14/0.46 @ ( image_5337237954834410540_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple7342073961973170484at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq2
% 0.14/0.46 thf(fact_2637_SUP__Sup__eq2,axiom,
% 0.14/0.46 ! [S5: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( ( comple493620192902636699_nat_o
% 0.14/0.46 @ ( image_6595146019508340652_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple4364388969068068532at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq2
% 0.14/0.46 thf(fact_2638_SUP__Sup__eq2,axiom,
% 0.14/0.46 ! [S5: set_se4826145725398303499at_num] :
% 0.14/0.46 ( ( comple4350791933526045961_num_o
% 0.14/0.46 @ ( image_2055017250723459638_num_o
% 0.14/0.46 @ ^ [I2: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple1400524285282149784at_num @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq2
% 0.14/0.46 thf(fact_2639_SUP__Sup__eq2,axiom,
% 0.14/0.46 ! [S5: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( ( comple3592611370556534995_nat_o
% 0.14/0.46 @ ( image_6923511907955291850_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple5685304695842803022at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq2
% 0.14/0.46 thf(fact_2640_SUP__Sup__eq2,axiom,
% 0.14/0.46 ! [S5: set_se6260736226359567993nt_int] :
% 0.14/0.46 ( ( comple7687260386943045147_int_o
% 0.14/0.46 @ ( image_4446226961036766042_int_o
% 0.14/0.46 @ ^ [I2: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple5382143125604098054nt_int @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq2
% 0.14/0.46 thf(fact_2641_SUP__Sup__eq,axiom,
% 0.14/0.46 ! [S5: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( ( comple1177764198577243945_nat_o
% 0.14/0.46 @ ( image_4859512832475012440_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple4364388969068068532at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq
% 0.14/0.46 thf(fact_2642_SUP__Sup__eq,axiom,
% 0.14/0.46 ! [S5: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( ( comple1901448594430626575_nat_o
% 0.14/0.46 @ ( image_5253903537071781336_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple5685304695842803022at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq
% 0.14/0.46 thf(fact_2643_SUP__Sup__eq,axiom,
% 0.14/0.46 ! [S5: set_set_o] :
% 0.14/0.46 ( ( complete_Sup_Sup_o_o
% 0.14/0.46 @ ( image_set_o_o_o
% 0.14/0.46 @ ^ [I2: set_o,X4: $o] : ( member_o @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: $o] : ( member_o @ X4 @ ( comple90263536869209701_set_o @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq
% 0.14/0.46 thf(fact_2644_SUP__Sup__eq,axiom,
% 0.14/0.46 ! [S5: set_set_int] :
% 0.14/0.46 ( ( comple6496622788309502864_int_o
% 0.14/0.46 @ ( image_set_int_int_o
% 0.14/0.46 @ ^ [I2: set_int,X4: int] : ( member_int @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: int] : ( member_int @ X4 @ ( comple3221217463730067765et_int @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq
% 0.14/0.46 thf(fact_2645_SUP__Sup__eq,axiom,
% 0.14/0.46 ! [S5: set_set_nat] :
% 0.14/0.46 ( ( comple8317665133742190828_nat_o
% 0.14/0.46 @ ( image_set_nat_nat_o
% 0.14/0.46 @ ^ [I2: set_nat,X4: nat] : ( member_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % SUP_Sup_eq
% 0.14/0.46 thf(fact_2646_INF__Int__eq,axiom,
% 0.14/0.46 ! [S5: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( ( comple8183010123678664591_nat_o
% 0.14/0.46 @ ( image_4859512832475012440_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple6751905152567503566at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq
% 0.14/0.46 thf(fact_2647_INF__Int__eq,axiom,
% 0.14/0.46 ! [S5: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( ( comple6265855634338933877_nat_o
% 0.14/0.46 @ ( image_5253903537071781336_nat_o
% 0.14/0.46 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple1930127330929219688at_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq
% 0.14/0.46 thf(fact_2648_INF__Int__eq,axiom,
% 0.14/0.46 ! [S5: set_set_o] :
% 0.14/0.46 ( ( complete_Inf_Inf_o_o
% 0.14/0.46 @ ( image_set_o_o_o
% 0.14/0.46 @ ^ [I2: set_o,X4: $o] : ( member_o @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: $o] : ( member_o @ X4 @ ( comple3063163877087187839_set_o @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq
% 0.14/0.46 thf(fact_2649_INF__Int__eq,axiom,
% 0.14/0.46 ! [S5: set_set_int] :
% 0.14/0.46 ( ( comple4393433247856107946_int_o
% 0.14/0.46 @ ( image_set_int_int_o
% 0.14/0.46 @ ^ [I2: set_int,X4: int] : ( member_int @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: int] : ( member_int @ X4 @ ( comple3628384868704368283et_int @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq
% 0.14/0.46 thf(fact_2650_INF__Int__eq,axiom,
% 0.14/0.46 ! [S5: set_set_nat] :
% 0.14/0.46 ( ( comple6214475593288795910_nat_o
% 0.14/0.46 @ ( image_set_nat_nat_o
% 0.14/0.46 @ ^ [I2: set_nat,X4: nat] : ( member_nat @ X4 @ I2 )
% 0.14/0.46 @ S5 ) )
% 0.14/0.46 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( comple7806235888213564991et_nat @ S5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INF_Int_eq
% 0.14/0.46 thf(fact_2651_Sup__set__def,axiom,
% 0.14/0.46 ( comple4364388969068068532at_nat
% 0.14/0.46 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( collec6321179662152712658at_nat
% 0.14/0.46 @ ^ [X4: produc3843707927480180839at_nat] : ( complete_Sup_Sup_o @ ( image_3568060456209098518_nat_o @ ( member8757157785044589968at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2652_Sup__set__def,axiom,
% 0.14/0.46 ( comple90263536869209701_set_o
% 0.14/0.46 = ( ^ [A6: set_set_o] :
% 0.14/0.46 ( collect_o
% 0.14/0.46 @ ^ [X4: $o] : ( complete_Sup_Sup_o @ ( image_set_o_o @ ( member_o @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2653_Sup__set__def,axiom,
% 0.14/0.46 ( comple3221217463730067765et_int
% 0.14/0.46 = ( ^ [A6: set_set_int] :
% 0.14/0.46 ( collect_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Sup_Sup_o @ ( image_set_int_o @ ( member_int @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2654_Sup__set__def,axiom,
% 0.14/0.46 ( comple5685304695842803022at_nat
% 0.14/0.46 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( collec3392354462482085612at_nat
% 0.14/0.46 @ ^ [X4: product_prod_nat_nat] : ( complete_Sup_Sup_o @ ( image_7457375456213313148_nat_o @ ( member8440522571783428010at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2655_Sup__set__def,axiom,
% 0.14/0.46 ( comple5382143125604098054nt_int
% 0.14/0.46 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 0.14/0.46 ( collec213857154873943460nt_int
% 0.14/0.46 @ ^ [X4: product_prod_int_int] : ( complete_Sup_Sup_o @ ( image_701744273176368580_int_o @ ( member5262025264175285858nt_int @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2656_Sup__set__def,axiom,
% 0.14/0.46 ( comple7399068483239264473et_nat
% 0.14/0.46 = ( ^ [A6: set_set_nat] :
% 0.14/0.46 ( collect_nat
% 0.14/0.46 @ ^ [X4: nat] : ( complete_Sup_Sup_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_set_def
% 0.14/0.46 thf(fact_2657_Inf__set__def,axiom,
% 0.14/0.46 ( comple6751905152567503566at_nat
% 0.14/0.46 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( collec6321179662152712658at_nat
% 0.14/0.46 @ ^ [X4: produc3843707927480180839at_nat] : ( complete_Inf_Inf_o @ ( image_3568060456209098518_nat_o @ ( member8757157785044589968at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2658_Inf__set__def,axiom,
% 0.14/0.46 ( comple3063163877087187839_set_o
% 0.14/0.46 = ( ^ [A6: set_set_o] :
% 0.14/0.46 ( collect_o
% 0.14/0.46 @ ^ [X4: $o] : ( complete_Inf_Inf_o @ ( image_set_o_o @ ( member_o @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2659_Inf__set__def,axiom,
% 0.14/0.46 ( comple3628384868704368283et_int
% 0.14/0.46 = ( ^ [A6: set_set_int] :
% 0.14/0.46 ( collect_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Inf_Inf_o @ ( image_set_int_o @ ( member_int @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2660_Inf__set__def,axiom,
% 0.14/0.46 ( comple1930127330929219688at_nat
% 0.14/0.46 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( collec3392354462482085612at_nat
% 0.14/0.46 @ ^ [X4: product_prod_nat_nat] : ( complete_Inf_Inf_o @ ( image_7457375456213313148_nat_o @ ( member8440522571783428010at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2661_Inf__set__def,axiom,
% 0.14/0.46 ( comple1626965760690514720nt_int
% 0.14/0.46 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 0.14/0.46 ( collec213857154873943460nt_int
% 0.14/0.46 @ ^ [X4: product_prod_int_int] : ( complete_Inf_Inf_o @ ( image_701744273176368580_int_o @ ( member5262025264175285858nt_int @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2662_Inf__set__def,axiom,
% 0.14/0.46 ( comple7806235888213564991et_nat
% 0.14/0.46 = ( ^ [A6: set_set_nat] :
% 0.14/0.46 ( collect_nat
% 0.14/0.46 @ ^ [X4: nat] : ( complete_Inf_Inf_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_set_def
% 0.14/0.46 thf(fact_2663_image__diff__subset,axiom,
% 0.14/0.46 ! [F: nat > rat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_rat @ ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_diff_subset
% 0.14/0.46 thf(fact_2664_image__diff__subset,axiom,
% 0.14/0.46 ! [F: nat > nat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_diff_subset
% 0.14/0.46 thf(fact_2665_image__diff__subset,axiom,
% 0.14/0.46 ! [F: nat > int,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_diff_subset
% 0.14/0.46 thf(fact_2666_image__diff__subset,axiom,
% 0.14/0.46 ! [F: int > nat,A4: set_int,B5: set_int] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_diff_subset
% 0.14/0.46 thf(fact_2667_image__diff__subset,axiom,
% 0.14/0.46 ! [F: int > int,A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % image_diff_subset
% 0.14/0.46 thf(fact_2668_Inf__INT__eq2,axiom,
% 0.14/0.46 ( comple5307621999477653941_nat_o
% 0.14/0.46 = ( ^ [S4: set_se7255092946006855566_nat_o,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple4403251139954110286at_nat @ ( image_5694205205332509994at_nat @ collec7872792499061297490at_nat @ ( image_5235725667318448191_nat_o @ produc9020218426428501292_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq2
% 0.14/0.46 thf(fact_2669_Inf__INT__eq2,axiom,
% 0.14/0.46 ( comple8322679762649017525_nat_o
% 0.14/0.46 = ( ^ [S4: set_se9180647916752606350_nat_o,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq2
% 0.14/0.46 thf(fact_2670_Inf__INT__eq2,axiom,
% 0.14/0.46 ( comple2433913294995299363_num_o
% 0.14/0.46 = ( ^ [S4: set_nat_num_o,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple6868718957223342258at_num @ ( image_6580737572886966642at_num @ collec4100598399430923318at_num @ ( image_8484515203959327177_num_o @ produc4927758841916487424_num_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq2
% 0.14/0.46 thf(fact_2671_Inf__INT__eq2,axiom,
% 0.14/0.46 ( comple1675732732025788397_nat_o
% 0.14/0.46 = ( ^ [S4: set_nat_nat_o,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq2
% 0.14/0.46 thf(fact_2672_Inf__INT__eq2,axiom,
% 0.14/0.46 ( comple5770381748412298549_int_o
% 0.14/0.46 = ( ^ [S4: set_int_int_o,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple1626965760690514720nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ ( image_1365644804893650413_int_o @ produc4947309494688390418_int_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Inf_INT_eq2
% 0.14/0.46 thf(fact_2673_Sup__SUP__eq2,axiom,
% 0.14/0.46 ( comple4502628867940267931_nat_o
% 0.14/0.46 = ( ^ [S4: set_se7255092946006855566_nat_o,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple7342073961973170484at_nat @ ( image_5694205205332509994at_nat @ collec7872792499061297490at_nat @ ( image_5235725667318448191_nat_o @ produc9020218426428501292_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq2
% 0.14/0.46 thf(fact_2674_Sup__SUP__eq2,axiom,
% 0.14/0.46 ( comple493620192902636699_nat_o
% 0.14/0.46 = ( ^ [S4: set_se9180647916752606350_nat_o,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq2
% 0.14/0.46 thf(fact_2675_Sup__SUP__eq2,axiom,
% 0.14/0.46 ( comple4350791933526045961_num_o
% 0.14/0.46 = ( ^ [S4: set_nat_num_o,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple1400524285282149784at_num @ ( image_6580737572886966642at_num @ collec4100598399430923318at_num @ ( image_8484515203959327177_num_o @ produc4927758841916487424_num_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq2
% 0.14/0.46 thf(fact_2676_Sup__SUP__eq2,axiom,
% 0.14/0.46 ( comple3592611370556534995_nat_o
% 0.14/0.46 = ( ^ [S4: set_nat_nat_o,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq2
% 0.14/0.46 thf(fact_2677_Sup__SUP__eq2,axiom,
% 0.14/0.46 ( comple7687260386943045147_int_o
% 0.14/0.46 = ( ^ [S4: set_int_int_o,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple5382143125604098054nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ ( image_1365644804893650413_int_o @ produc4947309494688390418_int_o @ S4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % Sup_SUP_eq2
% 0.14/0.46 thf(fact_2678_bot__empty__eq2,axiom,
% 0.14/0.46 ( bot_bo3364206721330744218_nat_o
% 0.14/0.46 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ bot_bo4948859079157340979at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % bot_empty_eq2
% 0.14/0.46 thf(fact_2679_bot__empty__eq2,axiom,
% 0.14/0.46 ( bot_bot_nat_num_o
% 0.14/0.46 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ bot_bo7038385379056416535at_num ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % bot_empty_eq2
% 0.14/0.46 thf(fact_2680_bot__empty__eq2,axiom,
% 0.14/0.46 ( bot_bot_int_int_o
% 0.14/0.46 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % bot_empty_eq2
% 0.14/0.46 thf(fact_2681_bot__empty__eq2,axiom,
% 0.14/0.46 ( bot_bo394778441745866138_nat_o
% 0.14/0.46 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % bot_empty_eq2
% 0.14/0.46 thf(fact_2682_bot__empty__eq2,axiom,
% 0.14/0.46 ( bot_bot_nat_nat_o
% 0.14/0.46 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % bot_empty_eq2
% 0.14/0.46 thf(fact_2683_top__empty__eq2,axiom,
% 0.14/0.46 ( top_to1326704617074743934_nat_o
% 0.14/0.46 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ top_to5281548843312042519at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % top_empty_eq2
% 0.14/0.46 thf(fact_2684_top__empty__eq2,axiom,
% 0.14/0.46 ( top_to8903224817164384382_nat_o
% 0.14/0.46 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ top_to6833984726390702231at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % top_empty_eq2
% 0.14/0.46 thf(fact_2685_top__empty__eq2,axiom,
% 0.14/0.46 ( top_top_nat_num_o
% 0.14/0.46 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ top_to385025497714130939at_num ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % top_empty_eq2
% 0.14/0.46 thf(fact_2686_top__empty__eq2,axiom,
% 0.14/0.46 ( top_top_nat_nat_o
% 0.14/0.46 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ top_to4669805908274784177at_nat ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % top_empty_eq2
% 0.14/0.46 thf(fact_2687_top__empty__eq2,axiom,
% 0.14/0.46 ( top_top_int_int_o
% 0.14/0.46 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ top_to4366644338036079209nt_int ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % top_empty_eq2
% 0.14/0.46 thf(fact_2688_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_set_int,X2: int,A4: set_int] :
% 0.14/0.46 ( ! [C2: set_int] :
% 0.14/0.46 ( ( member_set_int @ C2 @ B5 )
% 0.14/0.46 => ~ ( member_int @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member_set_int @ A4 @ ( image_524474410958335435et_int @ ( insert_int @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member_int @ X2 @ A4 )
% 0.14/0.46 & ( member_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2689_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_set_Product_unit,X2: product_unit,A4: set_Product_unit] :
% 0.14/0.46 ( ! [C2: set_Product_unit] :
% 0.14/0.46 ( ( member5877623283571906838t_unit @ C2 @ B5 )
% 0.14/0.46 => ~ ( member_Product_unit @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member5877623283571906838t_unit @ A4 @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member_Product_unit @ X2 @ A4 )
% 0.14/0.46 & ( member5877623283571906838t_unit @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2690_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_se5479201105039950375at_nat,X2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.46 ( ! [C2: set_Pr4329608150637261639at_nat] :
% 0.14/0.46 ( ( member6273874620674182256at_nat @ C2 @ B5 )
% 0.14/0.46 => ~ ( member8757157785044589968at_nat @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member6273874620674182256at_nat @ A4 @ ( image_4303274092540115909at_nat @ ( insert9069300056098147895at_nat @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member8757157785044589968at_nat @ X2 @ A4 )
% 0.14/0.46 & ( member6273874620674182256at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2691_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_se7855581050983116737at_nat,X2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.46 ( ! [C2: set_Pr1261947904930325089at_nat] :
% 0.14/0.46 ( ( member2643936169264416010at_nat @ C2 @ B5 )
% 0.14/0.46 => ~ ( member8440522571783428010at_nat @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member2643936169264416010at_nat @ A4 @ ( image_3684629450409544005at_nat @ ( insert8211810215607154385at_nat @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 0.14/0.46 & ( member2643936169264416010at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2692_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_set_o,X2: $o,A4: set_o] :
% 0.14/0.46 ( ! [C2: set_o] :
% 0.14/0.46 ( ( member_set_o @ C2 @ B5 )
% 0.14/0.46 => ~ ( member_o @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member_set_o @ A4 @ ( image_set_o_set_o @ ( insert_o @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member_o @ X2 @ A4 )
% 0.14/0.46 & ( member_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2693_in__image__insert__iff,axiom,
% 0.14/0.46 ! [B5: set_set_nat,X2: nat,A4: set_nat] :
% 0.14/0.46 ( ! [C2: set_nat] :
% 0.14/0.46 ( ( member_set_nat @ C2 @ B5 )
% 0.14/0.46 => ~ ( member_nat @ X2 @ C2 ) )
% 0.14/0.46 => ( ( member_set_nat @ A4 @ ( image_7916887816326733075et_nat @ ( insert_nat @ X2 ) @ B5 ) )
% 0.14/0.46 = ( ( member_nat @ X2 @ A4 )
% 0.14/0.46 & ( member_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % in_image_insert_iff
% 0.14/0.46 thf(fact_2694_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2695_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2696_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2697_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2698_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2699_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2700_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2701_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2702_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2703_INT__extend__simps_I3_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( minus_minus_set_nat @ top_top_set_nat @ B5 ) ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(3)
% 0.14/0.46 thf(fact_2704_INT__extend__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = A4 ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(4)
% 0.14/0.46 thf(fact_2705_INT__extend__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Pr4329608150637261639at_nat,A4: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = A4 ) )
% 0.14/0.46 & ( ( C3 != bot_bo228742789529271731at_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_3160451284896210088et_nat
% 0.14/0.46 @ ^ [X4: produc3843707927480180839at_nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(4)
% 0.14/0.46 thf(fact_2706_INT__extend__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = A4 ) )
% 0.14/0.46 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_15824709712370754et_nat
% 0.14/0.46 @ ^ [X4: product_prod_nat_nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(4)
% 0.14/0.46 thf(fact_2707_INT__extend__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = A4 ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_o_set_nat
% 0.14/0.46 @ ^ [X4: $o] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(4)
% 0.14/0.46 thf(fact_2708_INT__extend__simps_I4_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = A4 ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.46 = ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_nat_set_nat
% 0.14/0.46 @ ^ [X4: nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_extend_simps(4)
% 0.14/0.46 thf(fact_2709_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: set_Pr4329608150637261639at_nat] : ( order_1878278401035043452at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2710_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: int] : ( order_4471489696718655927on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2711_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: set_Pr1261947904930325089at_nat] : ( order_5942792088423767318at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2712_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: product_unit] : ( order_888282469287196226t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2713_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: produc3843707927480180839at_nat] : ( order_2711500226769404828at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2714_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: product_prod_nat_nat] : ( order_7480980593162297270at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2715_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: $o] : ( order_6238756238976269133r_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2716_linear__order__on__singleton,axiom,
% 0.14/0.46 ! [X2: nat] : ( order_4473980167227706203on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % linear_order_on_singleton
% 0.14/0.46 thf(fact_2717_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: set_Pr4329608150637261639at_nat] : ( total_5117575981256876747at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2718_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: int] : ( total_on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2719_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: set_Pr1261947904930325089at_nat] : ( total_7212417256332265445at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2720_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: product_unit] : ( total_5665700600833547665t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2721_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: produc3843707927480180839at_nat] : ( total_1513685709984341995at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2722_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: product_prod_nat_nat] : ( total_3592101749530773125at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2723_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: $o] : ( total_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2724_total__on__singleton,axiom,
% 0.14/0.46 ! [X2: nat] : ( total_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.14/0.46
% 0.14/0.46 % total_on_singleton
% 0.14/0.46 thf(fact_2725_relation__of__def,axiom,
% 0.14/0.46 ( order_8308734813930759573at_nat
% 0.14/0.46 = ( ^ [P4: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A6: set_se5479201105039950375at_nat] :
% 0.14/0.46 ( collec7872792499061297490at_nat
% 0.14/0.46 @ ( produc9020218426428501292_nat_o
% 0.14/0.46 @ ^ [A5: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 0.14/0.46 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A5 @ B4 )
% 0.14/0.46 @ ( produc6258361011560675592at_nat @ A6
% 0.14/0.46 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A6 ) )
% 0.14/0.46 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % relation_of_def
% 0.14/0.46 thf(fact_2726_relation__of__def,axiom,
% 0.14/0.46 ( order_8809246210994205103at_nat
% 0.14/0.46 = ( ^ [P4: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A6: set_se7855581050983116737at_nat] :
% 0.14/0.46 ( collec6321179662152712658at_nat
% 0.14/0.46 @ ( produc410239310623530412_nat_o
% 0.14/0.46 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.14/0.46 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ B4 )
% 0.14/0.46 @ ( produc7726050920695093128at_nat @ A6
% 0.14/0.46 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A6 ) )
% 0.14/0.46 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % relation_of_def
% 0.14/0.46 thf(fact_2727_relation__of__def,axiom,
% 0.14/0.46 ( order_1962693441708344834of_nat
% 0.14/0.46 = ( ^ [P4: nat > nat > $o,A6: set_nat] :
% 0.14/0.46 ( collec3392354462482085612at_nat
% 0.14/0.46 @ ( produc6081775807080527818_nat_o
% 0.14/0.46 @ ^ [A5: nat,B4: nat] :
% 0.14/0.46 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 )
% 0.14/0.46 @ ( produc457027306803732586at_nat @ A6
% 0.14/0.46 @ ^ [Uu: nat] : A6 ) )
% 0.14/0.46 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % relation_of_def
% 0.14/0.46 thf(fact_2728_relation__of__def,axiom,
% 0.14/0.46 ( order_1960202971199294558of_int
% 0.14/0.46 = ( ^ [P4: int > int > $o,A6: set_int] :
% 0.14/0.46 ( collec213857154873943460nt_int
% 0.14/0.46 @ ( produc4947309494688390418_int_o
% 0.14/0.46 @ ^ [A5: int,B4: int] :
% 0.14/0.46 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 )
% 0.14/0.46 @ ( produc1453890548195736866nt_int @ A6
% 0.14/0.46 @ ^ [Uu: int] : A6 ) )
% 0.14/0.46 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % relation_of_def
% 0.14/0.46 thf(fact_2729_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,B: product_unit,B5: set_Product_unit] :
% 0.14/0.46 ( ( produc5506539147108004339t_unit @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 = ( insert6804906068341198690t_unit @ ( produc3434450474625521892t_unit @ A @ B )
% 0.14/0.46 @ ( sup_su4209953369189666580t_unit
% 0.14/0.46 @ ( produc5506539147108004339t_unit @ A4
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 @ ( produc5506539147108004339t_unit @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2730_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,B: $o,B5: set_o] :
% 0.14/0.46 ( ( product_Sigma_nat_o @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 = ( insert2233377226759017069_nat_o @ ( product_Pair_nat_o @ A @ B )
% 0.14/0.46 @ ( sup_su503371503184139039_nat_o
% 0.14/0.46 @ ( product_Sigma_nat_o @ A4
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 @ ( product_Sigma_nat_o @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2731_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: product_unit,A4: set_Product_unit,B: nat,B5: set_nat] :
% 0.14/0.46 ( ( produc6875377002296012693it_nat @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_nat @ B @ B5 ) )
% 0.14/0.46 = ( insert6879346373837673660it_nat @ ( produc4803288329813530246it_nat @ A @ B )
% 0.14/0.46 @ ( sup_su1639320892072265582it_nat
% 0.14/0.46 @ ( produc6875377002296012693it_nat @ A4
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_nat @ B @ B5 ) )
% 0.14/0.46 @ ( produc6875377002296012693it_nat @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2732_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: product_unit,A4: set_Product_unit,B: product_unit,B5: set_Product_unit] :
% 0.14/0.46 ( ( produc6121607364029222536t_unit @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 = ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ A @ B )
% 0.14/0.46 @ ( sup_su6481247232241170203t_unit
% 0.14/0.46 @ ( produc6121607364029222536t_unit @ A4
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 @ ( produc6121607364029222536t_unit @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2733_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: product_unit,A4: set_Product_unit,B: $o,B5: set_o] :
% 0.14/0.46 ( ( produc4996980317674386579unit_o @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 = ( insert3586912282507785154unit_o @ ( produc8487917018914037602unit_o @ A @ B )
% 0.14/0.46 @ ( sup_su2851927382625014182unit_o
% 0.14/0.46 @ ( produc4996980317674386579unit_o @ A4
% 0.14/0.46 @ ^ [Uu: product_unit] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 @ ( produc4996980317674386579unit_o @ ( insert_Product_unit @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2734_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,B: nat,B5: set_nat] :
% 0.14/0.46 ( ( product_Sigma_o_nat @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 0.14/0.46 = ( insert7948214739558299847_o_nat @ ( product_Pair_o_nat @ A @ B )
% 0.14/0.46 @ ( sup_su8679140417860611193_o_nat
% 0.14/0.46 @ ( product_Sigma_o_nat @ A4
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 0.14/0.46 @ ( product_Sigma_o_nat @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2735_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,B: product_unit,B5: set_Product_unit] :
% 0.14/0.46 ( ( produc411009820408249917t_unit @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 = ( insert9112848208840649964t_unit @ ( produc3901946521647900940t_unit @ A @ B )
% 0.14/0.46 @ ( sup_su4058753791541417424t_unit
% 0.14/0.46 @ ( produc411009820408249917t_unit @ A4
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_Product_unit @ B @ B5 ) )
% 0.14/0.46 @ ( produc411009820408249917t_unit @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2736_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: $o,A4: set_o,B: $o,B5: set_o] :
% 0.14/0.46 ( ( product_Sigma_o_o @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 = ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B )
% 0.14/0.46 @ ( sup_su5769328420594410459od_o_o
% 0.14/0.46 @ ( product_Sigma_o_o @ A4
% 0.14/0.46 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 0.14/0.46 @ ( product_Sigma_o_o @ ( insert_o @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2737_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: nat,A4: set_nat,B: num,B5: set_num] :
% 0.14/0.46 ( ( produc6237731129814287028at_num @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_num @ B @ B5 ) )
% 0.14/0.46 = ( insert8920054152555992091at_num @ ( product_Pair_nat_num @ A @ B )
% 0.14/0.46 @ ( sup_su2042722026077122175at_num
% 0.14/0.46 @ ( produc6237731129814287028at_num @ A4
% 0.14/0.46 @ ^ [Uu: nat] : ( insert_num @ B @ B5 ) )
% 0.14/0.46 @ ( produc6237731129814287028at_num @ ( insert_nat @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2738_insert__Times__insert,axiom,
% 0.14/0.46 ! [A: int,A4: set_int,B: int,B5: set_int] :
% 0.14/0.46 ( ( produc1453890548195736866nt_int @ ( insert_int @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 0.14/0.46 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B )
% 0.14/0.46 @ ( sup_su6024340866399070445nt_int
% 0.14/0.46 @ ( produc1453890548195736866nt_int @ A4
% 0.14/0.46 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 0.14/0.46 @ ( produc1453890548195736866nt_int @ ( insert_int @ A @ A4 )
% 0.14/0.46 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % insert_Times_insert
% 0.14/0.46 thf(fact_2739_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_char,B5: product_unit > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2740_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_char,B5: $o > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_o_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2741_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_char,B5: nat > set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2742_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_rat,B5: product_unit > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2743_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_rat,B5: $o > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2744_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_rat,B5: nat > set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2745_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_int,B5: product_unit > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2746_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: set_int,B5: $o > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2747_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: set_int,B5: nat > set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2748_INT__simps_I2_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_nat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(2)
% 0.14/0.46 thf(fact_2749_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_5325685772115642575t_char
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2750_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_o_set_char
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2751_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_char ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple7965528767983648192t_char
% 0.14/0.46 @ ( image_nat_set_char
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2752_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_4665621433434589782et_rat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2753_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_o_set_rat
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2754_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_rat ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple4298007329820168263et_rat
% 0.14/0.46 @ ( image_nat_set_rat
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2755_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2756_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_o )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2757_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 0.14/0.46 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_int ) )
% 0.14/0.46 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.46 => ( ( comple3628384868704368283et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2758_INT__simps_I1_J,axiom,
% 0.14/0.46 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.46 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = top_top_set_nat ) )
% 0.14/0.46 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ( comple7806235888213564991et_nat
% 0.14/0.46 @ ( image_8173849991827986510et_nat
% 0.14/0.46 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.46 @ C3 ) )
% 0.14/0.46 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % INT_simps(1)
% 0.14/0.46 thf(fact_2759_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_int ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_int_set_int
% 0.14/0.46 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2760_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_Product_unit,F: product_unit > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_int_set_int
% 0.14/0.46 @ ^ [X4: int] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2761_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_o,F: $o > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_o ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_int_set_int
% 0.14/0.46 @ ^ [X4: int] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2762_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,B5: product_unit > set_int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_int ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_873079544045703924it_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2763_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,B5: product_unit > set_Product_unit,F: product_unit > int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_873079544045703924it_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2764_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_Product_unit,B5: product_unit > set_o,F: $o > int] :
% 0.14/0.46 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.46 => ( ! [X: product_unit] :
% 0.14/0.46 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_o ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_3995998972318789802et_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_873079544045703924it_int
% 0.14/0.46 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2765_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_o,B5: $o > set_int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_int ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_o_int
% 0.14/0.46 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2766_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_o,B5: $o > set_Product_unit,F: product_unit > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_o_int
% 0.14/0.46 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2767_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_o,B5: $o > set_o,F: $o > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_o )
% 0.14/0.46 => ( ! [X: $o] :
% 0.14/0.46 ( ( member_o @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_o ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_o_set_int
% 0.14/0.46 @ ^ [X4: $o] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_o_int
% 0.14/0.46 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2768_cSUP__UNION,axiom,
% 0.14/0.46 ! [A4: set_nat,B5: nat > set_int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_nat )
% 0.14/0.46 => ( ! [X: nat] :
% 0.14/0.46 ( ( member_nat @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_int ) )
% 0.14/0.46 => ( ( condit2212336002400062152ve_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_nat_set_int
% 0.14/0.46 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Sup_Sup_int
% 0.14/0.46 @ ( image_nat_int
% 0.14/0.46 @ ^ [X4: nat] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cSUP_UNION
% 0.14/0.46 thf(fact_2769_cINF__UNION,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_int,F: int > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bot_set_int ) )
% 0.14/0.46 => ( ( condit1735850657277959132ow_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_int_set_int
% 0.14/0.46 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.46 = ( complete_Inf_Inf_int
% 0.14/0.46 @ ( image_int_int
% 0.14/0.46 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.46 @ A4 ) ) ) ) ) ) ).
% 0.14/0.46
% 0.14/0.46 % cINF_UNION
% 0.14/0.46 thf(fact_2770_cINF__UNION,axiom,
% 0.14/0.46 ! [A4: set_int,B5: int > set_Product_unit,F: product_unit > int] :
% 0.14/0.46 ( ( A4 != bot_bot_set_int )
% 0.14/0.46 => ( ! [X: int] :
% 0.14/0.46 ( ( member_int @ X @ A4 )
% 0.14/0.46 => ( ( B5 @ X )
% 0.14/0.46 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.46 => ( ( condit1735850657277959132ow_int
% 0.14/0.46 @ ( comple3221217463730067765et_int
% 0.14/0.46 @ ( image_int_set_int
% 0.14/0.46 @ ^ [X4: int] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.46 @ A4 ) ) )
% 0.14/0.46 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2771_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_int,B5: int > set_o,F: $o > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_o ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_int_set_int
% 0.14/0.47 @ ^ [X4: int] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2772_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,B5: product_unit > set_int,F: int > int] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ! [X: product_unit] :
% 0.14/0.47 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_int ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_3995998972318789802et_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_873079544045703924it_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2773_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,B5: product_unit > set_Product_unit,F: product_unit > int] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ! [X: product_unit] :
% 0.14/0.47 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_3995998972318789802et_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_873079544045703924it_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2774_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,B5: product_unit > set_o,F: $o > int] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ! [X: product_unit] :
% 0.14/0.47 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_o ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_3995998972318789802et_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_873079544045703924it_int
% 0.14/0.47 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2775_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_o,B5: $o > set_int,F: int > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_int ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_o_set_int
% 0.14/0.47 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_o_int
% 0.14/0.47 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2776_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_o,B5: $o > set_Product_unit,F: product_unit > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_o_set_int
% 0.14/0.47 @ ^ [X4: $o] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_o_int
% 0.14/0.47 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2777_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_o,B5: $o > set_o,F: $o > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_o ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_o_set_int
% 0.14/0.47 @ ^ [X4: $o] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_o_int
% 0.14/0.47 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2778_cINF__UNION,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: nat > set_int,F: int > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ( B5 @ X )
% 0.14/0.47 != bot_bot_set_int ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( comple3221217463730067765et_int
% 0.14/0.47 @ ( image_nat_set_int
% 0.14/0.47 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.47 @ A4 ) ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_nat_int
% 0.14/0.47 @ ^ [X4: nat] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_UNION
% 0.14/0.47 thf(fact_2779_Ex__inj__on__UNION__Sigma,axiom,
% 0.14/0.47 ! [A4: nat > set_nat,I3: set_nat] :
% 0.14/0.47 ? [F5: nat > product_prod_nat_nat] :
% 0.14/0.47 ( ( inj_on5538052773655684606at_nat @ F5 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) @ ( produc457027306803732586at_nat @ I3 @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Ex_inj_on_UNION_Sigma
% 0.14/0.47 thf(fact_2780_prod__set__simps_I1_J,axiom,
% 0.14/0.47 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( basic_1274512288150691911at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.14/0.47 = ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % prod_set_simps(1)
% 0.14/0.47 thf(fact_2781_prod__set__simps_I1_J,axiom,
% 0.14/0.47 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( basic_3661821009137050567at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.14/0.47 = ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % prod_set_simps(1)
% 0.14/0.47 thf(fact_2782_prod__set__simps_I1_J,axiom,
% 0.14/0.47 ! [X2: int,Y3: int] :
% 0.14/0.47 ( ( basic_fsts_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.14/0.47 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 0.14/0.47
% 0.14/0.47 % prod_set_simps(1)
% 0.14/0.47 thf(fact_2783_prod__set__simps_I1_J,axiom,
% 0.14/0.47 ! [X2: nat,Y3: num] :
% 0.14/0.47 ( ( basic_fsts_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.14/0.47 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % prod_set_simps(1)
% 0.14/0.47 thf(fact_2784_prod__set__simps_I1_J,axiom,
% 0.14/0.47 ! [X2: nat,Y3: nat] :
% 0.14/0.47 ( ( basic_fsts_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.14/0.47 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % prod_set_simps(1)
% 0.14/0.47 thf(fact_2785_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: int > $o,F: int > nat,G: int > nat,S5: set_int] :
% 0.14/0.47 ( ( image_int_nat
% 0.14/0.47 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_sup_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ S5 @ ( collect_int @ P2 ) ) )
% 0.14/0.47 @ ( image_int_nat @ G
% 0.14/0.47 @ ( inf_inf_set_int @ S5
% 0.14/0.47 @ ( collect_int
% 0.14/0.47 @ ^ [X4: int] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2786_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: int > $o,F: int > int,G: int > int,S5: set_int] :
% 0.14/0.47 ( ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( if_int @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_sup_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ S5 @ ( collect_int @ P2 ) ) )
% 0.14/0.47 @ ( image_int_int @ G
% 0.14/0.47 @ ( inf_inf_set_int @ S5
% 0.14/0.47 @ ( collect_int
% 0.14/0.47 @ ^ [X4: int] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2787_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: nat > $o,F: nat > rat,G: nat > rat,S5: set_nat] :
% 0.14/0.47 ( ( image_nat_rat
% 0.14/0.47 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_sup_set_rat @ ( image_nat_rat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_nat_rat @ G
% 0.14/0.47 @ ( inf_inf_set_nat @ S5
% 0.14/0.47 @ ( collect_nat
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2788_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: nat > $o,F: nat > nat,G: nat > nat,S5: set_nat] :
% 0.14/0.47 ( ( image_nat_nat
% 0.14/0.47 @ ^ [X4: nat] : ( if_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_nat_nat @ G
% 0.14/0.47 @ ( inf_inf_set_nat @ S5
% 0.14/0.47 @ ( collect_nat
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2789_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: nat > $o,F: nat > int,G: nat > int,S5: set_nat] :
% 0.14/0.47 ( ( image_nat_int
% 0.14/0.47 @ ^ [X4: nat] : ( if_int @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_sup_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_nat_int @ G
% 0.14/0.47 @ ( inf_inf_set_nat @ S5
% 0.14/0.47 @ ( collect_nat
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2790_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: nat > $o,F: nat > produc859450856879609959at_nat,G: nat > produc859450856879609959at_nat,S5: set_nat] :
% 0.14/0.47 ( ( image_3276603626957510736at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( image_3276603626957510736at_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_3276603626957510736at_nat @ G
% 0.14/0.47 @ ( inf_inf_set_nat @ S5
% 0.14/0.47 @ ( collect_nat
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2791_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: product_prod_int_int > $o,F: product_prod_int_int > produc859450856879609959at_nat,G: product_prod_int_int > produc859450856879609959at_nat,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.47 ( ( image_8858061497167895027at_nat
% 0.14/0.47 @ ^ [X4: product_prod_int_int] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( image_8858061497167895027at_nat @ F @ ( inf_in2269163501485487111nt_int @ S5 @ ( collec213857154873943460nt_int @ P2 ) ) )
% 0.14/0.47 @ ( image_8858061497167895027at_nat @ G
% 0.14/0.47 @ ( inf_in2269163501485487111nt_int @ S5
% 0.14/0.47 @ ( collec213857154873943460nt_int
% 0.14/0.47 @ ^ [X4: product_prod_int_int] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2792_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > produc859450856879609959at_nat,G: product_prod_nat_nat > produc859450856879609959at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( image_1119892238107900587at_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( image_1119892238107900587at_nat @ F @ ( inf_in2572325071724192079at_nat @ S5 @ ( collec3392354462482085612at_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_1119892238107900587at_nat @ G
% 0.14/0.47 @ ( inf_in2572325071724192079at_nat @ S5
% 0.14/0.47 @ ( collec3392354462482085612at_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2793_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: nat > $o,F: nat > produc3843707927480180839at_nat,G: nat > produc3843707927480180839at_nat,S5: set_nat] :
% 0.14/0.47 ( ( image_2499013659892586576at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( if_Pro3594990065127090477at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( image_2499013659892586576at_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 0.14/0.47 @ ( image_2499013659892586576at_nat @ G
% 0.14/0.47 @ ( inf_inf_set_nat @ S5
% 0.14/0.47 @ ( collect_nat
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2794_if__image__distrib,axiom,
% 0.14/0.47 ! [P2: product_prod_int_int > $o,F: product_prod_int_int > produc3843707927480180839at_nat,G: product_prod_int_int > produc3843707927480180839at_nat,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.47 ( ( image_6029125644611338739at_nat
% 0.14/0.47 @ ^ [X4: product_prod_int_int] : ( if_Pro3594990065127090477at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ S5 )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( image_6029125644611338739at_nat @ F @ ( inf_in2269163501485487111nt_int @ S5 @ ( collec213857154873943460nt_int @ P2 ) ) )
% 0.14/0.47 @ ( image_6029125644611338739at_nat @ G
% 0.14/0.47 @ ( inf_in2269163501485487111nt_int @ S5
% 0.14/0.47 @ ( collec213857154873943460nt_int
% 0.14/0.47 @ ^ [X4: product_prod_int_int] :
% 0.14/0.47 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % if_image_distrib
% 0.14/0.47 thf(fact_2795_UN__Un,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2796_UN__Un,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2797_UN__Un,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2798_UN__Un,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2799_UN__Un,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2800_UN__Un,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_Un
% 0.14/0.47 thf(fact_2801_bdd__below__image__inf,axiom,
% 0.14/0.47 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 0.14/0.47 ( ( condit1103211067700513672ow_rat
% 0.14/0.47 @ ( image_nat_rat
% 0.14/0.47 @ ^ [X4: nat] : ( inf_inf_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.47 & ( condit1103211067700513672ow_rat @ ( image_nat_rat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below_image_inf
% 0.14/0.47 thf(fact_2802_bdd__below__image__inf,axiom,
% 0.14/0.47 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat
% 0.14/0.47 @ ( image_nat_nat
% 0.14/0.47 @ ^ [X4: nat] : ( inf_inf_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 & ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below_image_inf
% 0.14/0.47 thf(fact_2803_bdd__below__image__inf,axiom,
% 0.14/0.47 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( image_nat_int
% 0.14/0.47 @ ^ [X4: nat] : ( inf_inf_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 & ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below_image_inf
% 0.14/0.47 thf(fact_2804_bdd__below__image__inf,axiom,
% 0.14/0.47 ! [F: int > nat,G: int > nat,A4: set_int] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat
% 0.14/0.47 @ ( image_int_nat
% 0.14/0.47 @ ^ [X4: int] : ( inf_inf_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 & ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below_image_inf
% 0.14/0.47 thf(fact_2805_bdd__below__image__inf,axiom,
% 0.14/0.47 ! [F: int > int,G: int > int,A4: set_int] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( inf_inf_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 & ( condit1735850657277959132ow_int @ ( image_int_int @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below_image_inf
% 0.14/0.47 thf(fact_2806_bdd__above__image__sup,axiom,
% 0.14/0.47 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 0.14/0.47 ( ( condit1579696412822616692ve_rat
% 0.14/0.47 @ ( image_nat_rat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.47 & ( condit1579696412822616692ve_rat @ ( image_nat_rat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above_image_sup
% 0.14/0.47 thf(fact_2807_bdd__above__image__sup,axiom,
% 0.14/0.47 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( condit2214826472909112428ve_nat
% 0.14/0.47 @ ( image_nat_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 & ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above_image_sup
% 0.14/0.47 thf(fact_2808_bdd__above__image__sup,axiom,
% 0.14/0.47 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 0.14/0.47 ( ( condit2212336002400062152ve_int
% 0.14/0.47 @ ( image_nat_int
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 & ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above_image_sup
% 0.14/0.47 thf(fact_2809_bdd__above__image__sup,axiom,
% 0.14/0.47 ! [F: int > nat,G: int > nat,A4: set_int] :
% 0.14/0.47 ( ( condit2214826472909112428ve_nat
% 0.14/0.47 @ ( image_int_nat
% 0.14/0.47 @ ^ [X4: int] : ( sup_sup_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 & ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above_image_sup
% 0.14/0.47 thf(fact_2810_bdd__above__image__sup,axiom,
% 0.14/0.47 ! [F: int > int,G: int > int,A4: set_int] :
% 0.14/0.47 ( ( condit2212336002400062152ve_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( sup_sup_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ A4 ) )
% 0.14/0.47 = ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 & ( condit2212336002400062152ve_int @ ( image_int_int @ G @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above_image_sup
% 0.14/0.47 thf(fact_2811_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_Product_unit,B5: product_unit > set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_7778121751606633509t_unit
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_7778121751606633509t_unit
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2812_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_o,B5: product_unit > set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_6930536745178679216_set_o
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_6930536745178679216_set_o
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2813_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_Product_unit,B5: $o > set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_663195431845683034t_unit
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_663195431845683034t_unit
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2814_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_o,B5: $o > set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_o_set_o
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_o_set_o
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2815_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: set_Product_unit,B5: nat > set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_4824033694279209942t_unit
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_4824033694279209942t_unit
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2816_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: set_o,B5: nat > set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_nat_set_o
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_nat_set_o
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2817_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2818_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2819_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2820_UN__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_Pr1261947904930325089at_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo2099793752762293965at_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su6327502436637775413at_nat @ A4 @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(3)
% 0.14/0.47 thf(fact_2821_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_Product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_7778121751606633509t_unit
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_7778121751606633509t_unit
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2822_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_o,B5: set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_6930536745178679216_set_o
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_6930536745178679216_set_o
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2823_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_Product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_663195431845683034t_unit
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_663195431845683034t_unit
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2824_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_o,B5: set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_o_set_o
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_o_set_o
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_o_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2825_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_Product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_4824033694279209942t_unit
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple3349607820504768346t_unit
% 0.14/0.47 @ ( image_4824033694279209942t_unit
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2826_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_o,B5: set_o] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_nat_set_o
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_o ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple90263536869209701_set_o
% 0.14/0.47 @ ( image_nat_set_o
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2827_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2828_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2829_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bot_set_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2830_UN__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = bot_bo2099793752762293965at_nat ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) )
% 0.14/0.47 = ( sup_su6327502436637775413at_nat @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_simps(2)
% 0.14/0.47 thf(fact_2831_UN__insert,axiom,
% 0.14/0.47 ! [B5: nat > set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2832_UN__insert,axiom,
% 0.14/0.47 ! [B5: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2833_UN__insert,axiom,
% 0.14/0.47 ! [B5: $o > set_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2834_UN__insert,axiom,
% 0.14/0.47 ! [B5: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2835_UN__insert,axiom,
% 0.14/0.47 ! [B5: nat > set_Pr8693737435421807431at_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2836_UN__insert,axiom,
% 0.14/0.47 ! [B5: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2837_UN__insert,axiom,
% 0.14/0.47 ! [B5: $o > set_Pr8693737435421807431at_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2838_UN__insert,axiom,
% 0.14/0.47 ! [B5: product_prod_nat_nat > set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2839_UN__insert,axiom,
% 0.14/0.47 ! [B5: nat > set_Pr4329608150637261639at_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( B5 @ A ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2840_UN__insert,axiom,
% 0.14/0.47 ! [B5: product_unit > set_Pr4329608150637261639at_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( B5 @ A ) @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_insert
% 0.14/0.47 thf(fact_2841_inj__apsnd,axiom,
% 0.14/0.47 ! [F: code_integer > code_integer] :
% 0.14/0.47 ( ( inj_on20428373856169009nteger @ ( produc6499014454317279255nteger @ F ) @ top_to2363841527343591755nteger )
% 0.14/0.47 = ( inj_on1158064722259180589nteger @ F @ top_to4645266643341252675nteger ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_apsnd
% 0.14/0.47 thf(fact_2842_INT__insert,axiom,
% 0.14/0.47 ! [B5: nat > set_Pr1261947904930325089at_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2843_INT__insert,axiom,
% 0.14/0.47 ! [B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2844_INT__insert,axiom,
% 0.14/0.47 ! [B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2845_INT__insert,axiom,
% 0.14/0.47 ! [B5: product_unit > set_Pr1261947904930325089at_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2846_INT__insert,axiom,
% 0.14/0.47 ! [B5: $o > set_Pr1261947904930325089at_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2847_INT__insert,axiom,
% 0.14/0.47 ! [B5: nat > set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2848_INT__insert,axiom,
% 0.14/0.47 ! [B5: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2849_INT__insert,axiom,
% 0.14/0.47 ! [B5: produc3843707927480180839at_nat > set_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2850_INT__insert,axiom,
% 0.14/0.47 ! [B5: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2851_INT__insert,axiom,
% 0.14/0.47 ! [B5: $o > set_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_insert
% 0.14/0.47 thf(fact_2852_inj__on__apsnd,axiom,
% 0.14/0.47 ! [F: code_integer > code_integer,A4: set_Code_integer] :
% 0.14/0.47 ( ( inj_on20428373856169009nteger @ ( produc6499014454317279255nteger @ F )
% 0.14/0.47 @ ( produc5882431272649516420nteger @ top_to4645266643341252675nteger
% 0.14/0.47 @ ^ [Uu: code_integer] : A4 ) )
% 0.14/0.47 = ( inj_on1158064722259180589nteger @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_apsnd
% 0.14/0.47 thf(fact_2853_inj__on__insert,axiom,
% 0.14/0.47 ! [F: int > nat,A: int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ ( insert_int @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 & ~ ( member_nat @ ( F @ A ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2854_inj__on__insert,axiom,
% 0.14/0.47 ! [F: int > int,A: int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ ( insert_int @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 & ~ ( member_int @ ( F @ A ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2855_inj__on__insert,axiom,
% 0.14/0.47 ! [F: product_unit > $o,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( inj_on8854722734121536060unit_o @ F @ ( insert_Product_unit @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on8854722734121536060unit_o @ F @ A4 )
% 0.14/0.47 & ~ ( member_o @ ( F @ A ) @ ( image_Product_unit_o @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2856_inj__on__insert,axiom,
% 0.14/0.47 ! [F: product_unit > nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( inj_on8430439091780834860it_nat @ F @ ( insert_Product_unit @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on8430439091780834860it_nat @ F @ A4 )
% 0.14/0.47 & ~ ( member_nat @ ( F @ A ) @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2857_inj__on__insert,axiom,
% 0.14/0.47 ! [F: product_unit > int,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( inj_on8427948621271784584it_int @ F @ ( insert_Product_unit @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on8427948621271784584it_int @ F @ A4 )
% 0.14/0.47 & ~ ( member_int @ ( F @ A ) @ ( image_873079544045703924it_int @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2858_inj__on__insert,axiom,
% 0.14/0.47 ! [F: $o > $o,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ ( insert_o @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_o_o @ F @ A4 )
% 0.14/0.47 & ~ ( member_o @ ( F @ A ) @ ( image_o_o @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2859_inj__on__insert,axiom,
% 0.14/0.47 ! [F: $o > nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_nat @ F @ ( insert_o @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_o_nat @ F @ A4 )
% 0.14/0.47 & ~ ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2860_inj__on__insert,axiom,
% 0.14/0.47 ! [F: $o > int,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_int @ F @ ( insert_o @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_o_int @ F @ A4 )
% 0.14/0.47 & ~ ( member_int @ ( F @ A ) @ ( image_o_int @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2861_inj__on__insert,axiom,
% 0.14/0.47 ! [F: nat > rat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ ( insert_nat @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 & ~ ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2862_inj__on__insert,axiom,
% 0.14/0.47 ! [F: nat > $o,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ ( insert_nat @ A @ A4 ) )
% 0.14/0.47 = ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.47 & ~ ( member_o @ ( F @ A ) @ ( image_nat_o @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_insert
% 0.14/0.47 thf(fact_2863_inj__on__Un__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 => ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.47 = ( image_nat_rat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un_image_eq_iff
% 0.14/0.47 thf(fact_2864_inj__on__Un__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 => ( ( ( image_nat_nat @ F @ A4 )
% 0.14/0.47 = ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un_image_eq_iff
% 0.14/0.47 thf(fact_2865_inj__on__Un__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 => ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.47 = ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un_image_eq_iff
% 0.14/0.47 thf(fact_2866_inj__on__Un__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 => ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.47 = ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un_image_eq_iff
% 0.14/0.47 thf(fact_2867_inj__on__Un__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 => ( ( ( image_int_int @ F @ A4 )
% 0.14/0.47 = ( image_int_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un_image_eq_iff
% 0.14/0.47 thf(fact_2868_Sigma__Un__distrib1,axiom,
% 0.14/0.47 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ ( sup_sup_set_nat @ I3 @ J3 ) @ C3 )
% 0.14/0.47 = ( sup_su6327502436637775413at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib1
% 0.14/0.47 thf(fact_2869_Sigma__Un__distrib1,axiom,
% 0.14/0.47 ! [I3: set_Pr1261947904930325089at_nat,J3: set_Pr1261947904930325089at_nat,C3: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( produc2761391749766926216at_nat @ ( sup_su6327502436637775413at_nat @ I3 @ J3 ) @ C3 )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( produc2761391749766926216at_nat @ I3 @ C3 ) @ ( produc2761391749766926216at_nat @ J3 @ C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib1
% 0.14/0.47 thf(fact_2870_Sigma__Un__distrib1,axiom,
% 0.14/0.47 ! [I3: set_se7855581050983116737at_nat,J3: set_se7855581050983116737at_nat,C3: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.47 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ I3 @ J3 ) @ C3 )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I3 @ C3 ) @ ( produc7726050920695093128at_nat @ J3 @ C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib1
% 0.14/0.47 thf(fact_2871_Sigma__Int__distrib1,axiom,
% 0.14/0.47 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ I3 @ J3 ) @ C3 )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Int_distrib1
% 0.14/0.47 thf(fact_2872_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_rat @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_rat )
% 0.14/0.47 => ( inj_on_nat_rat
% 0.14/0.47 @ ^ [X4: nat] : ( if_rat @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2873_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,G: nat > int,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_int @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_int )
% 0.14/0.47 => ( inj_on_nat_int
% 0.14/0.47 @ ^ [X4: nat] : ( if_int @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2874_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,G: int > int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_int_int @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_int )
% 0.14/0.47 => ( inj_on_int_int
% 0.14/0.47 @ ^ [X4: int] : ( if_int @ ( member_int @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2875_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,G: $o > product_unit,B5: set_o] :
% 0.14/0.47 ( ( inj_on4268752236855399398t_unit @ F @ A4 )
% 0.14/0.47 => ( ( inj_on4268752236855399398t_unit @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_in4660618365625256667t_unit @ ( image_o_Product_unit @ F @ A4 ) @ ( image_o_Product_unit @ G @ B5 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( inj_on4268752236855399398t_unit
% 0.14/0.47 @ ^ [X4: $o] : ( if_Product_unit @ ( member_o @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2876_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,G: nat > product_unit,B5: set_nat] :
% 0.14/0.47 ( ( inj_on7061601236592826506t_unit @ F @ A4 )
% 0.14/0.47 => ( ( inj_on7061601236592826506t_unit @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_in4660618365625256667t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) @ ( image_8730104196221521654t_unit @ G @ B5 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( inj_on7061601236592826506t_unit
% 0.14/0.47 @ ^ [X4: nat] : ( if_Product_unit @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2877_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,G: int > product_unit,B5: set_int] :
% 0.14/0.47 ( ( inj_on4178023183795006766t_unit @ F @ A4 )
% 0.14/0.47 => ( ( inj_on4178023183795006766t_unit @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_in4660618365625256667t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( inj_on4178023183795006766t_unit
% 0.14/0.47 @ ^ [X4: int] : ( if_Product_unit @ ( member_int @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2878_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: $o > $o,A4: set_o,G: $o > $o,B5: set_o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_o_o @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_o @ ( image_o_o @ F @ A4 ) @ ( image_o_o @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_o )
% 0.14/0.47 => ( inj_on_o_o
% 0.14/0.47 @ ^ [X4: $o] :
% 0.14/0.47 ( ( ( member_o @ X4 @ A4 )
% 0.14/0.47 => ( F @ X4 ) )
% 0.14/0.47 & ( ~ ( member_o @ X4 @ A4 )
% 0.14/0.47 => ( G @ X4 ) ) )
% 0.14/0.47 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2879_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_o @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_o @ ( image_nat_o @ F @ A4 ) @ ( image_nat_o @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_o )
% 0.14/0.47 => ( inj_on_nat_o
% 0.14/0.47 @ ^ [X4: nat] :
% 0.14/0.47 ( ( ( member_nat @ X4 @ A4 )
% 0.14/0.47 => ( F @ X4 ) )
% 0.14/0.47 & ( ~ ( member_nat @ X4 @ A4 )
% 0.14/0.47 => ( G @ X4 ) ) )
% 0.14/0.47 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2880_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: int > $o,A4: set_int,G: int > $o,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_o @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_int_o @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_o @ ( image_int_o @ F @ A4 ) @ ( image_int_o @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_o )
% 0.14/0.47 => ( inj_on_int_o
% 0.14/0.47 @ ^ [X4: int] :
% 0.14/0.47 ( ( ( member_int @ X4 @ A4 )
% 0.14/0.47 => ( F @ X4 ) )
% 0.14/0.47 & ( ~ ( member_int @ X4 @ A4 )
% 0.14/0.47 => ( G @ X4 ) ) )
% 0.14/0.47 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2881_inj__on__disjoint__Un,axiom,
% 0.14/0.47 ! [F: $o > nat,A4: set_o,G: $o > nat,B5: set_o] :
% 0.14/0.47 ( ( inj_on_o_nat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_o_nat @ G @ B5 )
% 0.14/0.47 => ( ( ( inf_inf_set_nat @ ( image_o_nat @ F @ A4 ) @ ( image_o_nat @ G @ B5 ) )
% 0.14/0.47 = bot_bot_set_nat )
% 0.14/0.47 => ( inj_on_o_nat
% 0.14/0.47 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.47 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_disjoint_Un
% 0.14/0.47 thf(fact_2882_Sigma__Un__distrib2,axiom,
% 0.14/0.47 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ I3
% 0.14/0.47 @ ^ [I2: nat] : ( sup_sup_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 0.14/0.47 = ( sup_su6327502436637775413at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib2
% 0.14/0.47 thf(fact_2883_Sigma__Un__distrib2,axiom,
% 0.14/0.47 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( produc2761391749766926216at_nat @ I3
% 0.14/0.47 @ ^ [I2: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( produc2761391749766926216at_nat @ I3 @ A4 ) @ ( produc2761391749766926216at_nat @ I3 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib2
% 0.14/0.47 thf(fact_2884_Sigma__Un__distrib2,axiom,
% 0.14/0.47 ! [I3: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 0.14/0.47 ( ( produc7726050920695093128at_nat @ I3
% 0.14/0.47 @ ^ [I2: set_Pr1261947904930325089at_nat] : ( sup_su3642409539654194069at_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I3 @ A4 ) @ ( produc7726050920695093128at_nat @ I3 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Un_distrib2
% 0.14/0.47 thf(fact_2885_Times__Un__distrib1,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ ( sup_sup_set_nat @ A4 @ B5 )
% 0.14/0.47 @ ^ [Uu: nat] : C3 )
% 0.14/0.47 = ( sup_su6327502436637775413at_nat
% 0.14/0.47 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.47 @ ^ [Uu: nat] : C3 )
% 0.14/0.47 @ ( produc457027306803732586at_nat @ B5
% 0.14/0.47 @ ^ [Uu: nat] : C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Un_distrib1
% 0.14/0.47 thf(fact_2886_Times__Un__distrib1,axiom,
% 0.14/0.47 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( produc2761391749766926216at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 )
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : C3 )
% 0.14/0.47 = ( sup_su718114333110466843at_nat
% 0.14/0.47 @ ( produc2761391749766926216at_nat @ A4
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : C3 )
% 0.14/0.47 @ ( produc2761391749766926216at_nat @ B5
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Un_distrib1
% 0.14/0.47 thf(fact_2887_Times__Un__distrib1,axiom,
% 0.14/0.47 ! [A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat,C3: set_se7855581050983116737at_nat] :
% 0.14/0.47 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ A4 @ B5 )
% 0.14/0.47 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat
% 0.14/0.47 @ ( produc7726050920695093128at_nat @ A4
% 0.14/0.47 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 )
% 0.14/0.47 @ ( produc7726050920695093128at_nat @ B5
% 0.14/0.47 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Un_distrib1
% 0.14/0.47 thf(fact_2888_Times__Int__Times,axiom,
% 0.14/0.47 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( inf_in4302113700860409141at_nat
% 0.14/0.47 @ ( produc2761391749766926216at_nat @ A4
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 0.14/0.47 @ ( produc2761391749766926216at_nat @ C3
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : D ) )
% 0.14/0.47 = ( produc2761391749766926216at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ C3 )
% 0.14/0.47 @ ^ [Uu: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ B5 @ D ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Int_Times
% 0.14/0.47 thf(fact_2889_Times__Int__Times,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: set_nat,C3: set_nat,D: set_nat] :
% 0.14/0.47 ( ( inf_in2572325071724192079at_nat
% 0.14/0.47 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.47 @ ^ [Uu: nat] : B5 )
% 0.14/0.47 @ ( produc457027306803732586at_nat @ C3
% 0.14/0.47 @ ^ [Uu: nat] : D ) )
% 0.14/0.47 = ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ A4 @ C3 )
% 0.14/0.47 @ ^ [Uu: nat] : ( inf_inf_set_nat @ B5 @ D ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Int_Times
% 0.14/0.47 thf(fact_2890_Sigma__Int__distrib2,axiom,
% 0.14/0.47 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ I3
% 0.14/0.47 @ ^ [I2: nat] : ( inf_inf_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sigma_Int_distrib2
% 0.14/0.47 thf(fact_2891_Times__Int__distrib1,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 0.14/0.47 ( ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ A4 @ B5 )
% 0.14/0.47 @ ^ [Uu: nat] : C3 )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat
% 0.14/0.47 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.47 @ ^ [Uu: nat] : C3 )
% 0.14/0.47 @ ( produc457027306803732586at_nat @ B5
% 0.14/0.47 @ ^ [Uu: nat] : C3 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Times_Int_distrib1
% 0.14/0.47 thf(fact_2892_inj__on__Un,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 & ( inj_on_nat_rat @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_rat @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_rat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2893_inj__on__Un,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.47 & ( inj_on_nat_int @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_int @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_int ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2894_inj__on__Un,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 & ( inj_on_int_int @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_int @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_int ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2895_inj__on__Un,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.47 & ( inj_on_nat_nat @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_nat @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2896_inj__on__Un,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 & ( inj_on_int_nat @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_nat @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2897_inj__on__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( inj_on1041401102088758999t_unit @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on1041401102088758999t_unit @ F @ A4 )
% 0.14/0.47 & ( inj_on1041401102088758999t_unit @ F @ B5 )
% 0.14/0.47 & ( ( inf_in4660618365625256667t_unit @ ( image_8487516615895632747t_unit @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_8487516615895632747t_unit @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2898_inj__on__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > $o,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( inj_on991952103320416098_nat_o @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on991952103320416098_nat_o @ F @ A4 )
% 0.14/0.47 & ( inj_on991952103320416098_nat_o @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_o @ ( image_3275415580317762038_nat_o @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_3275415580317762038_nat_o @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_o ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2899_inj__on__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( inj_on490725545064285830at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on490725545064285830at_nat @ F @ A4 )
% 0.14/0.47 & ( inj_on490725545064285830at_nat @ F @ B5 )
% 0.14/0.47 & ( ( inf_inf_set_nat @ ( image_6160980552072806642at_nat @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_6160980552072806642at_nat @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bot_set_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2900_inj__on__Un,axiom,
% 0.14/0.47 ! [F: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( inj_on3108384905993948887t_unit @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on3108384905993948887t_unit @ F @ A4 )
% 0.14/0.47 & ( inj_on3108384905993948887t_unit @ F @ B5 )
% 0.14/0.47 & ( ( inf_in4660618365625256667t_unit @ ( image_7082456443403096939t_unit @ F @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) @ ( image_7082456443403096939t_unit @ F @ ( minus_3314409938677909166at_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2901_inj__on__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > product_prod_nat_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( inj_on229527429751349963at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( ( inj_on229527429751349963at_nat @ F @ A4 )
% 0.14/0.47 & ( inj_on229527429751349963at_nat @ F @ B5 )
% 0.14/0.47 & ( ( inf_in2572325071724192079at_nat @ ( image_6706873702294942047at_nat @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_6706873702294942047at_nat @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 0.14/0.47 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_Un
% 0.14/0.47 thf(fact_2902_inj__on__image,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ ( comple3221217463730067765et_int @ A4 ) )
% 0.14/0.47 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image
% 0.14/0.47 thf(fact_2903_inj__on__image,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ ( comple3221217463730067765et_int @ A4 ) )
% 0.14/0.47 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image
% 0.14/0.47 thf(fact_2904_inj__on__image,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 0.14/0.47 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image
% 0.14/0.47 thf(fact_2905_inj__on__image,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 0.14/0.47 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image
% 0.14/0.47 thf(fact_2906_inj__on__image,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 0.14/0.47 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image
% 0.14/0.47 thf(fact_2907_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,B5: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2908_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2909_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,B5: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2910_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2911_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,B5: set_o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2912_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2913_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2914_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,B5: set_o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2915_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2916_cSUP__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_union
% 0.14/0.47 thf(fact_2917_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,B5: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2918_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2919_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,B5: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2920_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2921_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,B5: set_o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2922_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2923_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2924_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,B5: set_o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2925_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,B5: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2926_cINF__union,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,B5: set_Product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_union
% 0.14/0.47 thf(fact_2927_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2928_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2929_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2930_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2931_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2932_inj__on__image__Int,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,C3: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( inj_on8969904277767023793at_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_le3146513528884898305at_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_le3146513528884898305at_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_5168914502847457605at_nat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ ( image_5168914502847457605at_nat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Int
% 0.14/0.47 thf(fact_2933_image__Int,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2934_image__Int,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2935_image__Int,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2936_image__Int,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2937_image__Int,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.47 => ( ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2938_image__Int,axiom,
% 0.14/0.47 ! [F: char > product_prod_nat_nat,A4: set_char,B5: set_char] :
% 0.14/0.47 ( ( inj_on1021528964648911549at_nat @ F @ top_top_set_char )
% 0.14/0.47 => ( ( image_8382823969816519465at_nat @ F @ ( inf_inf_set_char @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_8382823969816519465at_nat @ F @ A4 ) @ ( image_8382823969816519465at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2939_image__Int,axiom,
% 0.14/0.47 ! [F: rat > product_prod_nat_nat,A4: set_rat,B5: set_rat] :
% 0.14/0.47 ( ( inj_on8867882244352206326at_nat @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( image_9175953278516507234at_nat @ F @ ( inf_inf_set_rat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_9175953278516507234at_nat @ F @ A4 ) @ ( image_9175953278516507234at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2940_image__Int,axiom,
% 0.14/0.47 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on5538052773655684606at_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_5846123807819985514at_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ ( image_5846123807819985514at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2941_image__Int,axiom,
% 0.14/0.47 ! [F: int > product_prod_nat_nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on8575894858119818402at_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( image_8883965892284119310at_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_8883965892284119310at_nat @ F @ A4 ) @ ( image_8883965892284119310at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2942_image__Int,axiom,
% 0.14/0.47 ! [F: list_nat > product_prod_nat_nat,A4: set_list_nat,B5: set_list_nat] :
% 0.14/0.47 ( ( inj_on7574789179980466158at_nat @ F @ top_top_set_list_nat )
% 0.14/0.47 => ( ( image_2795870212791037530at_nat @ F @ ( inf_inf_set_list_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( image_2795870212791037530at_nat @ F @ A4 ) @ ( image_2795870212791037530at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int
% 0.14/0.47 thf(fact_2943_inj__on__image__Pow,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Pow
% 0.14/0.47 thf(fact_2944_inj__on__image__Pow,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.47 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Pow
% 0.14/0.47 thf(fact_2945_inj__on__image__Pow,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.47 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Pow
% 0.14/0.47 thf(fact_2946_inj__on__image__Pow,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Pow
% 0.14/0.47 thf(fact_2947_inj__on__image__Pow,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Pow
% 0.14/0.47 thf(fact_2948_inj__on__image__Fpow,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Fpow
% 0.14/0.47 thf(fact_2949_inj__on__image__Fpow,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.47 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Fpow
% 0.14/0.47 thf(fact_2950_inj__on__image__Fpow,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.47 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Fpow
% 0.14/0.47 thf(fact_2951_inj__on__image__Fpow,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Fpow
% 0.14/0.47 thf(fact_2952_inj__on__image__Fpow,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_Fpow
% 0.14/0.47 thf(fact_2953_inj__on__imageI2,axiom,
% 0.14/0.47 ! [F3: $o > $o,F: nat > $o,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_o @ ( comp_o_o_nat @ F3 @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_nat_o @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI2
% 0.14/0.47 thf(fact_2954_inj__on__imageI2,axiom,
% 0.14/0.47 ! [F3: nat > num,F: int > nat,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_num @ ( comp_nat_num_int @ F3 @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_int_nat @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI2
% 0.14/0.47 thf(fact_2955_inj__on__imageI2,axiom,
% 0.14/0.47 ! [F3: nat > nat,F: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_nat_nat @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI2
% 0.14/0.47 thf(fact_2956_inj__on__imageI2,axiom,
% 0.14/0.47 ! [F3: int > nat,F: int > int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ ( comp_int_nat_int @ F3 @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_int_int @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI2
% 0.14/0.47 thf(fact_2957_inj__on__imageI2,axiom,
% 0.14/0.47 ! [F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,A4: set_Code_integer] :
% 0.14/0.47 ( ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F3 @ F ) @ A4 )
% 0.14/0.47 => ( inj_on108595395805848489nteger @ F @ A4 ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI2
% 0.14/0.47 thf(fact_2958_SUP__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2959_SUP__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2960_SUP__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2961_SUP__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2962_SUP__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2963_SUP__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2964_SUP__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2965_SUP__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_union
% 0.14/0.47 thf(fact_2966_INF__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2967_INF__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2968_INF__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2969_INF__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2970_INF__union,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2971_INF__union,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_union
% 0.14/0.47 thf(fact_2972_image__Un,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( image_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_sup_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2973_image__Un,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2974_image__Un,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_sup_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2975_image__Un,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2976_image__Un,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_sup_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2977_image__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > produc859450856879609959at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( image_6321802852832981957at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( image_6321802852832981957at_nat @ F @ A4 ) @ ( image_6321802852832981957at_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2978_image__Un,axiom,
% 0.14/0.47 ! [F: produc859450856879609959at_nat > produc3843707927480180839at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( image_7637461350386011077at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( image_7637461350386011077at_nat @ F @ A4 ) @ ( image_7637461350386011077at_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2979_image__Un,axiom,
% 0.14/0.47 ! [F: produc3843707927480180839at_nat > produc859450856879609959at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( image_5653576389946358725at_nat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( image_5653576389946358725at_nat @ F @ A4 ) @ ( image_5653576389946358725at_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2980_image__Un,axiom,
% 0.14/0.47 ! [F: produc3843707927480180839at_nat > produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( image_960689587819713477at_nat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( image_960689587819713477at_nat @ F @ A4 ) @ ( image_960689587819713477at_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Un
% 0.14/0.47 thf(fact_2981_INT__Un,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_Un
% 0.14/0.47 thf(fact_2982_INT__Un,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_Un
% 0.14/0.47 thf(fact_2983_INT__Un,axiom,
% 0.14/0.47 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_Un
% 0.14/0.47 thf(fact_2984_INT__Un,axiom,
% 0.14/0.47 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_Un
% 0.14/0.47 thf(fact_2985_inj__on__convol__ident,axiom,
% 0.14/0.47 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X5: set_se5479201105039950375at_nat] :
% 0.14/0.47 ( inj_on1468925692805905105at_nat
% 0.14/0.47 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ ( F @ X4 ) )
% 0.14/0.47 @ X5 ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_convol_ident
% 0.14/0.47 thf(fact_2986_inj__on__convol__ident,axiom,
% 0.14/0.47 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X5: set_se7855581050983116737at_nat] :
% 0.14/0.47 ( inj_on699426629415580343at_nat
% 0.14/0.47 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ ( F @ X4 ) )
% 0.14/0.47 @ X5 ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_convol_ident
% 0.14/0.47 thf(fact_2987_inj__on__convol__ident,axiom,
% 0.14/0.47 ! [F: nat > num,X5: set_nat] :
% 0.14/0.47 ( inj_on6246296710604522312at_num
% 0.14/0.47 @ ^ [X4: nat] : ( product_Pair_nat_num @ X4 @ ( F @ X4 ) )
% 0.14/0.47 @ X5 ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_convol_ident
% 0.14/0.47 thf(fact_2988_inj__on__convol__ident,axiom,
% 0.14/0.47 ! [F: nat > nat,X5: set_nat] :
% 0.14/0.47 ( inj_on5538052773655684606at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ ( F @ X4 ) )
% 0.14/0.47 @ X5 ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_convol_ident
% 0.14/0.47 thf(fact_2989_inj__on__convol__ident,axiom,
% 0.14/0.47 ! [F: int > int,X5: set_int] :
% 0.14/0.47 ( inj_on5397397550511676250nt_int
% 0.14/0.47 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ ( F @ X4 ) )
% 0.14/0.47 @ X5 ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_convol_ident
% 0.14/0.47 thf(fact_2990_total__onI,axiom,
% 0.14/0.47 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
% 0.14/0.47 ( ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 0.14/0.47 ( ( member8757157785044589968at_nat @ X @ A4 )
% 0.14/0.47 => ( ( member8757157785044589968at_nat @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
% 0.14/0.47 | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_1513685709984341995at_nat @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2991_total__onI,axiom,
% 0.14/0.47 ! [A4: set_o,R: set_Product_prod_o_o] :
% 0.14/0.47 ( ! [X: $o,Y: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ( member_o @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 0.14/0.47 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_on_o @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2992_total__onI,axiom,
% 0.14/0.47 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat] :
% 0.14/0.47 ( ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( member6273874620674182256at_nat @ X @ A4 )
% 0.14/0.47 => ( ( member6273874620674182256at_nat @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ R )
% 0.14/0.47 | ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_5117575981256876747at_nat @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2993_total__onI,axiom,
% 0.14/0.47 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member2643936169264416010at_nat @ X @ A4 )
% 0.14/0.47 => ( ( member2643936169264416010at_nat @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
% 0.14/0.47 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_7212417256332265445at_nat @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2994_total__onI,axiom,
% 0.14/0.47 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ! [X: nat,Y: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ( member_nat @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.14/0.47 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_on_nat @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2995_total__onI,axiom,
% 0.14/0.47 ! [A4: set_int,R: set_Pr958786334691620121nt_int] :
% 0.14/0.47 ( ! [X: int,Y: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ( member_int @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.14/0.47 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_on_int @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2996_total__onI,axiom,
% 0.14/0.47 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.47 => ( ( member8440522571783428010at_nat @ Y @ A4 )
% 0.14/0.47 => ( ( X != Y )
% 0.14/0.47 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R )
% 0.14/0.47 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y @ X ) @ R ) ) ) ) )
% 0.14/0.47 => ( total_3592101749530773125at_nat @ A4 @ R ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_onI
% 0.14/0.47 thf(fact_2997_total__on__def,axiom,
% 0.14/0.47 ( total_5117575981256876747at_nat
% 0.14/0.47 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 0.14/0.47 ! [X4: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 0.14/0.47 => ! [Y5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 0.14/0.47 => ( ( X4 != Y5 )
% 0.14/0.47 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R5 )
% 0.14/0.47 | ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_on_def
% 0.14/0.47 thf(fact_2998_total__on__def,axiom,
% 0.14/0.47 ( total_7212417256332265445at_nat
% 0.14/0.47 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ! [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 0.14/0.47 => ! [Y5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 0.14/0.47 => ( ( X4 != Y5 )
% 0.14/0.47 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R5 )
% 0.14/0.47 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_on_def
% 0.14/0.47 thf(fact_2999_total__on__def,axiom,
% 0.14/0.47 ( total_on_nat
% 0.14/0.47 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ! [X4: nat] :
% 0.14/0.47 ( ( member_nat @ X4 @ A6 )
% 0.14/0.47 => ! [Y5: nat] :
% 0.14/0.47 ( ( member_nat @ Y5 @ A6 )
% 0.14/0.47 => ( ( X4 != Y5 )
% 0.14/0.47 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R5 )
% 0.14/0.47 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_on_def
% 0.14/0.47 thf(fact_3000_total__on__def,axiom,
% 0.14/0.47 ( total_on_int
% 0.14/0.47 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 0.14/0.47 ! [X4: int] :
% 0.14/0.47 ( ( member_int @ X4 @ A6 )
% 0.14/0.47 => ! [Y5: int] :
% 0.14/0.47 ( ( member_int @ Y5 @ A6 )
% 0.14/0.47 => ( ( X4 != Y5 )
% 0.14/0.47 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R5 )
% 0.14/0.47 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_on_def
% 0.14/0.47 thf(fact_3001_total__on__def,axiom,
% 0.14/0.47 ( total_3592101749530773125at_nat
% 0.14/0.47 = ( ^ [A6: set_Pr1261947904930325089at_nat,R5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ! [X4: product_prod_nat_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 0.14/0.47 => ! [Y5: product_prod_nat_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ Y5 @ A6 )
% 0.14/0.47 => ( ( X4 != Y5 )
% 0.14/0.47 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R5 )
% 0.14/0.47 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % total_on_def
% 0.14/0.47 thf(fact_3002_SUP__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_UNIV_bool_expand
% 0.14/0.47 thf(fact_3003_SUP__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_UNIV_bool_expand
% 0.14/0.47 thf(fact_3004_SUP__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > set_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_UNIV_bool_expand
% 0.14/0.47 thf(fact_3005_SUP__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > product_unit] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_UNIV_bool_expand
% 0.14/0.47 thf(fact_3006_INF__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_UNIV_bool_expand
% 0.14/0.47 thf(fact_3007_INF__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > set_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_UNIV_bool_expand
% 0.14/0.47 thf(fact_3008_INF__UNIV__bool__expand,axiom,
% 0.14/0.47 ! [A4: $o > product_unit] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_UNIV_bool_expand
% 0.14/0.47 thf(fact_3009_fun_Oinj__map,axiom,
% 0.14/0.47 ! [F: $o > $o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ top_top_set_o )
% 0.14/0.47 => ( inj_on_nat_o_nat_o @ ( comp_o_o_nat @ F ) @ top_top_set_nat_o ) ) ).
% 0.14/0.47
% 0.14/0.47 % fun.inj_map
% 0.14/0.47 thf(fact_3010_fun_Oinj__map,axiom,
% 0.14/0.47 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.47 ( ( inj_on3998011822705705585nteger @ F @ top_to3804862627464599871nteger )
% 0.14/0.47 => ( inj_on5500977043710295017nteger @ ( comp_C8797469213163452608nteger @ F ) @ top_to3639204395728341691nteger ) ) ).
% 0.14/0.47
% 0.14/0.47 % fun.inj_map
% 0.14/0.47 thf(fact_3011_fun_Oinj__map,axiom,
% 0.14/0.47 ! [F: nat > num] :
% 0.14/0.47 ( ( inj_on_nat_num @ F @ top_top_set_nat )
% 0.14/0.47 => ( inj_on5377432224680912883nt_num @ ( comp_nat_num_int @ F ) @ top_top_set_int_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % fun.inj_map
% 0.14/0.47 thf(fact_3012_fun_Oinj__map,axiom,
% 0.14/0.47 ! [F: nat > nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( inj_on2461717442902640625at_nat @ ( comp_nat_nat_nat @ F ) @ top_top_set_nat_nat ) ) ).
% 0.14/0.47
% 0.14/0.47 % fun.inj_map
% 0.14/0.47 thf(fact_3013_fun_Oinj__map,axiom,
% 0.14/0.47 ! [F: int > nat] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( inj_on856898432580761861nt_nat @ ( comp_int_nat_int @ F ) @ top_top_set_int_int ) ) ).
% 0.14/0.47
% 0.14/0.47 % fun.inj_map
% 0.14/0.47 thf(fact_3014_Un__eq__UN,axiom,
% 0.14/0.47 ( sup_su718114333110466843at_nat
% 0.14/0.47 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_8493167801588156084at_nat
% 0.14/0.47 @ ^ [B4: $o] : ( if_set1508868558775481357at_nat @ B4 @ A6 @ B6 )
% 0.14/0.47 @ top_top_set_o ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_eq_UN
% 0.14/0.47 thf(fact_3015_Un__eq__UN,axiom,
% 0.14/0.47 ( sup_su5525570899277871387at_nat
% 0.14/0.47 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( comple4364388969068068532at_nat
% 0.14/0.47 @ ( image_2496312346330513076at_nat
% 0.14/0.47 @ ^ [B4: $o] : ( if_set3208018901896979469at_nat @ B4 @ A6 @ B6 )
% 0.14/0.47 @ top_top_set_o ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_eq_UN
% 0.14/0.47 thf(fact_3016_Un__eq__UN,axiom,
% 0.14/0.47 ( sup_sup_set_nat
% 0.14/0.47 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.14/0.47 ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [B4: $o] : ( if_set_nat @ B4 @ A6 @ B6 )
% 0.14/0.47 @ top_top_set_o ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_eq_UN
% 0.14/0.47 thf(fact_3017_UN__bool__eq,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_bool_eq
% 0.14/0.47 thf(fact_3018_UN__bool__eq,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_bool_eq
% 0.14/0.47 thf(fact_3019_UN__bool__eq,axiom,
% 0.14/0.47 ! [A4: $o > set_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_bool_eq
% 0.14/0.47 thf(fact_3020_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,G: int > nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_nat
% 0.14/0.47 @ ( image_int_nat
% 0.14/0.47 @ ^ [A5: int] : ( sup_sup_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3021_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_nat
% 0.14/0.47 @ ( image_nat_nat
% 0.14/0.47 @ ^ [A5: nat] : ( sup_sup_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3022_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,G: int > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [A5: int] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3023_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,G: product_unit > int] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_int
% 0.14/0.47 @ ( image_873079544045703924it_int
% 0.14/0.47 @ ^ [A5: product_unit] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3024_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,G: $o > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_int
% 0.14/0.47 @ ( image_o_int
% 0.14/0.47 @ ^ [A5: $o] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3025_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Sup_Sup_int
% 0.14/0.47 @ ( image_nat_int
% 0.14/0.47 @ ^ [A5: nat] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3026_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,G: product_unit > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [A5: product_unit] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3027_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit
% 0.14/0.47 @ ( image_o_Product_unit
% 0.14/0.47 @ ^ [A5: $o] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3028_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit
% 0.14/0.47 @ ( image_8730104196221521654t_unit
% 0.14/0.47 @ ^ [A5: nat] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3029_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,G: product_unit > set_nat] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [A5: product_unit] : ( sup_sup_set_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % conditionally_complete_lattice_class.SUP_sup_distrib
% 0.14/0.47 thf(fact_3030_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,G: int > nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_nat
% 0.14/0.47 @ ( image_int_nat
% 0.14/0.47 @ ^ [A5: int] : ( inf_inf_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3031_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_nat
% 0.14/0.47 @ ( image_nat_nat
% 0.14/0.47 @ ^ [A5: nat] : ( inf_inf_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3032_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,G: int > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [A5: int] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3033_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,G: product_unit > int] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_873079544045703924it_int
% 0.14/0.47 @ ^ [A5: product_unit] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3034_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,G: $o > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_o_int
% 0.14/0.47 @ ^ [A5: $o] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3035_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ G @ A4 ) ) )
% 0.14/0.47 = ( complete_Inf_Inf_int
% 0.14/0.47 @ ( image_nat_int
% 0.14/0.47 @ ^ [A5: nat] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3036_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,G: product_unit > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [A5: product_unit] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3037_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_o_Product_unit
% 0.14/0.47 @ ^ [A5: $o] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3038_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_8730104196221521654t_unit
% 0.14/0.47 @ ^ [A5: nat] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3039_cINF__inf__distrib,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,G: product_unit > set_nat] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [A5: product_unit] : ( inf_inf_set_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 0.14/0.47 @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_inf_distrib
% 0.14/0.47 thf(fact_3040_fsts_Ointros,axiom,
% 0.14/0.47 ! [P: produc7812382424243267045t_unit] : ( member_ref_a @ ( produc473321116828791851t_unit @ P ) @ ( basic_685971451221398055t_unit @ P ) ) ).
% 0.14/0.47
% 0.14/0.47 % fsts.intros
% 0.14/0.47 thf(fact_3041_fsts_Osimps,axiom,
% 0.14/0.47 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 0.14/0.47 ( ( member_ref_a @ A @ ( basic_685971451221398055t_unit @ P ) )
% 0.14/0.47 = ( A
% 0.14/0.47 = ( produc473321116828791851t_unit @ P ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % fsts.simps
% 0.14/0.47 thf(fact_3042_fsts_Ocases,axiom,
% 0.14/0.47 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 0.14/0.47 ( ( member_ref_a @ A @ ( basic_685971451221398055t_unit @ P ) )
% 0.14/0.47 => ( A
% 0.14/0.47 = ( produc473321116828791851t_unit @ P ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % fsts.cases
% 0.14/0.47 thf(fact_3043_INT__bool__eq,axiom,
% 0.14/0.47 ! [A4: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_bool_eq
% 0.14/0.47 thf(fact_3044_INT__bool__eq,axiom,
% 0.14/0.47 ! [A4: $o > set_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_bool_eq
% 0.14/0.47 thf(fact_3045_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,A: nat] :
% 0.14/0.47 ( ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3046_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,A: int] :
% 0.14/0.47 ( ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 = ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3047_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: $o > int,A4: set_o,A: $o] :
% 0.14/0.47 ( ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3048_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,A: nat] :
% 0.14/0.47 ( ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3049_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,A: int] :
% 0.14/0.47 ( ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3050_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,A: $o] :
% 0.14/0.47 ( ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3051_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,A: nat] :
% 0.14/0.47 ( ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3052_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,A: int] :
% 0.14/0.47 ( ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3053_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A4: set_o,A: $o] :
% 0.14/0.47 ( ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3054_cSUP__eq__cINF__D,axiom,
% 0.14/0.47 ! [F: nat > set_nat,A4: set_nat,A: nat] :
% 0.14/0.47 ( ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ A @ A4 )
% 0.14/0.47 => ( ( F @ A )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_eq_cINF_D
% 0.14/0.47 thf(fact_3055_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,A: int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ ( insert_int @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_nat @ ( F @ A ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3056_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_nat @ ( F @ A ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3057_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,A: int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( insert_int @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3058_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3059_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,A: $o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3060_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3061_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3062_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,A: $o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3063_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3064_cSUP__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_insert
% 0.14/0.47 thf(fact_3065_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,A: int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ ( insert_int @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_nat @ ( F @ A ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3066_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_nat @ ( F @ A ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3067_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,A: int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( insert_int @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3068_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > int,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3069_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,A: $o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3070_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3071_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > product_unit,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3072_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > product_unit,A: $o] :
% 0.14/0.47 ( ( A4 != bot_bot_set_o )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3073_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > product_unit,A: nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3074_cINF__insert,axiom,
% 0.14/0.47 ! [A4: set_Product_unit,F: product_unit > set_nat,A: product_unit] :
% 0.14/0.47 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_insert
% 0.14/0.47 thf(fact_3075_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > $o,B5: set_o,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ B5 )
% 0.14/0.47 => ( ( member_o @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3076_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > nat,B5: set_o,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_nat @ F @ B5 )
% 0.14/0.47 => ( ( member_o @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3077_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > int,B5: set_o,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_int @ F @ B5 )
% 0.14/0.47 => ( ( member_o @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3078_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,B5: set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ B5 )
% 0.14/0.47 => ( ( member_nat @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.47 => ( ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.47 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3079_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: nat > $o,B5: set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ B5 )
% 0.14/0.47 => ( ( member_nat @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.47 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3080_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,B5: set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ B5 )
% 0.14/0.47 => ( ( member_nat @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3081_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: nat > int,B5: set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ B5 )
% 0.14/0.47 => ( ( member_nat @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3082_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: int > $o,B5: set_int,A: int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_o @ F @ B5 )
% 0.14/0.47 => ( ( member_int @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_int_o @ F @ A4 ) )
% 0.14/0.47 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3083_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: int > nat,B5: set_int,A: int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ B5 )
% 0.14/0.47 => ( ( member_int @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3084_inj__on__image__mem__iff,axiom,
% 0.14/0.47 ! [F: int > int,B5: set_int,A: int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ B5 )
% 0.14/0.47 => ( ( member_int @ A @ B5 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_mem_iff
% 0.14/0.47 thf(fact_3085_inj__on__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.47 = ( image_nat_rat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_eq_iff
% 0.14/0.47 thf(fact_3086_inj__on__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( ( image_nat_nat @ F @ A4 )
% 0.14/0.47 = ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_eq_iff
% 0.14/0.47 thf(fact_3087_inj__on__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.47 = ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_eq_iff
% 0.14/0.47 thf(fact_3088_inj__on__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.47 = ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_eq_iff
% 0.14/0.47 thf(fact_3089_inj__on__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( ( image_int_int @ F @ A4 )
% 0.14/0.47 = ( image_int_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_eq_iff
% 0.14/0.47 thf(fact_3090_subset__image__inj,axiom,
% 0.14/0.47 ! [S5: set_rat,F: nat > rat,T3: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_rat @ S5 @ ( image_nat_rat @ F @ T3 ) )
% 0.14/0.47 = ( ? [U2: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 0.14/0.47 & ( inj_on_nat_rat @ F @ U2 )
% 0.14/0.47 & ( S5
% 0.14/0.47 = ( image_nat_rat @ F @ U2 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % subset_image_inj
% 0.14/0.47 thf(fact_3091_subset__image__inj,axiom,
% 0.14/0.47 ! [S5: set_nat,F: nat > nat,T3: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_nat @ S5 @ ( image_nat_nat @ F @ T3 ) )
% 0.14/0.47 = ( ? [U2: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 0.14/0.47 & ( inj_on_nat_nat @ F @ U2 )
% 0.14/0.47 & ( S5
% 0.14/0.47 = ( image_nat_nat @ F @ U2 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % subset_image_inj
% 0.14/0.47 thf(fact_3092_subset__image__inj,axiom,
% 0.14/0.47 ! [S5: set_int,F: nat > int,T3: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_int @ S5 @ ( image_nat_int @ F @ T3 ) )
% 0.14/0.47 = ( ? [U2: set_nat] :
% 0.14/0.47 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 0.14/0.47 & ( inj_on_nat_int @ F @ U2 )
% 0.14/0.47 & ( S5
% 0.14/0.47 = ( image_nat_int @ F @ U2 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % subset_image_inj
% 0.14/0.47 thf(fact_3093_subset__image__inj,axiom,
% 0.14/0.47 ! [S5: set_nat,F: int > nat,T3: set_int] :
% 0.14/0.47 ( ( ord_less_eq_set_nat @ S5 @ ( image_int_nat @ F @ T3 ) )
% 0.14/0.47 = ( ? [U2: set_int] :
% 0.14/0.47 ( ( ord_less_eq_set_int @ U2 @ T3 )
% 0.14/0.47 & ( inj_on_int_nat @ F @ U2 )
% 0.14/0.47 & ( S5
% 0.14/0.47 = ( image_int_nat @ F @ U2 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % subset_image_inj
% 0.14/0.47 thf(fact_3094_subset__image__inj,axiom,
% 0.14/0.47 ! [S5: set_int,F: int > int,T3: set_int] :
% 0.14/0.47 ( ( ord_less_eq_set_int @ S5 @ ( image_int_int @ F @ T3 ) )
% 0.14/0.47 = ( ? [U2: set_int] :
% 0.14/0.47 ( ( ord_less_eq_set_int @ U2 @ T3 )
% 0.14/0.47 & ( inj_on_int_int @ F @ U2 )
% 0.14/0.47 & ( S5
% 0.14/0.47 = ( image_int_int @ F @ U2 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % subset_image_inj
% 0.14/0.47 thf(fact_3095_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: product_unit > product_unit,A4: set_Product_unit,X2: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( inj_on8151373323710067377t_unit @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 0.14/0.47 = ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 0.14/0.47 ( ~ ( member_Product_unit @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_Product_unit @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_405062704495631173t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3096_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,X2: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( inj_on4268752236855399398t_unit @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 0.14/0.47 = ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: $o,A8: set_o] :
% 0.14/0.47 ( ~ ( member_o @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_o @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_o_Product_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3097_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,X2: rat,B5: set_rat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_rat @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_rat @ X2 @ B5 )
% 0.14/0.47 = ( image_nat_rat @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: nat,A8: set_nat] :
% 0.14/0.47 ( ~ ( member_nat @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_nat @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_nat_rat @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3098_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,X2: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( inj_on7061601236592826506t_unit @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 0.14/0.47 = ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: nat,A8: set_nat] :
% 0.14/0.47 ( ~ ( member_nat @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_nat @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_8730104196221521654t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3099_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,X2: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( inj_on4178023183795006766t_unit @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 0.14/0.47 = ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: int,A8: set_int] :
% 0.14/0.47 ( ~ ( member_int @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_int @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_5846526143423701914t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3100_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: product_unit > $o,A4: set_Product_unit,X2: $o,B5: set_o] :
% 0.14/0.47 ( ( inj_on8854722734121536060unit_o @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_o @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_o @ X2 @ B5 )
% 0.14/0.47 = ( image_Product_unit_o @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 0.14/0.47 ( ~ ( member_Product_unit @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_Product_unit @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_Product_unit_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3101_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: $o > $o,A4: set_o,X2: $o,B5: set_o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_o @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_o @ X2 @ B5 )
% 0.14/0.47 = ( image_o_o @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: $o,A8: set_o] :
% 0.14/0.47 ( ~ ( member_o @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_o @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_o_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3102_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: nat > $o,A4: set_nat,X2: $o,B5: set_o] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_o @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_o @ X2 @ B5 )
% 0.14/0.47 = ( image_nat_o @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: nat,A8: set_nat] :
% 0.14/0.47 ( ~ ( member_nat @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_nat @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_nat_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3103_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: int > $o,A4: set_int,X2: $o,B5: set_o] :
% 0.14/0.47 ( ( inj_on_int_o @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_o @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_o @ X2 @ B5 )
% 0.14/0.47 = ( image_int_o @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: int,A8: set_int] :
% 0.14/0.47 ( ~ ( member_int @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_int @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_int_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3104_inj__img__insertE,axiom,
% 0.14/0.47 ! [F: product_unit > nat,A4: set_Product_unit,X2: nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on8430439091780834860it_nat @ F @ A4 )
% 0.14/0.47 => ( ~ ( member_nat @ X2 @ B5 )
% 0.14/0.47 => ( ( ( insert_nat @ X2 @ B5 )
% 0.14/0.47 = ( image_875570014554754200it_nat @ F @ A4 ) )
% 0.14/0.47 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 0.14/0.47 ( ~ ( member_Product_unit @ X8 @ A8 )
% 0.14/0.47 => ( ( A4
% 0.14/0.47 = ( insert_Product_unit @ X8 @ A8 ) )
% 0.14/0.47 => ( ( X2
% 0.14/0.47 = ( F @ X8 ) )
% 0.14/0.47 => ( B5
% 0.14/0.47 != ( image_875570014554754200it_nat @ F @ A8 ) ) ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_img_insertE
% 0.14/0.47 thf(fact_3105_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > $o,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ top_top_set_o )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3106_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_nat @ F @ top_top_set_o )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3107_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: $o > int,A: $o,A4: set_o] :
% 0.14/0.47 ( ( inj_on_o_int @ F @ top_top_set_o )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 = ( member_o @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3108_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: char > $o,A: char,A4: set_char] :
% 0.14/0.47 ( ( inj_on_char_o @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_char_o @ F @ A4 ) )
% 0.14/0.47 = ( member_char @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3109_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: char > nat,A: char,A4: set_char] :
% 0.14/0.47 ( ( inj_on_char_nat @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_char_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_char @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3110_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: char > int,A: char,A4: set_char] :
% 0.14/0.47 ( ( inj_on_char_int @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_char_int @ F @ A4 ) )
% 0.14/0.47 = ( member_char @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3111_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: rat > $o,A: rat,A4: set_rat] :
% 0.14/0.47 ( ( inj_on_rat_o @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_o @ ( F @ A ) @ ( image_rat_o @ F @ A4 ) )
% 0.14/0.47 = ( member_rat @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3112_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: rat > nat,A: rat,A4: set_rat] :
% 0.14/0.47 ( ( inj_on_rat_nat @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_nat @ ( F @ A ) @ ( image_rat_nat @ F @ A4 ) )
% 0.14/0.47 = ( member_rat @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3113_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: rat > int,A: rat,A4: set_rat] :
% 0.14/0.47 ( ( inj_on_rat_int @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_int @ ( F @ A ) @ ( image_rat_int @ F @ A4 ) )
% 0.14/0.47 = ( member_rat @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3114_inj__image__mem__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.47 = ( member_nat @ A @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_mem_iff
% 0.14/0.47 thf(fact_3115_inj__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ( image_nat_rat @ F @ A4 )
% 0.14/0.47 = ( image_nat_rat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_eq_iff
% 0.14/0.47 thf(fact_3116_inj__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ( image_nat_nat @ F @ A4 )
% 0.14/0.47 = ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_eq_iff
% 0.14/0.47 thf(fact_3117_inj__image__eq__iff,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ( image_nat_int @ F @ A4 )
% 0.14/0.47 = ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_eq_iff
% 0.14/0.47 thf(fact_3118_inj__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( ( image_int_nat @ F @ A4 )
% 0.14/0.47 = ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_eq_iff
% 0.14/0.47 thf(fact_3119_inj__image__eq__iff,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.47 => ( ( ( image_int_int @ F @ A4 )
% 0.14/0.47 = ( image_int_int @ F @ B5 ) )
% 0.14/0.47 = ( A4 = B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_eq_iff
% 0.14/0.47 thf(fact_3120_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: char > $o,B: $o] :
% 0.14/0.47 ( ( inj_on_char_o @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) )
% 0.14/0.47 = ( ? [X4: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3121_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: char > nat,B: nat] :
% 0.14/0.47 ( ( inj_on_char_nat @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) )
% 0.14/0.47 = ( ? [X4: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3122_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: char > int,B: int] :
% 0.14/0.47 ( ( inj_on_char_int @ F @ top_top_set_char )
% 0.14/0.47 => ( ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) )
% 0.14/0.47 = ( ? [X4: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: char] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3123_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: rat > $o,B: $o] :
% 0.14/0.47 ( ( inj_on_rat_o @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) )
% 0.14/0.47 = ( ? [X4: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3124_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: rat > nat,B: nat] :
% 0.14/0.47 ( ( inj_on_rat_nat @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) )
% 0.14/0.47 = ( ? [X4: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3125_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: rat > int,B: int] :
% 0.14/0.47 ( ( inj_on_rat_int @ F @ top_top_set_rat )
% 0.14/0.47 => ( ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) )
% 0.14/0.47 = ( ? [X4: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: rat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3126_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: nat > rat,B: rat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 0.14/0.47 = ( ? [X4: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3127_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: nat > $o,B: $o] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
% 0.14/0.47 = ( ? [X4: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3128_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: nat > nat,B: nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 0.14/0.47 = ( ? [X4: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3129_range__ex1__eq,axiom,
% 0.14/0.47 ! [F: nat > int,B: int] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) )
% 0.14/0.47 = ( ? [X4: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ X4 ) )
% 0.14/0.47 & ! [Y5: nat] :
% 0.14/0.47 ( ( B
% 0.14/0.47 = ( F @ Y5 ) )
% 0.14/0.47 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % range_ex1_eq
% 0.14/0.47 thf(fact_3130_comp__inj__on,axiom,
% 0.14/0.47 ! [F: nat > $o,A4: set_nat,G: $o > $o] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_o_o @ G @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.47 => ( inj_on_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on
% 0.14/0.47 thf(fact_3131_comp__inj__on,axiom,
% 0.14/0.47 ! [F: code_integer > code_integer > code_integer,A4: set_Code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.47 ( ( inj_on108595395805848489nteger @ F @ A4 )
% 0.14/0.47 => ( ( inj_on3998011822705705585nteger @ G @ ( image_2177946750938214461nteger @ F @ A4 ) )
% 0.14/0.47 => ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on
% 0.14/0.47 thf(fact_3132_comp__inj__on,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,G: nat > nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on
% 0.14/0.47 thf(fact_3133_comp__inj__on,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,G: nat > num] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_num @ G @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( inj_on_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on
% 0.14/0.47 thf(fact_3134_comp__inj__on,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,G: int > nat] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_int_nat @ G @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( inj_on_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on
% 0.14/0.47 thf(fact_3135_inj__on__imageI,axiom,
% 0.14/0.47 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_o_o @ G @ ( image_nat_o @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI
% 0.14/0.47 thf(fact_3136_inj__on__imageI,axiom,
% 0.14/0.47 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,A4: set_Code_integer] :
% 0.14/0.47 ( ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ A4 )
% 0.14/0.47 => ( inj_on3998011822705705585nteger @ G @ ( image_2177946750938214461nteger @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI
% 0.14/0.47 thf(fact_3137_inj__on__imageI,axiom,
% 0.14/0.47 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI
% 0.14/0.47 thf(fact_3138_inj__on__imageI,axiom,
% 0.14/0.47 ! [G: nat > num,F: int > nat,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI
% 0.14/0.47 thf(fact_3139_inj__on__imageI,axiom,
% 0.14/0.47 ! [G: int > nat,F: int > int,A4: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 )
% 0.14/0.47 => ( inj_on_int_nat @ G @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_imageI
% 0.14/0.47 thf(fact_3140_comp__inj__on__iff,axiom,
% 0.14/0.47 ! [F: nat > $o,A4: set_nat,F3: $o > $o] :
% 0.14/0.47 ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_o_o @ F3 @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.47 = ( inj_on_nat_o @ ( comp_o_o_nat @ F3 @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on_iff
% 0.14/0.47 thf(fact_3141_comp__inj__on__iff,axiom,
% 0.14/0.47 ! [F: code_integer > code_integer > code_integer,A4: set_Code_integer,F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.47 ( ( inj_on108595395805848489nteger @ F @ A4 )
% 0.14/0.47 => ( ( inj_on3998011822705705585nteger @ F3 @ ( image_2177946750938214461nteger @ F @ A4 ) )
% 0.14/0.47 = ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F3 @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on_iff
% 0.14/0.47 thf(fact_3142_comp__inj__on__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,F3: nat > nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_nat @ F3 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 = ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on_iff
% 0.14/0.47 thf(fact_3143_comp__inj__on__iff,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,F3: nat > num] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_nat_num @ F3 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 = ( inj_on_int_num @ ( comp_nat_num_int @ F3 @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on_iff
% 0.14/0.47 thf(fact_3144_comp__inj__on__iff,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,F3: int > nat] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.47 => ( ( inj_on_int_nat @ F3 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 = ( inj_on_int_nat @ ( comp_int_nat_int @ F3 @ F ) @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % comp_inj_on_iff
% 0.14/0.47 thf(fact_3145_inj__compose,axiom,
% 0.14/0.47 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer] :
% 0.14/0.47 ( ( inj_on3998011822705705585nteger @ F @ top_to3804862627464599871nteger )
% 0.14/0.47 => ( ( inj_on108595395805848489nteger @ G @ top_to4645266643341252675nteger )
% 0.14/0.47 => ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ top_to4645266643341252675nteger ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_compose
% 0.14/0.47 thf(fact_3146_inj__compose,axiom,
% 0.14/0.47 ! [F: $o > $o,G: nat > $o] :
% 0.14/0.47 ( ( inj_on_o_o @ F @ top_top_set_o )
% 0.14/0.47 => ( ( inj_on_nat_o @ G @ top_top_set_nat )
% 0.14/0.47 => ( inj_on_nat_o @ ( comp_o_o_nat @ F @ G ) @ top_top_set_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_compose
% 0.14/0.47 thf(fact_3147_inj__compose,axiom,
% 0.14/0.47 ! [F: nat > nat,G: nat > nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.14/0.47 => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ top_top_set_nat ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_compose
% 0.14/0.47 thf(fact_3148_inj__compose,axiom,
% 0.14/0.47 ! [F: nat > num,G: int > nat] :
% 0.14/0.47 ( ( inj_on_nat_num @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( inj_on_int_nat @ G @ top_top_set_int )
% 0.14/0.47 => ( inj_on_int_num @ ( comp_nat_num_int @ F @ G ) @ top_top_set_int ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_compose
% 0.14/0.47 thf(fact_3149_inj__compose,axiom,
% 0.14/0.47 ! [F: int > nat,G: int > int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( inj_on_int_int @ G @ top_top_set_int )
% 0.14/0.47 => ( inj_on_int_nat @ ( comp_int_nat_int @ F @ G ) @ top_top_set_int ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_compose
% 0.14/0.47 thf(fact_3150_inf__Sup,axiom,
% 0.14/0.47 ! [A: set_Pr1261947904930325089at_nat,B5: set_se7855581050983116737at_nat] :
% 0.14/0.47 ( ( inf_in2572325071724192079at_nat @ A @ ( comple5685304695842803022at_nat @ B5 ) )
% 0.14/0.47 = ( comple5685304695842803022at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inf_Sup
% 0.14/0.47 thf(fact_3151_inf__Sup,axiom,
% 0.14/0.47 ! [A: set_nat,B5: set_set_nat] :
% 0.14/0.47 ( ( inf_inf_set_nat @ A @ ( comple7399068483239264473et_nat @ B5 ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inf_Sup
% 0.14/0.47 thf(fact_3152_inf__Sup,axiom,
% 0.14/0.47 ! [A: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( inf_inf_Product_unit @ A @ ( comple4687483117567863418t_unit @ B5 ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ ( inf_inf_Product_unit @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inf_Sup
% 0.14/0.47 thf(fact_3153_sup__Inf,axiom,
% 0.14/0.47 ! [A: set_Pr8693737435421807431at_nat,B5: set_se6425085446898223655at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A @ ( comple6332534001959699150at_nat @ B5 ) )
% 0.14/0.47 = ( comple6332534001959699150at_nat @ ( image_1013614488123988933at_nat @ ( sup_su718114333110466843at_nat @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % sup_Inf
% 0.14/0.47 thf(fact_3154_sup__Inf,axiom,
% 0.14/0.47 ! [A: set_Pr4329608150637261639at_nat,B5: set_se5479201105039950375at_nat] :
% 0.14/0.47 ( ( sup_su5525570899277871387at_nat @ A @ ( comple6751905152567503566at_nat @ B5 ) )
% 0.14/0.47 = ( comple6751905152567503566at_nat @ ( image_4303274092540115909at_nat @ ( sup_su5525570899277871387at_nat @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % sup_Inf
% 0.14/0.47 thf(fact_3155_sup__Inf,axiom,
% 0.14/0.47 ! [A: set_nat,B5: set_set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A @ ( comple7806235888213564991et_nat @ B5 ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( sup_sup_set_nat @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % sup_Inf
% 0.14/0.47 thf(fact_3156_sup__Inf,axiom,
% 0.14/0.47 ! [A: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( sup_sup_Product_unit @ A @ ( comple2584293577114468500t_unit @ B5 ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ ( sup_sup_Product_unit @ A ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % sup_Inf
% 0.14/0.47 thf(fact_3157_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,M: nat,F: $o > nat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3158_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M: nat,F: nat > nat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3159_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,M: nat,F: int > nat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3160_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,M: int,F: $o > int] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3161_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M: int,F: nat > int] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3162_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,M: int,F: int > int] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3163_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,M: rat,F: $o > rat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3164_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M: rat,F: nat > rat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3165_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,M: rat,F: int > rat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3166_bdd__below_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,M: code_integer,F: $o > code_integer] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_le3102999989581377725nteger @ M @ ( F @ X ) ) )
% 0.14/0.47 => ( condit4933233095834890765nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_below.I2
% 0.14/0.47 thf(fact_3167_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_o,M3: nat,F: $o > nat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3168_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M3: nat,F: nat > nat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3169_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_int,M3: nat,F: int > nat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3170_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_o,M3: int,F: $o > int] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3171_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M3: int,F: nat > int] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3172_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_int,M3: int,F: int > int] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3173_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_o,M3: rat,F: $o > rat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3174_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_nat,M3: rat,F: nat > rat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3175_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_int,M3: rat,F: int > rat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit1103211067700513672ow_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3176_bdd__belowI2,axiom,
% 0.14/0.47 ! [A4: set_o,M3: code_integer,F: $o > code_integer] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_le3102999989581377725nteger @ M3 @ ( F @ X ) ) )
% 0.14/0.47 => ( condit4933233095834890765nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_belowI2
% 0.14/0.47 thf(fact_3177_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > nat,M: nat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3178_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > nat,M: nat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3179_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > nat,M: nat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3180_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > int,M: int] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3181_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > int,M: int] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3182_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > int,M: int] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3183_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > rat,M: rat] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit1579696412822616692ve_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3184_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > rat,M: rat] :
% 0.14/0.47 ( ! [X: nat] :
% 0.14/0.47 ( ( member_nat @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3185_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_int,F: int > rat,M: rat] :
% 0.14/0.47 ( ! [X: int] :
% 0.14/0.47 ( ( member_int @ X @ A4 )
% 0.14/0.47 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit1579696412822616692ve_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3186_bdd__above_OI2,axiom,
% 0.14/0.47 ! [A4: set_o,F: $o > code_integer,M: code_integer] :
% 0.14/0.47 ( ! [X: $o] :
% 0.14/0.47 ( ( member_o @ X @ A4 )
% 0.14/0.47 => ( ord_le3102999989581377725nteger @ ( F @ X ) @ M ) )
% 0.14/0.47 => ( condit1118808407379112185nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % bdd_above.I2
% 0.14/0.47 thf(fact_3187_image__Int__subset,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3188_image__Int__subset,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3189_image__Int__subset,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3190_image__Int__subset,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] : ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3191_image__Int__subset,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3192_image__Int__subset,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) @ ( inf_in2572325071724192079at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ ( image_5168914502847457605at_nat @ F @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_Int_subset
% 0.14/0.47 thf(fact_3193_swap__inj__on,axiom,
% 0.14/0.47 ! [A4: set_Pr7459493094073627847at_nat] :
% 0.14/0.47 ( inj_on3942866938762682161at_nat
% 0.14/0.47 @ ( produc5456455677105495163at_nat
% 0.14/0.47 @ ^ [I2: set_Pr4329608150637261639at_nat,J: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ J @ I2 ) )
% 0.14/0.47 @ A4 ) ).
% 0.14/0.47
% 0.14/0.47 % swap_inj_on
% 0.14/0.47 thf(fact_3194_swap__inj__on,axiom,
% 0.14/0.47 ! [A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( inj_on8430303779476321073at_nat
% 0.14/0.47 @ ( produc7548845685434208379at_nat
% 0.14/0.47 @ ^ [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ J @ I2 ) )
% 0.14/0.47 @ A4 ) ).
% 0.14/0.47
% 0.14/0.47 % swap_inj_on
% 0.14/0.47 thf(fact_3195_swap__inj__on,axiom,
% 0.14/0.47 ! [A4: set_Pr3280342998896498603um_nat] :
% 0.14/0.47 ( inj_on2339680571444523825at_num
% 0.14/0.47 @ ( produc5219324331026901427at_num
% 0.14/0.47 @ ^ [I2: num,J: nat] : ( product_Pair_nat_num @ J @ I2 ) )
% 0.14/0.47 @ A4 ) ).
% 0.14/0.47
% 0.14/0.47 % swap_inj_on
% 0.14/0.47 thf(fact_3196_swap__inj__on,axiom,
% 0.14/0.47 ! [A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( inj_on8969904277767023793at_nat
% 0.14/0.47 @ ( produc2626176000494625587at_nat
% 0.14/0.47 @ ^ [I2: nat,J: nat] : ( product_Pair_nat_nat @ J @ I2 ) )
% 0.14/0.47 @ A4 ) ).
% 0.14/0.47
% 0.14/0.47 % swap_inj_on
% 0.14/0.47 thf(fact_3197_swap__inj__on,axiom,
% 0.14/0.47 ! [A4: set_Pr958786334691620121nt_int] :
% 0.14/0.47 ( inj_on6454360653267994289nt_int
% 0.14/0.47 @ ( produc4245557441103728435nt_int
% 0.14/0.47 @ ^ [I2: int,J: int] : ( product_Pair_int_int @ J @ I2 ) )
% 0.14/0.47 @ A4 ) ).
% 0.14/0.47
% 0.14/0.47 % swap_inj_on
% 0.14/0.47 thf(fact_3198_SUP__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > product_unit] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3199_SUP__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > product_unit] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3200_SUP__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > product_unit] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3201_SUP__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3202_SUP__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3203_SUP__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3204_SUP__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > product_unit] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3205_SUP__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3206_SUP__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3207_SUP__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_absorb
% 0.14/0.47 thf(fact_3208_Sup__inf,axiom,
% 0.14/0.47 ! [B5: set_se7855581050983116737at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( inf_in2572325071724192079at_nat @ ( comple5685304695842803022at_nat @ B5 ) @ A )
% 0.14/0.47 = ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3684629450409544005at_nat
% 0.14/0.47 @ ^ [B4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sup_inf
% 0.14/0.47 thf(fact_3209_Sup__inf,axiom,
% 0.14/0.47 ! [B5: set_set_nat,A: set_nat] :
% 0.14/0.47 ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ B5 ) @ A )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_7916887816326733075et_nat
% 0.14/0.47 @ ^ [B4: set_nat] : ( inf_inf_set_nat @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sup_inf
% 0.14/0.47 thf(fact_3210_Sup__inf,axiom,
% 0.14/0.47 ! [B5: set_Product_unit,A: product_unit] :
% 0.14/0.47 ( ( inf_inf_Product_unit @ ( comple4687483117567863418t_unit @ B5 ) @ A )
% 0.14/0.47 = ( comple4687483117567863418t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [B4: product_unit] : ( inf_inf_Product_unit @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Sup_inf
% 0.14/0.47 thf(fact_3211_Inf__sup,axiom,
% 0.14/0.47 ! [B5: set_se6425085446898223655at_nat,A: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ ( comple6332534001959699150at_nat @ B5 ) @ A )
% 0.14/0.47 = ( comple6332534001959699150at_nat
% 0.14/0.47 @ ( image_1013614488123988933at_nat
% 0.14/0.47 @ ^ [B4: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Inf_sup
% 0.14/0.47 thf(fact_3212_Inf__sup,axiom,
% 0.14/0.47 ! [B5: set_se5479201105039950375at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( sup_su5525570899277871387at_nat @ ( comple6751905152567503566at_nat @ B5 ) @ A )
% 0.14/0.47 = ( comple6751905152567503566at_nat
% 0.14/0.47 @ ( image_4303274092540115909at_nat
% 0.14/0.47 @ ^ [B4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Inf_sup
% 0.14/0.47 thf(fact_3213_Inf__sup,axiom,
% 0.14/0.47 ! [B5: set_set_nat,A: set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ ( comple7806235888213564991et_nat @ B5 ) @ A )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_7916887816326733075et_nat
% 0.14/0.47 @ ^ [B4: set_nat] : ( sup_sup_set_nat @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Inf_sup
% 0.14/0.47 thf(fact_3214_Inf__sup,axiom,
% 0.14/0.47 ! [B5: set_Product_unit,A: product_unit] :
% 0.14/0.47 ( ( sup_sup_Product_unit @ ( comple2584293577114468500t_unit @ B5 ) @ A )
% 0.14/0.47 = ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [B4: product_unit] : ( sup_sup_Product_unit @ B4 @ A )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Inf_sup
% 0.14/0.47 thf(fact_3215_INF__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > product_unit] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3216_INF__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > product_unit] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3217_INF__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > product_unit] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3218_INF__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3219_INF__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3220_INF__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3221_INF__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > product_unit] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3222_INF__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3223_INF__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3224_INF__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_absorb
% 0.14/0.47 thf(fact_3225_translation__subtract__Int,axiom,
% 0.14/0.47 ! [A: int,S2: set_int,T2: set_int] :
% 0.14/0.47 ( ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.47 @ ( inf_inf_set_int @ S2 @ T2 ) )
% 0.14/0.47 = ( inf_inf_set_int
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.47 @ S2 )
% 0.14/0.47 @ ( image_int_int
% 0.14/0.47 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 0.14/0.47 @ T2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % translation_subtract_Int
% 0.14/0.47 thf(fact_3226_translation__subtract__Int,axiom,
% 0.14/0.47 ! [A: rat,S2: set_rat,T2: set_rat] :
% 0.14/0.47 ( ( image_rat_rat
% 0.14/0.47 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.47 @ ( inf_inf_set_rat @ S2 @ T2 ) )
% 0.14/0.47 = ( inf_inf_set_rat
% 0.14/0.47 @ ( image_rat_rat
% 0.14/0.47 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.47 @ S2 )
% 0.14/0.47 @ ( image_rat_rat
% 0.14/0.47 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 0.14/0.47 @ T2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % translation_subtract_Int
% 0.14/0.47 thf(fact_3227_translation__subtract__Int,axiom,
% 0.14/0.47 ! [A: code_integer,S2: set_Code_integer,T2: set_Code_integer] :
% 0.14/0.47 ( ( image_4470545334726330049nteger
% 0.14/0.47 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.47 @ ( inf_in1364745209274528805nteger @ S2 @ T2 ) )
% 0.14/0.47 = ( inf_in1364745209274528805nteger
% 0.14/0.47 @ ( image_4470545334726330049nteger
% 0.14/0.47 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.47 @ S2 )
% 0.14/0.47 @ ( image_4470545334726330049nteger
% 0.14/0.47 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 0.14/0.47 @ T2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % translation_subtract_Int
% 0.14/0.47 thf(fact_3228_UN__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3229_UN__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3230_UN__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3231_UN__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3232_UN__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3233_UN__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3234_UN__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_525487068563185620at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_525487068563185620at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3235_UN__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3236_UN__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( A4 @ K ) @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3237_UN__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( A4 @ K ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_absorb
% 0.14/0.47 thf(fact_3238_INT__absorb,axiom,
% 0.14/0.47 ! [K: produc3843707927480180839at_nat,I3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member8757157785044589968at_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3239_INT__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3240_INT__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3241_INT__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3242_INT__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3243_INT__absorb,axiom,
% 0.14/0.47 ! [K: produc3843707927480180839at_nat,I3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.47 ( ( member8757157785044589968at_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3244_INT__absorb,axiom,
% 0.14/0.47 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 0.14/0.47 ( ( member8440522571783428010at_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3245_INT__absorb,axiom,
% 0.14/0.47 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 0.14/0.47 ( ( member_o @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3246_INT__absorb,axiom,
% 0.14/0.47 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 0.14/0.47 ( ( member_nat @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3247_INT__absorb,axiom,
% 0.14/0.47 ! [K: int,I3: set_int,A4: int > set_nat] :
% 0.14/0.47 ( ( member_int @ K @ I3 )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_absorb
% 0.14/0.47 thf(fact_3248_Int__Union2,axiom,
% 0.14/0.47 ! [B5: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( inf_in2572325071724192079at_nat @ ( comple5685304695842803022at_nat @ B5 ) @ A4 )
% 0.14/0.47 = ( comple5685304695842803022at_nat
% 0.14/0.47 @ ( image_3684629450409544005at_nat
% 0.14/0.47 @ ^ [C5: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ C5 @ A4 )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Union2
% 0.14/0.47 thf(fact_3249_Int__Union2,axiom,
% 0.14/0.47 ! [B5: set_set_nat,A4: set_nat] :
% 0.14/0.47 ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ B5 ) @ A4 )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_7916887816326733075et_nat
% 0.14/0.47 @ ^ [C5: set_nat] : ( inf_inf_set_nat @ C5 @ A4 )
% 0.14/0.47 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Union2
% 0.14/0.47 thf(fact_3250_Int__Union,axiom,
% 0.14/0.47 ! [A4: set_Pr1261947904930325089at_nat,B5: set_se7855581050983116737at_nat] :
% 0.14/0.47 ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple5685304695842803022at_nat @ B5 ) )
% 0.14/0.47 = ( comple5685304695842803022at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A4 ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Union
% 0.14/0.47 thf(fact_3251_Int__Union,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: set_set_nat] :
% 0.14/0.47 ( ( inf_inf_set_nat @ A4 @ ( comple7399068483239264473et_nat @ B5 ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A4 ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Union
% 0.14/0.47 thf(fact_3252_Un__Inter,axiom,
% 0.14/0.47 ! [A4: set_Pr8693737435421807431at_nat,B5: set_se6425085446898223655at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple6332534001959699150at_nat @ B5 ) )
% 0.14/0.47 = ( comple6332534001959699150at_nat @ ( image_1013614488123988933at_nat @ ( sup_su718114333110466843at_nat @ A4 ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_Inter
% 0.14/0.47 thf(fact_3253_Un__Inter,axiom,
% 0.14/0.47 ! [A4: set_Pr4329608150637261639at_nat,B5: set_se5479201105039950375at_nat] :
% 0.14/0.47 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple6751905152567503566at_nat @ B5 ) )
% 0.14/0.47 = ( comple6751905152567503566at_nat @ ( image_4303274092540115909at_nat @ ( sup_su5525570899277871387at_nat @ A4 ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_Inter
% 0.14/0.47 thf(fact_3254_Un__Inter,axiom,
% 0.14/0.47 ! [A4: set_nat,B5: set_set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B5 ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( sup_sup_set_nat @ A4 ) @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Un_Inter
% 0.14/0.47 thf(fact_3255_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_rat,A7: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_rat )
% 0.14/0.47 => ( ( ? [F2: rat > nat] :
% 0.14/0.47 ( ( inj_on_rat_nat @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_nat @ ( image_rat_nat @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: nat > rat] :
% 0.14/0.47 ( ( image_nat_rat @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3256_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_int,A7: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( ? [F2: int > nat] :
% 0.14/0.47 ( ( inj_on_int_nat @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_nat @ ( image_int_nat @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: nat > int] :
% 0.14/0.47 ( ( image_nat_int @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3257_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_int,A7: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_int )
% 0.14/0.47 => ( ( ? [F2: int > int] :
% 0.14/0.47 ( ( inj_on_int_int @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_int @ ( image_int_int @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: int > int] :
% 0.14/0.47 ( ( image_int_int @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3258_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_nat,A7: set_rat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( ? [F2: nat > rat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: rat > nat] :
% 0.14/0.47 ( ( image_rat_nat @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3259_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_nat,A7: set_nat] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( ? [F2: nat > nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: nat > nat] :
% 0.14/0.47 ( ( image_nat_nat @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3260_inj__on__iff__surj,axiom,
% 0.14/0.47 ! [A4: set_nat,A7: set_int] :
% 0.14/0.47 ( ( A4 != bot_bot_set_nat )
% 0.14/0.47 => ( ( ? [F2: nat > int] :
% 0.14/0.47 ( ( inj_on_nat_int @ F2 @ A4 )
% 0.14/0.47 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ A4 ) @ A7 ) ) )
% 0.14/0.47 = ( ? [G3: int > nat] :
% 0.14/0.47 ( ( image_int_nat @ G3 @ A7 )
% 0.14/0.47 = A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_iff_surj
% 0.14/0.47 thf(fact_3261_Int__Inter__eq_I1_J,axiom,
% 0.14/0.47 ! [B8: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( B8 = bot_bo3083307316010499117at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ B8 ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( B8 != bot_bo3083307316010499117at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ B8 ) )
% 0.14/0.47 = ( comple1930127330929219688at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A4 ) @ B8 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Inter_eq(1)
% 0.14/0.47 thf(fact_3262_Int__Inter__eq_I1_J,axiom,
% 0.14/0.47 ! [B8: set_set_nat,A4: set_nat] :
% 0.14/0.47 ( ( ( B8 = bot_bot_set_set_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B8 ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( B8 != bot_bot_set_set_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B8 ) )
% 0.14/0.47 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A4 ) @ B8 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Inter_eq(1)
% 0.14/0.47 thf(fact_3263_Int__Inter__eq_I2_J,axiom,
% 0.14/0.47 ! [B8: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( B8 = bot_bo3083307316010499117at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ B8 ) @ A4 )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( B8 != bot_bo3083307316010499117at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ B8 ) @ A4 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_3684629450409544005at_nat
% 0.14/0.47 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B6 @ A4 )
% 0.14/0.47 @ B8 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Inter_eq(2)
% 0.14/0.47 thf(fact_3264_Int__Inter__eq_I2_J,axiom,
% 0.14/0.47 ! [B8: set_set_nat,A4: set_nat] :
% 0.14/0.47 ( ( ( B8 = bot_bot_set_set_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ B8 ) @ A4 )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( B8 != bot_bot_set_set_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ B8 ) @ A4 )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_7916887816326733075et_nat
% 0.14/0.47 @ ^ [B6: set_nat] : ( inf_inf_set_nat @ B6 @ A4 )
% 0.14/0.47 @ B8 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Int_Inter_eq(2)
% 0.14/0.47 thf(fact_3265_inj__image__subset__iff,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) )
% 0.14/0.47 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_subset_iff
% 0.14/0.47 thf(fact_3266_inj__image__subset__iff,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) )
% 0.14/0.47 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_subset_iff
% 0.14/0.47 thf(fact_3267_inj__image__subset__iff,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) )
% 0.14/0.47 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_subset_iff
% 0.14/0.47 thf(fact_3268_inj__image__subset__iff,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) )
% 0.14/0.47 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_subset_iff
% 0.14/0.47 thf(fact_3269_inj__image__subset__iff,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) )
% 0.14/0.47 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_image_subset_iff
% 0.14/0.47 thf(fact_3270_inj__on__image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_set_diff
% 0.14/0.47 thf(fact_3271_inj__on__image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_set_diff
% 0.14/0.47 thf(fact_3272_inj__on__image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 0.14/0.47 => ( ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_set_diff
% 0.14/0.47 thf(fact_3273_inj__on__image__set__diff,axiom,
% 0.14/0.47 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_set_diff
% 0.14/0.47 thf(fact_3274_inj__on__image__set__diff,axiom,
% 0.14/0.47 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ C3 )
% 0.14/0.47 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 0.14/0.47 => ( ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % inj_on_image_set_diff
% 0.14/0.47 thf(fact_3275_image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_set_diff
% 0.14/0.47 thf(fact_3276_image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_set_diff
% 0.14/0.47 thf(fact_3277_image__set__diff,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 0.14/0.47 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.47 => ( ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_set_diff
% 0.14/0.47 thf(fact_3278_image__set__diff,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.47 => ( ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_set_diff
% 0.14/0.47 thf(fact_3279_image__set__diff,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.47 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.47 => ( ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 0.14/0.47 = ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % image_set_diff
% 0.14/0.47 thf(fact_3280_cINF__lower2,axiom,
% 0.14/0.47 ! [F: $o > nat,A4: set_o,X2: $o,U: nat] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3281_cINF__lower2,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,X2: nat,U: nat] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3282_cINF__lower2,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,X2: int,U: nat] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3283_cINF__lower2,axiom,
% 0.14/0.47 ! [F: $o > int,A4: set_o,X2: $o,U: int] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3284_cINF__lower2,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,X2: nat,U: int] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3285_cINF__lower2,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,X2: int,U: int] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3286_cINF__lower2,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,X2: $o,U: product_unit] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3287_cINF__lower2,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,X2: nat,U: product_unit] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3288_cINF__lower2,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,X2: int,U: product_unit] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3289_cINF__lower2,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A4: set_o,X2: $o,U: set_nat] :
% 0.14/0.47 ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ ( F @ X2 ) @ U )
% 0.14/0.47 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower2
% 0.14/0.47 thf(fact_3290_cINF__lower,axiom,
% 0.14/0.47 ! [F: $o > nat,A4: set_o,X2: $o] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3291_cINF__lower,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,X2: nat] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3292_cINF__lower,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,X2: int] :
% 0.14/0.47 ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3293_cINF__lower,axiom,
% 0.14/0.47 ! [F: $o > int,A4: set_o,X2: $o] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3294_cINF__lower,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,X2: nat] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3295_cINF__lower,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,X2: int] :
% 0.14/0.47 ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3296_cINF__lower,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,X2: $o] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3297_cINF__lower,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,X2: nat] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3298_cINF__lower,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,X2: int] :
% 0.14/0.47 ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3299_cINF__lower,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A4: set_o,X2: $o] :
% 0.14/0.47 ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cINF_lower
% 0.14/0.47 thf(fact_3300_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: $o > nat,A4: set_o,X2: $o,U: nat] :
% 0.14/0.47 ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3301_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: nat > nat,A4: set_nat,X2: nat,U: nat] :
% 0.14/0.47 ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3302_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: int > nat,A4: set_int,X2: int,U: nat] :
% 0.14/0.47 ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3303_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: $o > int,A4: set_o,X2: $o,U: int] :
% 0.14/0.47 ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3304_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: nat > int,A4: set_nat,X2: nat,U: int] :
% 0.14/0.47 ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3305_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: int > int,A4: set_int,X2: int,U: int] :
% 0.14/0.47 ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3306_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A4: set_o,X2: $o,U: product_unit] :
% 0.14/0.47 ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3307_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A4: set_nat,X2: nat,U: product_unit] :
% 0.14/0.47 ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3308_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: int > product_unit,A4: set_int,X2: int,U: product_unit] :
% 0.14/0.47 ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3309_cSUP__upper2,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A4: set_o,X2: $o,U: set_nat] :
% 0.14/0.47 ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( ord_less_eq_set_nat @ U @ ( F @ X2 ) )
% 0.14/0.47 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper2
% 0.14/0.47 thf(fact_3310_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: $o,A4: set_o,F: $o > nat] :
% 0.14/0.47 ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3311_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 0.14/0.47 ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3312_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: int,A4: set_int,F: int > nat] :
% 0.14/0.47 ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3313_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: $o,A4: set_o,F: $o > int] :
% 0.14/0.47 ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3314_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: nat,A4: set_nat,F: nat > int] :
% 0.14/0.47 ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3315_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: int,A4: set_int,F: int > int] :
% 0.14/0.47 ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3316_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: $o,A4: set_o,F: $o > product_unit] :
% 0.14/0.47 ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3317_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: nat,A4: set_nat,F: nat > product_unit] :
% 0.14/0.47 ( ( member_nat @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3318_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: int,A4: set_int,F: int > product_unit] :
% 0.14/0.47 ( ( member_int @ X2 @ A4 )
% 0.14/0.47 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 0.14/0.47 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3319_cSUP__upper,axiom,
% 0.14/0.47 ! [X2: $o,A4: set_o,F: $o > set_nat] :
% 0.14/0.47 ( ( member_o @ X2 @ A4 )
% 0.14/0.47 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 0.14/0.47 => ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % cSUP_upper
% 0.14/0.47 thf(fact_3320_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_nat,F: product_unit > set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3321_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_nat,F: $o > set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ bot_bot_set_o ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3322_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_nat,F: nat > set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ bot_bot_set_nat ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3323_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_nat,F: product_prod_nat_nat > set_nat] :
% 0.14/0.47 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ bot_bo2099793752762293965at_nat ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3324_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr8693737435421807431at_nat,F: product_unit > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3325_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr8693737435421807431at_nat,F: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ bot_bot_set_o ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3326_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr8693737435421807431at_nat,F: nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ bot_bot_set_nat ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3327_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3328_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr8693737435421807431at_nat,F: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ bot_bo2099793752762293965at_nat ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3329_Union__image__empty,axiom,
% 0.14/0.47 ! [A4: set_Pr4329608150637261639at_nat,F: $o > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ F @ bot_bot_set_o ) ) )
% 0.14/0.47 = A4 ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_empty
% 0.14/0.47 thf(fact_3330_Union__image__insert,axiom,
% 0.14/0.47 ! [F: nat > set_nat,A: nat,B5: set_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3331_Union__image__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_nat,A: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3332_Union__image__insert,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A: $o,B5: set_o] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3333_Union__image__insert,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3334_Union__image__insert,axiom,
% 0.14/0.47 ! [F: nat > set_Pr8693737435421807431at_nat,A: nat,B5: set_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3335_Union__image__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3336_Union__image__insert,axiom,
% 0.14/0.47 ! [F: $o > set_Pr8693737435421807431at_nat,A: $o,B5: set_o] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ ( insert_o @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3337_Union__image__insert,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3338_Union__image__insert,axiom,
% 0.14/0.47 ! [F: nat > set_Pr4329608150637261639at_nat,A: nat,B5: set_nat] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( F @ A ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3339_Union__image__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_Pr4329608150637261639at_nat,A: product_unit,B5: set_Product_unit] :
% 0.14/0.47 ( ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 0.14/0.47 = ( sup_su5525570899277871387at_nat @ ( F @ A ) @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ B5 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % Union_image_insert
% 0.14/0.47 thf(fact_3340_SUP__insert,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3341_SUP__insert,axiom,
% 0.14/0.47 ! [F: product_unit > product_unit,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3342_SUP__insert,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3343_SUP__insert,axiom,
% 0.14/0.47 ! [F: nat > set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3344_SUP__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3345_SUP__insert,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3346_SUP__insert,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > product_unit,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3347_SUP__insert,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3348_SUP__insert,axiom,
% 0.14/0.47 ! [F: nat > set_Pr8693737435421807431at_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3349_SUP__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % SUP_insert
% 0.14/0.47 thf(fact_3350_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3351_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_o_Product_unit
% 0.14/0.47 @ ^ [I2: $o] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3352_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_8730104196221521654t_unit
% 0.14/0.47 @ ^ [I2: nat] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3353_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3354_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [I2: $o] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3355_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [I2: nat] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3356_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 0.14/0.47 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_6169909464789311569t_unit
% 0.14/0.47 @ ^ [I2: product_prod_nat_nat] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3357_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,F: product_unit > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3358_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_o,F: $o > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7077428525161401678at_nat
% 0.14/0.47 @ ^ [I2: $o] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3359_INF__inf__const2,axiom,
% 0.14/0.47 ! [I3: set_nat,F: nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7178329752028323786at_nat
% 0.14/0.47 @ ^ [I2: nat] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const2
% 0.14/0.47 thf(fact_3360_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,X2: product_unit,F: product_unit > product_unit] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_405062704495631173t_unit
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3361_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_o,X2: product_unit,F: $o > product_unit] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_o_Product_unit
% 0.14/0.47 @ ^ [I2: $o] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3362_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_nat,X2: product_unit,F: nat > product_unit] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_8730104196221521654t_unit
% 0.14/0.47 @ ^ [I2: nat] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3363_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,X2: set_nat,F: product_unit > set_nat] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3364_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_o,X2: set_nat,F: $o > set_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [I2: $o] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3365_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_nat,X2: set_nat,F: nat > set_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [I2: nat] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3366_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_Pr1261947904930325089at_nat,X2: product_unit,F: product_prod_nat_nat > product_unit] :
% 0.14/0.47 ( ( I3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( comple2584293577114468500t_unit
% 0.14/0.47 @ ( image_6169909464789311569t_unit
% 0.14/0.47 @ ^ [I2: product_prod_nat_nat] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3367_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_Product_unit,X2: set_Pr1261947904930325089at_nat,F: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [I2: product_unit] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3368_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_o,X2: set_Pr1261947904930325089at_nat,F: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_o )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7077428525161401678at_nat
% 0.14/0.47 @ ^ [I2: $o] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3369_INF__inf__const1,axiom,
% 0.14/0.47 ! [I3: set_nat,X2: set_Pr1261947904930325089at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( I3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7178329752028323786at_nat
% 0.14/0.47 @ ^ [I2: nat] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 0.14/0.47 @ I3 ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ I3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_inf_const1
% 0.14/0.47 thf(fact_3370_INF__insert,axiom,
% 0.14/0.47 ! [F: nat > product_unit,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3371_INF__insert,axiom,
% 0.14/0.47 ! [F: product_unit > product_unit,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3372_INF__insert,axiom,
% 0.14/0.47 ! [F: $o > product_unit,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3373_INF__insert,axiom,
% 0.14/0.47 ! [F: nat > set_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3374_INF__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3375_INF__insert,axiom,
% 0.14/0.47 ! [F: $o > set_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3376_INF__insert,axiom,
% 0.14/0.47 ! [F: product_prod_nat_nat > product_unit,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3377_INF__insert,axiom,
% 0.14/0.47 ! [F: nat > set_Pr1261947904930325089at_nat,A: nat,A4: set_nat] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3378_INF__insert,axiom,
% 0.14/0.47 ! [F: product_unit > set_Pr1261947904930325089at_nat,A: product_unit,A4: set_Product_unit] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3379_INF__insert,axiom,
% 0.14/0.47 ! [F: $o > set_Pr1261947904930325089at_nat,A: $o,A4: set_o] :
% 0.14/0.47 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 0.14/0.47 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INF_insert
% 0.14/0.47 thf(fact_3380_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3381_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3382_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3383_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_15824709712370754et_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3384_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_7288820656315755647at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3385_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_8493167801588156084at_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3386_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_4592875511192039216at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3387_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple4364388969068068532at_nat
% 0.14/0.47 @ ( image_5172358348707908735at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su5525570899277871387at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3388_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_5803077947706746251at_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3389_UN__extend__simps_I2_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple4364388969068068532at_nat
% 0.14/0.47 @ ( image_2496312346330513076at_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su5525570899277871387at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(2)
% 0.14/0.47 thf(fact_3390_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3391_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_o_set_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3392_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_nat_set_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3393_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple7399068483239264473et_nat
% 0.14/0.47 @ ( image_15824709712370754et_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3394_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_Pr8693737435421807431at_nat,B5: product_unit > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_7288820656315755647at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3395_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_Pr8693737435421807431at_nat,B5: $o > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_8493167801588156084at_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3396_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: set_Pr8693737435421807431at_nat,B5: nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_4592875511192039216at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3397_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: set_Pr4329608150637261639at_nat,B5: product_unit > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple4364388969068068532at_nat
% 0.14/0.47 @ ( image_5172358348707908735at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( sup_su5525570899277871387at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3398_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple2748534634209756852at_nat
% 0.14/0.47 @ ( image_5803077947706746251at_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3399_UN__extend__simps_I3_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: set_Pr4329608150637261639at_nat,B5: $o > set_Pr4329608150637261639at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = A4 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ B5 @ C3 ) ) )
% 0.14/0.47 = ( comple4364388969068068532at_nat
% 0.14/0.47 @ ( image_2496312346330513076at_nat
% 0.14/0.47 @ ^ [X4: $o] : ( sup_su5525570899277871387at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % UN_extend_simps(3)
% 0.14/0.47 thf(fact_3400_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_3617315916088684441at_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3401_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo228742789529271731at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7979982168039674559at_nat
% 0.14/0.47 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3402_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_5423882813909314213at_nat
% 0.14/0.47 @ ^ [X4: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3403_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_o,A4: $o > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_o )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7077428525161401678at_nat
% 0.14/0.47 @ ^ [X4: $o] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3404_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_nat,A4: nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.47 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple1930127330929219688at_nat
% 0.14/0.47 @ ( image_7178329752028323786at_nat
% 0.14/0.47 @ ^ [X4: nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3405_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_8173849991827986510et_nat
% 0.14/0.47 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3406_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo228742789529271731at_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_3160451284896210088et_nat
% 0.14/0.47 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.47 @ C3 ) ) ) ) ) ).
% 0.14/0.47
% 0.14/0.47 % INT_extend_simps(1)
% 0.14/0.47 thf(fact_3407_INT__extend__simps_I1_J,axiom,
% 0.14/0.47 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat,B5: set_nat] :
% 0.14/0.47 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = B5 ) )
% 0.14/0.47 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.47 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.47 = ( comple7806235888213564991et_nat
% 0.14/0.47 @ ( image_15824709712370754et_nat
% 0.14/0.48 @ ^ [X4: product_prod_nat_nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(1)
% 0.14/0.48 thf(fact_3408_INT__extend__simps_I1_J,axiom,
% 0.14/0.48 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.48 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.48 = B5 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_o )
% 0.14/0.48 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_o_set_nat
% 0.14/0.48 @ ^ [X4: $o] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(1)
% 0.14/0.48 thf(fact_3409_INT__extend__simps_I1_J,axiom,
% 0.14/0.48 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.48 = B5 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_nat_set_nat
% 0.14/0.48 @ ^ [X4: nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(1)
% 0.14/0.48 thf(fact_3410_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Product_unit,A4: set_Pr1261947904930325089at_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple1930127330929219688at_nat
% 0.14/0.48 @ ( image_3617315916088684441at_nat
% 0.14/0.48 @ ^ [X4: product_unit] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3411_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Pr4329608150637261639at_nat,A4: set_Pr1261947904930325089at_nat,B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo228742789529271731at_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple1930127330929219688at_nat
% 0.14/0.48 @ ( image_7979982168039674559at_nat
% 0.14/0.48 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3412_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple1930127330929219688at_nat
% 0.14/0.48 @ ( image_5423882813909314213at_nat
% 0.14/0.48 @ ^ [X4: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3413_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_o,A4: set_Pr1261947904930325089at_nat,B5: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_o )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple1930127330929219688at_nat
% 0.14/0.48 @ ( image_7077428525161401678at_nat
% 0.14/0.48 @ ^ [X4: $o] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3414_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_nat,A4: set_Pr1261947904930325089at_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple1930127330929219688at_nat
% 0.14/0.48 @ ( image_7178329752028323786at_nat
% 0.14/0.48 @ ^ [X4: nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3415_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_8173849991827986510et_nat
% 0.14/0.48 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3416_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Pr4329608150637261639at_nat,A4: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo228742789529271731at_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_3160451284896210088et_nat
% 0.14/0.48 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3417_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_15824709712370754et_nat
% 0.14/0.48 @ ^ [X4: product_prod_nat_nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3418_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_o )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_o )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_o_set_nat
% 0.14/0.48 @ ^ [X4: $o] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3419_INT__extend__simps_I2_J,axiom,
% 0.14/0.48 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 0.14/0.48 ( ( ( C3 = bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = A4 ) )
% 0.14/0.48 & ( ( C3 != bot_bot_set_nat )
% 0.14/0.48 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_nat_set_nat
% 0.14/0.48 @ ^ [X4: nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 0.14/0.48 @ C3 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % INT_extend_simps(2)
% 0.14/0.48 thf(fact_3420_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3421_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3422_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3423_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3424_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3425_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3426_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3427_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3428_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3429_le__cINF__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % le_cINF_iff
% 0.14/0.48 thf(fact_3430_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_int,F: nat > nat,A4: set_nat,G: int > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: int] :
% 0.14/0.48 ( ( member_int @ M4 @ B5 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3431_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_int,F: int > nat,A4: set_int,G: int > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: int] :
% 0.14/0.48 ( ( member_int @ M4 @ B5 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3432_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_Product_unit,F: nat > nat,A4: set_nat,G: product_unit > nat] :
% 0.14/0.48 ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ M4 @ B5 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3433_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_Product_unit,F: int > nat,A4: set_int,G: product_unit > nat] :
% 0.14/0.48 ( ( B5 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ M4 @ B5 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3434_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_o,F: nat > nat,A4: set_nat,G: $o > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: $o] :
% 0.14/0.48 ( ( member_o @ M4 @ B5 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3435_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_o,F: int > nat,A4: set_int,G: $o > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: $o] :
% 0.14/0.48 ( ( member_o @ M4 @ B5 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3436_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_nat,F: nat > nat,A4: set_nat,G: nat > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: nat] :
% 0.14/0.48 ( ( member_nat @ M4 @ B5 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3437_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_nat,F: int > nat,A4: set_int,G: nat > nat] :
% 0.14/0.48 ( ( B5 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: nat] :
% 0.14/0.48 ( ( member_nat @ M4 @ B5 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3438_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_int,F: nat > int,A4: set_nat,G: int > int] :
% 0.14/0.48 ( ( B5 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: int] :
% 0.14/0.48 ( ( member_int @ M4 @ B5 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3439_cINF__mono,axiom,
% 0.14/0.48 ! [B5: set_int,F: int > int,A4: set_int,G: int > int] :
% 0.14/0.48 ( ( B5 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ! [M4: int] :
% 0.14/0.48 ( ( member_int @ M4 @ B5 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ A4 )
% 0.14/0.48 & ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_mono
% 0.14/0.48 thf(fact_3440_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3441_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3442_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3443_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat,U: nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3444_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3445_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3446_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3447_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int,U: int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3448_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3449_cSUP__le__iff,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U )
% 0.14/0.48 = ( ! [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_le_iff
% 0.14/0.48 thf(fact_3450_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: nat > nat,B5: set_nat,F: int > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: int] :
% 0.14/0.48 ( ( member_int @ N2 @ A4 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3451_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: int] :
% 0.14/0.48 ( ( member_int @ N2 @ A4 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3452_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: nat > nat,B5: set_nat,F: product_unit > nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ N2 @ A4 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3453_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: int > nat,B5: set_int,F: product_unit > nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ N2 @ A4 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3454_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: nat > nat,B5: set_nat,F: $o > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: $o] :
% 0.14/0.48 ( ( member_o @ N2 @ A4 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3455_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: int > nat,B5: set_int,F: $o > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: $o] :
% 0.14/0.48 ( ( member_o @ N2 @ A4 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3456_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: nat] :
% 0.14/0.48 ( ( member_nat @ N2 @ A4 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3457_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: int > nat,B5: set_int,F: nat > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: nat] :
% 0.14/0.48 ( ( member_nat @ N2 @ A4 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3458_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: nat > int,B5: set_nat,F: int > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: int] :
% 0.14/0.48 ( ( member_int @ N2 @ A4 )
% 0.14/0.48 => ? [X6: nat] :
% 0.14/0.48 ( ( member_nat @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3459_cSUP__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ B5 ) )
% 0.14/0.48 => ( ! [N2: int] :
% 0.14/0.48 ( ( member_int @ N2 @ A4 )
% 0.14/0.48 => ? [X6: int] :
% 0.14/0.48 ( ( member_int @ X6 @ B5 )
% 0.14/0.48 & ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_mono
% 0.14/0.48 thf(fact_3460_prod__set__defs_I1_J,axiom,
% 0.14/0.48 ( basic_685971451221398055t_unit
% 0.14/0.48 = ( ^ [P3: produc7812382424243267045t_unit] : ( insert_ref_a @ ( produc473321116828791851t_unit @ P3 ) @ bot_bot_set_ref_a ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_defs(1)
% 0.14/0.48 thf(fact_3461_image__INT,axiom,
% 0.14/0.48 ! [F: int > int,C3: set_int,A4: set_o,B5: $o > set_int,J4: $o] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_o @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple3628384868704368283et_int
% 0.14/0.48 @ ( image_o_set_int
% 0.14/0.48 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3462_image__INT,axiom,
% 0.14/0.48 ! [F: int > int,C3: set_int,A4: set_nat,B5: nat > set_int,J4: nat] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_nat @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple3628384868704368283et_int
% 0.14/0.48 @ ( image_nat_set_int
% 0.14/0.48 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3463_image__INT,axiom,
% 0.14/0.48 ! [F: int > int,C3: set_int,A4: set_int,B5: int > set_int,J4: int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ C3 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_int @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple3628384868704368283et_int
% 0.14/0.48 @ ( image_int_set_int
% 0.14/0.48 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3464_image__INT,axiom,
% 0.14/0.48 ! [F: int > nat,C3: set_int,A4: set_o,B5: $o > set_int,J4: $o] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_o @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_o_set_nat
% 0.14/0.48 @ ^ [X4: $o] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3465_image__INT,axiom,
% 0.14/0.48 ! [F: int > nat,C3: set_int,A4: set_nat,B5: nat > set_int,J4: nat] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_nat @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_nat_set_nat
% 0.14/0.48 @ ^ [X4: nat] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3466_image__INT,axiom,
% 0.14/0.48 ! [F: int > nat,C3: set_int,A4: set_int,B5: int > set_int,J4: int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ C3 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_int @ J4 @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple7806235888213564991et_nat
% 0.14/0.48 @ ( image_int_set_nat
% 0.14/0.48 @ ^ [X4: int] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3467_image__INT,axiom,
% 0.14/0.48 ! [F: nat > rat,C3: set_nat,A4: set_o,B5: $o > set_nat,J4: $o] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ C3 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_o @ J4 @ A4 )
% 0.14/0.48 => ( ( image_nat_rat @ F @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple4298007329820168263et_rat
% 0.14/0.48 @ ( image_o_set_rat
% 0.14/0.48 @ ^ [X4: $o] : ( image_nat_rat @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3468_image__INT,axiom,
% 0.14/0.48 ! [F: nat > int,C3: set_nat,A4: set_o,B5: $o > set_nat,J4: $o] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ C3 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_o @ J4 @ A4 )
% 0.14/0.48 => ( ( image_nat_int @ F @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple3628384868704368283et_int
% 0.14/0.48 @ ( image_o_set_int
% 0.14/0.48 @ ^ [X4: $o] : ( image_nat_int @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3469_image__INT,axiom,
% 0.14/0.48 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: nat > set_nat,J4: nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ C3 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_nat @ J4 @ A4 )
% 0.14/0.48 => ( ( image_nat_rat @ F @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple4298007329820168263et_rat
% 0.14/0.48 @ ( image_nat_set_rat
% 0.14/0.48 @ ^ [X4: nat] : ( image_nat_rat @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3470_image__INT,axiom,
% 0.14/0.48 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: nat > set_nat,J4: nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ C3 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 0.14/0.48 => ( ( member_nat @ J4 @ A4 )
% 0.14/0.48 => ( ( image_nat_int @ F @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( comple3628384868704368283et_int
% 0.14/0.48 @ ( image_nat_set_int
% 0.14/0.48 @ ^ [X4: nat] : ( image_nat_int @ F @ ( B5 @ X4 ) )
% 0.14/0.48 @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_INT
% 0.14/0.48 thf(fact_3471_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3472_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > nat,B5: set_Product_unit,F: product_unit > nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3473_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: $o > nat,B5: set_o,F: $o > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3474_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3475_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3476_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > int,B5: set_Product_unit,F: product_unit > int] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3477_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: $o > int,B5: set_o,F: $o > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3478_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: nat > int,B5: set_nat,F: nat > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ B5 )
% 0.14/0.48 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3479_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > product_unit,B5: set_int,F: int > product_unit] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ B5 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3480_cINF__superset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > product_unit,B5: set_Product_unit,F: product_unit > product_unit] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ B5 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( G @ X ) @ ( F @ X ) ) )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cINF_superset_mono
% 0.14/0.48 thf(fact_3481_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3482_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > nat,B5: set_Product_unit,F: product_unit > nat] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3483_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: $o > nat,B5: set_o,F: $o > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3484_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3485_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3486_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > int,B5: set_Product_unit,F: product_unit > int] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3487_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_o,G: $o > int,B5: set_o,F: $o > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3488_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_nat,G: nat > int,B5: set_nat,F: nat > int] :
% 0.14/0.48 ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3489_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_int,G: int > product_unit,B5: set_int,F: int > product_unit] :
% 0.14/0.48 ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3490_cSUP__subset__mono,axiom,
% 0.14/0.48 ! [A4: set_Product_unit,G: product_unit > product_unit,B5: set_Product_unit,F: product_unit > product_unit] :
% 0.14/0.48 ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 0.14/0.48 => ( ! [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ A4 )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cSUP_subset_mono
% 0.14/0.48 thf(fact_3491_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: int > set_Product_unit,I: int,B5: set_Product_unit,J3: set_int] :
% 0.14/0.48 ( ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ ( fun_up5054257004045450754t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_Product_unit @ ( member_int @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3492_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: int > set_o,I: int,B5: set_o,J3: set_int] :
% 0.14/0.48 ( ( comple90263536869209701_set_o @ ( image_int_set_o @ ( fun_upd_int_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_int_set_o @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_o @ ( member_int @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3493_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: product_unit > set_Product_unit,I: product_unit,B5: set_Product_unit,J3: set_Product_unit] :
% 0.14/0.48 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ ( fun_up488859312337516701t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_Product_unit @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3494_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: product_unit > set_o,I: product_unit,B5: set_o,J3: set_Product_unit] :
% 0.14/0.48 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ ( fun_up1762901246852280360_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_o @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3495_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: $o > set_Product_unit,I: $o,B5: set_Product_unit,J3: set_o] :
% 0.14/0.48 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ ( fun_up4718931970374059986t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ A4 @ ( minus_minus_set_o @ J3 @ ( insert_o @ I @ bot_bot_set_o ) ) ) ) @ ( if_set_Product_unit @ ( member_o @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3496_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: $o > set_o,I: $o,B5: set_o,J3: set_o] :
% 0.14/0.48 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ ( fun_upd_o_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_o_set_o @ A4 @ ( minus_minus_set_o @ J3 @ ( insert_o @ I @ bot_bot_set_o ) ) ) ) @ ( if_set_o @ ( member_o @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3497_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: nat > set_Product_unit,I: nat,B5: set_Product_unit,J3: set_nat] :
% 0.14/0.48 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ ( fun_up1220017903161424222t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ A4 @ ( minus_minus_set_nat @ J3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) ) ) @ ( if_set_Product_unit @ ( member_nat @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3498_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: nat > set_o,I: nat,B5: set_o,J3: set_nat] :
% 0.14/0.48 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ ( fun_upd_nat_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ A4 @ ( minus_minus_set_nat @ J3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) ) ) @ ( if_set_o @ ( member_nat @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3499_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: int > set_nat,I: int,B5: set_nat,J3: set_int] :
% 0.14/0.48 ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ ( fun_upd_int_set_nat @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_nat @ ( member_int @ I @ J3 ) @ B5 @ bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3500_UNION__fun__upd,axiom,
% 0.14/0.48 ! [A4: product_unit > set_nat,I: product_unit,B5: set_nat,J3: set_Product_unit] :
% 0.14/0.48 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ ( fun_up4569834200710200790et_nat @ A4 @ I @ B5 ) @ J3 ) )
% 0.14/0.48 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_nat @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % UNION_fun_upd
% 0.14/0.48 thf(fact_3501_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( image_2021340605491722874at_rat
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_rat_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc8728714639637146746at_rat @ ( image_nat_rat @ F @ A4 )
% 0.14/0.48 @ ^ [X4: rat] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3502_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > rat,G: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( image_5529569163885119602at_nat
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_rat_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc140472662868866674at_nat @ ( image_nat_rat @ F @ A4 )
% 0.14/0.48 @ ^ [X4: rat] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3503_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > rat,G: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( image_1351718144375922894at_int
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_rat_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc137982192359816398at_int @ ( image_nat_rat @ F @ A4 )
% 0.14/0.48 @ ^ [X4: rat] : ( image_nat_int @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3504_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > int,G: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( image_3337248961327643342nt_rat
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_int_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc821250958618291406nt_rat @ ( image_nat_int @ F @ A4 )
% 0.14/0.48 @ ^ [X4: int] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3505_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( image_6845477519721040070nt_nat
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A4 )
% 0.14/0.48 @ ^ [X4: int] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3506_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: int > int,G: int > nat,A4: set_int] :
% 0.14/0.48 ( ( image_659947567330398058nt_nat
% 0.14/0.48 @ ^ [X4: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 0.14/0.48 @ ^ [X4: int] : ( image_int_nat @ G @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3507_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( image_2667626500211843362nt_int
% 0.14/0.48 @ ^ [X4: nat] : ( product_Pair_int_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc1453890548195736866nt_int @ ( image_nat_int @ F @ A4 )
% 0.14/0.48 @ ^ [X4: int] : ( image_nat_int @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3508_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: int > int,G: int > int,A4: set_int] :
% 0.14/0.48 ( ( image_5705468584675977158nt_int
% 0.14/0.48 @ ^ [X4: int] : ( product_Pair_int_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc1453890548195736866nt_int @ ( image_int_int @ F @ A4 )
% 0.14/0.48 @ ^ [X4: int] : ( image_int_int @ G @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3509_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > product_unit,G: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( image_469905907365485675it_rat
% 0.14/0.48 @ ^ [X4: nat] : ( produc4168158269727034510it_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc6240246942209516957it_rat @ ( image_8730104196221521654t_unit @ F @ A4 )
% 0.14/0.48 @ ^ [X4: product_unit] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3510_image__split__eq__Sigma,axiom,
% 0.14/0.48 ! [F: nat > product_unit,G: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( image_3978134465758882403it_nat
% 0.14/0.48 @ ^ [X4: nat] : ( produc4803288329813530246it_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.14/0.48 @ A4 )
% 0.14/0.48 = ( produc6875377002296012693it_nat @ ( image_8730104196221521654t_unit @ F @ A4 )
% 0.14/0.48 @ ^ [X4: product_unit] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_split_eq_Sigma
% 0.14/0.48 thf(fact_3511_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: num,C3: set_num,G: num > $o,X2: num] :
% 0.14/0.48 ( ( member_num @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_num_o @ G @ C3 )
% 0.14/0.48 => ( ( comp_o_num_num
% 0.14/0.48 @ ^ [I2: $o] : ( if_num @ ( member_o @ I2 @ ( image_num_o @ G @ C3 ) ) @ ( the_inv_into_num_o @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_num @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3512_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: num,C3: set_num,G: num > nat,X2: num] :
% 0.14/0.48 ( ( member_num @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_num_nat @ G @ C3 )
% 0.14/0.48 => ( ( comp_nat_num_num
% 0.14/0.48 @ ^ [I2: nat] : ( if_num @ ( member_nat @ I2 @ ( image_num_nat @ G @ C3 ) ) @ ( the_inv_into_num_nat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_num @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3513_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: num,C3: set_num,G: num > int,X2: num] :
% 0.14/0.48 ( ( member_num @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_num_int @ G @ C3 )
% 0.14/0.48 => ( ( comp_int_num_num
% 0.14/0.48 @ ^ [I2: int] : ( if_num @ ( member_int @ I2 @ ( image_num_int @ G @ C3 ) ) @ ( the_inv_into_num_int @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_num @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3514_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: $o,C3: set_o,G: $o > $o,X2: $o] :
% 0.14/0.48 ( ( member_o @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_o_o @ G @ C3 )
% 0.14/0.48 => ( ( comp_o_o_o
% 0.14/0.48 @ ^ [I2: $o] :
% 0.14/0.48 ( ( ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_o @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_o @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3515_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: $o,C3: set_o,G: $o > nat,X2: $o] :
% 0.14/0.48 ( ( member_o @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_o_nat @ G @ C3 )
% 0.14/0.48 => ( ( comp_nat_o_o
% 0.14/0.48 @ ^ [I2: nat] :
% 0.14/0.48 ( ( ( member_nat @ I2 @ ( image_o_nat @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_nat @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_nat @ I2 @ ( image_o_nat @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_o @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3516_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: $o,C3: set_o,G: $o > int,X2: $o] :
% 0.14/0.48 ( ( member_o @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_o_int @ G @ C3 )
% 0.14/0.48 => ( ( comp_int_o_o
% 0.14/0.48 @ ^ [I2: int] :
% 0.14/0.48 ( ( ( member_int @ I2 @ ( image_o_int @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_int @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_int @ I2 @ ( image_o_int @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_o @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3517_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: nat,C3: set_nat,G: nat > rat,X2: nat] :
% 0.14/0.48 ( ( member_nat @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_nat_rat @ G @ C3 )
% 0.14/0.48 => ( ( comp_rat_nat_nat
% 0.14/0.48 @ ^ [I2: rat] : ( if_nat @ ( member_rat @ I2 @ ( image_nat_rat @ G @ C3 ) ) @ ( the_inv_into_nat_rat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_nat @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3518_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: nat,C3: set_nat,G: nat > $o,X2: nat] :
% 0.14/0.48 ( ( member_nat @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_nat_o @ G @ C3 )
% 0.14/0.48 => ( ( comp_o_nat_nat
% 0.14/0.48 @ ^ [I2: $o] : ( if_nat @ ( member_o @ I2 @ ( image_nat_o @ G @ C3 ) ) @ ( the_inv_into_nat_o @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_nat @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3519_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: nat,C3: set_nat,G: nat > nat,X2: nat] :
% 0.14/0.48 ( ( member_nat @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_nat_nat @ G @ C3 )
% 0.14/0.48 => ( ( comp_nat_nat_nat
% 0.14/0.48 @ ^ [I2: nat] : ( if_nat @ ( member_nat @ I2 @ ( image_nat_nat @ G @ C3 ) ) @ ( the_inv_into_nat_nat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_nat @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3520_If__the__inv__into__f__f,axiom,
% 0.14/0.48 ! [I: nat,C3: set_nat,G: nat > int,X2: nat] :
% 0.14/0.48 ( ( member_nat @ I @ C3 )
% 0.14/0.48 => ( ( inj_on_nat_int @ G @ C3 )
% 0.14/0.48 => ( ( comp_int_nat_nat
% 0.14/0.48 @ ^ [I2: int] : ( if_nat @ ( member_int @ I2 @ ( image_nat_int @ G @ C3 ) ) @ ( the_inv_into_nat_int @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ G
% 0.14/0.48 @ I )
% 0.14/0.48 = ( id_nat @ I ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_f_f
% 0.14/0.48 thf(fact_3521_Field__insert,axiom,
% 0.14/0.48 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,R: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( field_1428494348145443988at_nat @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su474284620922681339at_nat @ ( insert2290795007606087959at_nat @ A @ ( insert2290795007606087959at_nat @ B @ bot_bo1534825418459847827at_nat ) ) @ ( field_1428494348145443988at_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3522_Field__insert,axiom,
% 0.14/0.48 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3523_Field__insert,axiom,
% 0.14/0.48 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_sup_set_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3524_Field__insert,axiom,
% 0.14/0.48 ! [A: produc859450856879609959at_nat,B: produc859450856879609959at_nat,R: set_Pr553994874890374343at_nat] :
% 0.14/0.48 ( ( field_3044959742847878580at_nat @ ( insert5475735164933346999at_nat @ ( produc4662710985925991255at_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su718114333110466843at_nat @ ( insert5050368324300391991at_nat @ A @ ( insert5050368324300391991at_nat @ B @ bot_bo5327735625951526323at_nat ) ) @ ( field_3044959742847878580at_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3525_Field__insert,axiom,
% 0.14/0.48 ! [A: product_unit,B: product_unit,R: set_Pr5094982260447487303t_unit] :
% 0.14/0.48 ( ( field_Product_unit @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( field_Product_unit @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3526_Field__insert,axiom,
% 0.14/0.48 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,R: set_Pr5564308138774400199at_nat] :
% 0.14/0.48 ( ( field_2862844103579723188at_nat @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) @ ( field_2862844103579723188at_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3527_Field__insert,axiom,
% 0.14/0.48 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,R: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( field_4706345496283612622at_nat @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) @ ( field_4706345496283612622at_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3528_Field__insert,axiom,
% 0.14/0.48 ! [A: $o,B: $o,R: set_Product_prod_o_o] :
% 0.14/0.48 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_sup_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3529_Field__insert,axiom,
% 0.14/0.48 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
% 0.14/0.48 = ( sup_sup_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_insert
% 0.14/0.48 thf(fact_3530_bdd__below__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( order_2045666486212196060at_rat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_antimono
% 0.14/0.48 thf(fact_3531_bdd__below__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_2680796546298691796at_nat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_antimono
% 0.14/0.48 thf(fact_3532_bdd__below__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_2678306075789641520at_int @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_antimono
% 0.14/0.48 thf(fact_3533_bdd__below__image__antimono,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_3680150258199746352nt_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_antimono
% 0.14/0.48 thf(fact_3534_bdd__below__image__antimono,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_3677659787690696076nt_int @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_antimono
% 0.14/0.48 thf(fact_3535_bdd__above__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( order_2045666486212196060at_rat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_antimono
% 0.14/0.48 thf(fact_3536_bdd__above__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_2680796546298691796at_nat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_antimono
% 0.14/0.48 thf(fact_3537_bdd__above__image__antimono,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_2678306075789641520at_int @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_antimono
% 0.14/0.48 thf(fact_3538_bdd__above__image__antimono,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_3680150258199746352nt_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_antimono
% 0.14/0.48 thf(fact_3539_bdd__above__image__antimono,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_3677659787690696076nt_int @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_antimono
% 0.14/0.48 thf(fact_3540_the__inv__f__o__f__id,axiom,
% 0.14/0.48 ! [F: nat > nat,Z2: nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( comp_nat_nat_nat @ ( the_inv_into_nat_nat @ top_top_set_nat @ F ) @ F @ Z2 )
% 0.14/0.48 = ( id_nat @ Z2 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_f_o_f_id
% 0.14/0.48 thf(fact_3541_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: product_unit > $o,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 0.14/0.48 ( ( inj_on8854722734121536060unit_o @ G @ C3 )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.48 => ( member2370919827131729009t_unit
% 0.14/0.48 @ ^ [I2: $o] : ( if_Product_unit @ ( member_o @ I2 @ ( image_Product_unit_o @ G @ C3 ) ) @ ( the_in43325605794470270unit_o @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We8730861560085513481t_unit @ top_top_set_o @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3542_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: $o > $o,C3: set_o,B5: set_o,X2: $o] :
% 0.14/0.48 ( ( inj_on_o_o @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 0.14/0.48 => ( member_o_o
% 0.14/0.48 @ ^ [I2: $o] :
% 0.14/0.48 ( ( ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_o @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ ( bNF_We7690717809131995284nc_o_o @ top_top_set_o @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3543_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: nat > $o,C3: set_nat,B5: set_nat,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_o @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 0.14/0.48 => ( member_o_nat
% 0.14/0.48 @ ^ [I2: $o] : ( if_nat @ ( member_o @ I2 @ ( image_nat_o @ G @ C3 ) ) @ ( the_inv_into_nat_o @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We6830391624356636116_o_nat @ top_top_set_o @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3544_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: product_unit > char,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 0.14/0.48 ( ( inj_on1959294024837303853t_char @ G @ C3 )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.48 => ( member379592906918970460t_unit
% 0.14/0.48 @ ^ [I2: char] : ( if_Product_unit @ ( member_char @ I2 @ ( image_7248553556944771225t_char @ G @ C3 ) ) @ ( the_in3194898024646563179t_char @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We7396736742984212070t_unit @ top_top_set_char @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3545_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: $o > char,C3: set_o,B5: set_o,X2: $o] :
% 0.14/0.48 ( ( inj_on_o_char @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 0.14/0.48 => ( member_char_o
% 0.14/0.48 @ ^ [I2: char] :
% 0.14/0.48 ( ( ( member_char @ I2 @ ( image_o_char @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_char @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_char @ I2 @ ( image_o_char @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ ( bNF_We6174688282833725809char_o @ top_top_set_char @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3546_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: nat > char,C3: set_nat,B5: set_nat,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_char @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 0.14/0.48 => ( member_char_nat
% 0.14/0.48 @ ^ [I2: char] : ( if_nat @ ( member_char @ I2 @ ( image_nat_char @ G @ C3 ) ) @ ( the_in9023905271258939222t_char @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We935846424581991991ar_nat @ top_top_set_char @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3547_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: product_unit > rat,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 0.14/0.48 ( ( inj_on7795309031694339124it_rat @ G @ C3 )
% 0.14/0.48 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 0.14/0.48 => ( member7011034171605722901t_unit
% 0.14/0.48 @ ^ [I2: rat] : ( if_Product_unit @ ( member_rat @ I2 @ ( image_240439954468258464it_rat @ G @ C3 ) ) @ ( the_in3915408195775746418it_rat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We8564238559827753503t_unit @ top_top_set_rat @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3548_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: $o > rat,C3: set_o,B5: set_o,X2: $o] :
% 0.14/0.48 ( ( inj_on_o_rat @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 0.14/0.48 => ( member_rat_o
% 0.14/0.48 @ ^ [I2: rat] :
% 0.14/0.48 ( ( ( member_rat @ I2 @ ( image_o_rat @ G @ C3 ) )
% 0.14/0.48 => ( the_inv_into_o_rat @ C3 @ G @ I2 ) )
% 0.14/0.48 & ( ~ ( member_rat @ I2 @ ( image_o_rat @ G @ C3 ) )
% 0.14/0.48 => X2 ) )
% 0.14/0.48 @ ( bNF_We6195730058148253354_rat_o @ top_top_set_rat @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3549_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: nat > rat,C3: set_nat,B5: set_nat,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 0.14/0.48 => ( member_rat_nat
% 0.14/0.48 @ ^ [I2: rat] : ( if_nat @ ( member_rat @ I2 @ ( image_nat_rat @ G @ C3 ) ) @ ( the_inv_into_nat_rat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We7223962090624190782at_nat @ top_top_set_rat @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3550_If__the__inv__into__in__Func,axiom,
% 0.14/0.48 ! [G: int > nat,C3: set_int,B5: set_int,X2: int] :
% 0.14/0.48 ( ( inj_on_int_nat @ G @ C3 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ C3 @ ( sup_sup_set_int @ B5 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 0.14/0.48 => ( member_nat_int
% 0.14/0.48 @ ^ [I2: nat] : ( if_int @ ( member_nat @ I2 @ ( image_int_nat @ G @ C3 ) ) @ ( the_inv_into_int_nat @ C3 @ G @ I2 ) @ X2 )
% 0.14/0.48 @ ( bNF_We7538026264050006418at_int @ top_top_set_nat @ ( sup_sup_set_int @ B5 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % If_the_inv_into_in_Func
% 0.14/0.48 thf(fact_3551_mono__cInf,axiom,
% 0.14/0.48 ! [F: $o > nat,A4: set_o] :
% 0.14/0.48 ( ( order_mono_o_nat @ F )
% 0.14/0.48 => ( ( condit5413489452508810728elow_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3552_mono__cInf,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3553_mono__cInf,axiom,
% 0.14/0.48 ! [F: $o > int,A4: set_o] :
% 0.14/0.48 ( ( order_mono_o_int @ F )
% 0.14/0.48 => ( ( condit5413489452508810728elow_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3554_mono__cInf,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3555_mono__cInf,axiom,
% 0.14/0.48 ! [F: $o > product_unit,A4: set_o] :
% 0.14/0.48 ( ( order_7782127260464396005t_unit @ F )
% 0.14/0.48 => ( ( condit5413489452508810728elow_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3556_mono__cInf,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.48 ( ( order_5727276828720722763t_unit @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3557_mono__cInf,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3558_mono__cInf,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_int @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3559_mono__cInf,axiom,
% 0.14/0.48 ! [F: int > product_unit,A4: set_int] :
% 0.14/0.48 ( ( order_2843698775922903023t_unit @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3560_mono__cInf,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit9161856309968323677t_unit @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cInf
% 0.14/0.48 thf(fact_3561_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: int > nat,I3: set_int] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_int_nat
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3562_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: nat > nat,I3: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_nat_nat
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3563_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > int,A4: int > nat,I3: set_int] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_int
% 0.14/0.48 @ ( image_int_int
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3564_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > int,A4: nat > nat,I3: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_int
% 0.14/0.48 @ ( image_nat_int
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3565_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: int > nat,I3: set_int] :
% 0.14/0.48 ( ( order_5727276828720722763t_unit @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( comple2584293577114468500t_unit
% 0.14/0.48 @ ( image_5846526143423701914t_unit
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3566_mono__cINF,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: nat > nat,I3: set_nat] :
% 0.14/0.48 ( ( order_5727276828720722763t_unit @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( comple2584293577114468500t_unit
% 0.14/0.48 @ ( image_8730104196221521654t_unit
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3567_mono__cINF,axiom,
% 0.14/0.48 ! [F: int > nat,A4: int > int,I3: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_int_int @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_int_nat
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3568_mono__cINF,axiom,
% 0.14/0.48 ! [F: int > nat,A4: product_unit > int,I3: set_Product_unit] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_875570014554754200it_nat
% 0.14/0.48 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3569_mono__cINF,axiom,
% 0.14/0.48 ! [F: int > nat,A4: $o > int,I3: set_o] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_o_int @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_o_nat
% 0.14/0.48 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3570_mono__cINF,axiom,
% 0.14/0.48 ! [F: int > nat,A4: nat > int,I3: set_nat] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_nat_int @ A4 @ I3 ) ) )
% 0.14/0.48 @ ( complete_Inf_Inf_nat
% 0.14/0.48 @ ( image_nat_nat
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cINF
% 0.14/0.48 thf(fact_3571_relcompp__distrib2,axiom,
% 0.14/0.48 ! [S5: product_prod_nat_nat > product_prod_nat_nat > $o,T3: product_prod_nat_nat > product_prod_nat_nat > $o,R3: product_prod_nat_nat > int > $o] :
% 0.14/0.48 ( ( relcom8911704206367525917at_int @ ( sup_su362511073950362882_nat_o @ S5 @ T3 ) @ R3 )
% 0.14/0.48 = ( sup_su5231854730092680051_int_o @ ( relcom8911704206367525917at_int @ S5 @ R3 ) @ ( relcom8911704206367525917at_int @ T3 @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % relcompp_distrib2
% 0.14/0.48 thf(fact_3572_relcompp__distrib2,axiom,
% 0.14/0.48 ! [S5: int > int > $o,T3: int > int > $o,R3: int > code_integer > $o] :
% 0.14/0.48 ( ( relcom967497705283160040nteger @ ( sup_sup_int_int_o @ S5 @ T3 ) @ R3 )
% 0.14/0.48 = ( sup_su1544571744061072657eger_o @ ( relcom967497705283160040nteger @ S5 @ R3 ) @ ( relcom967497705283160040nteger @ T3 @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % relcompp_distrib2
% 0.14/0.48 thf(fact_3573_relcompp__distrib,axiom,
% 0.14/0.48 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o] :
% 0.14/0.48 ( ( relcom8911704206367525917at_int @ R3 @ ( sup_su5231854730092680051_int_o @ S5 @ T3 ) )
% 0.14/0.48 = ( sup_su5231854730092680051_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ ( relcom8911704206367525917at_int @ R3 @ T3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % relcompp_distrib
% 0.14/0.48 thf(fact_3574_relcompp__distrib,axiom,
% 0.14/0.48 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o] :
% 0.14/0.48 ( ( relcom967497705283160040nteger @ R3 @ ( sup_su1544571744061072657eger_o @ S5 @ T3 ) )
% 0.14/0.48 = ( sup_su1544571744061072657eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ ( relcom967497705283160040nteger @ R3 @ T3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % relcompp_distrib
% 0.14/0.48 thf(fact_3575_Field__Union,axiom,
% 0.14/0.48 ! [R3: set_se7855581050983116737at_nat] :
% 0.14/0.48 ( ( field_nat @ ( comple5685304695842803022at_nat @ R3 ) )
% 0.14/0.48 = ( comple7399068483239264473et_nat @ ( image_5853224409075402146et_nat @ field_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Field_Union
% 0.14/0.48 thf(fact_3576_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( image_rat_nat @ ( the_inv_into_nat_rat @ A4 @ F ) @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3577_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: rat > nat,A4: set_rat] :
% 0.14/0.48 ( ( inj_on_rat_nat @ F @ A4 )
% 0.14/0.48 => ( ( image_nat_rat @ ( the_inv_into_rat_nat @ A4 @ F ) @ ( image_rat_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3578_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A4 @ F ) @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3579_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( image_nat_int @ ( the_inv_into_int_nat @ A4 @ F ) @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3580_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ ( the_inv_into_nat_int @ A4 @ F ) @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3581_the__inv__into__onto,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( image_int_int @ ( the_inv_into_int_int @ A4 @ F ) @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_onto
% 0.14/0.48 thf(fact_3582_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: char > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( image_8382823969816519465at_nat @ F @ ( vimage8942442433166402803at_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_8382823969816519465at_nat @ F @ top_top_set_char ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3583_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: list_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( image_2795870212791037530at_nat @ F @ ( vimage8527374361057053988at_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_2795870212791037530at_nat @ F @ top_top_set_list_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3584_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: rat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( image_9175953278516507234at_nat @ F @ ( vimage2119786153496215084at_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_9175953278516507234at_nat @ F @ top_top_set_rat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3585_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_rat] :
% 0.14/0.48 ( ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) )
% 0.14/0.48 = ( inf_inf_set_rat @ A4 @ ( image_nat_rat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3586_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( image_nat_nat @ F @ ( vimage_nat_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_inf_set_nat @ A4 @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3587_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_int] :
% 0.14/0.48 ( ( image_nat_int @ F @ ( vimage_nat_int @ F @ A4 ) )
% 0.14/0.48 = ( inf_inf_set_int @ A4 @ ( image_nat_int @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3588_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( image_5846123807819985514at_nat @ F @ ( vimage8013328719654469172at_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3589_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_nat] :
% 0.14/0.48 ( ( image_int_nat @ F @ ( vimage_int_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_inf_set_nat @ A4 @ ( image_int_nat @ F @ top_top_set_int ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3590_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( image_int_int @ F @ ( vimage_int_int @ F @ A4 ) )
% 0.14/0.48 = ( inf_inf_set_int @ A4 @ ( image_int_int @ F @ top_top_set_int ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3591_image__vimage__eq,axiom,
% 0.14/0.48 ! [F: int > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( image_8883965892284119310at_nat @ F @ ( vimage1827798767263827160at_nat @ F @ A4 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_8883965892284119310at_nat @ F @ top_top_set_int ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_eq
% 0.14/0.48 thf(fact_3592_vimage__comp,axiom,
% 0.14/0.48 ! [F: nat > $o,G: $o > $o,X2: set_o] :
% 0.14/0.48 ( ( vimage_nat_o @ F @ ( vimage_o_o @ G @ X2 ) )
% 0.14/0.48 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) @ X2 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_comp
% 0.14/0.48 thf(fact_3593_vimage__comp,axiom,
% 0.14/0.48 ! [F: int > nat,G: nat > num,X2: set_num] :
% 0.14/0.48 ( ( vimage_int_nat @ F @ ( vimage_nat_num @ G @ X2 ) )
% 0.14/0.48 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) @ X2 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_comp
% 0.14/0.48 thf(fact_3594_vimage__comp,axiom,
% 0.14/0.48 ! [F: nat > nat,G: nat > nat,X2: set_nat] :
% 0.14/0.48 ( ( vimage_nat_nat @ F @ ( vimage_nat_nat @ G @ X2 ) )
% 0.14/0.48 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ X2 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_comp
% 0.14/0.48 thf(fact_3595_vimage__comp,axiom,
% 0.14/0.48 ! [F: int > int,G: int > nat,X2: set_nat] :
% 0.14/0.48 ( ( vimage_int_int @ F @ ( vimage_int_nat @ G @ X2 ) )
% 0.14/0.48 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) @ X2 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_comp
% 0.14/0.48 thf(fact_3596_vimage__comp,axiom,
% 0.14/0.48 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,X2: set_Pr4111642102156807771nteger] :
% 0.14/0.48 ( ( vimage6029918387083761651nteger @ F @ ( vimage4289680085338140859nteger @ G @ X2 ) )
% 0.14/0.48 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ X2 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_comp
% 0.14/0.48 thf(fact_3597_set_Ocompositionality,axiom,
% 0.14/0.48 ! [F: nat > $o,G: $o > $o,Set: set_o] :
% 0.14/0.48 ( ( vimage_nat_o @ F @ ( vimage_o_o @ G @ Set ) )
% 0.14/0.48 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) @ Set ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.compositionality
% 0.14/0.48 thf(fact_3598_set_Ocompositionality,axiom,
% 0.14/0.48 ! [F: int > nat,G: nat > num,Set: set_num] :
% 0.14/0.48 ( ( vimage_int_nat @ F @ ( vimage_nat_num @ G @ Set ) )
% 0.14/0.48 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) @ Set ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.compositionality
% 0.14/0.48 thf(fact_3599_set_Ocompositionality,axiom,
% 0.14/0.48 ! [F: nat > nat,G: nat > nat,Set: set_nat] :
% 0.14/0.48 ( ( vimage_nat_nat @ F @ ( vimage_nat_nat @ G @ Set ) )
% 0.14/0.48 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ Set ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.compositionality
% 0.14/0.48 thf(fact_3600_set_Ocompositionality,axiom,
% 0.14/0.48 ! [F: int > int,G: int > nat,Set: set_nat] :
% 0.14/0.48 ( ( vimage_int_int @ F @ ( vimage_int_nat @ G @ Set ) )
% 0.14/0.48 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) @ Set ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.compositionality
% 0.14/0.48 thf(fact_3601_set_Ocompositionality,axiom,
% 0.14/0.48 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Set: set_Pr4111642102156807771nteger] :
% 0.14/0.48 ( ( vimage6029918387083761651nteger @ F @ ( vimage4289680085338140859nteger @ G @ Set ) )
% 0.14/0.48 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ Set ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.compositionality
% 0.14/0.48 thf(fact_3602_FieldI2,axiom,
% 0.14/0.48 ! [I: produc3843707927480180839at_nat,J4: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
% 0.14/0.48 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member8757157785044589968at_nat @ J4 @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3603_FieldI2,axiom,
% 0.14/0.48 ! [I: product_prod_nat_nat,J4: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member8440522571783428010at_nat @ J4 @ ( field_4706345496283612622at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3604_FieldI2,axiom,
% 0.14/0.48 ! [I: $o,J4: $o,R3: set_Product_prod_o_o] :
% 0.14/0.48 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_o @ J4 @ ( field_o @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3605_FieldI2,axiom,
% 0.14/0.48 ! [I: set_Pr4329608150637261639at_nat,J4: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member6273874620674182256at_nat @ J4 @ ( field_1428494348145443988at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3606_FieldI2,axiom,
% 0.14/0.48 ! [I: set_Pr1261947904930325089at_nat,J4: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member2643936169264416010at_nat @ J4 @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3607_FieldI2,axiom,
% 0.14/0.48 ! [I: nat,J4: nat,R3: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_nat @ J4 @ ( field_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3608_FieldI2,axiom,
% 0.14/0.48 ! [I: int,J4: int,R3: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_int @ J4 @ ( field_int @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI2
% 0.14/0.48 thf(fact_3609_FieldI1,axiom,
% 0.14/0.48 ! [I: produc3843707927480180839at_nat,J4: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
% 0.14/0.48 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3610_FieldI1,axiom,
% 0.14/0.48 ! [I: product_prod_nat_nat,J4: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member8440522571783428010at_nat @ I @ ( field_4706345496283612622at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3611_FieldI1,axiom,
% 0.14/0.48 ! [I: $o,J4: $o,R3: set_Product_prod_o_o] :
% 0.14/0.48 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_o @ I @ ( field_o @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3612_FieldI1,axiom,
% 0.14/0.48 ! [I: set_Pr4329608150637261639at_nat,J4: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member6273874620674182256at_nat @ I @ ( field_1428494348145443988at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3613_FieldI1,axiom,
% 0.14/0.48 ! [I: set_Pr1261947904930325089at_nat,J4: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3614_FieldI1,axiom,
% 0.14/0.48 ! [I: nat,J4: nat,R3: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_nat @ I @ ( field_nat @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3615_FieldI1,axiom,
% 0.14/0.48 ! [I: int,J4: int,R3: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J4 ) @ R3 )
% 0.14/0.48 => ( member_int @ I @ ( field_int @ R3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % FieldI1
% 0.14/0.48 thf(fact_3616_inf__Int__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( inf_in6969519006101653788_nat_o
% 0.14/0.48 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( inf_in2456762090751560885at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_Int_eq2
% 0.14/0.48 thf(fact_3617_inf__Int__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( inf_in6124848772414083356_nat_o
% 0.14/0.48 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( inf_in7913087082777306421at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_Int_eq2
% 0.14/0.48 thf(fact_3618_inf__Int__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 0.14/0.48 ( ( inf_inf_nat_num_o
% 0.14/0.48 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( inf_in7510916698018314649at_num @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_Int_eq2
% 0.14/0.48 thf(fact_3619_inf__Int__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( inf_inf_int_int_o
% 0.14/0.48 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( inf_in2269163501485487111nt_int @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_Int_eq2
% 0.14/0.48 thf(fact_3620_inf__Int__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( inf_inf_nat_nat_o
% 0.14/0.48 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( inf_in2572325071724192079at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_Int_eq2
% 0.14/0.48 thf(fact_3621_fun__upd__comp,axiom,
% 0.14/0.48 ! [F: $o > $o,G: nat > $o,X2: nat,Y3: $o] :
% 0.14/0.48 ( ( comp_o_o_nat @ F @ ( fun_upd_nat_o @ G @ X2 @ Y3 ) )
% 0.14/0.48 = ( fun_upd_nat_o @ ( comp_o_o_nat @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_comp
% 0.14/0.48 thf(fact_3622_fun__upd__comp,axiom,
% 0.14/0.48 ! [F: nat > num,G: int > nat,X2: int,Y3: nat] :
% 0.14/0.48 ( ( comp_nat_num_int @ F @ ( fun_upd_int_nat @ G @ X2 @ Y3 ) )
% 0.14/0.48 = ( fun_upd_int_num @ ( comp_nat_num_int @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_comp
% 0.14/0.48 thf(fact_3623_fun__upd__comp,axiom,
% 0.14/0.48 ! [F: nat > nat,G: nat > nat,X2: nat,Y3: nat] :
% 0.14/0.48 ( ( comp_nat_nat_nat @ F @ ( fun_upd_nat_nat @ G @ X2 @ Y3 ) )
% 0.14/0.48 = ( fun_upd_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_comp
% 0.14/0.48 thf(fact_3624_fun__upd__comp,axiom,
% 0.14/0.48 ! [F: int > nat,G: int > int,X2: int,Y3: int] :
% 0.14/0.48 ( ( comp_int_nat_int @ F @ ( fun_upd_int_int @ G @ X2 @ Y3 ) )
% 0.14/0.48 = ( fun_upd_int_nat @ ( comp_int_nat_int @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_comp
% 0.14/0.48 thf(fact_3625_fun__upd__comp,axiom,
% 0.14/0.48 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,Y3: code_integer > code_integer] :
% 0.14/0.48 ( ( comp_C8797469213163452608nteger @ F @ ( fun_up8056716234270145717nteger @ G @ X2 @ Y3 ) )
% 0.14/0.48 = ( fun_up8139772397987072257nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_comp
% 0.14/0.48 thf(fact_3626_image__vimage__subset,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_rat] : ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) ) @ A4 ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_subset
% 0.14/0.48 thf(fact_3627_image__vimage__subset,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( vimage_nat_nat @ F @ A4 ) ) @ A4 ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_subset
% 0.14/0.48 thf(fact_3628_image__vimage__subset,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_int] : ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( vimage_nat_int @ F @ A4 ) ) @ A4 ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_subset
% 0.14/0.48 thf(fact_3629_image__vimage__subset,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_nat] : ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( vimage_int_nat @ F @ A4 ) ) @ A4 ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_subset
% 0.14/0.48 thf(fact_3630_image__vimage__subset,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ F @ ( vimage_int_int @ F @ A4 ) ) @ A4 ) ).
% 0.14/0.48
% 0.14/0.48 % image_vimage_subset
% 0.14/0.48 thf(fact_3631_image__subset__iff__subset__vimage,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.14/0.48 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.14/0.48 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_rat @ F @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_subset_iff_subset_vimage
% 0.14/0.48 thf(fact_3632_image__subset__iff__subset__vimage,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_nat @ F @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_subset_iff_subset_vimage
% 0.14/0.48 thf(fact_3633_image__subset__iff__subset__vimage,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.14/0.48 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_int @ F @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_subset_iff_subset_vimage
% 0.14/0.48 thf(fact_3634_image__subset__iff__subset__vimage,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 = ( ord_less_eq_set_int @ A4 @ ( vimage_int_nat @ F @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_subset_iff_subset_vimage
% 0.14/0.48 thf(fact_3635_image__subset__iff__subset__vimage,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.14/0.48 = ( ord_less_eq_set_int @ A4 @ ( vimage_int_int @ F @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % image_subset_iff_subset_vimage
% 0.14/0.48 thf(fact_3636_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: char > char,A4: set_char] :
% 0.14/0.48 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( image_char_char @ F @ ( vimage_char_char @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3637_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: char > rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( image_char_rat @ F @ ( vimage_char_rat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3638_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: char > nat,A4: set_nat] :
% 0.14/0.48 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( image_char_nat @ F @ ( vimage_char_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3639_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: char > int,A4: set_int] :
% 0.14/0.48 ( ( ( image_char_int @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_int )
% 0.14/0.48 => ( ( image_char_int @ F @ ( vimage_char_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3640_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: rat > char,A4: set_char] :
% 0.14/0.48 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( image_rat_char @ F @ ( vimage_rat_char @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3641_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: rat > rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( image_rat_rat @ F @ ( vimage_rat_rat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3642_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: rat > nat,A4: set_nat] :
% 0.14/0.48 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( image_rat_nat @ F @ ( vimage_rat_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3643_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: rat > int,A4: set_int] :
% 0.14/0.48 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_int )
% 0.14/0.48 => ( ( image_rat_int @ F @ ( vimage_rat_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3644_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > char,A4: set_char] :
% 0.14/0.48 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( image_nat_char @ F @ ( vimage_nat_char @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3645_surj__image__vimage__eq,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_image_vimage_eq
% 0.14/0.48 thf(fact_3646_bdd__below__image__mono,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_rat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_mono
% 0.14/0.48 thf(fact_3647_bdd__below__image__mono,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_mono
% 0.14/0.48 thf(fact_3648_bdd__below__image__mono,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ A4 )
% 0.14/0.48 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_mono
% 0.14/0.48 thf(fact_3649_bdd__below__image__mono,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_mono
% 0.14/0.48 thf(fact_3650_bdd__below__image__mono,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_int @ F )
% 0.14/0.48 => ( ( condit1735850657277959132ow_int @ A4 )
% 0.14/0.48 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_image_mono
% 0.14/0.48 thf(fact_3651_bdd__above__image__mono,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_rat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_mono
% 0.14/0.48 thf(fact_3652_bdd__above__image__mono,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_mono
% 0.14/0.48 thf(fact_3653_bdd__above__image__mono,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_mono
% 0.14/0.48 thf(fact_3654_bdd__above__image__mono,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_mono
% 0.14/0.48 thf(fact_3655_bdd__above__image__mono,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_int @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_image_mono
% 0.14/0.48 thf(fact_3656_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( sup_su6164525874564267778_nat_o
% 0.14/0.48 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( sup_su5395584912770621083at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3657_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 0.14/0.48 ( ( sup_sup_nat_num_o
% 0.14/0.48 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( sup_su2042722026077122175at_num @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3658_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( sup_sup_nat_nat_o
% 0.14/0.48 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( sup_su6327502436637775413at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3659_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( sup_sup_int_int_o
% 0.14/0.48 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( sup_su6024340866399070445nt_int @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3660_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr8693737435421807431at_nat,S5: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( sup_su362511073950362882_nat_o
% 0.14/0.48 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ ( sup_su718114333110466843at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3661_sup__Un__eq2,axiom,
% 0.14/0.48 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( sup_su7519161239522478338_nat_o
% 0.14/0.48 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 0.14/0.48 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 0.14/0.48 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( sup_su5525570899277871387at_nat @ R3 @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % sup_Un_eq2
% 0.14/0.48 thf(fact_3662_vimage__Union,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_set_nat] :
% 0.14/0.48 ( ( vimage_nat_nat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 0.14/0.48 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( vimage_nat_nat @ F ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_Union
% 0.14/0.48 thf(fact_3663_vimage__Times,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 0.14/0.48 ( ( vimage2449269961533847803at_nat @ F
% 0.14/0.48 @ ( produc457027306803732586at_nat @ A4
% 0.14/0.48 @ ^ [Uu: nat] : B5 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ ( vimage4653281326611754070at_nat @ ( comp_P1567445206330693457at_nat @ product_fst_nat_nat @ F ) @ A4 ) @ ( vimage4653281326611754070at_nat @ ( comp_P1567445206330693457at_nat @ product_snd_nat_nat @ F ) @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_Times
% 0.14/0.48 thf(fact_3664_vimage__Times,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > produc7812382424243267045t_unit,A4: set_ref_a,B5: set_he8644174446132254637t_unit] :
% 0.14/0.48 ( ( vimage4308919176130087787t_unit @ F
% 0.14/0.48 @ ( produc3946373962484743846t_unit @ A4
% 0.14/0.48 @ ^ [Uu: ref_a] : B5 ) )
% 0.14/0.48 = ( inf_in2572325071724192079at_nat @ ( vimage7322659125625010723_ref_a @ ( comp_P7986581389989349338at_nat @ produc473321116828791851t_unit @ F ) @ A4 ) @ ( vimage1024995831485383111t_unit @ ( comp_P6390991081591698364at_nat @ produc1126150082675451753t_unit @ F ) @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_Times
% 0.14/0.48 thf(fact_3665_inj__on__fun__updI,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,Y3: rat,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ~ ( member_rat @ Y3 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_rat @ ( fun_upd_nat_rat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_fun_updI
% 0.14/0.48 thf(fact_3666_inj__on__fun__updI,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,Y3: nat,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ~ ( member_nat @ Y3 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_nat @ ( fun_upd_nat_nat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_fun_updI
% 0.14/0.48 thf(fact_3667_inj__on__fun__updI,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,Y3: nat,X2: int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ~ ( member_nat @ Y3 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( inj_on_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_fun_updI
% 0.14/0.48 thf(fact_3668_inj__on__fun__updI,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,Y3: int,X2: nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ~ ( member_int @ Y3 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_int @ ( fun_upd_nat_int @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_fun_updI
% 0.14/0.48 thf(fact_3669_inj__on__fun__updI,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,Y3: int,X2: int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ~ ( member_int @ Y3 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( inj_on_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_fun_updI
% 0.14/0.48 thf(fact_3670_set_Ocomp,axiom,
% 0.14/0.48 ! [F: nat > $o,G: $o > $o] :
% 0.14/0.48 ( ( comp_s9189197539837705563_set_o @ ( vimage_nat_o @ F ) @ ( vimage_o_o @ G ) )
% 0.14/0.48 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.comp
% 0.14/0.48 thf(fact_3671_set_Ocomp,axiom,
% 0.14/0.48 ! [F: int > nat,G: nat > num] :
% 0.14/0.48 ( ( comp_s6458263553158497821et_num @ ( vimage_int_nat @ F ) @ ( vimage_nat_num @ G ) )
% 0.14/0.48 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.comp
% 0.14/0.48 thf(fact_3672_set_Ocomp,axiom,
% 0.14/0.48 ! [F: nat > nat,G: nat > nat] :
% 0.14/0.48 ( ( comp_s8964582002068861047et_nat @ ( vimage_nat_nat @ F ) @ ( vimage_nat_nat @ G ) )
% 0.14/0.48 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.comp
% 0.14/0.48 thf(fact_3673_set_Ocomp,axiom,
% 0.14/0.48 ! [F: int > int,G: int > nat] :
% 0.14/0.48 ( ( comp_s7717450105097109807et_nat @ ( vimage_int_int @ F ) @ ( vimage_int_nat @ G ) )
% 0.14/0.48 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.comp
% 0.14/0.48 thf(fact_3674_set_Ocomp,axiom,
% 0.14/0.48 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 0.14/0.48 ( ( comp_s4786119426940707554nteger @ ( vimage6029918387083761651nteger @ F ) @ ( vimage4289680085338140859nteger @ G ) )
% 0.14/0.48 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % set.comp
% 0.14/0.48 thf(fact_3675_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 0.14/0.48 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 0.14/0.48 = top_to1996260823553986621t_unit )
% 0.14/0.48 => ( ( ( vimage7995052115951654139t_unit @ F @ A4 )
% 0.14/0.48 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 = ( A4 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3676_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: product_unit > $o,A4: set_o] :
% 0.14/0.48 ( ( ( image_Product_unit_o @ F @ top_to1996260823553986621t_unit )
% 0.14/0.48 = top_top_set_o )
% 0.14/0.48 => ( ( ( vimage8808348054653608838unit_o @ F @ A4 )
% 0.14/0.48 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 = ( A4 = bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3677_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: $o > product_unit,A4: set_Product_unit] :
% 0.14/0.48 ( ( ( image_o_Product_unit @ F @ top_top_set_o )
% 0.14/0.48 = top_to1996260823553986621t_unit )
% 0.14/0.48 => ( ( ( vimage4222377557387472176t_unit @ F @ A4 )
% 0.14/0.48 = bot_bot_set_o )
% 0.14/0.48 = ( A4 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3678_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: $o > $o,A4: set_o] :
% 0.14/0.48 ( ( ( image_o_o @ F @ top_top_set_o )
% 0.14/0.48 = top_top_set_o )
% 0.14/0.48 => ( ( ( vimage_o_o @ F @ A4 )
% 0.14/0.48 = bot_bot_set_o )
% 0.14/0.48 = ( A4 = bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3679_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: product_unit > char,A4: set_char] :
% 0.14/0.48 ( ( ( image_7248553556944771225t_char @ F @ top_to1996260823553986621t_unit )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( ( vimage2648087219933717859t_char @ F @ A4 )
% 0.14/0.48 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 = ( A4 = bot_bot_set_char ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3680_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: $o > char,A4: set_char] :
% 0.14/0.48 ( ( ( image_o_char @ F @ top_top_set_o )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( ( vimage_o_char @ F @ A4 )
% 0.14/0.48 = bot_bot_set_o )
% 0.14/0.48 = ( A4 = bot_bot_set_char ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3681_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: product_unit > rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_240439954468258464it_rat @ F @ top_to1996260823553986621t_unit )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( ( vimage5618198413390092650it_rat @ F @ A4 )
% 0.14/0.48 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 = ( A4 = bot_bot_set_rat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3682_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: $o > rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_o_rat @ F @ top_top_set_o )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( ( vimage_o_rat @ F @ A4 )
% 0.14/0.48 = bot_bot_set_o )
% 0.14/0.48 = ( A4 = bot_bot_set_rat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3683_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: set_nat] :
% 0.14/0.48 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( ( vimage6253328473476588386it_nat @ F @ A4 )
% 0.14/0.48 = bot_bo3957492148770167129t_unit )
% 0.14/0.48 = ( A4 = bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3684_surj__vimage__empty,axiom,
% 0.14/0.48 ! [F: $o > nat,A4: set_nat] :
% 0.14/0.48 ( ( ( image_o_nat @ F @ top_top_set_o )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( ( vimage_o_nat @ F @ A4 )
% 0.14/0.48 = bot_bot_set_o )
% 0.14/0.48 = ( A4 = bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_vimage_empty
% 0.14/0.48 thf(fact_3685_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: char > char,B5: set_char,A4: set_char] :
% 0.14/0.48 ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( ord_less_eq_set_char @ ( vimage_char_char @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_char @ B5 @ ( image_char_char @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3686_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: char > rat,B5: set_rat,A4: set_char] :
% 0.14/0.48 ( ( ( image_char_rat @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( ord_less_eq_set_char @ ( vimage_char_rat @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_rat @ B5 @ ( image_char_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3687_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: char > nat,B5: set_nat,A4: set_char] :
% 0.14/0.48 ( ( ( image_char_nat @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_char @ ( vimage_char_nat @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ B5 @ ( image_char_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3688_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: char > int,B5: set_int,A4: set_char] :
% 0.14/0.48 ( ( ( image_char_int @ F @ top_top_set_char )
% 0.14/0.48 = top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_char @ ( vimage_char_int @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ B5 @ ( image_char_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3689_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: rat > char,B5: set_char,A4: set_rat] :
% 0.14/0.48 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( vimage_rat_char @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_char @ B5 @ ( image_rat_char @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3690_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: rat > rat,B5: set_rat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( vimage_rat_rat @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_rat @ B5 @ ( image_rat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3691_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: rat > nat,B5: set_nat,A4: set_rat] :
% 0.14/0.48 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( vimage_rat_nat @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_nat @ B5 @ ( image_rat_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3692_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: rat > int,B5: set_int,A4: set_rat] :
% 0.14/0.48 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 0.14/0.48 = top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( vimage_rat_int @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_int @ B5 @ ( image_rat_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3693_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: nat > char,B5: set_char,A4: set_nat] :
% 0.14/0.48 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 0.14/0.48 = top_top_set_char )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( vimage_nat_char @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_char @ B5 @ ( image_nat_char @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3694_vimage__subsetD,axiom,
% 0.14/0.48 ! [F: nat > rat,B5: set_rat,A4: set_nat] :
% 0.14/0.48 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 0.14/0.48 = top_top_set_rat )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( vimage_nat_rat @ F @ B5 ) @ A4 )
% 0.14/0.48 => ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetD
% 0.14/0.48 thf(fact_3695_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: nat,A4: set_nat,F: nat > set_num] :
% 0.14/0.48 ( ( ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage5436458796434496692at_num @ ( product_Pair_nat_num @ X2 ) @ ( produc6237731129814287028at_num @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage5436458796434496692at_num @ ( product_Pair_nat_num @ X2 ) @ ( produc6237731129814287028at_num @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_num ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3696_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > set_int] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage7872673496510460816nt_int @ ( product_Pair_int_int @ X2 ) @ ( produc1453890548195736866nt_int @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage7872673496510460816nt_int @ ( product_Pair_int_int @ X2 ) @ ( produc1453890548195736866nt_int @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_int ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3697_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > set_Product_unit] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X2 ) @ ( produc411009820408249917t_unit @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X2 ) @ ( produc411009820408249917t_unit @ A4 @ F ) )
% 0.14/0.48 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3698_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: nat,A4: set_nat,F: nat > set_Product_unit] :
% 0.14/0.48 ( ( ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X2 ) @ ( produc5506539147108004339t_unit @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X2 ) @ ( produc5506539147108004339t_unit @ A4 @ F ) )
% 0.14/0.48 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3699_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > set_Product_unit] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X2 ) @ ( produc2622961094310184599t_unit @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X2 ) @ ( produc2622961094310184599t_unit @ A4 @ F ) )
% 0.14/0.48 = bot_bo3957492148770167129t_unit ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3700_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > set_o] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X2 ) @ ( product_Sigma_o_o @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X2 ) @ ( product_Sigma_o_o @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3701_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: nat,A4: set_nat,F: nat > set_o] :
% 0.14/0.48 ( ( ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X2 ) @ ( product_Sigma_nat_o @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_nat @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X2 ) @ ( product_Sigma_nat_o @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3702_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > set_o] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X2 ) @ ( product_Sigma_int_o @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X2 ) @ ( product_Sigma_int_o @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_o ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3703_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > set_nat] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X2 ) @ ( product_Sigma_o_nat @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X2 ) @ ( product_Sigma_o_nat @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3704_Pair__vimage__Sigma,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > set_nat] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X2 ) @ ( produc1456381018704787142nt_nat @ A4 @ F ) )
% 0.14/0.48 = ( F @ X2 ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X2 ) @ ( produc1456381018704787142nt_nat @ A4 @ F ) )
% 0.14/0.48 = bot_bot_set_nat ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pair_vimage_Sigma
% 0.14/0.48 thf(fact_3705_inj__vimage__image__eq,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( vimage_nat_rat @ F @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_vimage_image_eq
% 0.14/0.48 thf(fact_3706_inj__vimage__image__eq,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( vimage_nat_nat @ F @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_vimage_image_eq
% 0.14/0.48 thf(fact_3707_inj__vimage__image__eq,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( vimage_nat_int @ F @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_vimage_image_eq
% 0.14/0.48 thf(fact_3708_inj__vimage__image__eq,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.48 => ( ( vimage_int_nat @ F @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_vimage_image_eq
% 0.14/0.48 thf(fact_3709_inj__vimage__image__eq,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.48 => ( ( vimage_int_int @ F @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_vimage_image_eq
% 0.14/0.48 thf(fact_3710_inj__graph,axiom,
% 0.14/0.48 ( inj_on3412903767820855855at_nat
% 0.14/0.48 @ ^ [F2: nat > nat] :
% 0.14/0.48 ( collec3392354462482085612at_nat
% 0.14/0.48 @ ( produc6081775807080527818_nat_o
% 0.14/0.48 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.48 ( Y5
% 0.14/0.48 = ( F2 @ X4 ) ) ) )
% 0.14/0.48 @ top_top_set_nat_nat ) ).
% 0.14/0.48
% 0.14/0.48 % inj_graph
% 0.14/0.48 thf(fact_3711_inj__graph,axiom,
% 0.14/0.48 ( inj_on7039184780174133295nt_int
% 0.14/0.48 @ ^ [F2: int > int] :
% 0.14/0.48 ( collec213857154873943460nt_int
% 0.14/0.48 @ ( produc4947309494688390418_int_o
% 0.14/0.48 @ ^ [X4: int,Y5: int] :
% 0.14/0.48 ( Y5
% 0.14/0.48 = ( F2 @ X4 ) ) ) )
% 0.14/0.48 @ top_top_set_int_int ) ).
% 0.14/0.48
% 0.14/0.48 % inj_graph
% 0.14/0.48 thf(fact_3712_f__the__inv__into__f,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,Y3: rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( member_rat @ Y3 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ( F @ ( the_inv_into_nat_rat @ A4 @ F @ Y3 ) )
% 0.14/0.48 = Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % f_the_inv_into_f
% 0.14/0.48 thf(fact_3713_f__the__inv__into__f,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,Y3: nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( member_nat @ Y3 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( F @ ( the_inv_into_nat_nat @ A4 @ F @ Y3 ) )
% 0.14/0.48 = Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % f_the_inv_into_f
% 0.14/0.48 thf(fact_3714_f__the__inv__into__f,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,Y3: nat] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( member_nat @ Y3 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( F @ ( the_inv_into_int_nat @ A4 @ F @ Y3 ) )
% 0.14/0.48 = Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % f_the_inv_into_f
% 0.14/0.48 thf(fact_3715_f__the__inv__into__f,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,Y3: int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( member_int @ Y3 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ( F @ ( the_inv_into_nat_int @ A4 @ F @ Y3 ) )
% 0.14/0.48 = Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % f_the_inv_into_f
% 0.14/0.48 thf(fact_3716_f__the__inv__into__f,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,Y3: int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( member_int @ Y3 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ( F @ ( the_inv_into_int_int @ A4 @ F @ Y3 ) )
% 0.14/0.48 = Y3 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % f_the_inv_into_f
% 0.14/0.48 thf(fact_3717_inj__on__the__inv__into,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( inj_on_rat_nat @ ( the_inv_into_nat_rat @ A4 @ F ) @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_the_inv_into
% 0.14/0.48 thf(fact_3718_inj__on__the__inv__into,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A4 @ F ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_the_inv_into
% 0.14/0.48 thf(fact_3719_inj__on__the__inv__into,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( inj_on_int_nat @ ( the_inv_into_nat_int @ A4 @ F ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_the_inv_into
% 0.14/0.48 thf(fact_3720_inj__on__the__inv__into,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( inj_on_nat_int @ ( the_inv_into_int_nat @ A4 @ F ) @ ( image_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_the_inv_into
% 0.14/0.48 thf(fact_3721_inj__on__the__inv__into,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( inj_on_int_int @ ( the_inv_into_int_int @ A4 @ F ) @ ( image_int_int @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_the_inv_into
% 0.14/0.48 thf(fact_3722_vimage__fst,axiom,
% 0.14/0.48 ! [A4: set_ref_a] :
% 0.14/0.48 ( ( vimage2910454108108208703_ref_a @ produc473321116828791851t_unit @ A4 )
% 0.14/0.48 = ( produc3946373962484743846t_unit @ A4
% 0.14/0.48 @ ^ [Uu: ref_a] : top_to3956321331435058429t_unit ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_fst
% 0.14/0.48 thf(fact_3723_vimage__fst,axiom,
% 0.14/0.48 ! [A4: set_nat] :
% 0.14/0.48 ( ( vimage4653281326611754070at_nat @ product_fst_nat_nat @ A4 )
% 0.14/0.48 = ( produc457027306803732586at_nat @ A4
% 0.14/0.48 @ ^ [Uu: nat] : top_top_set_nat ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_fst
% 0.14/0.48 thf(fact_3724_vimage__snd,axiom,
% 0.14/0.48 ! [A4: set_he8644174446132254637t_unit] :
% 0.14/0.48 ( ( vimage6116673589273818795t_unit @ produc1126150082675451753t_unit @ A4 )
% 0.14/0.48 = ( produc3946373962484743846t_unit @ top_top_set_ref_a
% 0.14/0.48 @ ^ [Uu: ref_a] : A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_snd
% 0.14/0.48 thf(fact_3725_vimage__snd,axiom,
% 0.14/0.48 ! [A4: set_nat] :
% 0.14/0.48 ( ( vimage4653281326611754070at_nat @ product_snd_nat_nat @ A4 )
% 0.14/0.48 = ( produc457027306803732586at_nat @ top_top_set_nat
% 0.14/0.48 @ ^ [Uu: nat] : A4 ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_snd
% 0.14/0.48 thf(fact_3726_mono__Sup,axiom,
% 0.14/0.48 ! [F: set_nat > set_nat,A4: set_set_nat] :
% 0.14/0.48 ( ( order_1005506198798982270et_nat @ F )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ F @ A4 ) ) @ ( F @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Sup
% 0.14/0.48 thf(fact_3727_mono__Sup,axiom,
% 0.14/0.48 ! [F: product_unit > set_nat,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_509894322932672675et_nat @ F )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Sup
% 0.14/0.48 thf(fact_3728_mono__Sup,axiom,
% 0.14/0.48 ! [F: set_nat > product_unit,A4: set_set_nat] :
% 0.14/0.48 ( ( order_7928700340835332885t_unit @ F )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6369283972875870912t_unit @ F @ A4 ) ) @ ( F @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Sup
% 0.14/0.48 thf(fact_3729_mono__Sup,axiom,
% 0.14/0.48 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_4454465170704313136t_unit @ F )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Sup
% 0.14/0.48 thf(fact_3730_mono__Inf,axiom,
% 0.14/0.48 ! [F: set_nat > set_nat,A4: set_set_nat] :
% 0.14/0.48 ( ( order_1005506198798982270et_nat @ F )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( F @ ( comple7806235888213564991et_nat @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Inf
% 0.14/0.48 thf(fact_3731_mono__Inf,axiom,
% 0.14/0.48 ! [F: set_nat > product_unit,A4: set_set_nat] :
% 0.14/0.48 ( ( order_7928700340835332885t_unit @ F )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( comple7806235888213564991et_nat @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_6369283972875870912t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Inf
% 0.14/0.48 thf(fact_3732_mono__Inf,axiom,
% 0.14/0.48 ! [F: product_unit > set_nat,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_509894322932672675et_nat @ F )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Inf
% 0.14/0.48 thf(fact_3733_mono__Inf,axiom,
% 0.14/0.48 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_4454465170704313136t_unit @ F )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_Inf
% 0.14/0.48 thf(fact_3734_Pow__insert,axiom,
% 0.14/0.48 ! [A: nat,A4: set_nat] :
% 0.14/0.48 ( ( pow_nat @ ( insert_nat @ A @ A4 ) )
% 0.14/0.48 = ( sup_sup_set_set_nat @ ( pow_nat @ A4 ) @ ( image_7916887816326733075et_nat @ ( insert_nat @ A ) @ ( pow_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pow_insert
% 0.14/0.48 thf(fact_3735_Pow__insert,axiom,
% 0.14/0.48 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( pow_Pr3466873192417945886at_nat @ ( insert8211810215607154385at_nat @ A @ A4 ) )
% 0.14/0.48 = ( sup_su3642409539654194069at_nat @ ( pow_Pr3466873192417945886at_nat @ A4 ) @ ( image_3684629450409544005at_nat @ ( insert8211810215607154385at_nat @ A ) @ ( pow_Pr3466873192417945886at_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pow_insert
% 0.14/0.48 thf(fact_3736_Pow__insert,axiom,
% 0.14/0.48 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( pow_Pr1023649790151954692at_nat @ ( insert9069300056098147895at_nat @ A @ A4 ) )
% 0.14/0.48 = ( sup_su474284620922681339at_nat @ ( pow_Pr1023649790151954692at_nat @ A4 ) @ ( image_4303274092540115909at_nat @ ( insert9069300056098147895at_nat @ A ) @ ( pow_Pr1023649790151954692at_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pow_insert
% 0.14/0.48 thf(fact_3737_Pow__insert,axiom,
% 0.14/0.48 ! [A: product_unit,A4: set_Product_unit] :
% 0.14/0.48 ( ( pow_Product_unit @ ( insert_Product_unit @ A @ A4 ) )
% 0.14/0.48 = ( sup_su5975557051335651745t_unit @ ( pow_Product_unit @ A4 ) @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ A ) @ ( pow_Product_unit @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pow_insert
% 0.14/0.48 thf(fact_3738_Pow__insert,axiom,
% 0.14/0.48 ! [A: $o,A4: set_o] :
% 0.14/0.48 ( ( pow_o @ ( insert_o @ A @ A4 ) )
% 0.14/0.48 = ( sup_sup_set_set_o @ ( pow_o @ A4 ) @ ( image_set_o_set_o @ ( insert_o @ A ) @ ( pow_o @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Pow_insert
% 0.14/0.48 thf(fact_3739_vimage__subsetI,axiom,
% 0.14/0.48 ! [F: nat > rat,B5: set_rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( vimage_nat_rat @ F @ B5 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetI
% 0.14/0.48 thf(fact_3740_vimage__subsetI,axiom,
% 0.14/0.48 ! [F: nat > nat,B5: set_nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( vimage_nat_nat @ F @ B5 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetI
% 0.14/0.48 thf(fact_3741_vimage__subsetI,axiom,
% 0.14/0.48 ! [F: nat > int,B5: set_int,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_set_nat @ ( vimage_nat_int @ F @ B5 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetI
% 0.14/0.48 thf(fact_3742_vimage__subsetI,axiom,
% 0.14/0.48 ! [F: int > nat,B5: set_nat,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( vimage_int_nat @ F @ B5 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetI
% 0.14/0.48 thf(fact_3743_vimage__subsetI,axiom,
% 0.14/0.48 ! [F: int > int,B5: set_int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_set_int @ ( vimage_int_int @ F @ B5 ) @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_subsetI
% 0.14/0.48 thf(fact_3744_vimage__eq__UN,axiom,
% 0.14/0.48 ( vimage4884490618288580032t_unit
% 0.14/0.48 = ( ^ [F2: nat > product_unit,B6: set_Product_unit] :
% 0.14/0.48 ( comple7399068483239264473et_nat
% 0.14/0.48 @ ( image_8173849991827986510et_nat
% 0.14/0.48 @ ^ [Y5: product_unit] : ( vimage4884490618288580032t_unit @ F2 @ ( insert_Product_unit @ Y5 @ bot_bo3957492148770167129t_unit ) )
% 0.14/0.48 @ B6 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_eq_UN
% 0.14/0.48 thf(fact_3745_vimage__eq__UN,axiom,
% 0.14/0.48 ( vimage6435164912253009178at_nat
% 0.14/0.48 = ( ^ [F2: nat > produc3843707927480180839at_nat,B6: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( comple7399068483239264473et_nat
% 0.14/0.48 @ ( image_3160451284896210088et_nat
% 0.14/0.48 @ ^ [Y5: produc3843707927480180839at_nat] : ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ Y5 @ bot_bo228742789529271731at_nat ) )
% 0.14/0.48 @ B6 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_eq_UN
% 0.14/0.48 thf(fact_3746_vimage__eq__UN,axiom,
% 0.14/0.48 ( vimage8013328719654469172at_nat
% 0.14/0.48 = ( ^ [F2: nat > product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( comple7399068483239264473et_nat
% 0.14/0.48 @ ( image_15824709712370754et_nat
% 0.14/0.48 @ ^ [Y5: product_prod_nat_nat] : ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ Y5 @ bot_bo2099793752762293965at_nat ) )
% 0.14/0.48 @ B6 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_eq_UN
% 0.14/0.48 thf(fact_3747_vimage__eq__UN,axiom,
% 0.14/0.48 ( vimage_nat_o
% 0.14/0.48 = ( ^ [F2: nat > $o,B6: set_o] :
% 0.14/0.48 ( comple7399068483239264473et_nat
% 0.14/0.48 @ ( image_o_set_nat
% 0.14/0.48 @ ^ [Y5: $o] : ( vimage_nat_o @ F2 @ ( insert_o @ Y5 @ bot_bot_set_o ) )
% 0.14/0.48 @ B6 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_eq_UN
% 0.14/0.48 thf(fact_3748_vimage__eq__UN,axiom,
% 0.14/0.48 ( vimage_nat_nat
% 0.14/0.48 = ( ^ [F2: nat > nat,B6: set_nat] :
% 0.14/0.48 ( comple7399068483239264473et_nat
% 0.14/0.48 @ ( image_nat_set_nat
% 0.14/0.48 @ ^ [Y5: nat] : ( vimage_nat_nat @ F2 @ ( insert_nat @ Y5 @ bot_bot_set_nat ) )
% 0.14/0.48 @ B6 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % vimage_eq_UN
% 0.14/0.48 thf(fact_3749_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,X2: rat,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( member_nat @ ( the_inv_into_nat_rat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3750_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: $o > $o,A4: set_o,X2: $o,B5: set_o] :
% 0.14/0.48 ( ( inj_on_o_o @ F @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_o_o @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( member_o @ ( the_inv_into_o_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3751_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: nat > $o,A4: set_nat,X2: $o,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_o @ F @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( member_nat @ ( the_inv_into_nat_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3752_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: int > $o,A4: set_int,X2: $o,B5: set_int] :
% 0.14/0.48 ( ( inj_on_int_o @ F @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_int_o @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( member_int @ ( the_inv_into_int_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3753_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: $o > nat,A4: set_o,X2: nat,B5: set_o] :
% 0.14/0.48 ( ( inj_on_o_nat @ F @ A4 )
% 0.14/0.48 => ( ( member_nat @ X2 @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( member_o @ ( the_inv_into_o_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3754_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,X2: nat,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( member_nat @ X2 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( member_nat @ ( the_inv_into_nat_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3755_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,X2: nat,B5: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( member_nat @ X2 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( member_int @ ( the_inv_into_int_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3756_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: $o > int,A4: set_o,X2: int,B5: set_o] :
% 0.14/0.48 ( ( inj_on_o_int @ F @ A4 )
% 0.14/0.48 => ( ( member_int @ X2 @ ( image_o_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 0.14/0.48 => ( member_o @ ( the_inv_into_o_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3757_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,X2: int,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( member_int @ X2 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.14/0.48 => ( member_nat @ ( the_inv_into_nat_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3758_the__inv__into__into,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,X2: int,B5: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( member_int @ X2 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.14/0.48 => ( member_int @ ( the_inv_into_int_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_into
% 0.14/0.48 thf(fact_3759_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: nat > rat,G: nat > nat,A4: set_nat,X2: rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_nat_nat @ G @ A4 )
% 0.14/0.48 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_nat_rat @ A4 @ ( comp_nat_rat_nat @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_nat_nat_rat @ ( the_inv_into_nat_nat @ A4 @ G ) @ ( the_inv_into_nat_rat @ ( image_nat_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3760_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: nat > num,G: int > nat,A4: set_int,X2: num] :
% 0.14/0.48 ( ( inj_on_nat_num @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_int_nat @ G @ A4 )
% 0.14/0.48 => ( ( member_num @ X2 @ ( image_nat_num @ F @ ( image_int_nat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_int_num @ A4 @ ( comp_nat_num_int @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_nat_int_num @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_num @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3761_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: nat > rat,G: int > nat,A4: set_int,X2: rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_int_nat @ G @ A4 )
% 0.14/0.48 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ ( image_int_nat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_int_rat @ A4 @ ( comp_nat_rat_int @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_nat_int_rat @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_rat @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3762_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: $o > $o,G: nat > $o,A4: set_nat,X2: $o] :
% 0.14/0.48 ( ( inj_on_o_o @ F @ ( image_nat_o @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_nat_o @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_o_o @ F @ ( image_nat_o @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_nat_o @ A4 @ ( comp_o_o_nat @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_o_nat_o @ ( the_inv_into_nat_o @ A4 @ G ) @ ( the_inv_into_o_o @ ( image_nat_o @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3763_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: rat > $o,G: nat > rat,A4: set_nat,X2: $o] :
% 0.14/0.48 ( ( inj_on_rat_o @ F @ ( image_nat_rat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_nat_rat @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_rat_o @ F @ ( image_nat_rat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_nat_o @ A4 @ ( comp_rat_o_nat @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_rat_nat_o @ ( the_inv_into_nat_rat @ A4 @ G ) @ ( the_inv_into_rat_o @ ( image_nat_rat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3764_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: nat > $o,G: nat > nat,A4: set_nat,X2: $o] :
% 0.14/0.48 ( ( inj_on_nat_o @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_nat_nat @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_nat_o @ F @ ( image_nat_nat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_nat_o @ A4 @ ( comp_nat_o_nat @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_nat_nat_o @ ( the_inv_into_nat_nat @ A4 @ G ) @ ( the_inv_into_nat_o @ ( image_nat_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3765_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: int > $o,G: nat > int,A4: set_nat,X2: $o] :
% 0.14/0.48 ( ( inj_on_int_o @ F @ ( image_nat_int @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_nat_int @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_int_o @ F @ ( image_nat_int @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_nat_o @ A4 @ ( comp_int_o_nat @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_int_nat_o @ ( the_inv_into_nat_int @ A4 @ G ) @ ( the_inv_into_int_o @ ( image_nat_int @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3766_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: nat > $o,G: int > nat,A4: set_int,X2: $o] :
% 0.14/0.48 ( ( inj_on_nat_o @ F @ ( image_int_nat @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_int_nat @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_nat_o @ F @ ( image_int_nat @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_int_o @ A4 @ ( comp_nat_o_int @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_nat_int_o @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_o @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3767_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: int > $o,G: int > int,A4: set_int,X2: $o] :
% 0.14/0.48 ( ( inj_on_int_o @ F @ ( image_int_int @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_int_int @ G @ A4 )
% 0.14/0.48 => ( ( member_o @ X2 @ ( image_int_o @ F @ ( image_int_int @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_int_o @ A4 @ ( comp_int_o_int @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_int_int_o @ ( the_inv_into_int_int @ A4 @ G ) @ ( the_inv_into_int_o @ ( image_int_int @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3768_the__inv__into__comp,axiom,
% 0.14/0.48 ! [F: $o > nat,G: $o > $o,A4: set_o,X2: nat] :
% 0.14/0.48 ( ( inj_on_o_nat @ F @ ( image_o_o @ G @ A4 ) )
% 0.14/0.48 => ( ( inj_on_o_o @ G @ A4 )
% 0.14/0.48 => ( ( member_nat @ X2 @ ( image_o_nat @ F @ ( image_o_o @ G @ A4 ) ) )
% 0.14/0.48 => ( ( the_inv_into_o_nat @ A4 @ ( comp_o_nat_o @ F @ G ) @ X2 )
% 0.14/0.48 = ( comp_o_o_nat @ ( the_inv_into_o_o @ A4 @ G ) @ ( the_inv_into_o_nat @ ( image_o_o @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % the_inv_into_comp
% 0.14/0.48 thf(fact_3769_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > int,Y3: int] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_int @ Y3 @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_int_int @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3770_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > nat,Y3: nat] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_nat @ Y3 @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_int_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3771_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > product_unit,Y3: product_unit] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_5846526143423701914t_unit @ ( fun_up2220634978854545698t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_Product_unit @ Y3 @ ( image_5846526143423701914t_unit @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_5846526143423701914t_unit @ ( fun_up2220634978854545698t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3772_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: int,A4: set_int,F: int > $o,Y3: $o] :
% 0.14/0.48 ( ( ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_o @ Y3 @ ( image_int_o @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_int @ X2 @ A4 )
% 0.14/0.48 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_int_o @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3773_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > nat,Y3: nat] :
% 0.14/0.48 ( ( ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_nat @ Y3 @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3774_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > product_unit,Y3: product_unit] :
% 0.14/0.48 ( ( ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_Product_unit @ Y3 @ ( image_405062704495631173t_unit @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3775_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > $o,Y3: $o] :
% 0.14/0.48 ( ( ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_Product_unit_o @ ( fun_up5432024876597553480unit_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_o @ Y3 @ ( image_Product_unit_o @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 0.14/0.48 => ( ( image_Product_unit_o @ ( fun_up5432024876597553480unit_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_Product_unit_o @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3776_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > nat,Y3: nat] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_nat @ Y3 @ ( image_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_o_nat @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3777_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > product_unit,Y3: product_unit] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_Product_unit @ ( fun_up846054379331416818t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_Product_unit @ Y3 @ ( image_o_Product_unit @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_Product_unit @ ( fun_up846054379331416818t_unit @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3778_fun__upd__image,axiom,
% 0.14/0.48 ! [X2: $o,A4: set_o,F: $o > $o,Y3: $o] :
% 0.14/0.48 ( ( ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( insert_o @ Y3 @ ( image_o_o @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 0.14/0.48 & ( ~ ( member_o @ X2 @ A4 )
% 0.14/0.48 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X2 @ Y3 ) @ A4 )
% 0.14/0.48 = ( image_o_o @ F @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % fun_upd_image
% 0.14/0.48 thf(fact_3779_mono__cSUP,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: int > nat,I3: set_int] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_int_nat
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_nat @ ( image_int_nat @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3780_mono__cSUP,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: nat > nat,I3: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_nat_nat
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3781_mono__cSUP,axiom,
% 0.14/0.48 ! [F: int > nat,A4: int > int,I3: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_int_nat
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_int @ ( image_int_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3782_mono__cSUP,axiom,
% 0.14/0.48 ! [F: int > nat,A4: product_unit > int,I3: set_Product_unit] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_875570014554754200it_nat
% 0.14/0.48 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3783_mono__cSUP,axiom,
% 0.14/0.48 ! [F: int > nat,A4: $o > int,I3: set_o] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_o_nat
% 0.14/0.48 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_int @ ( image_o_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3784_mono__cSUP,axiom,
% 0.14/0.48 ! [F: int > nat,A4: nat > int,I3: set_nat] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_nat_nat
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( complete_Sup_Sup_int @ ( image_nat_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3785_mono__cSUP,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: int > product_unit,I3: set_int] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_int_nat
% 0.14/0.48 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3786_mono__cSUP,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: product_unit > product_unit,I3: set_Product_unit] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_875570014554754200it_nat
% 0.14/0.48 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3787_mono__cSUP,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: $o > product_unit,I3: set_o] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_o_nat
% 0.14/0.48 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3788_mono__cSUP,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: nat > product_unit,I3: set_nat] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) )
% 0.14/0.48 => ( ( I3 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat
% 0.14/0.48 @ ( complete_Sup_Sup_nat
% 0.14/0.48 @ ( image_nat_nat
% 0.14/0.48 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 0.14/0.48 @ I3 ) )
% 0.14/0.48 @ ( F @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSUP
% 0.14/0.48 thf(fact_3789_mono__cSup,axiom,
% 0.14/0.48 ! [F: $o > nat,A4: set_o] :
% 0.14/0.48 ( ( order_mono_o_nat @ F )
% 0.14/0.48 => ( ( condit5488710616941104124bove_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3790_mono__cSup,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_nat @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3791_mono__cSup,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_nat @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_int @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3792_mono__cSup,axiom,
% 0.14/0.48 ! [F: product_unit > nat,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_7096114683908731117it_nat @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3793_mono__cSup,axiom,
% 0.14/0.48 ! [F: $o > int,A4: set_o] :
% 0.14/0.48 ( ( order_mono_o_int @ F )
% 0.14/0.48 => ( ( condit5488710616941104124bove_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3794_mono__cSup,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( order_mono_nat_int @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3795_mono__cSup,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( order_mono_int_int @ F )
% 0.14/0.48 => ( ( condit2212336002400062152ve_int @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_int )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_int @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3796_mono__cSup,axiom,
% 0.14/0.48 ! [F: product_unit > int,A4: set_Product_unit] :
% 0.14/0.48 ( ( order_7093624213399680841it_int @ F )
% 0.14/0.48 => ( ( condit2080475194861589617t_unit @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3797_mono__cSup,axiom,
% 0.14/0.48 ! [F: $o > product_unit,A4: set_o] :
% 0.14/0.48 ( ( order_7782127260464396005t_unit @ F )
% 0.14/0.48 => ( ( condit5488710616941104124bove_o @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_o )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3798_mono__cSup,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.48 ( ( order_5727276828720722763t_unit @ F )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ A4 )
% 0.14/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.14/0.48 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % mono_cSup
% 0.14/0.48 thf(fact_3799_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > rat,A13: set_nat,B1: set_rat,F22: int > int,B22: set_int,A24: set_int] :
% 0.14/0.48 ( ( ( image_nat_rat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_int @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_int ) )
% 0.14/0.48 => ( ( bNF_We7904740386373615514nt_rat @ B22 @ B1 )
% 0.14/0.48 = ( image_1904597124500147013nt_rat @ ( bNF_We576767280138975660at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3800_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > nat,A13: set_nat,B1: set_nat,F22: int > int,B22: set_int,A24: set_int] :
% 0.14/0.48 ( ( ( image_nat_nat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_int @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_int ) )
% 0.14/0.48 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 0.14/0.48 = ( image_5412825682893543741nt_nat @ ( bNF_We893321924073841572at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3801_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > int,A13: set_nat,B1: set_int,F22: int > int,B22: set_int,A24: set_int] :
% 0.14/0.48 ( ( ( image_nat_int @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_int @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_int ) )
% 0.14/0.48 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 0.14/0.48 = ( image_1234974663384347033nt_int @ ( bNF_We1892675635974896128nt_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3802_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: int > nat,A13: set_int,B1: set_nat,F22: int > int,B22: set_int,A24: set_int] :
% 0.14/0.48 ( ( ( image_int_nat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_int @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_int ) )
% 0.14/0.48 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 0.14/0.48 = ( image_1600535827742230425nt_nat @ ( bNF_We1264975484310686208at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8537379975951060974nt_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3803_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: int > int,A13: set_int,B1: set_int,F22: int > int,B22: set_int,A24: set_int] :
% 0.14/0.48 ( ( ( image_int_int @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_int @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_int ) )
% 0.14/0.48 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 0.14/0.48 = ( image_6646056845087809525nt_int @ ( bNF_We2264329196211740764nt_int @ B22 @ F1 @ F22 ) @ ( bNF_We8537379975951060974nt_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3804_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > rat,A13: set_nat,B1: set_rat,F22: int > nat,B22: set_int,A24: set_nat] :
% 0.14/0.48 ( ( ( image_nat_rat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_nat ) )
% 0.14/0.48 => ( ( bNF_We7904740386373615514nt_rat @ B22 @ B1 )
% 0.14/0.48 = ( image_696479991571767017nt_rat @ ( bNF_We579257750648025936at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3805_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > nat,A13: set_nat,B1: set_nat,F22: int > nat,B22: set_int,A24: set_nat] :
% 0.14/0.48 ( ( ( image_nat_nat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_nat ) )
% 0.14/0.48 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 0.14/0.48 = ( image_4204708549965163745nt_nat @ ( bNF_We895812394582891848at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3806_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: nat > int,A13: set_nat,B1: set_int,F22: int > nat,B22: set_int,A24: set_nat] :
% 0.14/0.48 ( ( ( image_nat_int @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_nat ) )
% 0.14/0.48 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 0.14/0.48 = ( image_26857530455967037nt_int @ ( bNF_We1895166106483946404nt_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3807_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: int > nat,A13: set_int,B1: set_nat,F22: int > nat,B22: set_int,A24: set_nat] :
% 0.14/0.48 ( ( ( image_int_nat @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_nat ) )
% 0.14/0.48 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 0.14/0.48 = ( image_392418694813850429nt_nat @ ( bNF_We1267465954819736484at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7538026264050006418at_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3808_Func__map__surj,axiom,
% 0.14/0.48 ! [F1: int > int,A13: set_int,B1: set_int,F22: int > nat,B22: set_int,A24: set_nat] :
% 0.14/0.48 ( ( ( image_int_int @ F1 @ A13 )
% 0.14/0.48 = B1 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F22 @ B22 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 0.14/0.48 => ( ( ( B22 = bot_bot_set_int )
% 0.14/0.48 => ( A24 = bot_bot_set_nat ) )
% 0.14/0.48 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 0.14/0.48 = ( image_5437939712159429529nt_int @ ( bNF_We2266819666720791040nt_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7538026264050006418at_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Func_map_surj
% 0.14/0.48 thf(fact_3809_cofinal__def,axiom,
% 0.14/0.48 ( bNF_Ca6037544080215331608at_nat
% 0.14/0.48 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ! [X4: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member6273874620674182256at_nat @ X4 @ ( field_1428494348145443988at_nat @ R5 ) )
% 0.14/0.48 => ? [Y5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 0.14/0.48 & ( X4 != Y5 )
% 0.14/0.48 & ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cofinal_def
% 0.14/0.48 thf(fact_3810_cofinal__def,axiom,
% 0.14/0.48 ( bNF_Ca8448034394003515314at_nat
% 0.14/0.48 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ! [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member2643936169264416010at_nat @ X4 @ ( field_3145993188331922222at_nat @ R5 ) )
% 0.14/0.48 => ? [Y5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 0.14/0.48 & ( X4 != Y5 )
% 0.14/0.48 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cofinal_def
% 0.14/0.48 thf(fact_3811_cofinal__def,axiom,
% 0.14/0.48 ( bNF_Ca5159621140400407487al_nat
% 0.14/0.48 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ ( field_nat @ R5 ) )
% 0.14/0.48 => ? [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ A6 )
% 0.14/0.48 & ( X4 != Y5 )
% 0.14/0.48 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cofinal_def
% 0.14/0.48 thf(fact_3812_cofinal__def,axiom,
% 0.14/0.48 ( bNF_Ca5157130669891357211al_int
% 0.14/0.48 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ ( field_int @ R5 ) )
% 0.14/0.48 => ? [Y5: int] :
% 0.14/0.48 ( ( member_int @ Y5 @ A6 )
% 0.14/0.48 & ( X4 != Y5 )
% 0.14/0.48 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % cofinal_def
% 0.14/0.48 thf(fact_3813_Total__subset__Id,axiom,
% 0.14/0.48 ! [R: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( total_5117575981256876747at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 0.14/0.48 => ( ( ord_le5997549366648089703at_nat @ R @ id_set4888139568991089827at_nat )
% 0.14/0.48 => ( ( R = bot_bo4948859079157340979at_nat )
% 0.14/0.48 | ? [A3: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( R
% 0.14/0.48 = ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ A3 @ A3 ) @ bot_bo4948859079157340979at_nat ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Total_subset_Id
% 0.14/0.48 thf(fact_3814_Total__subset__Id,axiom,
% 0.14/0.48 ! [R: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( total_on_int @ ( field_int @ R ) @ R )
% 0.14/0.48 => ( ( ord_le2843351958646193337nt_int @ R @ id_int2 )
% 0.14/0.48 => ( ( R = bot_bo1796632182523588997nt_int )
% 0.14/0.48 | ? [A3: int] :
% 0.14/0.48 ( R
% 0.14/0.48 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A3 @ A3 ) @ bot_bo1796632182523588997nt_int ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Total_subset_Id
% 0.14/0.48 thf(fact_3815_Total__subset__Id,axiom,
% 0.14/0.48 ! [R: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( total_3592101749530773125at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 0.14/0.48 => ( ( ord_le3000389064537975527at_nat @ R @ id_Pro2258643101195443293at_nat )
% 0.14/0.48 => ( ( R = bot_bo5327735625951526323at_nat )
% 0.14/0.48 | ? [A3: product_prod_nat_nat] :
% 0.14/0.48 ( R
% 0.14/0.48 = ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A3 @ A3 ) @ bot_bo5327735625951526323at_nat ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Total_subset_Id
% 0.14/0.48 thf(fact_3816_Total__subset__Id,axiom,
% 0.14/0.48 ! [R: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( total_7212417256332265445at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 0.14/0.48 => ( ( ord_le1268244103169919719at_nat @ R @ id_set1796276052702428605at_nat )
% 0.14/0.48 => ( ( R = bot_bo228742789529271731at_nat )
% 0.14/0.48 | ? [A3: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( R
% 0.14/0.48 = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A3 @ A3 ) @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Total_subset_Id
% 0.14/0.48 thf(fact_3817_Total__subset__Id,axiom,
% 0.14/0.48 ! [R: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( total_on_nat @ ( field_nat @ R ) @ R )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ R @ id_nat2 )
% 0.14/0.48 => ( ( R = bot_bo2099793752762293965at_nat )
% 0.14/0.48 | ? [A3: nat] :
% 0.14/0.48 ( R
% 0.14/0.48 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A3 @ A3 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Total_subset_Id
% 0.14/0.48 thf(fact_3818_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ? [X: int] :
% 0.14/0.48 ( ( member_int @ X @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3819_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: rat] :
% 0.14/0.48 ( ( member_rat @ X @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3820_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: int] :
% 0.14/0.48 ( ( member_int @ X @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3821_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.48 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3822_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > $o,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3823_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ? [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3824_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3825_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ? [X: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3826_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ? [X: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3827_inf__img__fin__dom_H,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > $o,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_o @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ? [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 0.14/0.48 & ~ ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage2444243245536687506_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_dom'
% 0.14/0.48 thf(fact_3828_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ~ ! [Y: int] :
% 0.14/0.48 ( ( member_int @ Y @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3829_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: rat] :
% 0.14/0.48 ( ( member_rat @ Y @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ Y @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3830_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: int] :
% 0.14/0.48 ( ( member_int @ Y @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3831_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.48 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ Y @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3832_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > $o,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: $o] :
% 0.14/0.48 ( ( member_o @ Y @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ Y @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3833_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ~ ! [Y: nat] :
% 0.14/0.48 ( ( member_nat @ Y @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ F @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3834_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: nat] :
% 0.14/0.48 ( ( member_nat @ Y @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3835_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > int,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_int @ ( image_2483585944268220136at_int @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: int] :
% 0.14/0.48 ( ( member_int @ Y @ ( image_2483585944268220136at_int @ F @ A4 ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage4650790856102703794at_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3836_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ Y @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3837_inf__img__fin__domE_H,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ~ ! [Y: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ Y @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inf_img_fin_domE'
% 0.14/0.48 thf(fact_3838_prod__set__simps_I2_J,axiom,
% 0.14/0.48 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( basic_5713354656523905413at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 0.14/0.48 = ( insert2290795007606087959at_nat @ Y3 @ bot_bo1534825418459847827at_nat ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_simps(2)
% 0.14/0.48 thf(fact_3839_prod__set__simps_I2_J,axiom,
% 0.14/0.48 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( basic_484852565060450053at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 0.14/0.48 = ( insert9200635055090092081at_nat @ Y3 @ bot_bo3083307316010499117at_nat ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_simps(2)
% 0.14/0.48 thf(fact_3840_prod__set__simps_I2_J,axiom,
% 0.14/0.48 ! [X2: nat,Y3: num] :
% 0.14/0.48 ( ( basic_snds_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 0.14/0.48 = ( insert_num @ Y3 @ bot_bot_set_num ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_simps(2)
% 0.14/0.48 thf(fact_3841_prod__set__simps_I2_J,axiom,
% 0.14/0.48 ! [X2: int,Y3: int] :
% 0.14/0.48 ( ( basic_snds_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 0.14/0.48 = ( insert_int @ Y3 @ bot_bot_set_int ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_simps(2)
% 0.14/0.48 thf(fact_3842_prod__set__simps_I2_J,axiom,
% 0.14/0.48 ! [X2: nat,Y3: nat] :
% 0.14/0.48 ( ( basic_snds_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 0.14/0.48 = ( insert_nat @ Y3 @ bot_bot_set_nat ) ) ).
% 0.14/0.48
% 0.14/0.48 % prod_set_simps(2)
% 0.14/0.48 thf(fact_3843_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 0.14/0.48 => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
% 0.14/0.48 => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
% 0.14/0.48 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ A ) @ ( minus_8235382265540049710at_nat @ R @ id_Pro5428700290092274115at_nat ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3844_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Product_prod_o_o,A: $o,B: $o] :
% 0.14/0.48 ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
% 0.14/0.48 => ( ( member_o @ A @ ( field_o @ R ) )
% 0.14/0.48 => ( ( member_o @ B @ ( field_o @ R ) )
% 0.14/0.48 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ ( minus_7052513330764642158od_o_o @ R @ id_o2 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3845_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.14/0.48 ( ( order_7480980593162297270at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 0.14/0.48 => ( ( member8440522571783428010at_nat @ A @ ( field_4706345496283612622at_nat @ R ) )
% 0.14/0.48 => ( ( member8440522571783428010at_nat @ B @ ( field_4706345496283612622at_nat @ R ) )
% 0.14/0.48 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ B @ A ) @ ( minus_8321449233255521966at_nat @ R @ id_Pro2258643101195443293at_nat ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3846_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( order_1878278401035043452at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 0.14/0.48 => ( ( member6273874620674182256at_nat @ A @ ( field_1428494348145443988at_nat @ R ) )
% 0.14/0.48 => ( ( member6273874620674182256at_nat @ B @ ( field_1428494348145443988at_nat @ R ) )
% 0.14/0.48 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ B @ A ) @ ( minus_8674369445256047406at_nat @ R @ id_set4888139568991089827at_nat ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3847_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 0.14/0.48 => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
% 0.14/0.48 => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
% 0.14/0.48 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3848_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 0.14/0.48 ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
% 0.14/0.48 => ( ( member_nat @ A @ ( field_nat @ R ) )
% 0.14/0.48 => ( ( member_nat @ B @ ( field_nat @ R ) )
% 0.14/0.48 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( minus_1356011639430497352at_nat @ R @ id_nat2 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3849_Linear__order__in__diff__Id,axiom,
% 0.14/0.48 ! [R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 0.14/0.48 ( ( order_4471489696718655927on_int @ ( field_int @ R ) @ R )
% 0.14/0.48 => ( ( member_int @ A @ ( field_int @ R ) )
% 0.14/0.48 => ( ( member_int @ B @ ( field_int @ R ) )
% 0.14/0.48 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.14/0.48 = ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A ) @ ( minus_1052850069191792384nt_int @ R @ id_int2 ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_in_diff_Id
% 0.14/0.48 thf(fact_3850_aboveS__def,axiom,
% 0.14/0.48 ( order_4940263126897443436at_nat
% 0.14/0.48 = ( ^ [R5: set_Pr8693737435421807431at_nat,A5: product_prod_nat_nat] :
% 0.14/0.48 ( collec3392354462482085612at_nat
% 0.14/0.48 @ ^ [B4: product_prod_nat_nat] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3851_aboveS__def,axiom,
% 0.14/0.48 ( order_1761765819289301284nt_int
% 0.14/0.48 = ( ^ [R5: set_Pr2560585780119916871nt_int,A5: product_prod_int_int] :
% 0.14/0.48 ( collec213857154873943460nt_int
% 0.14/0.48 @ ^ [B4: product_prod_int_int] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3852_aboveS__def,axiom,
% 0.14/0.48 ( order_2442354982230848562at_nat
% 0.14/0.48 = ( ^ [R5: set_Pr7459493094073627847at_nat,A5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( collec4573900263915890866at_nat
% 0.14/0.48 @ ^ [B4: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3853_aboveS__def,axiom,
% 0.14/0.48 ( order_4440095836999870412at_nat
% 0.14/0.48 = ( ^ [R5: set_Pr4329608150637261639at_nat,A5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( collec5514110066124741708at_nat
% 0.14/0.48 @ ^ [B4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3854_aboveS__def,axiom,
% 0.14/0.48 ( order_aboveS_nat
% 0.14/0.48 = ( ^ [R5: set_Pr1261947904930325089at_nat,A5: nat] :
% 0.14/0.48 ( collect_nat
% 0.14/0.48 @ ^ [B4: nat] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3855_aboveS__def,axiom,
% 0.14/0.48 ( order_aboveS_int
% 0.14/0.48 = ( ^ [R5: set_Pr958786334691620121nt_int,A5: int] :
% 0.14/0.48 ( collect_int
% 0.14/0.48 @ ^ [B4: int] :
% 0.14/0.48 ( ( B4 != A5 )
% 0.14/0.48 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % aboveS_def
% 0.14/0.48 thf(fact_3856_card__vimage__inj,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ A4 @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 0.14/0.48 => ( ( finite_card_nat @ ( vimage_nat_rat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_rat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_vimage_inj
% 0.14/0.48 thf(fact_3857_card__vimage__inj,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 0.14/0.48 => ( ( finite_card_nat @ ( vimage_nat_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_vimage_inj
% 0.14/0.48 thf(fact_3858_card__vimage__inj,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ ( image_nat_int @ F @ top_top_set_nat ) )
% 0.14/0.48 => ( ( finite_card_nat @ ( vimage_nat_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_vimage_inj
% 0.14/0.48 thf(fact_3859_card__vimage__inj,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ A4 @ ( image_int_nat @ F @ top_top_set_int ) )
% 0.14/0.48 => ( ( finite_card_int @ ( vimage_int_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_vimage_inj
% 0.14/0.48 thf(fact_3860_card__vimage__inj,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ A4 @ ( image_int_int @ F @ top_top_set_int ) )
% 0.14/0.48 => ( ( finite_card_int @ ( vimage_int_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_vimage_inj
% 0.14/0.48 thf(fact_3861_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr7459493094073627847at_nat] :
% 0.14/0.48 ( ( order_1878278401035043452at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 0.14/0.48 => ( ( order_423636163458052581at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_se5479201105039950375at_nat] :
% 0.14/0.48 ( ( ord_le7966958417815640519at_nat @ A6 @ ( field_1428494348145443988at_nat @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bo1534825418459847827at_nat )
% 0.14/0.48 => ? [X4: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 0.14/0.48 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3862_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 0.14/0.48 => ( ( order_1968183844437341695at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_se7855581050983116737at_nat] :
% 0.14/0.48 ( ( ord_le2077887516847798113at_nat @ A6 @ ( field_3145993188331922222at_nat @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bo3083307316010499117at_nat )
% 0.14/0.48 => ? [X4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 0.14/0.48 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3863_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr958786334691620121nt_int] :
% 0.14/0.48 ( ( order_4471489696718655927on_int @ ( field_int @ R ) @ R )
% 0.14/0.48 => ( ( order_2886507596567047182on_int @ ( field_int @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ A6 @ ( field_int @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bot_set_int )
% 0.14/0.48 => ? [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: int] :
% 0.14/0.48 ( ( member_int @ Y5 @ A6 )
% 0.14/0.48 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3864_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr5094982260447487303t_unit] :
% 0.14/0.48 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R ) @ R )
% 0.14/0.48 => ( ( order_3164716736300062379t_unit @ ( field_Product_unit @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_Product_unit] :
% 0.14/0.48 ( ( ord_le3507040750410214029t_unit @ A6 @ ( field_Product_unit @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bo3957492148770167129t_unit )
% 0.14/0.48 => ? [X4: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: product_unit] :
% 0.14/0.48 ( ( member_Product_unit @ Y5 @ A6 )
% 0.14/0.48 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3865_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr5564308138774400199at_nat] :
% 0.14/0.48 ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 0.14/0.48 => ( ( order_2339240034117818117at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( ord_le1268244103169919719at_nat @ A6 @ ( field_2862844103579723188at_nat @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bo228742789529271731at_nat )
% 0.14/0.48 => ? [X4: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ Y5 @ A6 )
% 0.14/0.48 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3866_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr8693737435421807431at_nat] :
% 0.14/0.48 ( ( order_7480980593162297270at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 0.14/0.48 => ( ( order_8331247224601271455at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ord_le3146513528884898305at_nat @ A6 @ ( field_4706345496283612622at_nat @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bo2099793752762293965at_nat )
% 0.14/0.48 => ? [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ Y5 @ A6 )
% 0.14/0.48 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3867_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Product_prod_o_o] :
% 0.14/0.48 ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
% 0.14/0.48 => ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_o] :
% 0.14/0.48 ( ( ord_less_eq_set_o @ A6 @ ( field_o @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bot_set_o )
% 0.14/0.48 => ? [X4: $o] :
% 0.14/0.48 ( ( member_o @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: $o] :
% 0.14/0.48 ( ( member_o @ Y5 @ A6 )
% 0.14/0.48 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3868_Linear__order__Well__order__iff,axiom,
% 0.14/0.48 ! [R: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
% 0.14/0.48 => ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
% 0.14/0.48 = ( ! [A6: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ A6 @ ( field_nat @ R ) )
% 0.14/0.48 => ( ( A6 != bot_bot_set_nat )
% 0.14/0.48 => ? [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A6 )
% 0.14/0.48 & ! [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ A6 )
% 0.14/0.48 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % Linear_order_Well_order_iff
% 0.14/0.48 thf(fact_3869_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_int,H: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ F4 )
% 0.14/0.48 => ( finite_finite_int @ ( image_int_int @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3870_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_int,H: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ F4 )
% 0.14/0.48 => ( finite_finite_nat @ ( image_int_nat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3871_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_Pr1261947904930325089at_nat,H: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ F4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3872_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_Pr1261947904930325089at_nat,H: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ F4 )
% 0.14/0.48 => ( finite_finite_nat @ ( image_2486076414777270412at_nat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3873_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_nat,H: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ F4 )
% 0.14/0.48 => ( finite_finite_rat @ ( image_nat_rat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3874_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_nat,H: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ F4 )
% 0.14/0.48 => ( finite_finite_int @ ( image_nat_int @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3875_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_nat,H: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ F4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3876_finite__imageI,axiom,
% 0.14/0.48 ! [F4: set_nat,H: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ F4 )
% 0.14/0.48 => ( finite_finite_nat @ ( image_nat_nat @ H @ F4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_imageI
% 0.14/0.48 thf(fact_3877_IdI,axiom,
% 0.14/0.48 ! [A: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ id_Pro2258643101195443293at_nat ) ).
% 0.14/0.48
% 0.14/0.48 % IdI
% 0.14/0.48 thf(fact_3878_IdI,axiom,
% 0.14/0.48 ! [A: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ id_set4888139568991089827at_nat ) ).
% 0.14/0.48
% 0.14/0.48 % IdI
% 0.14/0.48 thf(fact_3879_IdI,axiom,
% 0.14/0.48 ! [A: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ id_set1796276052702428605at_nat ) ).
% 0.14/0.48
% 0.14/0.48 % IdI
% 0.14/0.48 thf(fact_3880_IdI,axiom,
% 0.14/0.48 ! [A: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ id_nat2 ) ).
% 0.14/0.48
% 0.14/0.48 % IdI
% 0.14/0.48 thf(fact_3881_IdI,axiom,
% 0.14/0.48 ! [A: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ id_int2 ) ).
% 0.14/0.48
% 0.14/0.48 % IdI
% 0.14/0.48 thf(fact_3882_pair__in__Id__conv,axiom,
% 0.14/0.48 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 0.14/0.48 = ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % pair_in_Id_conv
% 0.14/0.48 thf(fact_3883_pair__in__Id__conv,axiom,
% 0.14/0.48 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ id_set4888139568991089827at_nat )
% 0.14/0.48 = ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % pair_in_Id_conv
% 0.14/0.48 thf(fact_3884_pair__in__Id__conv,axiom,
% 0.14/0.48 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
% 0.14/0.48 = ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % pair_in_Id_conv
% 0.14/0.48 thf(fact_3885_pair__in__Id__conv,axiom,
% 0.14/0.48 ! [A: nat,B: nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 0.14/0.48 = ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % pair_in_Id_conv
% 0.14/0.48 thf(fact_3886_pair__in__Id__conv,axiom,
% 0.14/0.48 ! [A: int,B: int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 0.14/0.48 = ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % pair_in_Id_conv
% 0.14/0.48 thf(fact_3887_finite__UN,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN
% 0.14/0.48 thf(fact_3888_finite__UN,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN
% 0.14/0.48 thf(fact_3889_finite__UN,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN
% 0.14/0.48 thf(fact_3890_finite__UN,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: nat > set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN
% 0.14/0.48 thf(fact_3891_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite4343798906461161616at_nat @ A4 )
% 0.14/0.48 => ( ! [A3: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7979982168039674559at_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3892_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_o,B5: $o > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_o @ A4 )
% 0.14/0.48 => ( ! [A3: $o] :
% 0.14/0.48 ( ( member_o @ A3 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3893_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_int,B5: int > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ! [A3: int] :
% 0.14/0.48 ( ( member_int @ A3 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_8938366415781434990at_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3894_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ! [A3: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3895_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ! [A3: nat] :
% 0.14/0.48 ( ( member_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3896_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 0.14/0.48 ( ( finite4343798906461161616at_nat @ A4 )
% 0.14/0.48 => ( ! [A3: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3897_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_o,B5: $o > set_nat] :
% 0.14/0.48 ( ( finite_finite_o @ A4 )
% 0.14/0.48 => ( ! [A3: $o] :
% 0.14/0.48 ( ( member_o @ A3 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3898_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_int,B5: int > set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ! [A3: int] :
% 0.14/0.48 ( ( member_int @ A3 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3899_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ! [A3: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3900_finite__UN__I,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: nat > set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ! [A3: nat] :
% 0.14/0.48 ( ( member_nat @ A3 @ A4 )
% 0.14/0.48 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 0.14/0.48 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_UN_I
% 0.14/0.48 thf(fact_3901_bdd__below__UN,axiom,
% 0.14/0.48 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ I3 )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 0.14/0.48 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_UN
% 0.14/0.48 thf(fact_3902_bdd__below__UN,axiom,
% 0.14/0.48 ! [I3: set_nat,A4: nat > set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ I3 )
% 0.14/0.48 => ( ( condit1738341127787009408ow_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ I3 )
% 0.14/0.48 => ( condit1738341127787009408ow_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_below_UN
% 0.14/0.48 thf(fact_3903_bdd__above__UN,axiom,
% 0.14/0.48 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ I3 )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 0.14/0.48 = ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_UN
% 0.14/0.48 thf(fact_3904_bdd__above__UN,axiom,
% 0.14/0.48 ! [I3: set_nat,A4: nat > set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ I3 )
% 0.14/0.48 => ( ( condit2214826472909112428ve_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 0.14/0.48 = ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ I3 )
% 0.14/0.48 => ( condit2214826472909112428ve_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % bdd_above_UN
% 0.14/0.48 thf(fact_3905_card__image__le,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_int_nat @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image_le
% 0.14/0.48 thf(fact_3906_card__image__le,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_int @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image_le
% 0.14/0.48 thf(fact_3907_card__image__le,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image_le
% 0.14/0.48 thf(fact_3908_card__image__le,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image_le
% 0.14/0.48 thf(fact_3909_card__image__le,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image_le
% 0.14/0.48 thf(fact_3910_surj__card__le,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_nat,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_card_le
% 0.14/0.48 thf(fact_3911_surj__card__le,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_card_le
% 0.14/0.48 thf(fact_3912_surj__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_rat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_rat @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_card_le
% 0.14/0.48 thf(fact_3913_surj__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_card_le
% 0.14/0.48 thf(fact_3914_surj__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_int,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surj_card_le
% 0.14/0.48 thf(fact_3915_eq__card__imp__inj__on,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) )
% 0.14/0.48 => ( inj_on_int_nat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % eq_card_imp_inj_on
% 0.14/0.48 thf(fact_3916_eq__card__imp__inj__on,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) )
% 0.14/0.48 => ( inj_on_int_int @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % eq_card_imp_inj_on
% 0.14/0.48 thf(fact_3917_eq__card__imp__inj__on,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_rat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % eq_card_imp_inj_on
% 0.14/0.48 thf(fact_3918_eq__card__imp__inj__on,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % eq_card_imp_inj_on
% 0.14/0.48 thf(fact_3919_eq__card__imp__inj__on,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) )
% 0.14/0.48 => ( inj_on_nat_int @ F @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % eq_card_imp_inj_on
% 0.14/0.48 thf(fact_3920_inj__on__iff__eq__card,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 = ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_eq_card
% 0.14/0.48 thf(fact_3921_inj__on__iff__eq__card,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 = ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_eq_card
% 0.14/0.48 thf(fact_3922_inj__on__iff__eq__card,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 = ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_eq_card
% 0.14/0.48 thf(fact_3923_inj__on__iff__eq__card,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 = ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_eq_card
% 0.14/0.48 thf(fact_3924_inj__on__iff__eq__card,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 = ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_eq_card
% 0.14/0.48 thf(fact_3925_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( order_2339240034117818117at_nat @ A4 @ R )
% 0.14/0.48 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 0.14/0.48 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 0.14/0.48 & ( member8757157785044589968at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3926_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.14/0.48 ( ( order_8331247224601271455at_nat @ A4 @ R )
% 0.14/0.48 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 0.14/0.48 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 0.14/0.48 & ( member8440522571783428010at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3927_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_o,R: set_Product_prod_o_o,A: $o,B: $o] :
% 0.14/0.48 ( ( order_2615775362358406454r_on_o @ A4 @ R )
% 0.14/0.48 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 0.14/0.48 => ( ( member_o @ A @ A4 )
% 0.14/0.48 & ( member_o @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3928_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( order_423636163458052581at_nat @ A4 @ R )
% 0.14/0.48 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 0.14/0.48 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 0.14/0.48 & ( member6273874620674182256at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3929_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( order_1968183844437341695at_nat @ A4 @ R )
% 0.14/0.48 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 0.14/0.48 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 0.14/0.48 & ( member2643936169264416010at_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3930_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 0.14/0.48 ( ( order_2886507596567047182on_int @ A4 @ R )
% 0.14/0.48 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.14/0.48 => ( ( member_int @ A @ A4 )
% 0.14/0.48 & ( member_int @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3931_well__order__on__domain,axiom,
% 0.14/0.48 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 0.14/0.48 ( ( order_2888998067076097458on_nat @ A4 @ R )
% 0.14/0.48 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.14/0.48 => ( ( member_nat @ A @ A4 )
% 0.14/0.48 & ( member_nat @ B @ A4 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % well_order_on_domain
% 0.14/0.48 thf(fact_3932_infinite__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_rat] :
% 0.14/0.48 ( ~ ( finite_finite_rat @ S5 )
% 0.14/0.48 => ? [F5: nat > rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F5 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_countable_subset
% 0.14/0.48 thf(fact_3933_infinite__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_int] :
% 0.14/0.48 ( ~ ( finite_finite_int @ S5 )
% 0.14/0.48 => ? [F5: nat > int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F5 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_int @ ( image_nat_int @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_countable_subset
% 0.14/0.48 thf(fact_3934_infinite__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ~ ( finite6177210948735845034at_nat @ S5 )
% 0.14/0.48 => ? [F5: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on5538052773655684606at_nat @ F5 @ top_top_set_nat )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_countable_subset
% 0.14/0.48 thf(fact_3935_infinite__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_nat] :
% 0.14/0.48 ( ~ ( finite_finite_nat @ S5 )
% 0.14/0.48 => ? [F5: nat > nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F5 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_countable_subset
% 0.14/0.48 thf(fact_3936_infinite__iff__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_rat] :
% 0.14/0.48 ( ( ~ ( finite_finite_rat @ S5 ) )
% 0.14/0.48 = ( ? [F2: nat > rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F2 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_iff_countable_subset
% 0.14/0.48 thf(fact_3937_infinite__iff__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_int] :
% 0.14/0.48 ( ( ~ ( finite_finite_int @ S5 ) )
% 0.14/0.48 = ( ? [F2: nat > int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F2 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_iff_countable_subset
% 0.14/0.48 thf(fact_3938_infinite__iff__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ~ ( finite6177210948735845034at_nat @ S5 ) )
% 0.14/0.48 = ( ? [F2: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on5538052773655684606at_nat @ F2 @ top_top_set_nat )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_iff_countable_subset
% 0.14/0.48 thf(fact_3939_infinite__iff__countable__subset,axiom,
% 0.14/0.48 ! [S5: set_nat] :
% 0.14/0.48 ( ( ~ ( finite_finite_nat @ S5 ) )
% 0.14/0.48 = ( ? [F2: nat > nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.14/0.48 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % infinite_iff_countable_subset
% 0.14/0.48 thf(fact_3940_IdE,axiom,
% 0.14/0.48 ! [P: produc859450856879609959at_nat] :
% 0.14/0.48 ( ( member8206827879206165904at_nat @ P @ id_Pro2258643101195443293at_nat )
% 0.14/0.48 => ~ ! [X: product_prod_nat_nat] :
% 0.14/0.48 ( P
% 0.14/0.48 != ( produc6161850002892822231at_nat @ X @ X ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdE
% 0.14/0.48 thf(fact_3941_IdE,axiom,
% 0.14/0.48 ! [P: produc1319942482725812455at_nat] :
% 0.14/0.48 ( ( member1466754251312161552at_nat @ P @ id_set4888139568991089827at_nat )
% 0.14/0.48 => ~ ! [X: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( P
% 0.14/0.48 != ( produc9060074326276436823at_nat @ X @ X ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdE
% 0.14/0.48 thf(fact_3942_IdE,axiom,
% 0.14/0.48 ! [P: produc3843707927480180839at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ P @ id_set1796276052702428605at_nat )
% 0.14/0.48 => ~ ! [X: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( P
% 0.14/0.48 != ( produc2922128104949294807at_nat @ X @ X ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdE
% 0.14/0.48 thf(fact_3943_IdE,axiom,
% 0.14/0.48 ! [P: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ P @ id_nat2 )
% 0.14/0.48 => ~ ! [X: nat] :
% 0.14/0.48 ( P
% 0.14/0.48 != ( product_Pair_nat_nat @ X @ X ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdE
% 0.14/0.48 thf(fact_3944_IdE,axiom,
% 0.14/0.48 ! [P: product_prod_int_int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ P @ id_int2 )
% 0.14/0.48 => ~ ! [X: int] :
% 0.14/0.48 ( P
% 0.14/0.48 != ( product_Pair_int_int @ X @ X ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdE
% 0.14/0.48 thf(fact_3945_IdD,axiom,
% 0.14/0.48 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 0.14/0.48 => ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdD
% 0.14/0.48 thf(fact_3946_IdD,axiom,
% 0.14/0.48 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.14/0.48 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ id_set4888139568991089827at_nat )
% 0.14/0.48 => ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdD
% 0.14/0.48 thf(fact_3947_IdD,axiom,
% 0.14/0.48 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
% 0.14/0.48 => ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdD
% 0.14/0.48 thf(fact_3948_IdD,axiom,
% 0.14/0.48 ! [A: nat,B: nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 0.14/0.48 => ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdD
% 0.14/0.48 thf(fact_3949_IdD,axiom,
% 0.14/0.48 ! [A: int,B: int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 0.14/0.48 => ( A = B ) ) ).
% 0.14/0.48
% 0.14/0.48 % IdD
% 0.14/0.48 thf(fact_3950_card__bij__eq,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,B5: set_int,G: int > int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_int_int @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( finite_card_int @ A4 )
% 0.14/0.48 = ( finite_card_int @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3951_card__bij__eq,axiom,
% 0.14/0.48 ! [F: rat > nat,A4: set_rat,B5: set_nat,G: nat > rat] :
% 0.14/0.48 ( ( inj_on_rat_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_rat_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_nat_rat @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_rat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( finite_card_rat @ A4 )
% 0.14/0.48 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3952_card__bij__eq,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,B5: set_nat,G: nat > int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_nat_int @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( finite_card_int @ A4 )
% 0.14/0.48 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3953_card__bij__eq,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on8969904277767023793at_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( finite711546835091564841at_nat @ A4 )
% 0.14/0.48 = ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3954_card__bij__eq,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,B5: set_nat,G: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on5538052773655684606at_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( finite711546835091564841at_nat @ A4 )
% 0.14/0.48 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3955_card__bij__eq,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,B5: set_rat,G: rat > nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_rat_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_rat_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_rat @ B5 )
% 0.14/0.48 => ( ( finite_card_nat @ A4 )
% 0.14/0.48 = ( finite_card_rat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3956_card__bij__eq,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,B5: set_int,G: int > nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_int_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( finite_card_nat @ A4 )
% 0.14/0.48 = ( finite_card_int @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3957_card__bij__eq,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on2178005380612969504at_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( finite_card_nat @ A4 )
% 0.14/0.48 = ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3958_card__bij__eq,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,B5: set_nat,G: nat > nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( inj_on_nat_nat @ G @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ B5 ) @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( finite_card_nat @ A4 )
% 0.14/0.48 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_bij_eq
% 0.14/0.48 thf(fact_3959_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 0.14/0.48 => ? [F5: int > int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ ( image_int_int @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on_int_int @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3960_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) )
% 0.14/0.48 => ? [F5: int > nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on_int_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3961_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 0.14/0.48 => ? [F5: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on8969904277767023793at_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3962_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 0.14/0.48 => ? [F5: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on2178005380612969504at_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3963_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_rat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) )
% 0.14/0.48 => ? [F5: nat > rat] :
% 0.14/0.48 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on_nat_rat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3964_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) )
% 0.14/0.48 => ? [F5: nat > int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ ( image_nat_int @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on_nat_int @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3965_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 0.14/0.48 => ? [F5: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on5538052773655684606at_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3966_card__le__inj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 0.14/0.48 => ? [F5: nat > nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F5 @ A4 ) @ B5 )
% 0.14/0.48 & ( inj_on_nat_nat @ F5 @ A4 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_le_inj
% 0.14/0.48 thf(fact_3967_card__inj__on__le,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( finite_finite_rat @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_inj_on_le
% 0.14/0.48 thf(fact_3968_card__inj__on__le,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_inj_on_le
% 0.14/0.48 thf(fact_3969_card__inj__on__le,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_inj_on_le
% 0.14/0.48 thf(fact_3970_card__inj__on__le,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_inj_on_le
% 0.14/0.48 thf(fact_3971_card__inj__on__le,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_inj_on_le
% 0.14/0.48 thf(fact_3972_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ? [F2: int > int] :
% 0.14/0.48 ( ( inj_on_int_int @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_int @ ( image_int_int @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3973_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ? [F2: int > nat] :
% 0.14/0.48 ( ( inj_on_int_nat @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ ( image_int_nat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3974_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ? [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on8969904277767023793at_nat @ F2 @ A4 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3975_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ? [F2: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( inj_on2178005380612969504at_nat @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3976_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_rat @ B5 )
% 0.14/0.48 => ( ( ? [F2: nat > rat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3977_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ? [F2: nat > int] :
% 0.14/0.48 ( ( inj_on_nat_int @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3978_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ? [F2: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( inj_on5538052773655684606at_nat @ F2 @ A4 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3979_inj__on__iff__card__le,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ? [F2: nat > nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F2 @ A4 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A4 ) @ B5 ) ) )
% 0.14/0.48 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % inj_on_iff_card_le
% 0.14/0.48 thf(fact_3980_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_int,T3: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ S5 )
% 0.14/0.48 => ( ( finite_finite_int @ T3 )
% 0.14/0.48 => ( ( ( finite_card_int @ S5 )
% 0.14/0.48 = ( finite_card_int @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: int] :
% 0.14/0.48 ( ( member_int @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on_int_int @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3981_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_int,T3: set_nat,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ S5 )
% 0.14/0.48 => ( ( finite_finite_nat @ T3 )
% 0.14/0.48 => ( ( ( finite_card_int @ S5 )
% 0.14/0.48 = ( finite_card_nat @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: int] :
% 0.14/0.48 ( ( member_int @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on_int_nat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3982_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ S5 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ T3 )
% 0.14/0.48 => ( ( ( finite711546835091564841at_nat @ S5 )
% 0.14/0.48 = ( finite711546835091564841at_nat @ T3 ) )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on8969904277767023793at_nat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3983_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_Pr1261947904930325089at_nat,T3: set_nat,F: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ S5 )
% 0.14/0.48 => ( ( finite_finite_nat @ T3 )
% 0.14/0.48 => ( ( ( finite711546835091564841at_nat @ S5 )
% 0.14/0.48 = ( finite_card_nat @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on2178005380612969504at_nat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3984_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_nat,T3: set_rat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ S5 )
% 0.14/0.48 => ( ( finite_finite_rat @ T3 )
% 0.14/0.48 => ( ( ( finite_card_nat @ S5 )
% 0.14/0.48 = ( finite_card_rat @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: rat] :
% 0.14/0.48 ( ( member_rat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on_nat_rat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3985_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_nat,T3: set_int,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ S5 )
% 0.14/0.48 => ( ( finite_finite_int @ T3 )
% 0.14/0.48 => ( ( ( finite_card_nat @ S5 )
% 0.14/0.48 = ( finite_card_int @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: int] :
% 0.14/0.48 ( ( member_int @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on_nat_int @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3986_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_nat,T3: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ S5 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ T3 )
% 0.14/0.48 => ( ( ( finite_card_nat @ S5 )
% 0.14/0.48 = ( finite711546835091564841at_nat @ T3 ) )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on5538052773655684606at_nat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3987_surjective__iff__injective__gen,axiom,
% 0.14/0.48 ! [S5: set_nat,T3: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ S5 )
% 0.14/0.48 => ( ( finite_finite_nat @ T3 )
% 0.14/0.48 => ( ( ( finite_card_nat @ S5 )
% 0.14/0.48 = ( finite_card_nat @ T3 ) )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ S5 ) @ T3 )
% 0.14/0.48 => ( ( ! [X4: nat] :
% 0.14/0.48 ( ( member_nat @ X4 @ T3 )
% 0.14/0.48 => ? [Y5: nat] :
% 0.14/0.48 ( ( member_nat @ Y5 @ S5 )
% 0.14/0.48 & ( ( F @ Y5 )
% 0.14/0.48 = X4 ) ) ) )
% 0.14/0.48 = ( inj_on_nat_nat @ F @ S5 ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % surjective_iff_injective_gen
% 0.14/0.48 thf(fact_3988_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > int] :
% 0.14/0.48 ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ? [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_int
% 0.14/0.48 @ ( collect_int
% 0.14/0.48 @ ^ [A5: int] :
% 0.14/0.48 ( ( member_int @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3989_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > nat] :
% 0.14/0.48 ( ~ ( finite_finite_o @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( image_o_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_o
% 0.14/0.48 @ ( collect_o
% 0.14/0.48 @ ^ [A5: $o] :
% 0.14/0.48 ( ( member_o @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3990_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > nat] :
% 0.14/0.48 ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_int
% 0.14/0.48 @ ( collect_int
% 0.14/0.48 @ ^ [A5: int] :
% 0.14/0.48 ( ( member_int @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3991_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > rat] :
% 0.14/0.48 ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ? [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_nat
% 0.14/0.48 @ ( collect_nat
% 0.14/0.48 @ ^ [A5: nat] :
% 0.14/0.48 ( ( member_nat @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3992_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > int] :
% 0.14/0.48 ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ? [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_nat
% 0.14/0.48 @ ( collect_nat
% 0.14/0.48 @ ^ [A5: nat] :
% 0.14/0.48 ( ( member_nat @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3993_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.48 ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: nat] :
% 0.14/0.48 ( ( member_nat @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_nat
% 0.14/0.48 @ ( collect_nat
% 0.14/0.48 @ ^ [A5: nat] :
% 0.14/0.48 ( ( member_nat @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3994_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_o,F: $o > product_prod_nat_nat] :
% 0.14/0.48 ( ~ ( finite_finite_o @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ ( image_3855930084881510382at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: $o] :
% 0.14/0.48 ( ( member_o @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_o
% 0.14/0.48 @ ( collect_o
% 0.14/0.48 @ ^ [A5: $o] :
% 0.14/0.48 ( ( member_o @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3995_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_int,F: int > product_prod_nat_nat] :
% 0.14/0.48 ( ~ ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( finite6177210948735845034at_nat @ ( image_8883965892284119310at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: int] :
% 0.14/0.48 ( ( member_int @ X @ A4 )
% 0.14/0.48 & ~ ( finite_finite_int
% 0.14/0.48 @ ( collect_int
% 0.14/0.48 @ ^ [A5: int] :
% 0.14/0.48 ( ( member_int @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3996_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_Pr958786334691620121nt_int,F: product_prod_int_int > nat] :
% 0.14/0.48 ( ~ ( finite2998713641127702882nt_int @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( image_5044651549707136836nt_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: product_prod_int_int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ X @ A4 )
% 0.14/0.48 & ~ ( finite2998713641127702882nt_int
% 0.14/0.48 @ ( collec213857154873943460nt_int
% 0.14/0.48 @ ^ [A5: product_prod_int_int] :
% 0.14/0.48 ( ( member5262025264175285858nt_int @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3997_pigeonhole__infinite,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [X: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.14/0.48 & ~ ( finite6177210948735845034at_nat
% 0.14/0.48 @ ( collec3392354462482085612at_nat
% 0.14/0.48 @ ^ [A5: product_prod_nat_nat] :
% 0.14/0.48 ( ( member8440522571783428010at_nat @ A5 @ A4 )
% 0.14/0.48 & ( ( F @ A5 )
% 0.14/0.48 = ( F @ X ) ) ) ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % pigeonhole_infinite
% 0.14/0.48 thf(fact_3998_snds_Ointros,axiom,
% 0.14/0.48 ! [P: produc7812382424243267045t_unit] : ( member242389114213480694t_unit @ ( produc1126150082675451753t_unit @ P ) @ ( basic_1496934909540232809t_unit @ P ) ) ).
% 0.14/0.48
% 0.14/0.48 % snds.intros
% 0.14/0.48 thf(fact_3999_snds_Osimps,axiom,
% 0.14/0.48 ! [A: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 0.14/0.48 ( ( member242389114213480694t_unit @ A @ ( basic_1496934909540232809t_unit @ P ) )
% 0.14/0.48 = ( A
% 0.14/0.48 = ( produc1126150082675451753t_unit @ P ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % snds.simps
% 0.14/0.48 thf(fact_4000_snds_Ocases,axiom,
% 0.14/0.48 ! [A: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 0.14/0.48 ( ( member242389114213480694t_unit @ A @ ( basic_1496934909540232809t_unit @ P ) )
% 0.14/0.48 => ( A
% 0.14/0.48 = ( produc1126150082675451753t_unit @ P ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % snds.cases
% 0.14/0.48 thf(fact_4001_card__image,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.48 => ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image
% 0.14/0.48 thf(fact_4002_card__image,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.48 => ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image
% 0.14/0.48 thf(fact_4003_card__image,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.48 => ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_nat @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image
% 0.14/0.48 thf(fact_4004_card__image,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.48 => ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image
% 0.14/0.48 thf(fact_4005_card__image,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_card_int @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % card_image
% 0.14/0.48 thf(fact_4006_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 0.14/0.48 ( ( ! [B6: set_int] :
% 0.14/0.48 ( ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_int] :
% 0.14/0.48 ( ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4007_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 0.14/0.48 ( ( ! [B6: set_rat] :
% 0.14/0.48 ( ( ( finite_finite_rat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4008_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 0.14/0.48 ( ( ! [B6: set_int] :
% 0.14/0.48 ( ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4009_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.48 ( ( ! [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5168914502847457605at_nat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_5168914502847457605at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4010_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.48 ( ( ! [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5846123807819985514at_nat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_5846123807819985514at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4011_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.14/0.48 ( ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_int] :
% 0.14/0.48 ( ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4012_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,P2: set_nat > $o] :
% 0.14/0.48 ( ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_2486076414777270412at_nat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_2486076414777270412at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4013_all__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.14/0.48 ( ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) ) )
% 0.14/0.48 => ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ! [B6: set_nat] :
% 0.14/0.48 ( ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.14/0.48 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % all_finite_subset_image
% 0.14/0.48 thf(fact_4014_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 0.14/0.48 ( ( ? [B6: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4015_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 0.14/0.48 ( ( ? [B6: set_rat] :
% 0.14/0.48 ( ( finite_finite_rat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4016_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 0.14/0.48 ( ( ? [B6: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4017_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.48 ( ( ? [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_5168914502847457605at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4018_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > product_prod_nat_nat,A4: set_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 0.14/0.48 ( ( ? [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_5846123807819985514at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4019_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.14/0.48 ( ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_int @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4020_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,P2: set_nat > $o] :
% 0.14/0.48 ( ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B6 )
% 0.14/0.48 & ( ord_le3146513528884898305at_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_2486076414777270412at_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4021_ex__finite__subset__image,axiom,
% 0.14/0.48 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.14/0.48 ( ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 & ( P2 @ B6 ) ) )
% 0.14/0.48 = ( ? [B6: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B6 )
% 0.14/0.48 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.14/0.48 & ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % ex_finite_subset_image
% 0.14/0.48 thf(fact_4022_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_int,F: int > int,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_int @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_int_int @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4023_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_rat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_nat_rat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4024_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_int @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_nat_int @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4025_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ord_le3146513528884898305at_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite6177210948735845034at_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_5168914502847457605at_nat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4026_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_5846123807819985514at_nat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4027_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 0.14/0.48 ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_int] :
% 0.14/0.48 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_int @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_int_nat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4028_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_nat,F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_Pr1261947904930325089at_nat] :
% 0.14/0.48 ( ( ord_le3146513528884898305at_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite6177210948735845034at_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_2486076414777270412at_nat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4029_finite__subset__image,axiom,
% 0.14/0.48 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ B5 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ? [C2: set_nat] :
% 0.14/0.48 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 0.14/0.48 & ( finite_finite_nat @ C2 )
% 0.14/0.48 & ( B5
% 0.14/0.48 = ( image_nat_nat @ F @ C2 ) ) ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_subset_image
% 0.14/0.48 thf(fact_4030_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_int,F: int > int] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_int @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4031_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_int,B5: set_nat,F: int > nat] :
% 0.14/0.48 ( ( finite_finite_int @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4032_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4033_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat,F: product_prod_nat_nat > nat] :
% 0.14/0.48 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4034_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_rat,F: nat > rat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_rat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4035_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_int,F: nat > int] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_int @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4036_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4037_finite__surj,axiom,
% 0.14/0.48 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 0.14/0.48 ( ( finite_finite_nat @ A4 )
% 0.14/0.48 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.48 => ( finite_finite_nat @ B5 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_surj
% 0.14/0.48 thf(fact_4038_finite__image__iff,axiom,
% 0.14/0.48 ! [F: int > int,A4: set_int] :
% 0.14/0.48 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.48 => ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.48 = ( finite_finite_int @ A4 ) ) ) ).
% 0.14/0.48
% 0.14/0.48 % finite_image_iff
% 0.14/0.48 thf(fact_4039_finite__image__iff,axiom,
% 0.14/0.48 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.48 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.49 => ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.49 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4040_finite__image__iff,axiom,
% 0.14/0.49 ! [F: nat > int,A4: set_nat] :
% 0.14/0.49 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.49 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.49 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4041_finite__image__iff,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 0.14/0.49 => ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.49 = ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4042_finite__image__iff,axiom,
% 0.14/0.49 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.49 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 0.14/0.49 => ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.49 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4043_finite__image__iff,axiom,
% 0.14/0.49 ! [F: int > nat,A4: set_int] :
% 0.14/0.49 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.49 => ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.49 = ( finite_finite_int @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4044_finite__image__iff,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 0.14/0.49 => ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.49 = ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4045_finite__image__iff,axiom,
% 0.14/0.49 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.49 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.49 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.49 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_image_iff
% 0.14/0.49 thf(fact_4046_finite__imageD,axiom,
% 0.14/0.49 ! [F: int > int,A4: set_int] :
% 0.14/0.49 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.49 => ( finite_finite_int @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4047_finite__imageD,axiom,
% 0.14/0.49 ! [F: nat > rat,A4: set_nat] :
% 0.14/0.49 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4048_finite__imageD,axiom,
% 0.14/0.49 ! [F: nat > int,A4: set_nat] :
% 0.14/0.49 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4049_finite__imageD,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 0.14/0.49 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4050_finite__imageD,axiom,
% 0.14/0.49 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4051_finite__imageD,axiom,
% 0.14/0.49 ! [F: int > nat,A4: set_int] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.49 => ( finite_finite_int @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4052_finite__imageD,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 0.14/0.49 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4053_finite__imageD,axiom,
% 0.14/0.49 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.49 => ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_imageD
% 0.14/0.49 thf(fact_4054_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: char > nat,F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_char_nat @ G @ top_top_set_char ) )
% 0.14/0.49 => ( finite_finite_nat
% 0.14/0.49 @ ( image_char_nat
% 0.14/0.49 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_char ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4055_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: rat > nat,F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_rat_nat @ G @ top_top_set_rat ) )
% 0.14/0.49 => ( finite_finite_nat
% 0.14/0.49 @ ( image_rat_nat
% 0.14/0.49 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_rat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4056_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > rat,F: rat > rat] :
% 0.14/0.49 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_rat
% 0.14/0.49 @ ( image_nat_rat
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4057_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > rat,F: rat > int] :
% 0.14/0.49 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_int
% 0.14/0.49 @ ( image_nat_int
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4058_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > int,F: int > rat] :
% 0.14/0.49 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_rat
% 0.14/0.49 @ ( image_nat_rat
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4059_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > int,F: int > int] :
% 0.14/0.49 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_int
% 0.14/0.49 @ ( image_nat_int
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4060_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > rat,F: rat > nat] :
% 0.14/0.49 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_nat
% 0.14/0.49 @ ( image_nat_nat
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4061_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > int,F: int > nat] :
% 0.14/0.49 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_nat
% 0.14/0.49 @ ( image_nat_nat
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4062_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > nat,F: nat > rat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_rat
% 0.14/0.49 @ ( image_nat_rat
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4063_finite__range__imageI,axiom,
% 0.14/0.49 ! [G: nat > nat,F: nat > int] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.14/0.49 => ( finite_finite_int
% 0.14/0.49 @ ( image_nat_int
% 0.14/0.49 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.14/0.49 @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_range_imageI
% 0.14/0.49 thf(fact_4064_Id__fstsnd__eq,axiom,
% 0.14/0.49 ( id_Pro2258643101195443293at_nat
% 0.14/0.49 = ( collec7088162979684241874at_nat
% 0.14/0.49 @ ^ [X4: produc859450856879609959at_nat] :
% 0.14/0.49 ( ( produc3213797794245857475at_nat @ X4 )
% 0.14/0.49 = ( produc6408287024330202629at_nat @ X4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Id_fstsnd_eq
% 0.14/0.49 thf(fact_4065_Id__fstsnd__eq,axiom,
% 0.14/0.49 ( id_nat2
% 0.14/0.49 = ( collec3392354462482085612at_nat
% 0.14/0.49 @ ^ [X4: product_prod_nat_nat] :
% 0.14/0.49 ( ( product_fst_nat_nat @ X4 )
% 0.14/0.49 = ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Id_fstsnd_eq
% 0.14/0.49 thf(fact_4066_Id__fstsnd__eq,axiom,
% 0.14/0.49 ( id_int2
% 0.14/0.49 = ( collec213857154873943460nt_int
% 0.14/0.49 @ ^ [X4: product_prod_int_int] :
% 0.14/0.49 ( ( product_fst_int_int @ X4 )
% 0.14/0.49 = ( product_snd_int_int @ X4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Id_fstsnd_eq
% 0.14/0.49 thf(fact_4067_finite__surj__inj,axiom,
% 0.14/0.49 ! [A4: set_int,F: int > int] :
% 0.14/0.49 ( ( finite_finite_int @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_int @ A4 @ ( image_int_int @ F @ A4 ) )
% 0.14/0.49 => ( inj_on_int_int @ F @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_surj_inj
% 0.14/0.49 thf(fact_4068_finite__surj__inj,axiom,
% 0.14/0.49 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.49 => ( inj_on8969904277767023793at_nat @ F @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_surj_inj
% 0.14/0.49 thf(fact_4069_finite__surj__inj,axiom,
% 0.14/0.49 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_nat @ A4 @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.49 => ( inj_on_nat_nat @ F @ A4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_surj_inj
% 0.14/0.49 thf(fact_4070_inj__on__finite,axiom,
% 0.14/0.49 ! [F: int > int,A4: set_int,B5: set_int] :
% 0.14/0.49 ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_int @ B5 )
% 0.14/0.49 => ( finite_finite_int @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4071_inj__on__finite,axiom,
% 0.14/0.49 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 0.14/0.49 ( ( inj_on_nat_rat @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_rat @ B5 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4072_inj__on__finite,axiom,
% 0.14/0.49 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 0.14/0.49 ( ( inj_on_nat_int @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_int @ B5 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4073_inj__on__finite,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 0.14/0.49 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.49 => ( finite6177210948735845034at_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4074_inj__on__finite,axiom,
% 0.14/0.49 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 0.14/0.49 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4075_inj__on__finite,axiom,
% 0.14/0.49 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 0.14/0.49 ( ( inj_on_int_nat @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_nat @ B5 )
% 0.14/0.49 => ( finite_finite_int @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4076_inj__on__finite,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 0.14/0.49 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_nat @ B5 )
% 0.14/0.49 => ( finite6177210948735845034at_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4077_inj__on__finite,axiom,
% 0.14/0.49 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 0.14/0.49 ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 0.14/0.49 => ( ( finite_finite_nat @ B5 )
% 0.14/0.49 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inj_on_finite
% 0.14/0.49 thf(fact_4078_endo__inj__surj,axiom,
% 0.14/0.49 ! [A4: set_int,F: int > int] :
% 0.14/0.49 ( ( finite_finite_int @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ A4 )
% 0.14/0.49 => ( ( inj_on_int_int @ F @ A4 )
% 0.14/0.49 => ( ( image_int_int @ F @ A4 )
% 0.14/0.49 = A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % endo_inj_surj
% 0.14/0.49 thf(fact_4079_endo__inj__surj,axiom,
% 0.14/0.49 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ A4 )
% 0.14/0.49 => ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 0.14/0.49 => ( ( image_5168914502847457605at_nat @ F @ A4 )
% 0.14/0.49 = A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % endo_inj_surj
% 0.14/0.49 thf(fact_4080_endo__inj__surj,axiom,
% 0.14/0.49 ! [A4: set_nat,F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ A4 )
% 0.14/0.49 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ A4 )
% 0.14/0.49 => ( ( inj_on_nat_nat @ F @ A4 )
% 0.14/0.49 => ( ( image_nat_nat @ F @ A4 )
% 0.14/0.49 = A4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % endo_inj_surj
% 0.14/0.49 thf(fact_4081_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 0.14/0.49 => ( ( ( image_5168914502847457605at_nat @ F @ top_to4669805908274784177at_nat )
% 0.14/0.49 = top_to4669805908274784177at_nat )
% 0.14/0.49 => ( inj_on8969904277767023793at_nat @ F @ top_to4669805908274784177at_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4082_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: char > char] :
% 0.14/0.49 ( ( finite_finite_char @ top_top_set_char )
% 0.14/0.49 => ( ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.49 = top_top_set_char )
% 0.14/0.49 => ( inj_on_char_char @ F @ top_top_set_char ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4083_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: list_nat > list_nat] :
% 0.14/0.49 ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 0.14/0.49 => ( ( ( image_7976474329151083847st_nat @ F @ top_top_set_list_nat )
% 0.14/0.49 = top_top_set_list_nat )
% 0.14/0.49 => ( inj_on3049792774292151987st_nat @ F @ top_top_set_list_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4084_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: rat > rat] :
% 0.14/0.49 ( ( finite_finite_rat @ top_top_set_rat )
% 0.14/0.49 => ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.49 = top_top_set_rat )
% 0.14/0.49 => ( inj_on_rat_rat @ F @ top_top_set_rat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4085_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ top_top_set_nat )
% 0.14/0.49 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.14/0.49 = top_top_set_nat )
% 0.14/0.49 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4086_finite__UNIV__surj__inj,axiom,
% 0.14/0.49 ! [F: int > int] :
% 0.14/0.49 ( ( finite_finite_int @ top_top_set_int )
% 0.14/0.49 => ( ( ( image_int_int @ F @ top_top_set_int )
% 0.14/0.49 = top_top_set_int )
% 0.14/0.49 => ( inj_on_int_int @ F @ top_top_set_int ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_surj_inj
% 0.14/0.49 thf(fact_4087_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 0.14/0.49 => ( ( inj_on8969904277767023793at_nat @ F @ top_to4669805908274784177at_nat )
% 0.14/0.49 => ( ( image_5168914502847457605at_nat @ F @ top_to4669805908274784177at_nat )
% 0.14/0.49 = top_to4669805908274784177at_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4088_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: char > char] :
% 0.14/0.49 ( ( finite_finite_char @ top_top_set_char )
% 0.14/0.49 => ( ( inj_on_char_char @ F @ top_top_set_char )
% 0.14/0.49 => ( ( image_char_char @ F @ top_top_set_char )
% 0.14/0.49 = top_top_set_char ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4089_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: list_nat > list_nat] :
% 0.14/0.49 ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 0.14/0.49 => ( ( inj_on3049792774292151987st_nat @ F @ top_top_set_list_nat )
% 0.14/0.49 => ( ( image_7976474329151083847st_nat @ F @ top_top_set_list_nat )
% 0.14/0.49 = top_top_set_list_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4090_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: rat > rat] :
% 0.14/0.49 ( ( finite_finite_rat @ top_top_set_rat )
% 0.14/0.49 => ( ( inj_on_rat_rat @ F @ top_top_set_rat )
% 0.14/0.49 => ( ( image_rat_rat @ F @ top_top_set_rat )
% 0.14/0.49 = top_top_set_rat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4091_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: nat > nat] :
% 0.14/0.49 ( ( finite_finite_nat @ top_top_set_nat )
% 0.14/0.49 => ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.14/0.49 => ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.14/0.49 = top_top_set_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4092_finite__UNIV__inj__surj,axiom,
% 0.14/0.49 ! [F: int > int] :
% 0.14/0.49 ( ( finite_finite_int @ top_top_set_int )
% 0.14/0.49 => ( ( inj_on_int_int @ F @ top_top_set_int )
% 0.14/0.49 => ( ( image_int_int @ F @ top_top_set_int )
% 0.14/0.49 = top_top_set_int ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_UNIV_inj_surj
% 0.14/0.49 thf(fact_4093_finite__vimageD,axiom,
% 0.14/0.49 ! [H: char > char,F4: set_char] :
% 0.14/0.49 ( ( finite_finite_char @ ( vimage_char_char @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_char_char @ H @ top_top_set_char )
% 0.14/0.49 = top_top_set_char )
% 0.14/0.49 => ( finite_finite_char @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4094_finite__vimageD,axiom,
% 0.14/0.49 ! [H: char > rat,F4: set_rat] :
% 0.14/0.49 ( ( finite_finite_char @ ( vimage_char_rat @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_char_rat @ H @ top_top_set_char )
% 0.14/0.49 = top_top_set_rat )
% 0.14/0.49 => ( finite_finite_rat @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4095_finite__vimageD,axiom,
% 0.14/0.49 ! [H: char > nat,F4: set_nat] :
% 0.14/0.49 ( ( finite_finite_char @ ( vimage_char_nat @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_char_nat @ H @ top_top_set_char )
% 0.14/0.49 = top_top_set_nat )
% 0.14/0.49 => ( finite_finite_nat @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4096_finite__vimageD,axiom,
% 0.14/0.49 ! [H: char > int,F4: set_int] :
% 0.14/0.49 ( ( finite_finite_char @ ( vimage_char_int @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_char_int @ H @ top_top_set_char )
% 0.14/0.49 = top_top_set_int )
% 0.14/0.49 => ( finite_finite_int @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4097_finite__vimageD,axiom,
% 0.14/0.49 ! [H: rat > char,F4: set_char] :
% 0.14/0.49 ( ( finite_finite_rat @ ( vimage_rat_char @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_rat_char @ H @ top_top_set_rat )
% 0.14/0.49 = top_top_set_char )
% 0.14/0.49 => ( finite_finite_char @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4098_finite__vimageD,axiom,
% 0.14/0.49 ! [H: rat > rat,F4: set_rat] :
% 0.14/0.49 ( ( finite_finite_rat @ ( vimage_rat_rat @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_rat_rat @ H @ top_top_set_rat )
% 0.14/0.49 = top_top_set_rat )
% 0.14/0.49 => ( finite_finite_rat @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4099_finite__vimageD,axiom,
% 0.14/0.49 ! [H: rat > nat,F4: set_nat] :
% 0.14/0.49 ( ( finite_finite_rat @ ( vimage_rat_nat @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_rat_nat @ H @ top_top_set_rat )
% 0.14/0.49 = top_top_set_nat )
% 0.14/0.49 => ( finite_finite_nat @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4100_finite__vimageD,axiom,
% 0.14/0.49 ! [H: rat > int,F4: set_int] :
% 0.14/0.49 ( ( finite_finite_rat @ ( vimage_rat_int @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_rat_int @ H @ top_top_set_rat )
% 0.14/0.49 = top_top_set_int )
% 0.14/0.49 => ( finite_finite_int @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4101_finite__vimageD,axiom,
% 0.14/0.49 ! [H: nat > char,F4: set_char] :
% 0.14/0.49 ( ( finite_finite_nat @ ( vimage_nat_char @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_nat_char @ H @ top_top_set_nat )
% 0.14/0.49 = top_top_set_char )
% 0.14/0.49 => ( finite_finite_char @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4102_finite__vimageD,axiom,
% 0.14/0.49 ! [H: nat > rat,F4: set_rat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( vimage_nat_rat @ H @ F4 ) )
% 0.14/0.49 => ( ( ( image_nat_rat @ H @ top_top_set_nat )
% 0.14/0.49 = top_top_set_rat )
% 0.14/0.49 => ( finite_finite_rat @ F4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % finite_vimageD
% 0.14/0.49 thf(fact_4103_prod__set__defs_I2_J,axiom,
% 0.14/0.49 ( basic_1496934909540232809t_unit
% 0.14/0.49 = ( ^ [P3: produc7812382424243267045t_unit] : ( insert8563697753282147485t_unit @ ( produc1126150082675451753t_unit @ P3 ) @ bot_bo3686245532977126937t_unit ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % prod_set_defs(2)
% 0.14/0.49 thf(fact_4104_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: nat > product_unit,A4: set_nat] :
% 0.14/0.49 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.49 => ? [X: product_unit] :
% 0.14/0.49 ( ( member_Product_unit @ X @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4105_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: nat > $o,A4: set_nat] :
% 0.14/0.49 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.49 => ? [X: $o] :
% 0.14/0.49 ( ( member_o @ X @ ( image_nat_o @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_nat @ ( vimage_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4106_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: int > nat,A4: set_int] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_int @ A4 )
% 0.14/0.49 => ? [X: nat] :
% 0.14/0.49 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_int @ ( vimage_int_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4107_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: nat > nat,A4: set_nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.49 => ? [X: nat] :
% 0.14/0.49 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4108_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ? [X: product_unit] :
% 0.14/0.49 ( ( member_Product_unit @ X @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite6177210948735845034at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4109_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.49 => ? [X: product_prod_nat_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ X @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4110_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > $o,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite_finite_o @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ? [X: $o] :
% 0.14/0.49 ( ( member_o @ X @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite6177210948735845034at_nat @ ( vimage2444243245536687506_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4111_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ? [X: nat] :
% 0.14/0.49 ( ( member_nat @ X @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite6177210948735845034at_nat @ ( vimage4653281326611754070at_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4112_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 0.14/0.49 => ? [X: product_prod_nat_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ X @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite6177210948735845034at_nat @ ( vimage2449269961533847803at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4113_inf__img__fin__dom,axiom,
% 0.14/0.49 ! [F: nat > produc3843707927480180839at_nat,A4: set_nat] :
% 0.14/0.49 ( ( finite4343798906461161616at_nat @ ( image_2499013659892586576at_nat @ F @ A4 ) )
% 0.14/0.49 => ( ~ ( finite_finite_nat @ A4 )
% 0.14/0.49 => ? [X: produc3843707927480180839at_nat] :
% 0.14/0.49 ( ( member8757157785044589968at_nat @ X @ ( image_2499013659892586576at_nat @ F @ A4 ) )
% 0.14/0.49 & ~ ( finite_finite_nat @ ( vimage6435164912253009178at_nat @ F @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_img_fin_dom
% 0.14/0.49 thf(fact_4114_nat__descend__induct,axiom,
% 0.14/0.49 ! [N3: nat,P2: nat > $o,M3: nat] :
% 0.14/0.49 ( ! [K2: nat] :
% 0.14/0.49 ( ( ord_less_nat @ N3 @ K2 )
% 0.14/0.49 => ( P2 @ K2 ) )
% 0.14/0.49 => ( ! [K2: nat] :
% 0.14/0.49 ( ( ord_less_eq_nat @ K2 @ N3 )
% 0.14/0.49 => ( ! [I5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ K2 @ I5 )
% 0.14/0.49 => ( P2 @ I5 ) )
% 0.14/0.49 => ( P2 @ K2 ) ) )
% 0.14/0.49 => ( P2 @ M3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat_descend_induct
% 0.14/0.49 thf(fact_4115_Field__natLeq__on,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( field_nat
% 0.14/0.49 @ ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 0.14/0.49 = ( collect_nat
% 0.14/0.49 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Field_natLeq_on
% 0.14/0.49 thf(fact_4116_natLeq__on__well__order__on,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( order_2888998067076097458on_nat
% 0.14/0.49 @ ( collect_nat
% 0.14/0.49 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) )
% 0.14/0.49 @ ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % natLeq_on_well_order_on
% 0.14/0.49 thf(fact_4117_natLeq__on__Well__order,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( order_2888998067076097458on_nat
% 0.14/0.49 @ ( field_nat
% 0.14/0.49 @ ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 0.14/0.49 @ ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % natLeq_on_Well_order
% 0.14/0.49 thf(fact_4118_natLeq__on__wo__rel,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( bNF_We3818239936649020644el_nat
% 0.14/0.49 @ ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % natLeq_on_wo_rel
% 0.14/0.49 thf(fact_4119_wf__less,axiom,
% 0.14/0.49 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.14/0.49
% 0.14/0.49 % wf_less
% 0.14/0.49 thf(fact_4120_natLess__def,axiom,
% 0.14/0.49 ( bNF_Ca8459412986667044542atLess
% 0.14/0.49 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % natLess_def
% 0.14/0.49 thf(fact_4121_card_Ocomp__fun__commute__on,axiom,
% 0.14/0.49 ( ( comp_nat_nat_nat @ suc @ suc )
% 0.14/0.49 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.14/0.49
% 0.14/0.49 % card.comp_fun_commute_on
% 0.14/0.49 thf(fact_4122_pred__nat__def,axiom,
% 0.14/0.49 ( pred_nat
% 0.14/0.49 = ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [M5: nat,N4: nat] :
% 0.14/0.49 ( N4
% 0.14/0.49 = ( suc @ M5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % pred_nat_def
% 0.14/0.49 thf(fact_4123_zero__notin__Suc__image,axiom,
% 0.14/0.49 ! [A4: set_nat] :
% 0.14/0.49 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 0.14/0.49
% 0.14/0.49 % zero_notin_Suc_image
% 0.14/0.49 thf(fact_4124_Restr__natLeq2,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.14/0.49 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N3 )
% 0.14/0.49 @ ^ [Uu: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N3 ) ) )
% 0.14/0.49 = ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Restr_natLeq2
% 0.14/0.49 thf(fact_4125_Restr__natLeq,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.14/0.49 @ ( produc457027306803732586at_nat
% 0.14/0.49 @ ( collect_nat
% 0.14/0.49 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) )
% 0.14/0.49 @ ^ [Uu: nat] :
% 0.14/0.49 ( collect_nat
% 0.14/0.49 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) ) ) )
% 0.14/0.49 = ( collec3392354462482085612at_nat
% 0.14/0.49 @ ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( ( ord_less_nat @ X4 @ N3 )
% 0.14/0.49 & ( ord_less_nat @ Y5 @ N3 )
% 0.14/0.49 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Restr_natLeq
% 0.14/0.49 thf(fact_4126_natLeq__def,axiom,
% 0.14/0.49 ( bNF_Ca8665028551170535155natLeq
% 0.14/0.49 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % natLeq_def
% 0.14/0.49 thf(fact_4127_rat__denum,axiom,
% 0.14/0.49 ? [F5: nat > rat] :
% 0.14/0.49 ( ( image_nat_rat @ F5 @ top_top_set_nat )
% 0.14/0.49 = top_top_set_rat ) ).
% 0.14/0.49
% 0.14/0.49 % rat_denum
% 0.14/0.49 thf(fact_4128_greaterThan__0,axiom,
% 0.14/0.49 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.14/0.49 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.14/0.49
% 0.14/0.49 % greaterThan_0
% 0.14/0.49 thf(fact_4129_image__Suc__atLeastLessThan,axiom,
% 0.14/0.49 ! [I: nat,J4: nat] :
% 0.14/0.49 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J4 ) )
% 0.14/0.49 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_Suc_atLeastLessThan
% 0.14/0.49 thf(fact_4130_INT__greaterThan__UNIV,axiom,
% 0.14/0.49 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.14/0.49 = bot_bot_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % INT_greaterThan_UNIV
% 0.14/0.49 thf(fact_4131_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N3 ) )
% 0.14/0.49 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % atLeast0_lessThan_Suc_eq_insert_0
% 0.14/0.49 thf(fact_4132_image__minus__const__atLeastLessThan__nat,axiom,
% 0.14/0.49 ! [C: nat,Y3: nat,X2: nat] :
% 0.14/0.49 ( ( ( ord_less_nat @ C @ Y3 )
% 0.14/0.49 => ( ( image_nat_nat
% 0.14/0.49 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.14/0.49 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 0.14/0.49 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 0.14/0.49 & ( ~ ( ord_less_nat @ C @ Y3 )
% 0.14/0.49 => ( ( ( ord_less_nat @ X2 @ Y3 )
% 0.14/0.49 => ( ( image_nat_nat
% 0.14/0.49 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.14/0.49 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 0.14/0.49 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.14/0.49 & ( ~ ( ord_less_nat @ X2 @ Y3 )
% 0.14/0.49 => ( ( image_nat_nat
% 0.14/0.49 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.14/0.49 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 0.14/0.49 = bot_bot_set_nat ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_minus_const_atLeastLessThan_nat
% 0.14/0.49 thf(fact_4133_surj__nat__to__rat__surj,axiom,
% 0.14/0.49 ( ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat )
% 0.14/0.49 = top_top_set_rat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_nat_to_rat_surj
% 0.14/0.49 thf(fact_4134_range__mod,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.14/0.49 => ( ( image_nat_nat
% 0.14/0.49 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N3 )
% 0.14/0.49 @ top_top_set_nat )
% 0.14/0.49 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % range_mod
% 0.14/0.49 thf(fact_4135_divmod__nat__if,axiom,
% 0.14/0.49 ( divmod_nat
% 0.14/0.49 = ( ^ [M5: nat,N4: nat] :
% 0.14/0.49 ( if_Pro6206227464963214023at_nat
% 0.14/0.49 @ ( ( N4 = zero_zero_nat )
% 0.14/0.49 | ( ord_less_nat @ M5 @ N4 ) )
% 0.14/0.49 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [Q3: nat] : ( product_Pair_nat_nat @ ( suc @ Q3 ) )
% 0.14/0.49 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_nat_if
% 0.14/0.49 thf(fact_4136_Rats__eq__range__nat__to__rat__surj,axiom,
% 0.14/0.49 ( field_6020823756834552118ts_rat
% 0.14/0.49 = ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat ) ) ).
% 0.14/0.49
% 0.14/0.49 % Rats_eq_range_nat_to_rat_surj
% 0.14/0.49 thf(fact_4137_image__Suc__atLeastAtMost,axiom,
% 0.14/0.49 ! [I: nat,J4: nat] :
% 0.14/0.49 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J4 ) )
% 0.14/0.49 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_Suc_atLeastAtMost
% 0.14/0.49 thf(fact_4138_UN__atMost__UNIV,axiom,
% 0.14/0.49 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % UN_atMost_UNIV
% 0.14/0.49 thf(fact_4139_atMost__Suc__eq__insert__0,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( set_ord_atMost_nat @ ( suc @ N3 ) )
% 0.14/0.49 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % atMost_Suc_eq_insert_0
% 0.14/0.49 thf(fact_4140_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N3 ) )
% 0.14/0.49 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % atLeast0_atMost_Suc_eq_insert_0
% 0.14/0.49 thf(fact_4141_image__Suc__lessThan,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N3 ) )
% 0.14/0.49 = ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_Suc_lessThan
% 0.14/0.49 thf(fact_4142_UN__lessThan__UNIV,axiom,
% 0.14/0.49 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % UN_lessThan_UNIV
% 0.14/0.49 thf(fact_4143_lessThan__Suc__eq__insert__0,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( set_ord_lessThan_nat @ ( suc @ N3 ) )
% 0.14/0.49 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % lessThan_Suc_eq_insert_0
% 0.14/0.49 thf(fact_4144_image__Suc__atMost,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N3 ) )
% 0.14/0.49 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_Suc_atMost
% 0.14/0.49 thf(fact_4145_image__int__atLeastAtMost,axiom,
% 0.14/0.49 ! [A: nat,B: nat] :
% 0.14/0.49 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.14/0.49 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_int_atLeastAtMost
% 0.14/0.49 thf(fact_4146_image__int__atLeastLessThan,axiom,
% 0.14/0.49 ! [A: nat,B: nat] :
% 0.14/0.49 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.14/0.49 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_int_atLeastLessThan
% 0.14/0.49 thf(fact_4147_image__add__int__atLeastLessThan,axiom,
% 0.14/0.49 ! [L: int,U: int] :
% 0.14/0.49 ( ( image_int_int
% 0.14/0.49 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 0.14/0.49 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.14/0.49 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_add_int_atLeastLessThan
% 0.14/0.49 thf(fact_4148_pair__lessI2,axiom,
% 0.14/0.49 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 0.14/0.49 ( ( ord_less_eq_nat @ A @ B )
% 0.14/0.49 => ( ( ord_less_nat @ S2 @ T2 )
% 0.14/0.49 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_less ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_lessI2
% 0.14/0.49 thf(fact_4149_pair__less__iff1,axiom,
% 0.14/0.49 ! [X2: nat,Y3: nat,Z2: nat] :
% 0.14/0.49 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( product_Pair_nat_nat @ X2 @ Z2 ) ) @ fun_pair_less )
% 0.14/0.49 = ( ord_less_nat @ Y3 @ Z2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_less_iff1
% 0.14/0.49 thf(fact_4150_total__pair__less,axiom,
% 0.14/0.49 ! [A4: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A4 @ fun_pair_less ) ).
% 0.14/0.49
% 0.14/0.49 % total_pair_less
% 0.14/0.49 thf(fact_4151_Inf__int__def,axiom,
% 0.14/0.49 ( complete_Inf_Inf_int
% 0.14/0.49 = ( ^ [X9: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X9 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Inf_int_def
% 0.14/0.49 thf(fact_4152_wf__pair__less,axiom,
% 0.14/0.49 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 0.14/0.49
% 0.14/0.49 % wf_pair_less
% 0.14/0.49 thf(fact_4153_pair__lessI1,axiom,
% 0.14/0.49 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 0.14/0.49 ( ( ord_less_nat @ A @ B )
% 0.14/0.49 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_less ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_lessI1
% 0.14/0.49 thf(fact_4154_bij__betw__Suc,axiom,
% 0.14/0.49 ! [M: set_nat,N: set_nat] :
% 0.14/0.49 ( ( bij_betw_nat_nat @ suc @ M @ N )
% 0.14/0.49 = ( ( image_nat_nat @ suc @ M )
% 0.14/0.49 = N ) ) ).
% 0.14/0.49
% 0.14/0.49 % bij_betw_Suc
% 0.14/0.49 thf(fact_4155_pair__leqI2,axiom,
% 0.14/0.49 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 0.14/0.49 ( ( ord_less_eq_nat @ A @ B )
% 0.14/0.49 => ( ( ord_less_eq_nat @ S2 @ T2 )
% 0.14/0.49 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_leq ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_leqI2
% 0.14/0.49 thf(fact_4156_pair__leqI1,axiom,
% 0.14/0.49 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 0.14/0.49 ( ( ord_less_nat @ A @ B )
% 0.14/0.49 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_leq ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_leqI1
% 0.14/0.49 thf(fact_4157_pair__leq__def,axiom,
% 0.14/0.49 ( fun_pair_leq
% 0.14/0.49 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_leq_def
% 0.14/0.49 thf(fact_4158_wmax__insertI,axiom,
% 0.14/0.49 ! [Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ Y3 @ YS )
% 0.14/0.49 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 0.14/0.49 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % wmax_insertI
% 0.14/0.49 thf(fact_4159_wmin__insertI,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 0.14/0.49 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 0.14/0.49 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % wmin_insertI
% 0.14/0.49 thf(fact_4160_smax__insertI,axiom,
% 0.14/0.49 ! [Y3: product_prod_nat_nat,Y4: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,X5: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ Y3 @ Y4 )
% 0.14/0.49 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 0.14/0.49 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ Y4 ) @ fun_max_strict )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ X5 ) @ Y4 ) @ fun_max_strict ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % smax_insertI
% 0.14/0.49 thf(fact_4161_smin__insertI,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 0.14/0.49 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 0.14/0.49 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % smin_insertI
% 0.14/0.49 thf(fact_4162_max__rpair__set,axiom,
% 0.14/0.49 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 0.14/0.49
% 0.14/0.49 % max_rpair_set
% 0.14/0.49 thf(fact_4163_min__rpair__set,axiom,
% 0.14/0.49 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 0.14/0.49
% 0.14/0.49 % min_rpair_set
% 0.14/0.49 thf(fact_4164_wmax__emptyI,axiom,
% 0.14/0.49 ! [X5: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ X5 )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X5 ) @ fun_max_weak ) ) ).
% 0.14/0.49
% 0.14/0.49 % wmax_emptyI
% 0.14/0.49 thf(fact_4165_smax__emptyI,axiom,
% 0.14/0.49 ! [Y4: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( finite6177210948735845034at_nat @ Y4 )
% 0.14/0.49 => ( ( Y4 != bot_bo2099793752762293965at_nat )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y4 ) @ fun_max_strict ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % smax_emptyI
% 0.14/0.49 thf(fact_4166_smin__emptyI,axiom,
% 0.14/0.49 ! [X5: set_Pr1261947904930325089at_nat] :
% 0.14/0.49 ( ( X5 != bot_bo2099793752762293965at_nat )
% 0.14/0.49 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 0.14/0.49
% 0.14/0.49 % smin_emptyI
% 0.14/0.49 thf(fact_4167_wmin__emptyI,axiom,
% 0.14/0.49 ! [X5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 0.14/0.49
% 0.14/0.49 % wmin_emptyI
% 0.14/0.49 thf(fact_4168_max__strict__def,axiom,
% 0.14/0.49 ( fun_max_strict
% 0.14/0.49 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 0.14/0.49
% 0.14/0.49 % max_strict_def
% 0.14/0.49 thf(fact_4169_min__strict__def,axiom,
% 0.14/0.49 ( fun_min_strict
% 0.14/0.49 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 0.14/0.49
% 0.14/0.49 % min_strict_def
% 0.14/0.49 thf(fact_4170_min__weak__def,axiom,
% 0.14/0.49 ( fun_min_weak
% 0.14/0.49 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % min_weak_def
% 0.14/0.49 thf(fact_4171_max__weak__def,axiom,
% 0.14/0.49 ( fun_max_weak
% 0.14/0.49 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % max_weak_def
% 0.14/0.49 thf(fact_4172_image__atLeastZeroLessThan__int,axiom,
% 0.14/0.49 ! [U: int] :
% 0.14/0.49 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.14/0.49 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.14/0.49 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % image_atLeastZeroLessThan_int
% 0.14/0.49 thf(fact_4173_UN__atLeast__UNIV,axiom,
% 0.14/0.49 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % UN_atLeast_UNIV
% 0.14/0.49 thf(fact_4174_trans__pair__less,axiom,
% 0.14/0.49 trans_4347625901269045472at_nat @ fun_pair_less ).
% 0.14/0.49
% 0.14/0.49 % trans_pair_less
% 0.14/0.49 thf(fact_4175_less__eq__int_Orep__eq,axiom,
% 0.14/0.49 ( ord_less_eq_int
% 0.14/0.49 = ( ^ [X4: int,Xa3: int] :
% 0.14/0.49 ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [Y5: nat,Z4: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V3 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 0.14/0.49 @ ( rep_Integ @ X4 )
% 0.14/0.49 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_eq_int.rep_eq
% 0.14/0.49 thf(fact_4176_nat_Orep__eq,axiom,
% 0.14/0.49 ( nat2
% 0.14/0.49 = ( ^ [X4: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat.rep_eq
% 0.14/0.49 thf(fact_4177_less__int_Orep__eq,axiom,
% 0.14/0.49 ( ord_less_int
% 0.14/0.49 = ( ^ [X4: int,Xa3: int] :
% 0.14/0.49 ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [Y5: nat,Z4: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V3 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 0.14/0.49 @ ( rep_Integ @ X4 )
% 0.14/0.49 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_int.rep_eq
% 0.14/0.49 thf(fact_4178_less__eq__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re717283939379294677_int_o @ pcr_int
% 0.14/0.49 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.14/0.49 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 0.14/0.49 @ ord_less_eq_int ) ).
% 0.14/0.49
% 0.14/0.49 % less_eq_int.transfer
% 0.14/0.49 thf(fact_4179_less__eq__int_Oabs__eq,axiom,
% 0.14/0.49 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) )
% 0.14/0.49 @ Xa2
% 0.14/0.49 @ X2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_eq_int.abs_eq
% 0.14/0.49 thf(fact_4180_int__ge__less__than2__def,axiom,
% 0.14/0.49 ( int_ge_less_than2
% 0.14/0.49 = ( ^ [D3: int] :
% 0.14/0.49 ( collec213857154873943460nt_int
% 0.14/0.49 @ ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [Z6: int,Z4: int] :
% 0.14/0.49 ( ( ord_less_eq_int @ D3 @ Z4 )
% 0.14/0.49 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % int_ge_less_than2_def
% 0.14/0.49 thf(fact_4181_int__ge__less__than__def,axiom,
% 0.14/0.49 ( int_ge_less_than
% 0.14/0.49 = ( ^ [D3: int] :
% 0.14/0.49 ( collec213857154873943460nt_int
% 0.14/0.49 @ ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [Z6: int,Z4: int] :
% 0.14/0.49 ( ( ord_less_eq_int @ D3 @ Z6 )
% 0.14/0.49 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % int_ge_less_than_def
% 0.14/0.49 thf(fact_4182_less__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re717283939379294677_int_o @ pcr_int
% 0.14/0.49 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.14/0.49 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 0.14/0.49 @ ord_less_int ) ).
% 0.14/0.49
% 0.14/0.49 % less_int.transfer
% 0.14/0.49 thf(fact_4183_minus__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) )
% 0.14/0.49 @ minus_minus_int ) ).
% 0.14/0.49
% 0.14/0.49 % minus_int.transfer
% 0.14/0.49 thf(fact_4184_plus__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) )
% 0.14/0.49 @ plus_plus_int ) ).
% 0.14/0.49
% 0.14/0.49 % plus_int.transfer
% 0.14/0.49 thf(fact_4185_nat_Oabs__eq,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( nat2 @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat.abs_eq
% 0.14/0.49 thf(fact_4186_nat_Otransfer,axiom,
% 0.14/0.49 ( bNF_re4555766996558763186at_nat @ pcr_int
% 0.14/0.49 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.49 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.14/0.49 @ nat2 ) ).
% 0.14/0.49
% 0.14/0.49 % nat.transfer
% 0.14/0.49 thf(fact_4187_uminus__int_Oabs__eq,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( abs_Integ
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 )
% 0.14/0.49 @ X2 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % uminus_int.abs_eq
% 0.14/0.49 thf(fact_4188_uminus__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 0.14/0.49 @ uminus_uminus_int ) ).
% 0.14/0.49
% 0.14/0.49 % uminus_int.transfer
% 0.14/0.49 thf(fact_4189_times__int_Oabs__eq,axiom,
% 0.14/0.49 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( abs_Integ
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) )
% 0.14/0.49 @ Xa2
% 0.14/0.49 @ X2 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % times_int.abs_eq
% 0.14/0.49 thf(fact_4190_plus__int_Oabs__eq,axiom,
% 0.14/0.49 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( abs_Integ
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) )
% 0.14/0.49 @ Xa2
% 0.14/0.49 @ X2 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % plus_int.abs_eq
% 0.14/0.49 thf(fact_4191_minus__int_Oabs__eq,axiom,
% 0.14/0.49 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( abs_Integ
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) )
% 0.14/0.49 @ Xa2
% 0.14/0.49 @ X2 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % minus_int.abs_eq
% 0.14/0.49 thf(fact_4192_times__int_Otransfer,axiom,
% 0.14/0.49 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) )
% 0.14/0.49 @ times_times_int ) ).
% 0.14/0.49
% 0.14/0.49 % times_int.transfer
% 0.14/0.49 thf(fact_4193_less__int_Oabs__eq,axiom,
% 0.14/0.49 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.14/0.49 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 0.14/0.49 = ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) )
% 0.14/0.49 @ Xa2
% 0.14/0.49 @ X2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_int.abs_eq
% 0.14/0.49 thf(fact_4194_uminus__int__def,axiom,
% 0.14/0.49 ( uminus_uminus_int
% 0.14/0.49 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % uminus_int_def
% 0.14/0.49 thf(fact_4195_times__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % times_int.rsp
% 0.14/0.49 thf(fact_4196_nat__def,axiom,
% 0.14/0.49 ( nat2
% 0.14/0.49 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat_def
% 0.14/0.49 thf(fact_4197_minus__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % minus_int.rsp
% 0.14/0.49 thf(fact_4198_plus__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % plus_int.rsp
% 0.14/0.49 thf(fact_4199_less__eq__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re4202695980764964119_nat_o @ intrel
% 0.14/0.49 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.14/0.49 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_eq_int.rsp
% 0.14/0.49 thf(fact_4200_uminus__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 0.14/0.49 @ ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % uminus_int.rsp
% 0.14/0.49 thf(fact_4201_nat_Orsp,axiom,
% 0.14/0.49 ( bNF_re8246922863344978751at_nat @ intrel
% 0.14/0.49 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.49 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.14/0.49 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat.rsp
% 0.14/0.49 thf(fact_4202_intrel__def,axiom,
% 0.14/0.49 ( intrel
% 0.14/0.49 = ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] :
% 0.14/0.49 ( ( plus_plus_nat @ X4 @ V3 )
% 0.14/0.49 = ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % intrel_def
% 0.14/0.49 thf(fact_4203_less__int_Orsp,axiom,
% 0.14/0.49 ( bNF_re4202695980764964119_nat_o @ intrel
% 0.14/0.49 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.14/0.49 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_int.rsp
% 0.14/0.49 thf(fact_4204_times__int__def,axiom,
% 0.14/0.49 ( times_times_int
% 0.14/0.49 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % times_int_def
% 0.14/0.49 thf(fact_4205_minus__int__def,axiom,
% 0.14/0.49 ( minus_minus_int
% 0.14/0.49 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % minus_int_def
% 0.14/0.49 thf(fact_4206_plus__int__def,axiom,
% 0.14/0.49 ( plus_plus_int
% 0.14/0.49 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.14/0.49 @ ( produc27273713700761075at_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % plus_int_def
% 0.14/0.49 thf(fact_4207_rat__less__code,axiom,
% 0.14/0.49 ( ord_less_rat
% 0.14/0.49 = ( ^ [P3: rat,Q3: rat] :
% 0.14/0.49 ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( ord_less_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) )
% 0.14/0.49 @ ( quotient_of @ Q3 ) )
% 0.14/0.49 @ ( quotient_of @ P3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_less_code
% 0.14/0.49 thf(fact_4208_rat__less__eq__code,axiom,
% 0.14/0.49 ( ord_less_eq_rat
% 0.14/0.49 = ( ^ [P3: rat,Q3: rat] :
% 0.14/0.49 ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4947309494688390418_int_o
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) )
% 0.14/0.49 @ ( quotient_of @ Q3 ) )
% 0.14/0.49 @ ( quotient_of @ P3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_less_eq_code
% 0.14/0.49 thf(fact_4209_rat__uminus__code,axiom,
% 0.14/0.49 ! [P: rat] :
% 0.14/0.49 ( ( quotient_of @ ( uminus_uminus_rat @ P ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_uminus_code
% 0.14/0.49 thf(fact_4210_less__int__def,axiom,
% 0.14/0.49 ( ord_less_int
% 0.14/0.49 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_int_def
% 0.14/0.49 thf(fact_4211_less__eq__int__def,axiom,
% 0.14/0.49 ( ord_less_eq_int
% 0.14/0.49 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.14/0.49 @ ( produc8739625826339149834_nat_o
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] :
% 0.14/0.49 ( produc6081775807080527818_nat_o
% 0.14/0.49 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % less_eq_int_def
% 0.14/0.49 thf(fact_4212_rat__minus__code,axiom,
% 0.14/0.49 ! [P: rat,Q: rat] :
% 0.14/0.49 ( ( quotient_of @ ( minus_minus_rat @ P @ Q ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 0.14/0.49 @ ( quotient_of @ Q ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_minus_code
% 0.14/0.49 thf(fact_4213_rat__plus__code,axiom,
% 0.14/0.49 ! [P: rat,Q: rat] :
% 0.14/0.49 ( ( quotient_of @ ( plus_plus_rat @ P @ Q ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 0.14/0.49 @ ( quotient_of @ Q ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_plus_code
% 0.14/0.49 thf(fact_4214_rat__divide__code,axiom,
% 0.14/0.49 ! [P: rat,Q: rat] :
% 0.14/0.49 ( ( quotient_of @ ( divide_divide_rat @ P @ Q ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) ) )
% 0.14/0.49 @ ( quotient_of @ Q ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_divide_code
% 0.14/0.49 thf(fact_4215_rat__times__code,axiom,
% 0.14/0.49 ! [P: rat,Q: rat] :
% 0.14/0.49 ( ( quotient_of @ ( times_times_rat @ P @ Q ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int,C4: int] :
% 0.14/0.49 ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C4 @ D3 ) ) )
% 0.14/0.49 @ ( quotient_of @ Q ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_times_code
% 0.14/0.49 thf(fact_4216_pcr__int__def,axiom,
% 0.14/0.49 ( pcr_int
% 0.14/0.49 = ( relcom8911704206367525917at_int
% 0.14/0.49 @ ( basic_5328504652464829177at_nat
% 0.14/0.49 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 0.14/0.49 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.14/0.49 @ cr_int ) ) ).
% 0.14/0.49
% 0.14/0.49 % pcr_int_def
% 0.14/0.49 thf(fact_4217_UNIV__unit,axiom,
% 0.14/0.49 ( top_to1996260823553986621t_unit
% 0.14/0.49 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 0.14/0.49
% 0.14/0.49 % UNIV_unit
% 0.14/0.49 thf(fact_4218_top__unit__def,axiom,
% 0.14/0.49 top_top_Product_unit = product_Unity ).
% 0.14/0.49
% 0.14/0.49 % top_unit_def
% 0.14/0.49 thf(fact_4219_uminus__unit__def,axiom,
% 0.14/0.49 ( uminus2952777764628376836t_unit
% 0.14/0.49 = ( ^ [Uu2: product_unit] : product_Unity ) ) ).
% 0.14/0.49
% 0.14/0.49 % uminus_unit_def
% 0.14/0.49 thf(fact_4220_inf__unit__def,axiom,
% 0.14/0.49 ( inf_inf_Product_unit
% 0.14/0.49 = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 0.14/0.49
% 0.14/0.49 % inf_unit_def
% 0.14/0.49 thf(fact_4221_old_Ounit_Oexhaust,axiom,
% 0.14/0.49 ! [Y3: product_unit] : ( Y3 = product_Unity ) ).
% 0.14/0.49
% 0.14/0.49 % old.unit.exhaust
% 0.14/0.49 thf(fact_4222_Inf__unit__def,axiom,
% 0.14/0.49 ( comple2584293577114468500t_unit
% 0.14/0.49 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 0.14/0.49
% 0.14/0.49 % Inf_unit_def
% 0.14/0.49 thf(fact_4223_Sup__unit__def,axiom,
% 0.14/0.49 ( comple4687483117567863418t_unit
% 0.14/0.49 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 0.14/0.49
% 0.14/0.49 % Sup_unit_def
% 0.14/0.49 thf(fact_4224_sup__unit__def,axiom,
% 0.14/0.49 ( sup_sup_Product_unit
% 0.14/0.49 = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 0.14/0.49
% 0.14/0.49 % sup_unit_def
% 0.14/0.49 thf(fact_4225_bot__unit__def,axiom,
% 0.14/0.49 bot_bot_Product_unit = product_Unity ).
% 0.14/0.49
% 0.14/0.49 % bot_unit_def
% 0.14/0.49 thf(fact_4226_default__unit__def,axiom,
% 0.14/0.49 defaul566961228789861419t_unit = product_Unity ).
% 0.14/0.49
% 0.14/0.49 % default_unit_def
% 0.14/0.49 thf(fact_4227_Gcd__eq__Max,axiom,
% 0.14/0.49 ! [M: set_nat] :
% 0.14/0.49 ( ( finite_finite_nat @ M )
% 0.14/0.49 => ( ( M != bot_bot_set_nat )
% 0.14/0.49 => ( ~ ( member_nat @ zero_zero_nat @ M )
% 0.14/0.49 => ( ( gcd_Gcd_nat @ M )
% 0.14/0.49 = ( lattic8265883725875713057ax_nat
% 0.14/0.49 @ ( comple7806235888213564991et_nat
% 0.14/0.49 @ ( image_nat_set_nat
% 0.14/0.49 @ ^ [M5: nat] :
% 0.14/0.49 ( collect_nat
% 0.14/0.49 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ M5 ) )
% 0.14/0.49 @ M ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Gcd_eq_Max
% 0.14/0.49 thf(fact_4228_Gcd__int__eq,axiom,
% 0.14/0.49 ! [N: set_nat] :
% 0.14/0.49 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N ) )
% 0.14/0.49 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Gcd_int_eq
% 0.14/0.49 thf(fact_4229_Gcd__int__def,axiom,
% 0.14/0.49 ( gcd_Gcd_int
% 0.14/0.49 = ( ^ [K3: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K3 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Gcd_int_def
% 0.14/0.49 thf(fact_4230_Gcd__nat__abs__eq,axiom,
% 0.14/0.49 ! [K4: set_int] :
% 0.14/0.49 ( ( gcd_Gcd_nat
% 0.14/0.49 @ ( image_int_nat
% 0.14/0.49 @ ^ [K5: int] : ( nat2 @ ( abs_abs_int @ K5 ) )
% 0.14/0.49 @ K4 ) )
% 0.14/0.49 = ( nat2 @ ( gcd_Gcd_int @ K4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Gcd_nat_abs_eq
% 0.14/0.49 thf(fact_4231_range__abs__Nats,axiom,
% 0.14/0.49 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 0.14/0.49 = semiring_1_Nats_int ) ).
% 0.14/0.49
% 0.14/0.49 % range_abs_Nats
% 0.14/0.49 thf(fact_4232_Gcd__abs__eq,axiom,
% 0.14/0.49 ! [K4: set_int] :
% 0.14/0.49 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K4 ) )
% 0.14/0.49 = ( gcd_Gcd_int @ K4 ) ) ).
% 0.14/0.49
% 0.14/0.49 % Gcd_abs_eq
% 0.14/0.49 thf(fact_4233_int__in__range__abs,axiom,
% 0.14/0.49 ! [N3: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N3 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 0.14/0.49
% 0.14/0.49 % int_in_range_abs
% 0.14/0.49 thf(fact_4234_measure__function__int,axiom,
% 0.14/0.49 fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 0.14/0.49
% 0.14/0.49 % measure_function_int
% 0.14/0.49 thf(fact_4235_rat__abs__code,axiom,
% 0.14/0.49 ! [P: rat] :
% 0.14/0.49 ( ( quotient_of @ ( abs_abs_rat @ P ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_abs_code
% 0.14/0.49 thf(fact_4236_surj__int__encode,axiom,
% 0.14/0.49 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_int_encode
% 0.14/0.49 thf(fact_4237_surj__int__decode,axiom,
% 0.14/0.49 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 0.14/0.49 = top_top_set_int ) ).
% 0.14/0.49
% 0.14/0.49 % surj_int_decode
% 0.14/0.49 thf(fact_4238_Lcm__abs__eq,axiom,
% 0.14/0.49 ! [K4: set_int] :
% 0.14/0.49 ( ( gcd_Lcm_int @ ( image_int_int @ abs_abs_int @ K4 ) )
% 0.14/0.49 = ( gcd_Lcm_int @ K4 ) ) ).
% 0.14/0.49
% 0.14/0.49 % Lcm_abs_eq
% 0.14/0.49 thf(fact_4239_Lcm__int__def,axiom,
% 0.14/0.49 ( gcd_Lcm_int
% 0.14/0.49 = ( ^ [K3: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K3 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Lcm_int_def
% 0.14/0.49 thf(fact_4240_Lcm__int__eq,axiom,
% 0.14/0.49 ! [N: set_nat] :
% 0.14/0.49 ( ( gcd_Lcm_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N ) )
% 0.14/0.49 = ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ N ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Lcm_int_eq
% 0.14/0.49 thf(fact_4241_Lcm__nat__abs__eq,axiom,
% 0.14/0.49 ! [K4: set_int] :
% 0.14/0.49 ( ( gcd_Lcm_nat
% 0.14/0.49 @ ( image_int_nat
% 0.14/0.49 @ ^ [K5: int] : ( nat2 @ ( abs_abs_int @ K5 ) )
% 0.14/0.49 @ K4 ) )
% 0.14/0.49 = ( nat2 @ ( gcd_Lcm_int @ K4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Lcm_nat_abs_eq
% 0.14/0.49 thf(fact_4242_rat__inverse__code,axiom,
% 0.14/0.49 ! [P: rat] :
% 0.14/0.49 ( ( quotient_of @ ( inverse_inverse_rat @ P ) )
% 0.14/0.49 = ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 0.14/0.49 @ ( quotient_of @ P ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_inverse_code
% 0.14/0.49 thf(fact_4243_euclidean__size__int__def,axiom,
% 0.14/0.49 ( euclid4774559944035922753ze_int
% 0.14/0.49 = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 0.14/0.49
% 0.14/0.49 % euclidean_size_int_def
% 0.14/0.49 thf(fact_4244_Unity__def,axiom,
% 0.14/0.49 ( product_Unity
% 0.14/0.49 = ( product_Abs_unit @ $true ) ) ).
% 0.14/0.49
% 0.14/0.49 % Unity_def
% 0.14/0.49 thf(fact_4245_prod__encode__def,axiom,
% 0.14/0.49 ( nat_prod_encode
% 0.14/0.49 = ( produc6842872674320459806at_nat
% 0.14/0.49 @ ^ [M5: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M5 @ N4 ) ) @ M5 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % prod_encode_def
% 0.14/0.49 thf(fact_4246_Abs__unit__cases,axiom,
% 0.14/0.49 ! [X2: product_unit] :
% 0.14/0.49 ~ ! [Y: $o] :
% 0.14/0.49 ( ( X2
% 0.14/0.49 = ( product_Abs_unit @ Y ) )
% 0.14/0.49 => ~ ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Abs_unit_cases
% 0.14/0.49 thf(fact_4247_Abs__unit__induct,axiom,
% 0.14/0.49 ! [P2: product_unit > $o,X2: product_unit] :
% 0.14/0.49 ( ! [Y: $o] :
% 0.14/0.49 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ( P2 @ ( product_Abs_unit @ Y ) ) )
% 0.14/0.49 => ( P2 @ X2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % Abs_unit_induct
% 0.14/0.49 thf(fact_4248_Abs__unit__inject,axiom,
% 0.14/0.49 ! [X2: $o,Y3: $o] :
% 0.14/0.49 ( ( member_o @ X2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ( ( ( product_Abs_unit @ X2 )
% 0.14/0.49 = ( product_Abs_unit @ Y3 ) )
% 0.14/0.49 = ( X2 = Y3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Abs_unit_inject
% 0.14/0.49 thf(fact_4249_surj__prod__encode,axiom,
% 0.14/0.49 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_prod_encode
% 0.14/0.49 thf(fact_4250_type__definition__unit,axiom,
% 0.14/0.49 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 0.14/0.49
% 0.14/0.49 % type_definition_unit
% 0.14/0.49 thf(fact_4251_Rep__unit__inject,axiom,
% 0.14/0.49 ! [X2: product_unit,Y3: product_unit] :
% 0.14/0.49 ( ( ( product_Rep_unit @ X2 )
% 0.14/0.49 = ( product_Rep_unit @ Y3 ) )
% 0.14/0.49 = ( X2 = Y3 ) ) ).
% 0.14/0.49
% 0.14/0.49 % Rep_unit_inject
% 0.14/0.49 thf(fact_4252_Rep__unit__induct,axiom,
% 0.14/0.49 ! [Y3: $o,P2: $o > $o] :
% 0.14/0.49 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ( ! [X: product_unit] : ( P2 @ ( product_Rep_unit @ X ) )
% 0.14/0.49 => ( P2 @ Y3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Rep_unit_induct
% 0.14/0.49 thf(fact_4253_Rep__unit__cases,axiom,
% 0.14/0.49 ! [Y3: $o] :
% 0.14/0.49 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ~ ! [X: product_unit] :
% 0.14/0.49 ( Y3
% 0.14/0.49 = ( ~ ( product_Rep_unit @ X ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Rep_unit_cases
% 0.14/0.49 thf(fact_4254_Rep__unit,axiom,
% 0.14/0.49 ! [X2: product_unit] : ( member_o @ ( product_Rep_unit @ X2 ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 0.14/0.49
% 0.14/0.49 % Rep_unit
% 0.14/0.49 thf(fact_4255_Rep__unit__inverse,axiom,
% 0.14/0.49 ! [X2: product_unit] :
% 0.14/0.49 ( ( product_Abs_unit @ ( product_Rep_unit @ X2 ) )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 % Rep_unit_inverse
% 0.14/0.49 thf(fact_4256_Abs__unit__inverse,axiom,
% 0.14/0.49 ! [Y3: $o] :
% 0.14/0.49 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.14/0.49 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y3 ) )
% 0.14/0.49 = Y3 ) ) ).
% 0.14/0.49
% 0.14/0.49 % Abs_unit_inverse
% 0.14/0.49 thf(fact_4257_surj__prod__decode,axiom,
% 0.14/0.49 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 0.14/0.49 = top_to4669805908274784177at_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_prod_decode
% 0.14/0.49 thf(fact_4258_pair__less__def,axiom,
% 0.14/0.49 ( fun_pair_less
% 0.14/0.49 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 0.14/0.49
% 0.14/0.49 % pair_less_def
% 0.14/0.49 thf(fact_4259_list__decode_Oelims,axiom,
% 0.14/0.49 ! [X2: nat,Y3: list_nat] :
% 0.14/0.49 ( ( ( nat_list_decode @ X2 )
% 0.14/0.49 = Y3 )
% 0.14/0.49 => ( ( ( X2 = zero_zero_nat )
% 0.14/0.49 => ( Y3 != nil_nat ) )
% 0.14/0.49 => ~ ! [N2: nat] :
% 0.14/0.49 ( ( X2
% 0.14/0.49 = ( suc @ N2 ) )
% 0.14/0.49 => ( Y3
% 0.14/0.49 != ( produc2761476792215241774st_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 0.14/0.49 @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % list_decode.elims
% 0.14/0.49 thf(fact_4260_nat__to__rat__surj__def,axiom,
% 0.14/0.49 ( nat_to_rat_surj
% 0.14/0.49 = ( ^ [N4: nat] :
% 0.14/0.49 ( produc6207742614233964070at_rat
% 0.14/0.49 @ ^ [A5: nat,B4: nat] : ( fract @ ( nat_int_decode @ A5 ) @ ( nat_int_decode @ B4 ) )
% 0.14/0.49 @ ( nat_prod_decode @ N4 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat_to_rat_surj_def
% 0.14/0.49 thf(fact_4261_list__decode_Osimps_I2_J,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( nat_list_decode @ ( suc @ N3 ) )
% 0.14/0.49 = ( produc2761476792215241774st_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 0.14/0.49 @ ( nat_prod_decode @ N3 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % list_decode.simps(2)
% 0.14/0.49 thf(fact_4262_list__decode_Opelims,axiom,
% 0.14/0.49 ! [X2: nat,Y3: list_nat] :
% 0.14/0.49 ( ( ( nat_list_decode @ X2 )
% 0.14/0.49 = Y3 )
% 0.14/0.49 => ( ( accp_nat @ nat_list_decode_rel @ X2 )
% 0.14/0.49 => ( ( ( X2 = zero_zero_nat )
% 0.14/0.49 => ( ( Y3 = nil_nat )
% 0.14/0.49 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.14/0.49 => ~ ! [N2: nat] :
% 0.14/0.49 ( ( X2
% 0.14/0.49 = ( suc @ N2 ) )
% 0.14/0.49 => ( ( Y3
% 0.14/0.49 = ( produc2761476792215241774st_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 0.14/0.49 @ ( nat_prod_decode @ N2 ) ) )
% 0.14/0.49 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % list_decode.pelims
% 0.14/0.49 thf(fact_4263_surj__list__decode,axiom,
% 0.14/0.49 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 0.14/0.49 = top_top_set_list_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_list_decode
% 0.14/0.49 thf(fact_4264_list__decode_Opsimps_I2_J,axiom,
% 0.14/0.49 ! [N3: nat] :
% 0.14/0.49 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 0.14/0.49 => ( ( nat_list_decode @ ( suc @ N3 ) )
% 0.14/0.49 = ( produc2761476792215241774st_nat
% 0.14/0.49 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 0.14/0.49 @ ( nat_prod_decode @ N3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % list_decode.psimps(2)
% 0.14/0.49 thf(fact_4265_surj__sum__encode,axiom,
% 0.14/0.49 ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_sum_encode
% 0.14/0.49 thf(fact_4266_surj__list__encode,axiom,
% 0.14/0.49 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 0.14/0.49 = top_top_set_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_list_encode
% 0.14/0.49 thf(fact_4267_surj__sum__decode,axiom,
% 0.14/0.49 ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 0.14/0.49 = top_to6661820994512907621at_nat ) ).
% 0.14/0.49
% 0.14/0.49 % surj_sum_decode
% 0.14/0.49 thf(fact_4268_divmod__step__int__def,axiom,
% 0.14/0.49 ( unique5024387138958732305ep_int
% 0.14/0.49 = ( ^ [L3: num] :
% 0.14/0.49 ( produc4245557441103728435nt_int
% 0.14/0.49 @ ^ [Q3: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_step_int_def
% 0.14/0.49 thf(fact_4269_divmod__step__nat__def,axiom,
% 0.14/0.49 ( unique5026877609467782581ep_nat
% 0.14/0.49 = ( ^ [L3: num] :
% 0.14/0.49 ( produc2626176000494625587at_nat
% 0.14/0.49 @ ^ [Q3: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_step_nat_def
% 0.14/0.49 thf(fact_4270_divmod__step__integer__def,axiom,
% 0.14/0.49 ( unique4921790084139445826nteger
% 0.14/0.49 = ( ^ [L3: num] :
% 0.14/0.49 ( produc6916734918728496179nteger
% 0.14/0.49 @ ^ [Q3: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_step_integer_def
% 0.14/0.49 thf(fact_4271_nat__of__integer__code,axiom,
% 0.14/0.49 ( code_nat_of_integer
% 0.14/0.49 = ( ^ [K5: code_integer] :
% 0.14/0.49 ( if_nat @ ( ord_le3102999989581377725nteger @ K5 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.14/0.49 @ ( produc1555791787009142072er_nat
% 0.14/0.49 @ ^ [L3: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 0.14/0.49 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % nat_of_integer_code
% 0.14/0.49 thf(fact_4272_num__of__integer__code,axiom,
% 0.14/0.49 ( code_num_of_integer
% 0.14/0.49 = ( ^ [K5: code_integer] :
% 0.14/0.49 ( if_num @ ( ord_le3102999989581377725nteger @ K5 @ one_one_Code_integer ) @ one
% 0.14/0.49 @ ( produc7336495610019696514er_num
% 0.14/0.49 @ ^ [L3: code_integer,J: code_integer] : ( if_num @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 0.14/0.49 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % num_of_integer_code
% 0.14/0.49 thf(fact_4273_divmod__integer__code,axiom,
% 0.14/0.49 ( code_divmod_integer
% 0.14/0.49 = ( ^ [K5: code_integer,L3: code_integer] :
% 0.14/0.49 ( if_Pro6119634080678213985nteger @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K5 ) @ ( code_divmod_abs @ K5 @ L3 )
% 0.14/0.49 @ ( produc6916734918728496179nteger
% 0.14/0.49 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L3 @ S ) ) )
% 0.14/0.49 @ ( code_divmod_abs @ K5 @ L3 ) ) )
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K5 )
% 0.14/0.49 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K5 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K5 @ L3 )
% 0.14/0.49 @ ( produc6916734918728496179nteger
% 0.14/0.49 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L3 ) @ S ) ) )
% 0.14/0.49 @ ( code_divmod_abs @ K5 @ L3 ) ) ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_integer_code
% 0.14/0.49 thf(fact_4274_int__of__integer__code,axiom,
% 0.14/0.49 ( code_int_of_integer
% 0.14/0.49 = ( ^ [K5: code_integer] :
% 0.14/0.49 ( if_int @ ( ord_le6747313008572928689nteger @ K5 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K5 ) ) )
% 0.14/0.49 @ ( if_int @ ( K5 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.14/0.49 @ ( produc1553301316500091796er_int
% 0.14/0.49 @ ^ [L3: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 0.14/0.49 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % int_of_integer_code
% 0.14/0.49 thf(fact_4275_Code__Numeral_Onegative__def,axiom,
% 0.14/0.49 ( code_negative
% 0.14/0.49 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.14/0.49
% 0.14/0.49 % Code_Numeral.negative_def
% 0.14/0.49 thf(fact_4276_bit__cut__integer__code,axiom,
% 0.14/0.49 ( code_bit_cut_integer
% 0.14/0.49 = ( ^ [K5: code_integer] :
% 0.14/0.49 ( if_Pro5737122678794959658eger_o @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.14/0.49 @ ( produc9125791028180074456eger_o
% 0.14/0.49 @ ^ [R5: code_integer,S: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K5 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S ) ) @ ( S = one_one_Code_integer ) )
% 0.14/0.49 @ ( code_divmod_abs @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % bit_cut_integer_code
% 0.14/0.49 thf(fact_4277_divmod__integer__eq__cases,axiom,
% 0.14/0.49 ( code_divmod_integer
% 0.14/0.49 = ( ^ [K5: code_integer,L3: code_integer] :
% 0.14/0.49 ( if_Pro6119634080678213985nteger @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K5 )
% 0.14/0.49 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 0.14/0.49 @ ( if_Pro6119634080678213985nteger
% 0.14/0.49 @ ( ( sgn_sgn_Code_integer @ K5 )
% 0.14/0.49 = ( sgn_sgn_Code_integer @ L3 ) )
% 0.14/0.49 @ ( code_divmod_abs @ K5 @ L3 )
% 0.14/0.49 @ ( produc6916734918728496179nteger
% 0.14/0.49 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L3 ) @ S ) ) )
% 0.14/0.49 @ ( code_divmod_abs @ K5 @ L3 ) ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % divmod_integer_eq_cases
% 0.14/0.49 thf(fact_4278_UNIV__char__of__nat,axiom,
% 0.14/0.49 ( top_top_set_char
% 0.14/0.49 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % UNIV_char_of_nat
% 0.14/0.49 thf(fact_4279_num__of__integer__def,axiom,
% 0.14/0.49 ( code_num_of_integer
% 0.14/0.49 = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % num_of_integer_def
% 0.14/0.49 thf(fact_4280_range__nat__of__char,axiom,
% 0.14/0.49 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.14/0.49 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % range_nat_of_char
% 0.14/0.49 thf(fact_4281_num__of__integer_Orsp,axiom,
% 0.14/0.49 ( bNF_re7626690874201225453um_num
% 0.14/0.49 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.49 @ ^ [Y2: num,Z: num] : ( Y2 = Z )
% 0.14/0.49 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.14/0.49 @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 0.14/0.49
% 0.14/0.49 % num_of_integer.rsp
% 0.14/0.49 thf(fact_4282_num__of__integer_Otransfer,axiom,
% 0.14/0.49 ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 0.14/0.49 @ ^ [Y2: num,Z: num] : ( Y2 = Z )
% 0.14/0.49 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.14/0.49 @ code_num_of_integer ) ).
% 0.14/0.49
% 0.14/0.49 % num_of_integer.transfer
% 0.14/0.49 thf(fact_4283_pcr__integer__def,axiom,
% 0.14/0.49 ( code_pcr_integer
% 0.14/0.49 = ( relcom967497705283160040nteger
% 0.14/0.49 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 0.14/0.49 @ code_cr_integer ) ) ).
% 0.14/0.49
% 0.14/0.49 % pcr_integer_def
% 0.14/0.49 thf(fact_4284_Random__Pred_Onot__randompred__def,axiom,
% 0.14/0.49 ( random6974930770145893639ompred
% 0.14/0.49 = ( ^ [P4: produc7822875418678951345atural > produc4675096598859438275atural,S: produc7822875418678951345atural] :
% 0.14/0.49 ( produc6665183775751917029atural
% 0.14/0.49 @ ^ [P5: pred_Product_unit,S7: produc7822875418678951345atural] : ( if_Pro3444522238938527101atural @ ( eval_Product_unit @ P5 @ product_Unity ) @ ( produc5069803637994805237atural @ bot_bo2717538794563056311t_unit @ S7 ) @ ( produc5069803637994805237atural @ ( single_Product_unit @ product_Unity ) @ S7 ) )
% 0.14/0.49 @ ( P4 @ S ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Random_Pred.not_randompred_def
% 0.14/0.49 thf(fact_4285_rat__floor__code,axiom,
% 0.14/0.49 ( archim3151403230148437115or_rat
% 0.14/0.49 = ( ^ [P3: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P3 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % rat_floor_code
% 0.14/0.49 thf(fact_4286_Divides_Oadjust__div__def,axiom,
% 0.14/0.49 ( adjust_div
% 0.14/0.49 = ( produc8211389475949308722nt_int
% 0.14/0.49 @ ^ [Q3: int,R5: int] : ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % Divides.adjust_div_def
% 0.14/0.49 thf(fact_4287_take__bit__num__code,axiom,
% 0.14/0.49 ( bit_take_bit_num
% 0.14/0.49 = ( ^ [N4: nat,M5: num] :
% 0.14/0.49 ( produc478579273971653890on_num
% 0.14/0.49 @ ^ [A5: nat,X4: num] :
% 0.14/0.49 ( case_nat_option_num @ none_num
% 0.14/0.49 @ ^ [O: nat] :
% 0.14/0.49 ( case_num_option_num @ ( some_num @ one )
% 0.14/0.49 @ ^ [P3: num] :
% 0.14/0.49 ( case_o6005452278849405969um_num @ none_num
% 0.14/0.49 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 0.14/0.49 @ ( bit_take_bit_num @ O @ P3 ) )
% 0.14/0.49 @ ^ [P3: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P3 ) ) )
% 0.14/0.49 @ X4 )
% 0.14/0.49 @ A5 )
% 0.14/0.49 @ ( product_Pair_nat_num @ N4 @ M5 ) ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % take_bit_num_code
% 0.14/0.49 thf(fact_4288_list__ex__iff__not__all__inverval__nat,axiom,
% 0.14/0.49 ! [P2: nat > $o,I: nat,J4: nat] :
% 0.14/0.49 ( ( list_ex_nat @ P2 @ ( upt @ I @ J4 ) )
% 0.14/0.49 = ( ~ ( all_interval_nat @ ( comp_o_o_nat @ (~) @ P2 ) @ I @ J4 ) ) ) ).
% 0.14/0.49
% 0.14/0.49 % list_ex_iff_not_all_inverval_nat
% 0.14/0.49
% 0.14/0.49 % Helper facts (39)
% 0.14/0.49 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.14/0.49 ! [X2: int,Y3: int] :
% 0.14/0.49 ( ( if_int @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.14/0.49 ! [X2: int,Y3: int] :
% 0.14/0.49 ( ( if_int @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.14/0.49 ! [X2: nat,Y3: nat] :
% 0.14/0.49 ( ( if_nat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.14/0.49 ! [X2: nat,Y3: nat] :
% 0.14/0.49 ( ( if_nat @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.14/0.49 ! [X2: num,Y3: num] :
% 0.14/0.49 ( ( if_num @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.14/0.49 ! [X2: num,Y3: num] :
% 0.14/0.49 ( ( if_num @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.14/0.49 ! [X2: rat,Y3: rat] :
% 0.14/0.49 ( ( if_rat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.14/0.49 ! [X2: rat,Y3: rat] :
% 0.14/0.49 ( ( if_rat @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 0.14/0.49 ! [X2: set_o,Y3: set_o] :
% 0.14/0.49 ( ( if_set_o @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 0.14/0.49 ! [X2: set_o,Y3: set_o] :
% 0.14/0.49 ( ( if_set_o @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Ounit_T,axiom,
% 0.14/0.49 ! [X2: product_unit,Y3: product_unit] :
% 0.14/0.49 ( ( if_Product_unit @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Ounit_T,axiom,
% 0.14/0.49 ! [X2: product_unit,Y3: product_unit] :
% 0.14/0.49 ( ( if_Product_unit @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.14/0.49 ! [X2: code_integer,Y3: code_integer] :
% 0.14/0.49 ( ( if_Code_integer @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.14/0.49 ! [X2: code_integer,Y3: code_integer] :
% 0.14/0.49 ( ( if_Code_integer @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.14/0.49 ! [X2: set_nat,Y3: set_nat] :
% 0.14/0.49 ( ( if_set_nat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.14/0.49 ! [X2: set_nat,Y3: set_nat] :
% 0.14/0.49 ( ( if_set_nat @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 0.14/0.49 ! [X2: set_Product_unit,Y3: set_Product_unit] :
% 0.14/0.49 ( ( if_set_Product_unit @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 0.14/0.49 ! [X2: set_Product_unit,Y3: set_Product_unit] :
% 0.14/0.49 ( ( if_set_Product_unit @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Heap____Monad__OHeap_It__Heap__Oref_Itf__a_J_J_T,axiom,
% 0.14/0.49 ! [X2: heap_Heap_ref_a,Y3: heap_Heap_ref_a] :
% 0.14/0.49 ( ( if_Heap_Heap_ref_a @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Heap____Monad__OHeap_It__Heap__Oref_Itf__a_J_J_T,axiom,
% 0.14/0.49 ! [X2: heap_Heap_ref_a,Y3: heap_Heap_ref_a] :
% 0.14/0.49 ( ( if_Heap_Heap_ref_a @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.14/0.49 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 0.14/0.49 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.14/0.49 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 0.14/0.49 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.14/0.49 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.14/0.49 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.14/0.49 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.14/0.49 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 0.14/0.49 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.14/0.49 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 0.14/0.49 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.14/0.49 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 0.14/0.49 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.14/0.49 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 0.14/0.49 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 0.14/0.49 ! [X2: produc859450856879609959at_nat,Y3: produc859450856879609959at_nat] :
% 0.14/0.49 ( ( if_Pro4507677147265585453at_nat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 0.14/0.49 ! [X2: produc859450856879609959at_nat,Y3: produc859450856879609959at_nat] :
% 0.14/0.49 ( ( if_Pro4507677147265585453at_nat @ $true @ X2 @ Y3 )
% 0.14/0.49 = X2 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 0.14/0.49 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 0.14/0.49 ( ( if_set1508868558775481357at_nat @ $false @ X2 @ Y3 )
% 0.14/0.49 = Y3 ) ).
% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
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% 0.14/0.49
% 0.14/0.49 thf(help_If_2_1_If_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_T,axiom,
% 0.14/0.49 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.14/0.49 ( ( if_set3208018901896979469at_nat @ $false @ X2 @ Y3 )
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% 0.14/0.49
% 0.14/0.49 thf(help_If_1_1_If_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_T,axiom,
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% 0.14/0.49
% 0.14/0.49 % Conjectures (2)
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% 0.14/0.49 thf(conj_1,conjecture,
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% 0.14/0.49 %------------------------------------------------------------------------------
% 0.14/0.49 ------------------------
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% 6.18/2.31 %%% Generated on Tue Feb 24 03:29:42 EST 2026
% 6.18/2.31 %%% using '$$dhol' embedding, version 1.3.0.
% 6.18/2.31 %%% Logic specification used:
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% 6.18/2.31
% 6.18/2.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2DTF14919.p
% See solution above
% 6.18/2.33 ------------------------
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% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr_int_nat: set_int > ( int > nat ) > set_Pr3448869479623346877nt_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr_nat_int: set_nat > ( nat > int ) > set_Pr7995236796853374141at_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr_nat_nat: set_nat > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr_nat_num: set_nat > ( nat > num ) > set_Pr6200539531224447659at_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Gr_nat_rat: set_nat > ( nat > rat ) > set_Pr4105333604307423337at_rat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr_num_num: set_num > ( num > num ) > set_Pr8218934625190621173um_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_Gr1527221351080490466at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGr_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 7.68/3.89 bNF_Gr7888059597227825506at_nat: set_se5479201105039950375at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr7459493094073627847at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Code____Numeral__Ointeger_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_M_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_J,type,
% 7.68/3.89 bNF_Gr1453458339979195462nteger: set_Co4375521073081744395nteger > ( ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 7.68/3.89 bNF_Gr4092539093814444494nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr2243168462153404386nt_nat: set_int_int > ( ( int > int ) > int > nat ) > ( int > int ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_Gr6763702254253555408nt_num: set_int_nat > ( ( int > nat ) > int > num ) > ( int > nat ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_Gr318824752125099290nt_num: set_int_num > ( ( int > num ) > int > num ) > ( int > num ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.68/3.89 bNF_Gr952524912132828525nt_int: set_in6154042108061588260nt_int > ( ( int > product_prod_int_int ) > int > int ) > ( int > product_prod_int_int ) > ( int > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr1462982377596425817nt_nat: set_in7748886932685137004at_nat > ( ( int > product_prod_nat_nat ) > int > nat ) > ( int > product_prod_nat_nat ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_Gr5590197745039885111nt_num: set_in3169746454734514176um_num > ( ( int > product_prod_num_num ) > int > num ) > ( int > product_prod_num_num ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr1532745923208276441at_nat: set_li2168235667650531768at_nat > ( ( list_nat > product_prod_nat_nat ) > list_nat > nat ) > ( list_nat > product_prod_nat_nat ) > ( list_nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_Grp_nat_o_nat_o: set_nat_o > ( ( nat > $o ) > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr3847987472475283150at_nat: set_nat_nat > ( ( nat > nat ) > nat > nat ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Nat__Onat_Mt__Int__Oint_J,type,
% 7.68/3.89 bNF_Gr2878093617000900205at_int: set_na7251125088705586816nt_int > ( ( nat > product_prod_int_int ) > nat > int ) > ( nat > product_prod_int_int ) > ( nat > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr3388551082464497497at_nat: set_na8845969913329135560at_nat > ( ( nat > product_prod_nat_nat ) > nat > nat ) > ( nat > product_prod_nat_nat ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Rat__Orat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Int__Oint_J,type,
% 7.68/3.89 bNF_Gr6858100456814184557at_int: set_ra518564293221149304nt_int > ( ( rat > product_prod_int_int ) > rat > int ) > ( rat > product_prod_int_int ) > ( rat > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__Rat__Orat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Rat__Orat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr7368557922277781849at_nat: set_ra2113409117844698048at_nat > ( ( rat > product_prod_nat_nat ) > rat > nat ) > ( rat > product_prod_nat_nat ) > ( rat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__String__Ochar_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__String__Ochar_Mt__Int__Oint_J,type,
% 7.68/3.89 bNF_Gr6947267152677263533ar_int: set_ch6383161263842509759nt_int > ( ( char > product_prod_int_int ) > char > int ) > ( char > product_prod_int_int ) > ( char > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_062_It__String__Ochar_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__String__Ochar_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr1779741795384719769ar_nat: set_ch7978006088466058503at_nat > ( ( char > product_prod_nat_nat ) > char > nat ) > ( char > product_prod_nat_nat ) > ( char > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_Grp_o_o: set_o > ( $o > $o ) > $o > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_Eo_001t__Product____Type__Ounit,type,
% 7.68/3.89 bNF_Gr395642070819736771t_unit: set_o > ( $o > product_unit ) > $o > product_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_Eo_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Grp_o_rat: set_o > ( $o > rat ) > $o > rat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001_Eo_001t__String__Ochar,type,
% 7.68/3.89 bNF_Grp_o_char: set_o > ( $o > char ) > $o > char > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr6045950513751025625er_int: set_Code_integer > ( code_integer > int ) > code_integer > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 7.68/3.89 bNF_Gr6510375311308651680t_unit: set_ref_a > ( ref_a > heap_e7401611519738050253t_unit ) > ref_a > heap_e7401611519738050253t_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_Gr6684649993275963353nteger: set_int > ( int > code_integer ) > int > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_Grp_int_int: set_int > ( int > int ) > int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Grp_int_nat: set_int > ( int > nat ) > int > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Num__Onum,type,
% 7.68/3.89 bNF_Grp_int_num: set_int > ( int > num ) > int > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr6591314147588017797at_nat: set_int > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Grp_int_rat: set_int > ( int > rat ) > int > rat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Int__Oint_001t__String__Ochar,type,
% 7.68/3.89 bNF_Grp_int_char: set_int > ( int > char ) > int > char > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__Int__Oint,type,
% 7.68/3.89 bNF_Grp_list_nat_int: set_list_nat > ( list_nat > int ) > list_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr600725020315365264st_nat: set_list_nat > ( list_nat > list_nat ) > list_nat > list_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr4119388860389678161at_nat: set_list_nat > ( list_nat > product_prod_nat_nat ) > list_nat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_Grp_nat_o: set_nat > ( nat > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.89 bNF_Grp_nat_int: set_nat > ( nat > int ) > nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Grp_nat_nat: set_nat > ( nat > nat ) > nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Grp_nat_num: set_nat > ( nat > num ) > nat > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr3553472063123884001at_nat: set_nat > ( nat > product_prod_nat_nat ) > nat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 7.68/3.89 bNF_Gr1993012052113314029t_unit: set_nat > ( nat > product_unit ) > nat > product_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Grp_nat_rat: set_nat > ( nat > rat ) > nat > rat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__String__Ochar,type,
% 7.68/3.89 bNF_Grp_nat_char: set_nat > ( nat > char ) > nat > char > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_Grp_num_num: set_num > ( num > num ) > num > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 7.68/3.89 bNF_Gr5237703264515865432t_unit: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J,type,
% 7.68/3.89 bNF_Gr5964920315653434322_ref_a: set_Pr1133966238863718811t_unit > ( produc7812382424243267045t_unit > ref_a ) > produc7812382424243267045t_unit > ref_a > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr2749509334501985047nt_int: set_Pr958786334691620121nt_int > ( product_prod_int_int > int ) > product_prod_int_int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr8532703628021589765nt_num: set_Pr958786334691620121nt_int > ( product_prod_int_int > num ) > product_prod_int_int > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_Gr8859634586176591525_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr190934199572118623at_int: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > int ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr193424670081168899at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr5974128493091723341at_num: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > num ) > product_prod_nat_nat > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr7275288873855648526at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Int__Oint,type,
% 7.68/3.89 bNF_Grp_rat_int: set_rat > ( rat > int ) > rat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Grp_rat_nat: set_rat > ( rat > nat ) > rat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr6883301533820405721at_nat: set_rat > ( rat > product_prod_nat_nat ) > rat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Grp_rat_rat: set_rat > ( rat > rat ) > rat > rat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Rat__Orat_001t__String__Ochar,type,
% 7.68/3.89 bNF_Grp_rat_char: set_rat > ( rat > char ) > rat > char > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_Gr6677838525845560078at_nat: set_se7855581050983116737at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Int__Oint,type,
% 7.68/3.89 bNF_Grp_char_int: set_char > ( char > int ) > char > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Grp_char_nat: set_char > ( char > nat ) > char > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_Gr8982933507515605408at_nat: set_char > ( char > product_prod_nat_nat ) > char > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__Rat__Orat,type,
% 7.68/3.89 bNF_Grp_char_rat: set_char > ( char > rat ) > char > rat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OGrp_001t__String__Ochar_001t__String__Ochar,type,
% 7.68/3.89 bNF_Grp_char_char: set_char > ( char > char ) > char > char > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_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,type,
% 7.68/3.89 bNF_co1764293801198077070nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > produc101387210554329899nteger ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_Eo_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_convol_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > product_prod_o_o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_Eo_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_convol_o_o_nat: ( $o > $o ) > ( $o > nat ) > $o > product_prod_o_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_convol_o_nat_o: ( $o > nat ) > ( $o > $o ) > $o > product_prod_nat_o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_convol_o_nat_nat: ( $o > nat ) > ( $o > nat ) > $o > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001_Eo_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_convol_o_num_nat: ( $o > num ) > ( $o > nat ) > $o > product_prod_num_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.89 bNF_co6169604788974073338nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > produc723880050079548563nteger ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_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_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,type,
% 7.68/3.89 bNF_co3156833790671340178nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc101387210554329899nteger ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_co2174166945328636015nt_int: ( int > int ) > ( int > int ) > int > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co2176657415837686291nt_nat: ( int > int ) > ( int > nat ) > int > product_prod_int_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.89 bNF_co1174813233427581459at_int: ( int > nat ) > ( int > int ) > int > product_prod_nat_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co1177303703936631735at_nat: ( int > nat ) > ( int > nat ) > int > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_co6958007526947186177at_num: ( int > nat ) > ( int > num ) > int > product_prod_nat_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co8531006144098876929um_nat: ( int > num ) > ( int > nat ) > int > product_prod_num_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_co5088337930254655563um_num: ( int > num ) > ( int > num ) > int > product_prod_num_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_convol_nat_o_o: ( nat > $o ) > ( nat > $o ) > nat > product_prod_o_o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_convol_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > product_prod_o_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_convol_nat_nat_o: ( nat > nat ) > ( nat > $o ) > nat > product_prod_nat_o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co805650143699787099at_nat: ( nat > nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 7.68/3.89 bNF_convol_nat_num_o: ( nat > num ) > ( nat > $o ) > nat > product_prod_num_o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co8159352583862032293um_nat: ( nat > num ) > ( nat > nat ) > nat > product_prod_num_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_co4716684370017810927um_num: ( nat > num ) > ( nat > num ) > nat > product_prod_num_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_convol_num_o_nat: ( num > $o ) > ( num > nat ) > num > product_prod_o_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co7969830008525221797at_nat: ( num > nat ) > ( num > nat ) > num > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co6100160411832691183um_nat: ( num > num ) > ( num > nat ) > num > product_prod_num_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_co6607689160745551784nt_int: ( produc7812382424243267045t_unit > int ) > ( produc7812382424243267045t_unit > int ) > produc7812382424243267045t_unit > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co5610825919353547504at_nat: ( produc7812382424243267045t_unit > nat ) > ( produc7812382424243267045t_unit > nat ) > produc7812382424243267045t_unit > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_co3748779267718262122nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co2751916026326257842at_nat: ( product_prod_int_int > nat ) > ( product_prod_int_int > nat ) > product_prod_int_int > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_co49787548815638194nt_int: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_co8276296344278409722at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Oconvol_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_co147202357524637304at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.89 bNF_cs4943907971211754724nteger: set_Pr8415741480598773322nteger > ( product_prod_int_int > int ) > ( produc2963269191615333738nteger > int ) > ( produc2963269191615333738nteger > product_prod_int_int ) > ( produc2963269191615333738nteger > produc2963269191615333738nteger ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 7.68/3.89 bNF_cs7194553038297458973at_int: set_Pr49084382684228242at_int > ( produc859450856879609959at_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > ( produc4196048018000912732at_int > produc859450856879609959at_nat ) > ( produc4196048018000912732at_int > produc4196048018000912732at_int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 7.68/3.89 bNF_fs409234558581511823t_unit: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_fs4543836202474805097nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_fs8167890477030535480nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_fs6799373675401686564at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_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,
% 7.68/3.89 bNF_fs6342258632037972510at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc859450856879609959at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OfstOp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_fs1946732770515719151at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Opick__middlep_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_pi4515785505327359899nteger: ( int > int > $o ) > ( int > code_integer > $o ) > int > code_integer > int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Opick__middlep_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,
% 7.68/3.89 bNF_pi770922605693484880at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 7.68/3.89 bNF_re6580757339198446453_nat_o: ( ( $o > $o ) > ( $o > $o ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re7413876800493218871nt_nat: ( ( $o > $o ) > ( int > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re1515921786380824775at_nat: ( ( $o > $o ) > ( nat > nat ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re7387973359137000979nt_num: ( ( $o > $o ) > ( nat > num ) > $o ) > ( ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re2961086658867094474nt_num: ( ( int > int ) > ( int > code_integer ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re2034674868506727813nt_nat: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re7492190849051111027nt_num: ( ( int > int ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > num ) > $o ) > ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re5502197115626545091er_num: ( ( int > nat ) > ( code_integer > nat ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re3642433447925381491nt_nat: ( ( int > nat ) > ( int > int ) > $o ) > ( ( int > num ) > ( int > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re6307232852808291833nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re4099335476084980305nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re9099949428469764705nt_num: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re7435575058205011731_nat_o: ( ( int > nat ) > ( nat > $o ) > $o ) > ( ( int > num ) > ( nat > $o ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re717418264989850719at_nat: ( ( int > nat ) > ( nat > nat ) > $o ) > ( ( int > num ) > ( nat > nat ) > $o ) > ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re4310571189260822741nt_num: ( ( int > nat ) > ( nat > num ) > $o ) > ( ( ( int > int ) > int > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( int > nat ) > ( int > int ) > int > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re7839584876883444355nt_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( ( int > int ) > int > num ) > ( ( int > code_integer ) > int > num ) > $o ) > ( ( int > num ) > ( int > int ) > int > num ) > ( ( code_integer > num ) > ( int > code_integer ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re6292805115969292119er_num: ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > ( code_integer > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re4768042542643474933nt_num: ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > ( int > num ) > $o ) > ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re1982657550219213441nt_nat: ( ( nat > $o ) > ( int > int ) > $o ) > ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re4102725726183926567nt_num: ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > ( int > num ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re2697311982885662685_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re2144779315220482269at_nat: ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > $o ) > nat > $o ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 7.68/3.89 bNF_re3930744952143938759_nat_o: ( ( nat > nat ) > ( $o > $o ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re8622501330148003679nt_num: ( ( nat > nat ) > ( int > nat ) > $o ) > ( ( nat > nat ) > ( int > num ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re7744223787735169245_nat_o: ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > ( nat > $o ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re3262823321055862553at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re1160762158786734233nt_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ) > ( ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( nat > nat ) > ( int > nat ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re239970166668089693at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re584878643992547173nt_num: ( ( nat > nat ) > ( nat > num ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 7.68/3.89 bNF_re3931674169038344211_nat_o: ( ( nat > num ) > ( $o > $o ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > $o ) > nat > $o ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( $o > $o ) > ( nat > $o ) > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re5843449549409830101nt_nat: ( ( nat > num ) > ( int > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > int ) > int > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( int > nat ) > ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_re6524732562925676389at_nat: ( ( nat > num ) > ( nat > nat ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_M_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re2655444144887082515er_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( code_integer > nat ) > code_integer > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( code_integer > nat ) > code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re3846787885862361009nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( int > nat ) > int > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( int > nat ) > int > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_It__Nat__Onat_Mt__Num__Onum_J_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re2742285375668209089nt_num: ( ( nat > num ) > ( nat > num ) > $o ) > ( ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ) > ( ( nat > num ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( nat > num ) > ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_M_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re4105200416192800571er_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( code_integer > num ) > code_integer > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( code_integer > num ) > code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_It__Num__Onum_Mt__Num__Onum_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J_001_062_I_062_It__Int__Oint_Mt__Num__Onum_J_M_062_It__Int__Oint_Mt__Num__Onum_J_J,type,
% 7.68/3.89 bNF_re5446066262214944985nt_num: ( ( num > num ) > ( num > num ) > $o ) > ( ( ( int > num ) > int > num ) > ( ( int > num ) > int > num ) > $o ) > ( ( num > num ) > ( int > num ) > int > num ) > ( ( num > num ) > ( int > num ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re3284331099615978085nt_nat: ( ( product_prod_nat_nat > int ) > ( int > int ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > int ) > product_prod_nat_nat > nat ) > ( ( int > int ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.68/3.89 bNF_re8419181437172746013nt_nat: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ) > ( ( int > nat ) > int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J,type,
% 7.68/3.89 bNF_re2682547871993127601nt_num: ( ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ) > ( ( product_prod_nat_nat > num ) > ( int > num ) > $o ) > ( ( product_prod_nat_nat > nat ) > product_prod_nat_nat > num ) > ( ( int > nat ) > int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_rel_fun_o_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4895681925607069953_o_nat: ( $o > int > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4209105892566519389_o_nat: ( $o > nat > $o ) > ( $o > nat > $o ) > ( $o > $o ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_Eo_001t__Num__Onum,type,
% 7.68/3.89 bNF_re766437678722298023_o_num: ( $o > nat > $o ) > ( $o > num > $o ) > ( $o > $o ) > ( nat > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 7.68/3.89 bNF_re1181178334029315097nteger: ( code_integer > code_integer > $o ) > ( ( code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( code_integer > code_integer > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re40212662316476751um_num: ( code_integer > code_integer > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re8313794964846168862um_num: ( code_integer > int > $o ) > ( num > num > $o ) > ( code_integer > num ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 7.68/3.89 bNF_re1366391616432607057unit_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( ref_a > ref_a > $o ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 7.68/3.89 bNF_re5775369113877777_int_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ref_a > int > $o ) > ( heap_e7401611519738050253t_unit > int > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re9202112420002600977_nat_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ref_a > nat > $o ) > ( heap_e7401611519738050253t_unit > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re1850668159662942673it_o_o: ( ref_a > heap_e7401611519738050253t_unit > $o ) > ( $o > $o > $o ) > ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.68/3.89 bNF_re2828929484557863493at_int: ( int > code_integer > $o ) > ( product_prod_nat_nat > int > $o ) > ( int > product_prod_nat_nat ) > ( code_integer > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 7.68/3.89 bNF_re5404797796594736747unit_o: ( int > int > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( int > ref_a > $o ) > ( int > heap_e7401611519738050253t_unit > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 7.68/3.89 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4715010359784256181nt_nat: ( int > int > $o ) > ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.89 bNF_re3713166177374151349at_int: ( int > int > $o ) > ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_re272988434038980259at_num: ( int > int > $o ) > ( nat > num > $o ) > ( int > nat ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re1845987051190671011um_nat: ( int > int > $o ) > ( num > nat > $o ) > ( int > num ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_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,type,
% 7.68/3.89 bNF_re8766404587435608311at_nat: ( int > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_re4914077030771115051_nat_o: ( int > nat > $o ) > ( nat > $o > $o ) > ( int > nat ) > ( nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re3344003087646356989at_nat: ( int > nat > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_re9124706910656911431at_num: ( int > nat > $o ) > ( nat > num > $o ) > ( int > nat ) > ( nat > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 7.68/3.89 bNF_re3760060065607074657_num_o: ( int > nat > $o ) > ( num > $o > $o ) > ( int > num ) > ( nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re1474333490953826375um_nat: ( int > nat > $o ) > ( num > nat > $o ) > ( int > num ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4629543205785817921at_nat: ( list_nat > list_nat > $o ) > ( nat > nat > $o ) > ( list_nat > nat ) > ( list_nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_re439150893885221597_nat_o: ( nat > $o > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( $o > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001t__Num__Onum_001_Eo,type,
% 7.68/3.89 bNF_re8508505965575957011_num_o: ( nat > $o > $o ) > ( num > $o > $o ) > ( nat > num ) > ( $o > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
% 7.68/3.89 bNF_re8207659476513966505_o_int: ( nat > int > $o ) > ( $o > int > $o ) > ( nat > $o ) > ( int > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re8210149947023016781_o_nat: ( nat > int > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001t__Num__Onum,type,
% 7.68/3.89 bNF_re4767481733178795415_o_num: ( nat > int > $o ) > ( $o > num > $o ) > ( nat > $o ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re6025474579976152573at_nat: ( nat > int > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_re2582806366131931207at_num: ( nat > int > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4155804983283621959um_nat: ( nat > int > $o ) > ( num > nat > $o ) > ( nat > num ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Heap__Oref_Itf__a_J_M_Eo_J_001_062_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
% 7.68/3.89 bNF_re5655699643857186083unit_o: ( nat > nat > $o ) > ( ( ref_a > $o ) > ( heap_e7401611519738050253t_unit > $o ) > $o ) > ( nat > ref_a > $o ) > ( nat > heap_e7401611519738050253t_unit > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 7.68/3.89 bNF_re605504016728627135_int_o: ( nat > nat > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( nat > int > $o ) > ( nat > int > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 7.68/3.89 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re7523573913982466217_o_nat: ( nat > nat > $o ) > ( $o > nat > $o ) > ( nat > $o ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_re1402873238235875719_nat_o: ( nat > nat > $o ) > ( nat > $o > $o ) > ( nat > nat ) > ( nat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_re2211152805895086571at_num: ( nat > nat > $o ) > ( nat > num > $o ) > ( nat > nat ) > ( nat > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re3784151423046777323um_nat: ( nat > nat > $o ) > ( num > nat > $o ) > ( nat > num ) > ( nat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re341483209202555957um_num: ( nat > nat > $o ) > ( num > num > $o ) > ( nat > num ) > ( nat > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 7.68/3.89 bNF_re4702136315717946289at_rat: ( nat > nat > $o ) > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re4736500879113541833um_num: ( num > num > $o ) > ( num > num > $o ) > ( num > num ) > ( num > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 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,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_re6202762543029211035nteger: ( product_prod_nat_nat > int > $o ) > ( int > code_integer > $o ) > ( product_prod_nat_nat > int ) > ( int > code_integer ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re5552630237950767466nt_int: ( product_prod_nat_nat > int > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( int > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.89 bNF_re8466801222876787014um_num: ( product_prod_nat_nat > int > $o ) > ( num > num > $o ) > ( product_prod_nat_nat > num ) > ( int > num ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re20414067882207223nt_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.89 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 ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re1865807574169326223at_o_o: ( rat > rat > $o ) > ( $o > $o > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re7554818335971813481nt_int: ( rat > rat > $o ) > ( int > int > $o ) > ( rat > int ) > ( rat > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re6557955094579809201at_nat: ( rat > rat > $o ) > ( nat > nat > $o ) > ( rat > nat ) > ( rat > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_re1692451286490762625ar_o_o: ( char > char > $o ) > ( $o > $o > $o ) > ( char > $o ) > ( char > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001t__Int__Oint,type,
% 7.68/3.89 bNF_re4780507660726531203_o_int: ( char > char > $o ) > ( $o > int > $o ) > ( char > $o ) > ( char > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001_Eo_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4782998131235581479_o_nat: ( char > char > $o ) > ( $o > nat > $o ) > ( char > $o ) > ( char > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_re6064627146911078825_int_o: ( char > char > $o ) > ( int > $o > $o ) > ( char > int ) > ( char > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_re4731199128827642459nt_int: ( char > char > $o ) > ( int > int > $o ) > ( char > int ) > ( char > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re4733689599336692735nt_nat: ( char > char > $o ) > ( int > nat > $o ) > ( char > int ) > ( char > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_re7885669492343766789_nat_o: ( char > char > $o ) > ( nat > $o > $o ) > ( char > nat ) > ( char > $o ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.89 bNF_re3731845416926587903at_int: ( char > char > $o ) > ( nat > int > $o ) > ( char > nat ) > ( char > int ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Orel__fun_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_re3734335887435638179at_nat: ( char > char > $o ) > ( nat > nat > $o ) > ( char > nat ) > ( char > nat ) > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_001t__Heap__Oref_Itf__a_J_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 7.68/3.89 bNF_sn8323453914685745821t_unit: ( ref_a > ref_a > $o ) > ( ref_a > heap_e7401611519738050253t_unit > $o ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.68/3.89 bNF_sn8000174127721201323nteger: ( int > int > $o ) > ( int > code_integer > $o ) > produc2963269191615333738nteger > produc2963269191615333738nteger ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_sn1062102010912252026nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_sn8916957246138178918at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_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,
% 7.68/3.89 bNF_sn649997494946348640at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > produc4196048018000912732at_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_OsndOp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.68/3.89 bNF_sn1857951156667551021at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Heap__Oref_Itf__a_J_001t__Int__Oint_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi7828673959370436579_int_o: ( ref_a > int ) > ( heap_e7401611519738050253t_unit > int ) > ( int > int > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Heap__Oref_Itf__a_J_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi4623496019404053219_nat_o: ( ref_a > nat ) > ( heap_e7401611519738050253t_unit > nat ) > ( nat > nat > $o ) > ref_a > heap_e7401611519738050253t_unit > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_Eo,type,
% 7.68/3.89 bNF_vi699694178825965831eger_o: ( int > int ) > ( code_integer > code_integer ) > ( int > code_integer > $o ) > int > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi2125572119366604152_int_o: ( int > int ) > ( code_integer > int ) > ( int > int > $o ) > int > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi3884084463199473129_int_o: ( int > int ) > ( int > int ) > ( int > int > $o ) > int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi3197508430158922565_int_o: ( int > int ) > ( nat > int ) > ( int > int > $o ) > int > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi5018550775591610529_nat_o: ( int > int ) > ( nat > nat ) > ( int > nat > $o ) > int > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Rat__Orat_001_Eo,type,
% 7.68/3.89 bNF_vi1281217848275042457_rat_o: ( int > int ) > ( nat > rat ) > ( int > rat > $o ) > int > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__String__Ochar_001_Eo,type,
% 7.68/3.89 bNF_vi9149698133064535136char_o: ( int > int ) > ( nat > char ) > ( int > char > $o ) > int > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi2193923016096921761_nat_o: ( int > nat ) > ( int > nat ) > ( nat > nat > $o ) > int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__Rat__Orat_001_Eo,type,
% 7.68/3.89 bNF_vi7769575839906753835_rat_o: ( int > nat ) > ( num > rat ) > ( nat > rat > $o ) > int > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum_001t__String__Ochar_001_Eo,type,
% 7.68/3.89 bNF_vi1300075849944819442char_o: ( int > nat ) > ( num > char ) > ( nat > char > $o ) > int > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum_001_Eo,type,
% 7.68/3.89 bNF_vi2326032003723069084_num_o: ( int > num ) > ( code_integer > num ) > ( num > num > $o ) > int > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum_001_Eo,type,
% 7.68/3.89 bNF_vi2107963681178519309_num_o: ( int > num ) > ( int > num ) > ( num > num > $o ) > int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi2881549544236934259_int_o: ( int > product_prod_nat_nat ) > ( code_integer > int ) > ( product_prod_nat_nat > int > $o ) > int > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi1204582724742824157_nat_o: ( int > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__List__Olist_It__Nat__Onat_J_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi467646977814820164_int_o: ( list_nat > int ) > ( code_integer > int ) > ( int > int > $o ) > list_nat > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi5202502398764838569_nat_o: ( list_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > list_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__Product____Type__Ounit_001_Eo,type,
% 7.68/3.89 bNF_vi5856767400800367702unit_o: ( nat > $o ) > ( $o > product_unit ) > ( $o > product_unit > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__Rat__Orat_001_Eo,type,
% 7.68/3.89 bNF_vi3868162310295888627_rat_o: ( nat > $o ) > ( $o > rat ) > ( $o > rat > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001_Eo_001_Eo_001t__String__Ochar_001_Eo,type,
% 7.68/3.89 bNF_vi8816436626763797690char_o: ( nat > $o ) > ( $o > char ) > ( $o > char > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi7331807916455492308_int_o: ( nat > int ) > ( code_integer > int ) > ( int > int > $o ) > nat > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi8357618154448083105_int_o: ( nat > int ) > ( nat > int ) > ( int > int > $o ) > nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi1731478210338170163_nat_o: ( nat > int ) > ( num > nat ) > ( int > nat > $o ) > nat > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_vi6818137723729380987_o_o_o: ( nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001t__Product____Type__Ounit_001_Eo,type,
% 7.68/3.89 bNF_vi1443435967014148806unit_o: ( nat > nat ) > ( $o > product_unit ) > ( nat > product_unit > $o ) > nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi6667456707345531737_nat_o: ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001_Eo,type,
% 7.68/3.89 bNF_vi2930123780028963665_rat_o: ( nat > nat ) > ( nat > rat ) > ( nat > rat > $o ) > nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__String__Ochar_001_Eo,type,
% 7.68/3.89 bNF_vi8943400373106913048char_o: ( nat > nat ) > ( nat > char ) > ( nat > char > $o ) > nat > nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi190728152058600505_nat_o: ( nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi1633389952966819264_nat_o: ( product_prod_int_int > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_int_int > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_Eo,type,
% 7.68/3.89 bNF_vi5082502771524357669nt_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 7.68/3.89 bNF_vi8966365312794588230_int_o: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo,type,
% 7.68/3.89 bNF_vi33923956287962137eger_o: ( product_prod_nat_nat > int ) > ( int > code_integer ) > ( int > code_integer > $o ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi9094538908245281400_nat_o: ( product_prod_nat_nat > int ) > ( num > nat ) > ( int > nat > $o ) > product_prod_nat_nat > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi2682369418337388893_int_o: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > int ) > ( int > int > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001_Eo_001_Eo_001_Eo,type,
% 7.68/3.89 bNF_vi9025507403824386624_o_o_o: ( product_prod_nat_nat > nat ) > ( $o > $o ) > ( nat > $o > $o ) > product_prod_nat_nat > $o > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
% 7.68/3.89 bNF_vi5493721401438417730_nat_o: ( product_prod_nat_nat > nat ) > ( int > nat ) > ( nat > nat > $o ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_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_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi5426221348228882691_int_o: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi763171854521451549_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 ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Rat__Orat_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi508398028314858188_int_o: ( rat > int ) > ( code_integer > int ) > ( int > int > $o ) > rat > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__Rat__Orat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi2997284877290766385_nat_o: ( rat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > rat > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__String__Ochar_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo,type,
% 7.68/3.89 bNF_vi7262943168399475603_int_o: ( char > int ) > ( code_integer > int ) > ( int > int > $o ) > char > code_integer > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Def_Ovimage2p_001t__String__Ochar_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.89 bNF_vi728936465572800120_nat_o: ( char > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > char > int > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr2943678036615987864nt_int: set_o > ( $o > int ) > ( $o > int ) > set_Pr958786334691620121nt_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr1946814795223983584at_nat: set_o > ( $o > nat ) > ( $o > nat ) > set_Pr1261947904930325089at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr7727518618234538026at_num: set_o > ( $o > nat ) > ( $o > num ) > set_Pr6200539531224447659at_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr8686673574714534880nt_int: set_int > ( int > int ) > ( int > int ) > set_Pr958786334691620121nt_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr7689810333322530600at_nat: set_int > ( int > nat ) > ( int > nat ) > set_Pr1261947904930325089at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Int__Oint_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr4247142119478309234at_num: set_int > ( int > nat ) > ( int > num ) > set_Pr6200539531224447659at_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 7.68/3.89 bNF_Gr8315020014477690244nt_int: set_nat > ( nat > int ) > ( nat > int ) > set_Pr958786334691620121nt_int ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.89 bNF_Gr7318156773085685964at_nat: set_nat > ( nat > nat ) > ( nat > nat ) > set_Pr1261947904930325089at_nat ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr3875488559241464598at_num: set_nat > ( nat > nat ) > ( nat > num ) > set_Pr6200539531224447659at_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr5511461681843259283at_num: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > num ) > set_Pr6200539531224447659at_num ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_001t__Int__Oint_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 7.68/3.89 bNF_Gr166583433173494904er_num: ( int > num ) > ( code_integer > num ) > ( int > code_integer > $o ) > num > num > $o ).
% 7.68/3.89
% 7.68/3.89 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2p_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
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% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001_Eo_001t__Nat__Onat,type,
% 7.68/3.90 finite4703585013658510744_o_nat: set_o > ( $o > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.90 finite366418920864469932nteger: set_Code_integer > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Int__Oint_001_Eo,type,
% 7.68/3.90 finite5985214029334008090_int_o: set_int > ( int > $o > $o ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.90 finite4582259249640653518nt_nat: set_int > ( int > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Nat__Onat_001_Eo,type,
% 7.68/3.90 finite7806256374766696054_nat_o: set_nat > ( nat > $o > $o ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.90 finite3582905537739598962at_nat: set_nat > ( nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.68/3.90 finite1496024664758132007_nat_o: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o > $o ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.68/3.90 finite2110315540964234241at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_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,
% 7.68/3.90 finite2818816984019561153_nat_o: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > $o > $o ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__commute__on_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,
% 7.68/3.90 finite8619596206551965927at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.90 finite954763878425697269nteger: set_Co726186806682698383nteger > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001_Eo_001t__Nat__Onat,type,
% 7.68/3.90 finite2426395113773319005_o_nat: set_o > ( $o > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.90 finite917065715488314481nteger: set_Code_integer > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.90 finite8981753823465611337nt_nat: set_int > ( int > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.90 finite7982400111564556781at_nat: set_nat > ( nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.68/3.90 finite5150387867909132486at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ocomp__fun__idem__on_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,
% 7.68/3.90 finite352855791390415404at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > nat > nat ) > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 7.68/3.90 finite_finite_o: set_o > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 7.68/3.90 finite_finite_int: set_int > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 7.68/3.90 finite8100373058378681591st_nat: set_list_nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 7.68/3.90 finite_finite_nat: set_nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.68/3.90 finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.68/3.90 finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_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,
% 7.68/3.90 finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Ounit,type,
% 7.68/3.90 finite4290736615968046902t_unit: set_Product_unit > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 7.68/3.90 finite_finite_rat: set_rat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Finite__Set_Ofinite_001t__String__Ochar,type,
% 7.68/3.90 finite_finite_char: set_char > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.90 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 7.68/3.90 comp_C2822359487432382964nteger: ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.90 comp_C3983183376822107068nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 7.68/3.90 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_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,type,
% 7.68/3.90 comp_C7826480081638475456nteger: ( ( code_integer > code_integer ) > code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_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_M_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_J_001t__Code____Numeral__Ointeger,type,
% 7.68/3.90 comp_C6484513282182537548nteger: ( ( code_integer > code_integer ) > produc101387210554329899nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc101387210554329899nteger ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_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_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,
% 7.68/3.90 comp_P3928908779438215820nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
% 7.68/3.90 comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Int__Oint,type,
% 7.68/3.90 comp_o_o_int: ( $o > $o ) > ( int > $o ) > int > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Num__Onum,type,
% 7.68/3.90 comp_o_o_num: ( $o > $o ) > ( num > $o ) > num > $o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_int_nat: ( $o > int ) > ( nat > $o ) > nat > int ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Nat__Onat_001_Eo,type,
% 7.68/3.90 comp_o_nat_o: ( $o > nat ) > ( $o > $o ) > $o > nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Nat__Onat_001t__Int__Oint,type,
% 7.68/3.90 comp_o_nat_int: ( $o > nat ) > ( int > $o ) > int > nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_nat_nat: ( $o > nat ) > ( nat > $o ) > nat > nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Num__Onum_001_Eo,type,
% 7.68/3.90 comp_o_num_o: ( $o > num ) > ( $o > $o ) > $o > num ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Num__Onum_001t__Int__Oint,type,
% 7.68/3.90 comp_o_num_int: ( $o > num ) > ( int > $o ) > int > num ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Num__Onum_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_num_nat: ( $o > num ) > ( nat > $o ) > nat > num ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Num__Onum_001t__Num__Onum,type,
% 7.68/3.90 comp_o_num_num: ( $o > num ) > ( num > $o ) > num > num ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Nat__Onat,type,
% 7.68/3.90 comp_o7658611401268416066_o_nat: ( $o > product_prod_o_o ) > ( nat > $o ) > nat > product_prod_o_o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_I_Eo_J_001t__Product____Type__Ounit,type,
% 7.68/3.90 comp_o6895741221744486154t_unit: ( $o > set_o ) > ( product_unit > $o ) > product_unit > set_o ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Int__Oint_J_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_set_int_nat: ( $o > set_int ) > ( nat > $o ) > nat > set_int ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Int__Oint_J_001t__Product____Type__Ounit,type,
% 7.68/3.90 comp_o1521574261646630388t_unit: ( $o > set_int ) > ( product_unit > $o ) > product_unit > set_int ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_set_nat_nat: ( $o > set_nat ) > ( nat > $o ) > nat > set_nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Ounit,type,
% 7.68/3.90 comp_o9190160103024335696t_unit: ( $o > set_nat ) > ( product_unit > $o ) > product_unit > set_nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Ounit,type,
% 7.68/3.90 comp_o2254869825208929t_unit: ( $o > set_Pr1261947904930325089at_nat ) > ( product_unit > $o ) > product_unit > set_Pr1261947904930325089at_nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Product____Type__Ounit,type,
% 7.68/3.90 comp_o4913564575355137019t_unit: ( $o > set_Pr4329608150637261639at_nat ) > ( product_unit > $o ) > product_unit > set_Pr4329608150637261639at_nat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 7.68/3.90 comp_o_set_rat_nat: ( $o > set_rat ) > ( nat > $o ) > nat > set_rat ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001_Eo_001t__String__Ochar_001_Eo,type,
% 7.68/3.90 comp_o_char_o: ( $o > char ) > ( $o > $o ) > $o > char ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 7.68/3.90 comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 7.68/3.90
% 7.68/3.90 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,
% 7.68/3.90 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 7.68/3.90 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 7.68/3.90 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.68/3.90 comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Int__Oint,type,
% 7.68/3.90 comp_C2177396528461469320um_int: ( code_integer > num ) > ( int > code_integer ) > int > num ).
% 7.68/3.90
% 7.68/3.90 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
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% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
% 7.78/3.90 comp_nat_rat_rat: ( nat > rat ) > ( rat > nat ) > rat > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__String__Ochar,type,
% 7.78/3.90 comp_nat_rat_char: ( nat > rat ) > ( char > nat ) > char > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_nat_set_nat_int: ( nat > set_nat ) > ( int > nat ) > int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_nat_set_nat_nat: ( nat > set_nat ) > ( nat > nat ) > nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_nat_set_rat_int: ( nat > set_rat ) > ( int > nat ) > int > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_nat_set_rat_nat: ( nat > set_rat ) > ( nat > nat ) > nat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__String__Ochar_001t__String__Ochar,type,
% 7.78/3.90 comp_nat_char_char: ( nat > char ) > ( char > nat ) > char > char ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001_Eo,type,
% 7.78/3.90 comp_num_o_o: ( num > $o ) > ( $o > num ) > $o > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Int__Oint,type,
% 7.78/3.90 comp_num_o_int: ( num > $o ) > ( int > num ) > int > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Nat__Onat,type,
% 7.78/3.90 comp_num_o_nat: ( num > $o ) > ( nat > num ) > nat > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001_Eo_001t__Num__Onum,type,
% 7.78/3.90 comp_num_o_num: ( num > $o ) > ( num > num ) > num > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 comp_num_nat_int: ( num > nat ) > ( int > num ) > int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 comp_num_nat_nat: ( num > nat ) > ( nat > num ) > nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 7.78/3.90 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 7.78/3.90 comp_num_num_o: ( num > num ) > ( $o > num ) > $o > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
% 7.78/3.90 comp_n8557746072492896886nteger: ( num > num ) > ( code_integer > num ) > code_integer > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint,type,
% 7.78/3.90 comp_num_num_int: ( num > num ) > ( int > num ) > int > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
% 7.78/3.90 comp_num_num_nat: ( num > num ) > ( nat > num ) > nat > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 7.78/3.90 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint,type,
% 7.78/3.90 comp_num_set_int_int: ( num > set_int ) > ( int > num ) > int > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_num_set_nat_int: ( num > set_nat ) > ( int > num ) > int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_num_set_rat_int: ( num > set_rat ) > ( int > num ) > int > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_I_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_M_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_J_001t__Code____Numeral__Ointeger,type,
% 7.78/3.90 comp_P8564252314792299288nteger: ( produc723880050079548563nteger > produc101387210554329899nteger ) > ( code_integer > produc723880050079548563nteger ) > code_integer > produc101387210554329899nteger ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001_Eo,type,
% 7.78/3.90 comp_P2137996956111167876_o_o_o: ( product_prod_o_o > $o ) > ( $o > product_prod_o_o ) > $o > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
% 7.78/3.90 comp_P551574746845053877_o_o_o: ( product_prod_o_o > product_prod_o_o ) > ( $o > product_prod_o_o ) > $o > product_prod_o_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P7034811116587396339_o_nat: ( product_prod_o_o > product_prod_o_o ) > ( nat > product_prod_o_o ) > nat > product_prod_o_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P4785046977597218846at_nat: ( product_prod_o_o > product_prod_o_o ) > ( product_prod_nat_nat > product_prod_o_o ) > product_prod_nat_nat > product_prod_o_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001_Eo,type,
% 7.78/3.90 comp_P1471321874221585045at_o_o: ( product_prod_o_o > product_prod_nat_o ) > ( $o > product_prod_o_o ) > $o > product_prod_nat_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P465755969289462830at_int: ( product_prod_o_int > product_prod_o_nat ) > ( product_prod_nat_int > product_prod_o_int ) > product_prod_nat_int > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
% 7.78/3.90 comp_P1422407636550552773_nat_o: ( product_prod_o_nat > product_prod_o_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P1391661485614827491at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( nat > product_prod_o_nat ) > nat > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P4962864564169660718at_nat: ( product_prod_o_nat > product_prod_o_nat ) > ( product_prod_nat_nat > product_prod_o_nat ) > product_prod_nat_nat > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P9057111047297513408at_int: ( product_prod_o_nat > product_prod_o_num ) > ( product_prod_nat_int > product_prod_o_nat ) > product_prod_nat_int > product_prod_o_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
% 7.78/3.90 comp_P196761593691424337_nat_o: ( product_prod_o_nat > product_prod_nat_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001_Eo,type,
% 7.78/3.90 comp_P972951341003599239_nat_o: ( product_prod_o_nat > product_prod_num_nat ) > ( $o > product_prod_o_nat ) > $o > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.78/3.90 comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P8237986404257982958t_unit: ( produc8126358835630522215t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc8126358835630522215t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P3239167524078694454t_unit: ( produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P1287623958910499840t_unit: ( produc1799199577659733785_ref_a > ref_a ) > ( produc7812382424243267045t_unit > produc1799199577659733785_ref_a ) > produc7812382424243267045t_unit > ref_a ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J,type,
% 7.78/3.90 comp_P2006160480335490974_ref_a: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( produc1799199577659733785_ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P8019343326919024234t_unit: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( produc7812382424243267045t_unit > produc7812382424243267045t_unit ) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P6390991081591698364at_nat: ( produc7812382424243267045t_unit > heap_e7401611519738050253t_unit ) > ( product_prod_nat_nat > produc7812382424243267045t_unit ) > product_prod_nat_nat > heap_e7401611519738050253t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oref_Itf__a_J_J,type,
% 7.78/3.90 comp_P7254561687666694144_ref_a: ( produc7812382424243267045t_unit > ref_a ) > ( produc1799199577659733785_ref_a > produc7812382424243267045t_unit ) > produc1799199577659733785_ref_a > ref_a ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P4044372497395451596t_unit: ( produc7812382424243267045t_unit > ref_a ) > ( produc7812382424243267045t_unit > produc7812382424243267045t_unit ) > produc7812382424243267045t_unit > ref_a ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P7986581389989349338at_nat: ( produc7812382424243267045t_unit > ref_a ) > ( product_prod_nat_nat > produc7812382424243267045t_unit ) > product_prod_nat_nat > ref_a ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oref_Itf__a_J_J_001t__Heap__Oref_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oref_Itf__a_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 comp_P9134237804721252988t_unit: ( produc5288414631154139675_ref_a > ref_a ) > ( produc7812382424243267045t_unit > produc5288414631154139675_ref_a ) > produc7812382424243267045t_unit > ref_a ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P9034173210191959223nt_int: ( product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
% 7.78/3.90 comp_P6651465171681656048nt_int: ( product_prod_int_int > int ) > ( int > product_prod_int_int ) > int > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 comp_P6653955642190706324nt_nat: ( product_prod_int_int > int ) > ( nat > product_prod_int_int ) > nat > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P5356232565778667509nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Rat__Orat,type,
% 7.78/3.90 comp_P6018825582104210588nt_rat: ( product_prod_int_int > int ) > ( rat > product_prod_int_int ) > rat > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__String__Ochar,type,
% 7.78/3.90 comp_P4161745170962941589t_char: ( product_prod_int_int > int ) > ( char > product_prod_int_int ) > char > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P2318390481314533713nt_int: ( product_prod_int_int > nat ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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,
% 7.78/3.90 comp_P2788356708182965334nt_int: ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_P2134349925370910487at_int: ( product_prod_int_int > product_prod_nat_nat ) > ( int > product_prod_int_int ) > int > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P3488689526429045841nt_nat: ( product_prod_int_nat > nat ) > ( product_prod_int_nat > product_prod_int_nat ) > product_prod_int_nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Int__Oint,type,
% 7.78/3.90 comp_P1145193044942399421um_int: ( product_prod_int_nat > product_prod_nat_num ) > ( int > product_prod_int_nat ) > int > product_prod_nat_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P5799945282029801519_o_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_nat_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P8901546994122883554at_nat: ( product_prod_nat_o > product_prod_nat_o ) > ( product_prod_nat_nat > product_prod_nat_o ) > product_prod_nat_nat > product_prod_nat_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Num__Onum_M_Eo_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P6576135029341976421_o_nat: ( product_prod_nat_o > product_prod_num_o ) > ( nat > product_prod_nat_o ) > nat > product_prod_num_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Num__Onum_M_Eo_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P5807473265676440968nt_nat: ( product_prod_nat_o > product_prod_num_o ) > ( product_prod_int_nat > product_prod_nat_o ) > product_prod_int_nat > product_prod_num_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P397146161216181329at_int: ( product_prod_nat_int > nat ) > ( product_prod_nat_int > product_prod_nat_int ) > product_prod_nat_int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_P8376639181999047357at_int: ( product_prod_nat_int > product_prod_num_nat ) > ( int > product_prod_nat_int ) > int > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P3772045228931366376nt_int: ( product_prod_nat_int > product_prod_num_nat ) > ( product_prod_int_int > product_prod_nat_int ) > product_prod_int_int > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P2002127591014248037at_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 ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P7900071416159368952at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P3913276677246710332at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P4524073163769703009at_int: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > product_prod_nat_nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P4605287290794827253at_nat: ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 comp_P1953119740877977564at_int: ( product_prod_nat_nat > nat ) > ( int > product_prod_nat_nat ) > int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 7.78/3.90 comp_P5292260908303971472st_nat: ( product_prod_nat_nat > nat ) > ( list_nat > product_prod_nat_nat ) > list_nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P1567445206330693457at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P8635049891247748876at_int: ( product_prod_nat_nat > nat ) > ( produc4196048018000912732at_int > product_prod_nat_nat ) > produc4196048018000912732at_int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.78/3.90 comp_P1320480151300532104at_rat: ( product_prod_nat_nat > nat ) > ( rat > product_prod_nat_nat ) > rat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__String__Ochar,type,
% 7.78/3.90 comp_P1491501995297412481t_char: ( product_prod_nat_nat > nat ) > ( char > product_prod_nat_nat ) > char > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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,
% 7.78/3.90 comp_P7428279379633703887at_int: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > product_prod_nat_nat ) > int > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P7430769850142754163at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > ( nat > product_prod_nat_nat ) > nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P6334688330072917552at_int: ( product_prod_nat_nat > product_prod_nat_num ) > ( product_prod_nat_int > product_prod_nat_nat ) > product_prod_nat_int > product_prod_nat_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_P5371577678113413053at_nat: ( product_prod_nat_nat > product_prod_num_nat ) > ( nat > product_prod_nat_nat ) > nat > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P5124699952429557552nt_nat: ( product_prod_nat_nat > product_prod_num_nat ) > ( product_prod_int_nat > product_prod_nat_nat ) > product_prod_int_nat > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Int__Oint,type,
% 7.78/3.90 comp_P7387482301570536291um_int: ( product_prod_nat_nat > product_prod_num_num ) > ( int > product_prod_nat_nat ) > int > product_prod_num_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.78/3.90 comp_P9218946435557410242nt_int: ( product_prod_nat_nat > product_prod_num_num ) > ( product_prod_int_int > product_prod_nat_nat ) > product_prod_int_int > product_prod_num_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P8336958949797789649um_nat: ( product_prod_nat_num > nat ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Num__Onum_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J,type,
% 7.78/3.90 comp_P5051845089628979463um_nat: ( product_prod_nat_num > num ) > ( product_prod_num_nat > product_prod_nat_num ) > product_prod_num_nat > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 7.78/3.90 comp_P3192427084145116251at_num: ( product_prod_num_nat > product_prod_o_nat ) > ( num > product_prod_num_nat ) > num > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 7.78/3.90 comp_P2539519431309506803at_num: ( product_prod_num_nat > product_prod_nat_nat ) > ( num > product_prod_num_nat ) > num > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Num__Onum_Mt__Nat__Onat_J_001t__Num__Onum,type,
% 7.78/3.90 comp_P480327259280165693at_num: ( product_prod_num_nat > product_prod_num_nat ) > ( num > product_prod_num_nat ) > num > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Int__Oint,type,
% 7.78/3.90 comp_P4305060815297604026um_int: ( product_prod_num_num > num ) > ( int > product_prod_num_num ) > int > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
% 7.78/3.90 comp_P864883071962432936um_num: ( product_prod_num_num > num ) > ( num > product_prod_num_num ) > num > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_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,
% 7.78/3.90 comp_P4974406650942564362at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_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__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.78/3.90 comp_P4528037747288561284at_nat: ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 7.78/3.90 comp_P3728553842126764068at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( produc1319942482725812455at_nat > produc1319942482725812455at_nat ) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 7.78/3.90 comp_P8235817900121468292at_nat: ( produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat ) > ( set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_Eo_001_Eo,type,
% 7.78/3.90 comp_P5156358013004227690it_o_o: ( product_unit > $o ) > ( $o > product_unit ) > $o > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_Eo_001t__Nat__Onat,type,
% 7.78/3.90 comp_P4985893458130756478_o_nat: ( product_unit > $o ) > ( nat > product_unit ) > nat > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001_Eo_001_Eo,type,
% 7.78/3.90 comp_rat_o_o: ( rat > $o ) > ( $o > rat ) > $o > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001_Eo_001t__Nat__Onat,type,
% 7.78/3.90 comp_rat_o_nat: ( rat > $o ) > ( nat > rat ) > nat > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__Int__Oint,type,
% 7.78/3.90 comp_rat_int_int: ( rat > int ) > ( int > rat ) > int > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 comp_rat_int_nat: ( rat > int ) > ( nat > rat ) > nat > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Int__Oint_001t__String__Ochar,type,
% 7.78/3.90 comp_rat_int_char: ( rat > int ) > ( char > rat ) > char > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001_Eo,type,
% 7.78/3.90 comp_rat_nat_o: ( rat > nat ) > ( $o > rat ) > $o > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 comp_rat_nat_int: ( rat > nat ) > ( int > rat ) > int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.78/3.90 comp_rat_nat_rat: ( rat > nat ) > ( rat > rat ) > rat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__String__Ochar,type,
% 7.78/3.90 comp_rat_nat_char: ( rat > nat ) > ( char > rat ) > char > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Num__Onum_001t__Nat__Onat,type,
% 7.78/3.90 comp_rat_num_nat: ( rat > num ) > ( nat > rat ) > nat > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Num__Onum_001t__Num__Onum,type,
% 7.78/3.90 comp_rat_num_num: ( rat > num ) > ( num > rat ) > num > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Nat__Onat,type,
% 7.78/3.90 comp_rat_rat_nat: ( rat > rat ) > ( nat > rat ) > nat > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__String__Ochar,type,
% 7.78/3.90 comp_rat_rat_char: ( rat > rat ) > ( char > rat ) > char > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__String__Ochar_001t__String__Ochar,type,
% 7.78/3.90 comp_rat_char_char: ( rat > char ) > ( char > rat ) > char > char ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Set__Oset_I_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_J,type,
% 7.78/3.90 comp_s4786119426940707554nteger: ( set_Co726186806682698383nteger > set_Code_integer ) > ( set_Pr4111642102156807771nteger > set_Co726186806682698383nteger ) > set_Pr4111642102156807771nteger > set_Code_integer ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_I_Eo_J,type,
% 7.78/3.90 comp_s9189197539837705563_set_o: ( set_o > set_nat ) > ( set_o > set_o ) > set_o > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 7.78/3.90 comp_s7717450105097109807et_nat: ( set_int > set_int ) > ( set_nat > set_int ) > set_nat > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 7.78/3.90 comp_s2487324123861929025et_int: ( set_int > set_int ) > ( set_set_int > set_int ) > set_set_int > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 7.78/3.90 comp_s5712175470073906149et_int: ( set_int > set_nat ) > ( set_set_int > set_int ) > set_set_int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001_Eo,type,
% 7.78/3.90 comp_s7011316712748663051_int_o: ( set_nat > set_int ) > ( $o > set_nat ) > $o > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint,type,
% 7.78/3.90 comp_s5617672292595496825nt_int: ( set_nat > set_int ) > ( int > set_nat ) > int > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_s5620162763104547101nt_nat: ( set_nat > set_int ) > ( nat > set_nat ) > nat > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Num__Onum_J,type,
% 7.78/3.90 comp_s6458263553158497821et_num: ( set_nat > set_int ) > ( set_num > set_nat ) > set_num > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s3768223441818958217et_nat: ( set_nat > set_int ) > ( set_set_nat > set_nat ) > set_set_nat > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
% 7.78/3.90 comp_s33089643564333159_nat_o: ( set_nat > set_nat ) > ( $o > set_nat ) > $o > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_s3430750717902475037at_int: ( set_nat > set_nat ) > ( int > set_nat ) > int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_s3433241188411525313at_nat: ( set_nat > set_nat ) > ( nat > set_nat ) > nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 7.78/3.90 comp_s8964582002068861047et_nat: ( set_nat > set_nat ) > ( set_nat > set_nat ) > set_nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s6993074788030935341et_nat: ( set_nat > set_nat ) > ( set_set_nat > set_nat ) > set_set_nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001_Eo,type,
% 7.78/3.90 comp_s8507027185284273247_rat_o: ( set_nat > set_rat ) > ( $o > set_nat ) > $o > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_s8253438564248248613at_int: ( set_nat > set_rat ) > ( int > set_nat ) > int > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_s8255929034757298889at_nat: ( set_nat > set_rat ) > ( nat > set_nat ) > nat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Rat__Orat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s6435139744279249717et_nat: ( set_nat > set_rat ) > ( set_set_nat > set_nat ) > set_set_nat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_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,
% 7.78/3.90 comp_s7355055891894327172at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 7.78/3.90 comp_s8709038167382007543et_int: ( set_set_int > set_int ) > ( set_set_int > set_set_int ) > set_set_int > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s1975749275458958491et_nat: ( set_set_int > set_int ) > ( set_set_nat > set_set_int ) > set_set_nat > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 7.78/3.90 comp_s6907669228194913343et_int: ( set_set_nat > set_nat ) > ( set_set_int > set_set_nat ) > set_set_int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s174380336271864291et_nat: ( set_set_nat > set_nat ) > ( set_set_nat > set_set_nat ) > set_set_nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Set__Oset_It__Rat__Orat_J_J_001t__Set__Oset_It__Rat__Orat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 comp_s703482200030188019et_nat: ( set_set_rat > set_rat ) > ( set_set_nat > set_set_rat ) > set_set_nat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001_Eo_001_Eo,type,
% 7.78/3.90 comp_char_o_o: ( char > $o ) > ( $o > char ) > $o > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001_Eo_001t__String__Ochar,type,
% 7.78/3.90 comp_char_o_char: ( char > $o ) > ( char > char ) > char > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Int__Oint_001t__String__Ochar,type,
% 7.78/3.90 comp_char_int_char: ( char > int ) > ( char > char ) > char > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 comp_char_nat_int: ( char > nat ) > ( int > char ) > int > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 comp_char_nat_nat: ( char > nat ) > ( nat > char ) > nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Nat__Onat_001t__String__Ochar,type,
% 7.78/3.90 comp_char_nat_char: ( char > nat ) > ( char > char ) > char > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Num__Onum_001t__Nat__Onat,type,
% 7.78/3.90 comp_char_num_nat: ( char > num ) > ( nat > char ) > nat > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Num__Onum_001t__Num__Onum,type,
% 7.78/3.90 comp_char_num_num: ( char > num ) > ( num > char ) > num > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Num__Onum_001t__String__Ochar,type,
% 7.78/3.90 comp_char_num_char: ( char > num ) > ( char > char ) > char > num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Rat__Orat_001t__String__Ochar,type,
% 7.78/3.90 comp_char_rat_char: ( char > rat ) > ( char > char ) > char > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Int__Oint_J_001_Eo,type,
% 7.78/3.90 comp_char_set_int_o: ( char > set_int ) > ( $o > char ) > $o > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Int__Oint_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_c3102392033783471720nt_nat: ( char > set_int ) > ( nat > char ) > nat > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Int__Oint_J_001t__Num__Onum,type,
% 7.78/3.90 comp_c8883095856794026162nt_num: ( char > set_int ) > ( num > char ) > num > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
% 7.78/3.90 comp_char_set_nat_o: ( char > set_nat ) > ( $o > char ) > $o > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_c912979988581399656at_int: ( char > set_nat ) > ( int > char ) > int > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_c915470459090449932at_nat: ( char > set_nat ) > ( nat > char ) > nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Nat__Onat_J_001t__Num__Onum,type,
% 7.78/3.90 comp_c6696174282101004374at_num: ( char > set_nat ) > ( num > char ) > num > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Rat__Orat_J_001_Eo,type,
% 7.78/3.90 comp_char_set_rat_o: ( char > set_rat ) > ( $o > char ) > $o > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Rat__Orat_J_001t__Int__Oint,type,
% 7.78/3.90 comp_c5735667834927173232at_int: ( char > set_rat ) > ( int > char ) > int > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Rat__Orat_J_001t__Nat__Onat,type,
% 7.78/3.90 comp_c5738158305436223508at_nat: ( char > set_rat ) > ( nat > char ) > nat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__Set__Oset_It__Rat__Orat_J_001t__Num__Onum,type,
% 7.78/3.90 comp_c2295490091592002142at_num: ( char > set_rat ) > ( num > char ) > num > set_rat ).
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% 7.78/3.90
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% 7.78/3.90 sup_su5231854730092680051_int_o: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_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,
% 7.78/3.90 sup_su362511073950362882_nat_o: ( 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 > $o ).
% 7.78/3.90
% 7.78/3.90 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,
% 7.78/3.90 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 ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
% 7.78/3.90 sup_su6164525874564267778_nat_o: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 7.78/3.90 sup_sup_int: int > int > int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 7.78/3.90 sup_sup_nat: nat > nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 7.78/3.90 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 7.78/3.90 sup_sup_rat: rat > rat > rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 7.78/3.90 sup_sup_set_o: set_o > set_o > set_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 7.78/3.90 sup_sup_set_int: set_int > set_int > set_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 7.78/3.90 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 7.78/3.90 sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 7.78/3.90 sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Ounit_J_J,type,
% 7.78/3.90 sup_su4058753791541417424t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 7.78/3.90 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 7.78/3.90 sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.78/3.90 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 7.78/3.90 sup_su2042722026077122175at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Ounit_J_J,type,
% 7.78/3.90 sup_su4209953369189666580t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 7.78/3.90 sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_M_Eo_J_J,type,
% 7.78/3.90 sup_su2851927382625014182unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Nat__Onat_J_J,type,
% 7.78/3.90 sup_su1639320892072265582it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 7.78/3.90 sup_su6481247232241170203t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 7.78/3.90 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
% 7.78/3.90 sup_su5395584912770621083at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 7.78/3.90 sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 7.78/3.90 sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 7.78/3.90 sup_sup_set_set_o: set_set_o > set_set_o > set_set_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 7.78/3.90 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 7.78/3.90 sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 7.78/3.90 sup_su474284620922681339at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
% 7.78/3.90 sup_su5975557051335651745t_unit: set_set_Product_unit > set_set_Product_unit > set_set_Product_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 7.78/3.90 lattic8265883725875713057ax_nat: set_nat > nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 7.78/3.90 quotie9062115205763428814nteger: ( ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > code_integer > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 7.78/3.90 quotie8207154290130328982nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_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,
% 7.78/3.90 quotie8803226531959296410nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001_Eo_001_Eo,type,
% 7.78/3.90 quotient_o_o: ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > ( $o > $o > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001_Eo_001t__Nat__Onat,type,
% 7.78/3.90 quotient_o_nat: ( $o > $o > $o ) > ( $o > nat ) > ( nat > $o ) > ( $o > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 7.78/3.90 quotie2291698863146621601nteger: ( int > int > $o ) > ( int > code_integer ) > ( code_integer > int ) > ( int > code_integer > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Int__Oint,type,
% 7.78/3.90 quotient_int_int: ( int > int > $o ) > ( int > int ) > ( int > int ) > ( int > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 quotient_int_nat: ( int > int > $o ) > ( int > nat ) > ( nat > int ) > ( int > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Num__Onum,type,
% 7.78/3.90 quotient_int_num: ( int > int > $o ) > ( int > num ) > ( num > int ) > ( int > num > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001_Eo,type,
% 7.78/3.90 quotient_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( $o > nat ) > ( nat > $o > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 quotient_nat_int: ( nat > nat > $o ) > ( nat > int ) > ( int > nat ) > ( nat > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 quotient_nat_nat: ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Num__Onum,type,
% 7.78/3.90 quotient_nat_num: ( nat > nat > $o ) > ( nat > num ) > ( num > nat ) > ( nat > num > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.78/3.90 quotient_nat_rat: ( nat > nat > $o ) > ( nat > rat ) > ( rat > nat ) > ( nat > rat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__String__Ochar,type,
% 7.78/3.90 quotient_nat_char: ( nat > nat > $o ) > ( nat > char ) > ( char > nat ) > ( nat > char > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Num__Onum_001t__Int__Oint,type,
% 7.78/3.90 quotient_num_int: ( num > num > $o ) > ( num > int ) > ( int > num ) > ( num > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Num__Onum_001t__Nat__Onat,type,
% 7.78/3.90 quotient_num_nat: ( num > num > $o ) > ( num > nat ) > ( nat > num ) > ( num > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 7.78/3.90 quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.78/3.90 quotie4166942682936818134at_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 ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Rat__Orat_001t__Int__Oint,type,
% 7.78/3.90 quotient_rat_int: ( rat > rat > $o ) > ( rat > int ) > ( int > rat ) > ( rat > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Rat__Orat_001t__Nat__Onat,type,
% 7.78/3.90 quotient_rat_nat: ( rat > rat > $o ) > ( rat > nat ) > ( nat > rat ) > ( rat > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Rat__Orat_001t__Rat__Orat,type,
% 7.78/3.90 quotient_rat_rat: ( rat > rat > $o ) > ( rat > rat ) > ( rat > rat ) > ( rat > rat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__Rat__Orat_001t__String__Ochar,type,
% 7.78/3.90 quotient_rat_char: ( rat > rat > $o ) > ( rat > char ) > ( char > rat ) > ( rat > char > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__String__Ochar_001t__Int__Oint,type,
% 7.78/3.90 quotient_char_int: ( char > char > $o ) > ( char > int ) > ( int > char ) > ( char > int > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__String__Ochar_001t__Nat__Onat,type,
% 7.78/3.90 quotient_char_nat: ( char > char > $o ) > ( char > nat ) > ( nat > char ) > ( char > nat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__String__Ochar_001t__Rat__Orat,type,
% 7.78/3.90 quotient_char_rat: ( char > char > $o ) > ( char > rat ) > ( rat > char ) > ( char > rat > $o ) > $o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Lifting_OQuotient_001t__String__Ochar_001t__String__Ochar,type,
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% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001_Eo_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
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% 7.78/3.90
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% 7.78/3.90 produc3628557804203378146at_num: ( $o > $o ) > ( nat > num ) > product_prod_o_nat > product_prod_o_num ).
% 7.78/3.90
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% 7.78/3.90 produc9141321880750005618at_o_o: ( $o > nat ) > ( $o > $o ) > product_prod_o_o > product_prod_nat_o ).
% 7.78/3.90
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% 7.78/3.90 produc6587185857518356756at_nat: ( $o > nat ) > ( nat > nat ) > product_prod_o_nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001_Eo_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc4527993685489015646at_nat: ( $o > num ) > ( nat > nat ) > product_prod_o_nat > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 7.78/3.90 produc1802105962441033582nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Heap__Oref_Itf__a_J_001t__Heap__Oref_Itf__a_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 7.78/3.90 produc3456481717235892722t_unit: ( ref_a > ref_a ) > ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ) > produc7812382424243267045t_unit > produc7812382424243267045t_unit ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.78/3.90 produc4404592263388028922at_rat: ( int > int ) > ( nat > rat ) > product_prod_int_nat > product_prod_int_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 7.78/3.90 produc5664932004629684302nt_int: ( int > nat ) > ( int > int ) > product_prod_int_int > product_prod_nat_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 produc5667422475138734578nt_nat: ( int > nat ) > ( int > nat ) > product_prod_int_int > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum,type,
% 7.78/3.90 produc2224754261294513212nt_num: ( int > nat ) > ( int > num ) > product_prod_int_int > product_prod_nat_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 7.78/3.90 produc8298419091753553490_nat_o: ( int > nat ) > ( nat > $o ) > product_prod_int_nat > product_prod_nat_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 7.78/3.90 produc4665578292728629746at_int: ( int > nat ) > ( nat > int ) > product_prod_int_nat > product_prod_nat_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc4668068763237680022at_nat: ( int > nat ) > ( nat > nat ) > product_prod_int_nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
% 7.78/3.90 produc1225400549393458656at_num: ( int > nat ) > ( nat > num ) > product_prod_int_nat > product_prod_nat_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 7.78/3.90 produc4032938703151184286at_rat: ( int > nat ) > ( nat > rat ) > product_prod_int_nat > product_prod_nat_rat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 7.78/3.90 produc165562089265172102nt_num: ( int > num ) > ( int > num ) > product_prod_int_int > product_prod_num_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001_Eo,type,
% 7.78/3.90 produc9074608839065728392_nat_o: ( int > num ) > ( nat > $o ) > product_prod_int_nat > product_prod_num_o ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc2608876591208338912at_nat: ( int > num ) > ( nat > nat ) > product_prod_int_nat > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
% 7.78/3.90 produc8248099538878400170nt_int: ( nat > $o ) > ( int > int ) > product_prod_nat_int > product_prod_o_int ).
% 7.78/3.90
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% 7.78/3.90 produc8250590009387450446nt_nat: ( nat > $o ) > ( int > nat ) > product_prod_nat_int > product_prod_o_nat ).
% 7.78/3.90
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% 7.78/3.90 produc4807921795543229080nt_num: ( nat > $o ) > ( int > num ) > product_prod_nat_int > product_prod_o_num ).
% 7.78/3.90
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% 7.78/3.90 produc6957950696844810486_nat_o: ( nat > $o ) > ( nat > $o ) > product_prod_nat_nat > product_prod_o_o ).
% 7.78/3.90
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% 7.78/3.90 produc7251236297486395890at_nat: ( nat > $o ) > ( nat > nat ) > product_prod_nat_nat > product_prod_o_nat ).
% 7.78/3.90
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% 7.78/3.90 produc8346403496959479886nt_int: ( nat > int ) > ( int > int ) > product_prod_nat_int > product_prod_int_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 produc8348893967468530162nt_nat: ( nat > int ) > ( int > nat ) > product_prod_nat_int > product_prod_int_nat ).
% 7.78/3.90
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint,type,
% 7.78/3.90 produc5477380188365894716um_int: ( nat > int ) > ( num > int ) > product_prod_nat_num > product_prod_int_int ).
% 7.78/3.90
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% 7.78/3.90 produc2001155298098703512at_o_o: ( nat > nat ) > ( $o > $o ) > product_prod_nat_o > product_prod_nat_o ).
% 7.78/3.90
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% 7.78/3.90 produc7974749936722635250nt_int: ( nat > nat ) > ( int > int ) > product_prod_nat_int > product_prod_nat_int ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 produc7977240407231685526nt_nat: ( nat > nat ) > ( int > nat ) > product_prod_nat_int > product_prod_nat_nat ).
% 7.78/3.90
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% 7.78/3.90 produc4534572193387464160nt_num: ( nat > nat ) > ( int > num ) > product_prod_nat_int > product_prod_nat_num ).
% 7.78/3.90
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% 7.78/3.90 produc4787215299218314158_nat_o: ( nat > nat ) > ( nat > $o ) > product_prod_nat_nat > product_prod_nat_o ).
% 7.78/3.90
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% 7.78/3.90
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% 7.78/3.90 produc3535218481486409604at_num: ( nat > nat ) > ( nat > num ) > product_prod_nat_nat > product_prod_nat_num ).
% 7.78/3.90
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% 7.78/3.90
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo_001_Eo,type,
% 7.78/3.90 produc3264868786340801506um_o_o: ( nat > num ) > ( $o > $o ) > product_prod_nat_o > product_prod_num_o ).
% 7.78/3.90
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% 7.78/3.90
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% 7.78/3.90
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% 7.78/3.90 produc1476026309457068494at_num: ( nat > num ) > ( nat > num ) > product_prod_nat_nat > product_prod_num_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint_001t__Int__Oint,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint_001t__Nat__Onat,type,
% 7.78/3.90 produc8749313216793205150nt_nat: ( nat > rat ) > ( int > nat ) > product_prod_nat_int > product_prod_rat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Num__Onum_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.78/3.90 produc170006858110003436at_nat: ( nat > set_Pr1261947904930325089at_nat ) > ( num > set_Pr1261947904930325089at_nat ) > product_prod_nat_num > produc3843707927480180839at_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Num__Onum_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc8319293927732033832at_nat: ( num > $o ) > ( nat > nat ) > product_prod_num_nat > product_prod_o_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc4208724500416182148at_nat: ( num > nat ) > ( nat > nat ) > product_prod_num_nat > product_prod_nat_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.78/3.90 produc2149532328386841038at_nat: ( num > num ) > ( nat > nat ) > product_prod_num_nat > product_prod_num_nat ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 7.78/3.90 produc3932168101365401472at_num: ( set_Pr1261947904930325089at_nat > nat ) > ( set_Pr1261947904930325089at_nat > num ) > produc3843707927480180839at_nat > product_prod_nat_num ).
% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__Rat__Orat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat_001t__String__Ochar,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Rat__Orat_001t__Int__Oint,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Rat__Orat_001t__Nat__Onat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Rat__Orat_001t__Rat__Orat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__Rat__Orat_001t__String__Ochar,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__String__Ochar_001t__Int__Oint,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__String__Ochar_001t__Nat__Onat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__String__Ochar_001t__Rat__Orat,type,
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% 7.78/3.90
% 7.78/3.90 thf(sy_c_Product__Type_Omap__prod_001t__String__Ochar_001t__String__Ochar_001t__String__Ochar_001t__String__Ochar,type,
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% 7.78/3.90
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Int__Oint_001t__Nat__Onat,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001_Eo,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Int__Oint,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Num__Onum,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Rat__Orat,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__String__Ochar,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Num__Onum_001t__Nat__Onat,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Num__Onum_001t__Num__Onum,type,
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% 7.78/3.91 conver4368408235330554745_ref_a: ( produc7812382424243267045t_unit > ref_a > $o ) > ref_a > produc7812382424243267045t_unit > $o ).
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Int__Oint,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Nat__Onat,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__Rat__Orat,type,
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% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__Rat__Orat_001t__String__Ochar,type,
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% 7.78/3.91 conver5243090411617913141at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 7.78/3.91
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% 7.78/3.91 conver9095369822871743413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Int__Oint,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Nat__Onat,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__Rat__Orat,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oconversep_001t__String__Ochar_001t__String__Ochar,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Int__Oint,type,
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% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Nat__Onat,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Int__Oint,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
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% 7.78/3.91 inv_im2354225701593503139at_nat: set_Pr1261947904930325089at_nat > ( set_Pr4329608150637261639at_nat > nat ) > set_Pr7459493094073627847at_nat ).
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% 7.78/3.91 inv_im4434751243573137211at_int: set_Pr4329608150637261639at_nat > ( int > set_Pr1261947904930325089at_nat ) > set_Pr958786334691620121nt_int ).
% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 7.78/3.91 inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > ( nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 7.78/3.91 inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).
% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Int__Oint,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orefl__on_001_Eo,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orefl__on_001t__Product____Type__Ounit,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orefl__on_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,
% 7.78/3.91 refl_o6272981002401706822at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o ).
% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
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% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
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% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Int__Oint_Mt__Num__Onum_J_001_062_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
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% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
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% 7.78/3.91
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% 7.78/3.91
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% 7.78/3.91
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% 7.78/3.91
% 7.78/3.91 thf(sy_c_Relation_Orelcompp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
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% 7.78/3.91 ( ( present_a @ ( set_a @ R @ V @ H ) )
% 7.78/3.91 = ( present_a @ H ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_13_effect__refE,axiom,
% 7.78/3.91 ! [V: a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( ref_a2 @ V ) @ H @ H2 @ R )
% 7.78/3.91 => ~ ( ( ( get_a @ H2 @ R )
% 7.78/3.91 = V )
% 7.78/3.91 => ( ( present_a @ H2 @ R )
% 7.78/3.91 => ( present_a @ H @ R ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_14_alloc__set,axiom,
% 7.78/3.91 ! [X2: a,R: ref_a,X3: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( produc473321116828791851t_unit @ ( alloc_a @ X2 @ ( set_a @ R @ X3 @ H ) ) )
% 7.78/3.91 = ( produc473321116828791851t_unit @ ( alloc_a @ X2 @ H ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_15_ref_H__def,axiom,
% 7.78/3.91 ref_a3 = ref_a2 ).
% 7.78/3.91
% 7.78/3.91 thf(fact_16_get__alloc__neq,axiom,
% 7.78/3.91 ! [R: ref_a,V: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( noteq_a_a @ R @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) )
% 7.78/3.91 => ( ( get_a @ ( produc1126150082675451753t_unit @ ( alloc_a @ V @ H ) ) @ R )
% 7.78/3.91 = ( get_a @ H @ R ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_17_effect__changeE,axiom,
% 7.78/3.91 ! [F: a > a,R2: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: a] :
% 7.78/3.91 ( ( heap_effect_a @ ( change_a @ F @ R2 ) @ H @ H2 @ R )
% 7.78/3.91 => ~ ( ( H2
% 7.78/3.91 = ( set_a @ R2 @ ( F @ ( get_a @ H @ R2 ) ) @ H ) )
% 7.78/3.91 => ( R
% 7.78/3.91 != ( F @ ( get_a @ H @ R2 ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_18_effect__changeE,axiom,
% 7.78/3.91 ! [F: ref_a > ref_a,R2: ref_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( change_ref_a @ F @ R2 ) @ H @ H2 @ R )
% 7.78/3.91 => ~ ( ( H2
% 7.78/3.91 = ( set_ref_a2 @ R2 @ ( F @ ( get_ref_a @ H @ R2 ) ) @ H ) )
% 7.78/3.91 => ( R
% 7.78/3.91 != ( F @ ( get_ref_a @ H @ R2 ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_19_effect__changeI,axiom,
% 7.78/3.91 ! [H2: heap_e7401611519738050253t_unit,R: ref_a,F: a > a,H: heap_e7401611519738050253t_unit,X2: a] :
% 7.78/3.91 ( ( H2
% 7.78/3.91 = ( set_a @ R @ ( F @ ( get_a @ H @ R ) ) @ H ) )
% 7.78/3.91 => ( ( X2
% 7.78/3.91 = ( F @ ( get_a @ H @ R ) ) )
% 7.78/3.91 => ( heap_effect_a @ ( change_a @ F @ R ) @ H @ H2 @ X2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_20_effect__changeI,axiom,
% 7.78/3.91 ! [H2: heap_e7401611519738050253t_unit,R: ref_ref_a,F: ref_a > ref_a,H: heap_e7401611519738050253t_unit,X2: ref_a] :
% 7.78/3.91 ( ( H2
% 7.78/3.91 = ( set_ref_a2 @ R @ ( F @ ( get_ref_a @ H @ R ) ) @ H ) )
% 7.78/3.91 => ( ( X2
% 7.78/3.91 = ( F @ ( get_ref_a @ H @ R ) ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( change_ref_a @ F @ R ) @ H @ H2 @ X2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_21_present__alloc__neq,axiom,
% 7.78/3.91 ! [H: heap_e7401611519738050253t_unit,R: ref_a,V: a] :
% 7.78/3.91 ( ( present_a @ H @ R )
% 7.78/3.91 => ( noteq_a_a @ R @ ( produc473321116828791851t_unit @ ( alloc_a @ V @ H ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_22_Ref_Oget__set__neq,axiom,
% 7.78/3.91 ! [R: ref_a,S2: ref_a,X2: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( noteq_a_a @ R @ S2 )
% 7.78/3.91 => ( ( get_a @ ( set_a @ S2 @ X2 @ H ) @ R )
% 7.78/3.91 = ( get_a @ H @ R ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_23_ref__def,axiom,
% 7.78/3.91 ( ref_a2
% 7.78/3.91 = ( ^ [V3: a] : ( heap_heap_ref_a @ ( alloc_a @ V3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_24_effect__lookupE,axiom,
% 7.78/3.91 ! [R: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: a] :
% 7.78/3.91 ( ( heap_effect_a @ ( lookup_a @ R ) @ H @ H2 @ X2 )
% 7.78/3.91 => ~ ( ( H2 = H )
% 7.78/3.91 => ( X2
% 7.78/3.91 != ( get_a @ H @ R ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_25_effect__lookupE,axiom,
% 7.78/3.91 ! [R: ref_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( lookup_ref_a @ R ) @ H @ H2 @ X2 )
% 7.78/3.91 => ~ ( ( H2 = H )
% 7.78/3.91 => ( X2
% 7.78/3.91 != ( get_ref_a @ H @ R ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_26_effect__lookupI,axiom,
% 7.78/3.91 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,X2: a,R: ref_a] :
% 7.78/3.91 ( ( H2 = H )
% 7.78/3.91 => ( ( X2
% 7.78/3.91 = ( get_a @ H @ R ) )
% 7.78/3.91 => ( heap_effect_a @ ( lookup_a @ R ) @ H @ H2 @ X2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_27_effect__lookupI,axiom,
% 7.78/3.91 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,X2: ref_a,R: ref_ref_a] :
% 7.78/3.91 ( ( H2 = H )
% 7.78/3.91 => ( ( X2
% 7.78/3.91 = ( get_ref_a @ H @ R ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( lookup_ref_a @ R ) @ H @ H2 @ X2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_28_effect__refI,axiom,
% 7.78/3.91 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,V: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 7.78/3.91 = ( alloc_a @ V @ H ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( ref_a2 @ V ) @ H @ H2 @ R ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_29_snd__swap,axiom,
% 7.78/3.91 ! [X2: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( produc6369869760173755749_ref_a @ ( produc970745769005243767t_unit @ X2 ) )
% 7.78/3.91 = ( produc473321116828791851t_unit @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_30_snd__swap,axiom,
% 7.78/3.91 ! [X2: produc1799199577659733785_ref_a] :
% 7.78/3.91 ( ( produc1126150082675451753t_unit @ ( produc6214465446503547763_ref_a @ X2 ) )
% 7.78/3.91 = ( produc5717040794327095847_ref_a @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_31_fst__swap,axiom,
% 7.78/3.91 ! [X2: produc1799199577659733785_ref_a] :
% 7.78/3.91 ( ( produc473321116828791851t_unit @ ( produc6214465446503547763_ref_a @ X2 ) )
% 7.78/3.91 = ( produc6369869760173755749_ref_a @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_32_fst__swap,axiom,
% 7.78/3.91 ! [X2: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( produc5717040794327095847_ref_a @ ( produc970745769005243767t_unit @ X2 ) )
% 7.78/3.91 = ( produc1126150082675451753t_unit @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_33_prod_Oinject,axiom,
% 7.78/3.91 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat,Y1: set_Pr4329608150637261639at_nat,Y22: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( ( produc9060074326276436823at_nat @ X1 @ X22 )
% 7.78/3.91 = ( produc9060074326276436823at_nat @ Y1 @ Y22 ) )
% 7.78/3.91 = ( ( X1 = Y1 )
% 7.78/3.91 & ( X22 = Y22 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_34_prod_Oinject,axiom,
% 7.78/3.91 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat,Y1: set_Pr1261947904930325089at_nat,Y22: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( ( produc2922128104949294807at_nat @ X1 @ X22 )
% 7.78/3.91 = ( produc2922128104949294807at_nat @ Y1 @ Y22 ) )
% 7.78/3.91 = ( ( X1 = Y1 )
% 7.78/3.91 & ( X22 = Y22 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_35_prod_Oinject,axiom,
% 7.78/3.91 ! [X1: nat,X22: num,Y1: nat,Y22: num] :
% 7.78/3.91 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 7.78/3.91 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 7.78/3.91 = ( ( X1 = Y1 )
% 7.78/3.91 & ( X22 = Y22 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_36_prod_Oinject,axiom,
% 7.78/3.91 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 7.78/3.91 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 7.78/3.91 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 7.78/3.91 = ( ( X1 = Y1 )
% 7.78/3.91 & ( X22 = Y22 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_37_prod_Oinject,axiom,
% 7.78/3.91 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 7.78/3.91 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 7.78/3.91 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 7.78/3.91 = ( ( X1 = Y1 )
% 7.78/3.91 & ( X22 = Y22 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_38_old_Oprod_Oinject,axiom,
% 7.78/3.91 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( ( produc9060074326276436823at_nat @ A @ B )
% 7.78/3.91 = ( produc9060074326276436823at_nat @ A2 @ B2 ) )
% 7.78/3.91 = ( ( A = A2 )
% 7.78/3.91 & ( B = B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_39_old_Oprod_Oinject,axiom,
% 7.78/3.91 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 7.78/3.91 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 7.78/3.91 = ( ( A = A2 )
% 7.78/3.91 & ( B = B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_40_old_Oprod_Oinject,axiom,
% 7.78/3.91 ! [A: nat,B: num,A2: nat,B2: num] :
% 7.78/3.91 ( ( ( product_Pair_nat_num @ A @ B )
% 7.78/3.91 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 7.78/3.91 = ( ( A = A2 )
% 7.78/3.91 & ( B = B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_41_old_Oprod_Oinject,axiom,
% 7.78/3.91 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 7.78/3.91 ( ( ( product_Pair_nat_nat @ A @ B )
% 7.78/3.91 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 7.78/3.91 = ( ( A = A2 )
% 7.78/3.91 & ( B = B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_42_old_Oprod_Oinject,axiom,
% 7.78/3.91 ! [A: int,B: int,A2: int,B2: int] :
% 7.78/3.91 ( ( ( product_Pair_int_int @ A @ B )
% 7.78/3.91 = ( product_Pair_int_int @ A2 @ B2 ) )
% 7.78/3.91 = ( ( A = A2 )
% 7.78/3.91 & ( B = B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_43_swap__simp,axiom,
% 7.78/3.91 ! [X2: num,Y3: nat] :
% 7.78/3.91 ( ( product_swap_num_nat @ ( product_Pair_num_nat @ X2 @ Y3 ) )
% 7.78/3.91 = ( product_Pair_nat_num @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_44_swap__simp,axiom,
% 7.78/3.91 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( produc5396952528824381687at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = ( produc9060074326276436823at_nat @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_45_swap__simp,axiom,
% 7.78/3.91 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( produc3946833401584108663at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = ( produc2922128104949294807at_nat @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_46_swap__simp,axiom,
% 7.78/3.91 ! [X2: nat,Y3: num] :
% 7.78/3.91 ( ( product_swap_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.91 = ( product_Pair_num_nat @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_47_swap__simp,axiom,
% 7.78/3.91 ! [X2: nat,Y3: nat] :
% 7.78/3.91 ( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.91 = ( product_Pair_nat_nat @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_48_swap__simp,axiom,
% 7.78/3.91 ! [X2: int,Y3: int] :
% 7.78/3.91 ( ( product_swap_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.91 = ( product_Pair_int_int @ Y3 @ X2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_49_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: produc1319942482725812455at_nat] :
% 7.78/3.91 ( ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ Prod ) @ ( produc826222791318859909at_nat @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_50_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: produc3843707927480180839at_nat] :
% 7.78/3.91 ( ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ Prod ) @ ( produc2937545259423399429at_nat @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_51_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: product_prod_nat_num] :
% 7.78/3.91 ( ( product_Pair_nat_num @ ( product_fst_nat_num @ Prod ) @ ( product_snd_nat_num @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_52_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: product_prod_nat_nat] :
% 7.78/3.91 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_53_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: product_prod_int_int] :
% 7.78/3.91 ( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_54_prod_Ocollapse,axiom,
% 7.78/3.91 ! [Prod: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ Prod ) @ ( produc1126150082675451753t_unit @ Prod ) )
% 7.78/3.91 = Prod ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_55_old_Oprod_Oexhaust,axiom,
% 7.78/3.91 ! [Y3: produc1319942482725812455at_nat] :
% 7.78/3.91 ~ ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( Y3
% 7.78/3.91 != ( produc9060074326276436823at_nat @ A3 @ B3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_56_old_Oprod_Oexhaust,axiom,
% 7.78/3.91 ! [Y3: produc3843707927480180839at_nat] :
% 7.78/3.91 ~ ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( Y3
% 7.78/3.91 != ( produc2922128104949294807at_nat @ A3 @ B3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_57_old_Oprod_Oexhaust,axiom,
% 7.78/3.91 ! [Y3: product_prod_nat_num] :
% 7.78/3.91 ~ ! [A3: nat,B3: num] :
% 7.78/3.91 ( Y3
% 7.78/3.91 != ( product_Pair_nat_num @ A3 @ B3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_58_old_Oprod_Oexhaust,axiom,
% 7.78/3.91 ! [Y3: product_prod_nat_nat] :
% 7.78/3.91 ~ ! [A3: nat,B3: nat] :
% 7.78/3.91 ( Y3
% 7.78/3.91 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_59_old_Oprod_Oexhaust,axiom,
% 7.78/3.91 ! [Y3: product_prod_int_int] :
% 7.78/3.91 ~ ! [A3: int,B3: int] :
% 7.78/3.91 ( Y3
% 7.78/3.91 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_60_surj__pair,axiom,
% 7.78/3.91 ! [P: produc1319942482725812455at_nat] :
% 7.78/3.91 ? [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc9060074326276436823at_nat @ X @ Y ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_61_surj__pair,axiom,
% 7.78/3.91 ! [P: produc3843707927480180839at_nat] :
% 7.78/3.91 ? [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc2922128104949294807at_nat @ X @ Y ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_62_surj__pair,axiom,
% 7.78/3.91 ! [P: product_prod_nat_num] :
% 7.78/3.91 ? [X: nat,Y: num] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_num @ X @ Y ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_63_surj__pair,axiom,
% 7.78/3.91 ! [P: product_prod_nat_nat] :
% 7.78/3.91 ? [X: nat,Y: nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_nat @ X @ Y ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_64_surj__pair,axiom,
% 7.78/3.91 ! [P: product_prod_int_int] :
% 7.78/3.91 ? [X: int,Y: int] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_int_int @ X @ Y ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_65_prod__cases,axiom,
% 7.78/3.91 ! [P2: produc1319942482725812455at_nat > $o,P: produc1319942482725812455at_nat] :
% 7.78/3.91 ( ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( P2 @ ( produc9060074326276436823at_nat @ A3 @ B3 ) )
% 7.78/3.91 => ( P2 @ P ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_66_prod__cases,axiom,
% 7.78/3.91 ! [P2: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
% 7.78/3.91 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P2 @ ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 7.78/3.91 => ( P2 @ P ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_67_prod__cases,axiom,
% 7.78/3.91 ! [P2: product_prod_nat_num > $o,P: product_prod_nat_num] :
% 7.78/3.91 ( ! [A3: nat,B3: num] : ( P2 @ ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.91 => ( P2 @ P ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_68_prod__cases,axiom,
% 7.78/3.91 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 7.78/3.91 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 7.78/3.91 => ( P2 @ P ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_69_prod__cases,axiom,
% 7.78/3.91 ! [P2: product_prod_int_int > $o,P: product_prod_int_int] :
% 7.78/3.91 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 7.78/3.91 => ( P2 @ P ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_70_Pair__inject,axiom,
% 7.78/3.91 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( ( produc9060074326276436823at_nat @ A @ B )
% 7.78/3.91 = ( produc9060074326276436823at_nat @ A2 @ B2 ) )
% 7.78/3.91 => ~ ( ( A = A2 )
% 7.78/3.91 => ( B != B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_71_Pair__inject,axiom,
% 7.78/3.91 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 7.78/3.91 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 7.78/3.91 => ~ ( ( A = A2 )
% 7.78/3.91 => ( B != B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_72_Pair__inject,axiom,
% 7.78/3.91 ! [A: nat,B: num,A2: nat,B2: num] :
% 7.78/3.91 ( ( ( product_Pair_nat_num @ A @ B )
% 7.78/3.91 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 7.78/3.91 => ~ ( ( A = A2 )
% 7.78/3.91 => ( B != B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_73_Pair__inject,axiom,
% 7.78/3.91 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 7.78/3.91 ( ( ( product_Pair_nat_nat @ A @ B )
% 7.78/3.91 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 7.78/3.91 => ~ ( ( A = A2 )
% 7.78/3.91 => ( B != B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_74_Pair__inject,axiom,
% 7.78/3.91 ! [A: int,B: int,A2: int,B2: int] :
% 7.78/3.91 ( ( ( product_Pair_int_int @ A @ B )
% 7.78/3.91 = ( product_Pair_int_int @ A2 @ B2 ) )
% 7.78/3.91 => ~ ( ( A = A2 )
% 7.78/3.91 => ( B != B2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_75_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: produc3843707927480180839at_nat,P2: produc3843707927480180839at_nat > $o] :
% 7.78/3.91 ( ( member8757157785044589968at_nat @ A @ ( collec6321179662152712658at_nat @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_76_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: $o,P2: $o > $o] :
% 7.78/3.91 ( ( member_o @ A @ ( collect_o @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_77_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: int,P2: int > $o] :
% 7.78/3.91 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_78_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 7.78/3.91 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_79_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: nat,P2: nat > $o] :
% 7.78/3.91 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_80_mem__Collect__eq,axiom,
% 7.78/3.91 ! [A: product_prod_int_int,P2: product_prod_int_int > $o] :
% 7.78/3.91 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P2 ) )
% 7.78/3.91 = ( P2 @ A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_81_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( collec6321179662152712658at_nat
% 7.78/3.91 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_82_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_o] :
% 7.78/3.91 ( ( collect_o
% 7.78/3.91 @ ^ [X4: $o] : ( member_o @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_83_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_int] :
% 7.78/3.91 ( ( collect_int
% 7.78/3.91 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_84_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( collec3392354462482085612at_nat
% 7.78/3.91 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_85_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_nat] :
% 7.78/3.91 ( ( collect_nat
% 7.78/3.91 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_86_Collect__mem__eq,axiom,
% 7.78/3.91 ! [A4: set_Pr958786334691620121nt_int] :
% 7.78/3.91 ( ( collec213857154873943460nt_int
% 7.78/3.91 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A4 ) )
% 7.78/3.91 = A4 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_87_Collect__cong,axiom,
% 7.78/3.91 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 7.78/3.91 ( ! [X: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ X )
% 7.78/3.91 = ( Q2 @ X ) )
% 7.78/3.91 => ( ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.91 = ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_88_Collect__cong,axiom,
% 7.78/3.91 ! [P2: nat > $o,Q2: nat > $o] :
% 7.78/3.91 ( ! [X: nat] :
% 7.78/3.91 ( ( P2 @ X )
% 7.78/3.91 = ( Q2 @ X ) )
% 7.78/3.91 => ( ( collect_nat @ P2 )
% 7.78/3.91 = ( collect_nat @ Q2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_89_Collect__cong,axiom,
% 7.78/3.91 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > $o] :
% 7.78/3.91 ( ! [X: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ X )
% 7.78/3.91 = ( Q2 @ X ) )
% 7.78/3.91 => ( ( collec213857154873943460nt_int @ P2 )
% 7.78/3.91 = ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_90_fst__eqD,axiom,
% 7.78/3.91 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_91_fst__eqD,axiom,
% 7.78/3.91 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_92_fst__eqD,axiom,
% 7.78/3.91 ! [X2: nat,Y3: num,A: nat] :
% 7.78/3.91 ( ( ( product_fst_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_93_fst__eqD,axiom,
% 7.78/3.91 ! [X2: nat,Y3: nat,A: nat] :
% 7.78/3.91 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_94_fst__eqD,axiom,
% 7.78/3.91 ! [X2: int,Y3: int,A: int] :
% 7.78/3.91 ( ( ( product_fst_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_95_fst__eqD,axiom,
% 7.78/3.91 ! [X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: ref_a] :
% 7.78/3.91 ( ( ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( X2 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_96_fst__conv,axiom,
% 7.78/3.91 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_97_fst__conv,axiom,
% 7.78/3.91 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_98_fst__conv,axiom,
% 7.78/3.91 ! [X1: nat,X22: num] :
% 7.78/3.91 ( ( product_fst_nat_num @ ( product_Pair_nat_num @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_99_fst__conv,axiom,
% 7.78/3.91 ! [X1: nat,X22: nat] :
% 7.78/3.91 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_100_fst__conv,axiom,
% 7.78/3.91 ! [X1: int,X22: int] :
% 7.78/3.91 ( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_101_fst__conv,axiom,
% 7.78/3.91 ! [X1: ref_a,X22: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X1 @ X22 ) )
% 7.78/3.91 = X1 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_102_snd__eqD,axiom,
% 7.78/3.91 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_103_snd__eqD,axiom,
% 7.78/3.91 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_104_snd__eqD,axiom,
% 7.78/3.91 ! [X2: nat,Y3: num,A: num] :
% 7.78/3.91 ( ( ( product_snd_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_105_snd__eqD,axiom,
% 7.78/3.91 ! [X2: nat,Y3: nat,A: nat] :
% 7.78/3.91 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_106_snd__eqD,axiom,
% 7.78/3.91 ! [X2: int,Y3: int,A: int] :
% 7.78/3.91 ( ( ( product_snd_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_107_snd__eqD,axiom,
% 7.78/3.91 ! [X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 7.78/3.91 = A )
% 7.78/3.91 => ( Y3 = A ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_108_snd__conv,axiom,
% 7.78/3.91 ! [X1: set_Pr4329608150637261639at_nat,X22: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_109_snd__conv,axiom,
% 7.78/3.91 ! [X1: set_Pr1261947904930325089at_nat,X22: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_110_snd__conv,axiom,
% 7.78/3.91 ! [X1: nat,X22: num] :
% 7.78/3.91 ( ( product_snd_nat_num @ ( product_Pair_nat_num @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_111_snd__conv,axiom,
% 7.78/3.91 ! [X1: nat,X22: nat] :
% 7.78/3.91 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_112_snd__conv,axiom,
% 7.78/3.91 ! [X1: int,X22: int] :
% 7.78/3.91 ( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_113_snd__conv,axiom,
% 7.78/3.91 ! [X1: ref_a,X22: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X1 @ X22 ) )
% 7.78/3.91 = X22 ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_114_prod_Oswap__def,axiom,
% 7.78/3.91 ( produc5396952528824381687at_nat
% 7.78/3.91 = ( ^ [P3: produc1319942482725812455at_nat] : ( produc9060074326276436823at_nat @ ( produc826222791318859909at_nat @ P3 ) @ ( produc4486455499028916547at_nat @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_115_prod_Oswap__def,axiom,
% 7.78/3.91 ( produc3946833401584108663at_nat
% 7.78/3.91 = ( ^ [P3: produc3843707927480180839at_nat] : ( produc2922128104949294807at_nat @ ( produc2937545259423399429at_nat @ P3 ) @ ( produc6011863565407846595at_nat @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_116_prod_Oswap__def,axiom,
% 7.78/3.91 ( product_swap_num_nat
% 7.78/3.91 = ( ^ [P3: product_prod_num_nat] : ( product_Pair_nat_num @ ( product_snd_num_nat @ P3 ) @ ( product_fst_num_nat @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_117_prod_Oswap__def,axiom,
% 7.78/3.91 ( product_swap_nat_nat
% 7.78/3.91 = ( ^ [P3: product_prod_nat_nat] : ( product_Pair_nat_nat @ ( product_snd_nat_nat @ P3 ) @ ( product_fst_nat_nat @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_118_prod_Oswap__def,axiom,
% 7.78/3.91 ( product_swap_int_int
% 7.78/3.91 = ( ^ [P3: product_prod_int_int] : ( product_Pair_int_int @ ( product_snd_int_int @ P3 ) @ ( product_fst_int_int @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_119_prod_Oswap__def,axiom,
% 7.78/3.91 ( produc970745769005243767t_unit
% 7.78/3.91 = ( ^ [P3: produc7812382424243267045t_unit] : ( produc2564672488694626579_ref_a @ ( produc1126150082675451753t_unit @ P3 ) @ ( produc473321116828791851t_unit @ P3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_120_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: produc1319942482725812455at_nat] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ Prod ) @ ( produc826222791318859909at_nat @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_121_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: produc3843707927480180839at_nat] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ Prod ) @ ( produc2937545259423399429at_nat @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_122_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: product_prod_nat_num] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( product_Pair_nat_num @ ( product_fst_nat_num @ Prod ) @ ( product_snd_nat_num @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_123_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: product_prod_nat_nat] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_124_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: product_prod_int_int] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_125_prod_Oexhaust__sel,axiom,
% 7.78/3.91 ! [Prod: produc7812382424243267045t_unit] :
% 7.78/3.91 ( Prod
% 7.78/3.91 = ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ Prod ) @ ( produc1126150082675451753t_unit @ Prod ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_126_exI__realizer,axiom,
% 7.78/3.91 ! [P2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) @ ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_127_exI__realizer,axiom,
% 7.78/3.91 ! [P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Y3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) @ ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_128_exI__realizer,axiom,
% 7.78/3.91 ! [P2: num > nat > $o,Y3: num,X2: nat] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( product_snd_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) ) @ ( product_fst_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_129_exI__realizer,axiom,
% 7.78/3.91 ! [P2: nat > nat > $o,Y3: nat,X2: nat] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_130_exI__realizer,axiom,
% 7.78/3.91 ! [P2: int > int > $o,Y3: int,X2: int] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( product_snd_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_131_exI__realizer,axiom,
% 7.78/3.91 ! [P2: heap_e7401611519738050253t_unit > ref_a > $o,Y3: heap_e7401611519738050253t_unit,X2: ref_a] :
% 7.78/3.91 ( ( P2 @ Y3 @ X2 )
% 7.78/3.91 => ( P2 @ ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) ) @ ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ X2 @ Y3 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_132_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: set_Pr4329608150637261639at_nat > $o,P: set_Pr4329608150637261639at_nat,Q2: set_Pr4329608150637261639at_nat > $o,Q: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( produc4486455499028916547at_nat @ ( produc9060074326276436823at_nat @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( produc826222791318859909at_nat @ ( produc9060074326276436823at_nat @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_133_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: set_Pr1261947904930325089at_nat > $o,P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat > $o,Q: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( produc6011863565407846595at_nat @ ( produc2922128104949294807at_nat @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( produc2937545259423399429at_nat @ ( produc2922128104949294807at_nat @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_134_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: nat > $o,P: nat,Q2: num > $o,Q: num] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( product_fst_nat_num @ ( product_Pair_nat_num @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( product_snd_nat_num @ ( product_Pair_nat_num @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_135_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: nat > $o,P: nat,Q2: nat > $o,Q: nat] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_136_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: int > $o,P: int,Q2: int > $o,Q: int] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( product_fst_int_int @ ( product_Pair_int_int @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( product_snd_int_int @ ( product_Pair_int_int @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_137_conjI__realizer,axiom,
% 7.78/3.91 ! [P2: ref_a > $o,P: ref_a,Q2: heap_e7401611519738050253t_unit > $o,Q: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( P2 @ P )
% 7.78/3.91 => ( ( Q2 @ Q )
% 7.78/3.91 => ( ( P2 @ ( produc473321116828791851t_unit @ ( produc6544324848051098391t_unit @ P @ Q ) ) )
% 7.78/3.91 & ( Q2 @ ( produc1126150082675451753t_unit @ ( produc6544324848051098391t_unit @ P @ Q ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_138_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: produc1319942482725812455at_nat] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( produc9060074326276436823at_nat @ ( produc4486455499028916547at_nat @ T2 ) @ ( produc826222791318859909at_nat @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_139_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: produc3843707927480180839at_nat] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( produc2922128104949294807at_nat @ ( produc6011863565407846595at_nat @ T2 ) @ ( produc2937545259423399429at_nat @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_140_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: product_prod_nat_num] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( product_Pair_nat_num @ ( product_fst_nat_num @ T2 ) @ ( product_snd_nat_num @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_141_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: product_prod_nat_nat] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T2 ) @ ( product_snd_nat_nat @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_142_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: product_prod_int_int] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ T2 ) @ ( product_snd_int_int @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_143_surjective__pairing,axiom,
% 7.78/3.91 ! [T2: produc7812382424243267045t_unit] :
% 7.78/3.91 ( T2
% 7.78/3.91 = ( produc6544324848051098391t_unit @ ( produc473321116828791851t_unit @ T2 ) @ ( produc1126150082675451753t_unit @ T2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_144_Ref_Oset__set__swap,axiom,
% 7.78/3.91 ! [R: ref_a,R2: ref_a,X2: a,X3: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( noteq_a_a @ R @ R2 )
% 7.78/3.91 => ( ( set_a @ R @ X2 @ ( set_a @ R2 @ X3 @ H ) )
% 7.78/3.91 = ( set_a @ R2 @ X3 @ ( set_a @ R @ X2 @ H ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_145_next__fresh,axiom,
% 7.78/3.91 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,X2: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 7.78/3.91 = ( alloc_a @ X2 @ H ) )
% 7.78/3.91 => ~ ( present_a @ H @ R ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_146_next__present,axiom,
% 7.78/3.91 ! [R: ref_a,H2: heap_e7401611519738050253t_unit,X2: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( ( produc6544324848051098391t_unit @ R @ H2 )
% 7.78/3.91 = ( alloc_a @ X2 @ H ) )
% 7.78/3.91 => ( present_a @ H2 @ R ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_147_noteq__I,axiom,
% 7.78/3.91 ! [H: heap_e7401611519738050253t_unit,R: ref_a,R2: ref_a] :
% 7.78/3.91 ( ( present_a @ H @ R )
% 7.78/3.91 => ( ~ ( present_a @ H @ R2 )
% 7.78/3.91 => ( noteq_a_a @ R @ R2 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_148_effect__heapE,axiom,
% 7.78/3.91 ! [F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( heap_heap_ref_a @ F ) @ H @ H2 @ R )
% 7.78/3.91 => ~ ( ( H2
% 7.78/3.91 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( R
% 7.78/3.91 != ( produc473321116828791851t_unit @ ( F @ H ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_149_effect__heapI,axiom,
% 7.78/3.91 ! [H2: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( H2
% 7.78/3.91 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( ( R
% 7.78/3.91 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( heap_heap_ref_a @ F ) @ H @ H2 @ R ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_150_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A: produc1319942482725812455at_nat] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( produc4486455499028916547at_nat @ A ) @ ( produc826222791318859909at_nat @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_151_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A: produc3843707927480180839at_nat] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( produc6011863565407846595at_nat @ A ) @ ( produc2937545259423399429at_nat @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_152_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: nat > num > $o,X2: nat,Y3: num,A: product_prod_nat_num] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( product_fst_nat_num @ A ) @ ( product_snd_nat_num @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_153_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: nat > nat > $o,X2: nat,Y3: nat,A: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_154_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: int > int > $o,X2: int,Y3: int,A: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( product_fst_int_int @ A ) @ ( product_snd_int_int @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_155_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 7.78/3.91 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o,X2: ref_a,Y3: heap_e7401611519738050253t_unit,A: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( P2 @ X2 @ Y3 )
% 7.78/3.91 => ( ( A
% 7.78/3.91 = ( produc6544324848051098391t_unit @ X2 @ Y3 ) )
% 7.78/3.91 => ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( produc1126150082675451753t_unit @ A ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_156_sndI,axiom,
% 7.78/3.91 ! [X2: produc1319942482725812455at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc9060074326276436823at_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc826222791318859909at_nat @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_157_sndI,axiom,
% 7.78/3.91 ! [X2: produc3843707927480180839at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc2922128104949294807at_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc2937545259423399429at_nat @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_158_sndI,axiom,
% 7.78/3.91 ! [X2: product_prod_nat_num,Y3: nat,Z2: num] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_nat_num @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_snd_nat_num @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_159_sndI,axiom,
% 7.78/3.91 ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_snd_nat_nat @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_160_sndI,axiom,
% 7.78/3.91 ! [X2: product_prod_int_int,Y3: int,Z2: int] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_int_int @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_snd_int_int @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_161_sndI,axiom,
% 7.78/3.91 ! [X2: produc7812382424243267045t_unit,Y3: ref_a,Z2: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc6544324848051098391t_unit @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc1126150082675451753t_unit @ X2 )
% 7.78/3.91 = Z2 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_162_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( produc826222791318859909at_nat @ P ) )
% 7.78/3.91 = ( ? [A5: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc9060074326276436823at_nat @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_163_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( produc2937545259423399429at_nat @ P ) )
% 7.78/3.91 = ( ? [A5: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc2922128104949294807at_nat @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_164_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: num,P: product_prod_nat_num] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( product_snd_nat_num @ P ) )
% 7.78/3.91 = ( ? [A5: nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_num @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_165_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: nat,P: product_prod_nat_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( product_snd_nat_nat @ P ) )
% 7.78/3.91 = ( ? [A5: nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_nat @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_166_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: int,P: product_prod_int_int] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( product_snd_int_int @ P ) )
% 7.78/3.91 = ( ? [A5: int] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_int_int @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_167_eq__snd__iff,axiom,
% 7.78/3.91 ! [B: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( produc1126150082675451753t_unit @ P ) )
% 7.78/3.91 = ( ? [A5: ref_a] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc6544324848051098391t_unit @ A5 @ B ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_168_fstI,axiom,
% 7.78/3.91 ! [X2: produc1319942482725812455at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc9060074326276436823at_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc4486455499028916547at_nat @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_169_fstI,axiom,
% 7.78/3.91 ! [X2: produc3843707927480180839at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc2922128104949294807at_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc6011863565407846595at_nat @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_170_fstI,axiom,
% 7.78/3.91 ! [X2: product_prod_nat_num,Y3: nat,Z2: num] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_nat_num @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_fst_nat_num @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_171_fstI,axiom,
% 7.78/3.91 ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_fst_nat_nat @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_172_fstI,axiom,
% 7.78/3.91 ! [X2: product_prod_int_int,Y3: int,Z2: int] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( product_Pair_int_int @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( product_fst_int_int @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_173_fstI,axiom,
% 7.78/3.91 ! [X2: produc7812382424243267045t_unit,Y3: ref_a,Z2: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( X2
% 7.78/3.91 = ( produc6544324848051098391t_unit @ Y3 @ Z2 ) )
% 7.78/3.91 => ( ( produc473321116828791851t_unit @ X2 )
% 7.78/3.91 = Y3 ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_174_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( produc4486455499028916547at_nat @ P ) )
% 7.78/3.91 = ( ? [B4: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc9060074326276436823at_nat @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_175_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( produc6011863565407846595at_nat @ P ) )
% 7.78/3.91 = ( ? [B4: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc2922128104949294807at_nat @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_176_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: nat,P: product_prod_nat_num] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( product_fst_nat_num @ P ) )
% 7.78/3.91 = ( ? [B4: num] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_num @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_177_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: nat,P: product_prod_nat_nat] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( product_fst_nat_nat @ P ) )
% 7.78/3.91 = ( ? [B4: nat] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_nat_nat @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_178_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: int,P: product_prod_int_int] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( product_fst_int_int @ P ) )
% 7.78/3.91 = ( ? [B4: int] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( product_Pair_int_int @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_179_eq__fst__iff,axiom,
% 7.78/3.91 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 7.78/3.91 ( ( A
% 7.78/3.91 = ( produc473321116828791851t_unit @ P ) )
% 7.78/3.91 = ( ? [B4: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( P
% 7.78/3.91 = ( produc6544324848051098391t_unit @ A @ B4 ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_180_effect__guardE,axiom,
% 7.78/3.91 ! [P2: heap_e7401611519738050253t_unit > $o,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( heap_guard_ref_a @ P2 @ F ) @ H @ H2 @ R )
% 7.78/3.91 => ~ ( ( H2
% 7.78/3.91 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( ( R
% 7.78/3.91 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ~ ( P2 @ H ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_181_effect__guardI,axiom,
% 7.78/3.91 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,R: ref_a] :
% 7.78/3.91 ( ( P2 @ H )
% 7.78/3.91 => ( ( H2
% 7.78/3.91 = ( produc1126150082675451753t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( ( R
% 7.78/3.91 = ( produc473321116828791851t_unit @ ( F @ H ) ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( heap_guard_ref_a @ P2 @ F ) @ H @ H2 @ R ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_182_effect__ifI,axiom,
% 7.78/3.91 ! [C: $o,T2: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a,E: heap_Heap_ref_a] :
% 7.78/3.91 ( ( C
% 7.78/3.91 => ( heap_effect_ref_a @ T2 @ H @ H2 @ R ) )
% 7.78/3.91 => ( ( ~ C
% 7.78/3.91 => ( heap_effect_ref_a @ E @ H @ H2 @ R ) )
% 7.78/3.91 => ( heap_effect_ref_a @ ( if_Heap_Heap_ref_a @ C @ T2 @ E ) @ H @ H2 @ R ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_183_effect__deterministic_I2_J,axiom,
% 7.78/3.91 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,A: ref_a,H3: heap_e7401611519738050253t_unit,B: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ F @ H @ H2 @ A )
% 7.78/3.91 => ( ( heap_effect_ref_a @ F @ H @ H3 @ B )
% 7.78/3.91 => ( H2 = H3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_184_effect__deterministic_I1_J,axiom,
% 7.78/3.91 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,A: ref_a,H3: heap_e7401611519738050253t_unit,B: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ F @ H @ H2 @ A )
% 7.78/3.91 => ( ( heap_effect_ref_a @ F @ H @ H3 @ B )
% 7.78/3.91 => ( A = B ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_185_effect__ifE,axiom,
% 7.78/3.91 ! [C: $o,T2: heap_Heap_ref_a,E: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ( ( heap_effect_ref_a @ ( if_Heap_Heap_ref_a @ C @ T2 @ E ) @ H @ H2 @ R )
% 7.78/3.91 => ( ( C
% 7.78/3.91 => ~ ( heap_effect_ref_a @ T2 @ H @ H2 @ R ) )
% 7.78/3.91 => ~ ( ~ C
% 7.78/3.91 => ~ ( heap_effect_ref_a @ E @ H @ H2 @ R ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_186_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: $o > nat,X2: $o,C: num,G: $o > num,A4: set_o] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_o @ X2 @ A4 )
% 7.78/3.91 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr7727518618234538026at_num @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_187_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: nat > nat,X2: nat,C: num,G: nat > num,A4: set_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.91 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr3875488559241464598at_num @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_188_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: int > nat,X2: int,C: num,G: int > num,A4: set_int] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_int @ X2 @ A4 )
% 7.78/3.91 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr4247142119478309234at_num @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_189_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: $o > nat,X2: $o,C: nat,G: $o > nat,A4: set_o] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_o @ X2 @ A4 )
% 7.78/3.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr1946814795223983584at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_190_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: nat > nat,X2: nat,C: nat,G: nat > nat,A4: set_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr7318156773085685964at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_191_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: int > nat,X2: int,C: nat,G: int > nat,A4: set_int] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_int @ X2 @ A4 )
% 7.78/3.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( bNF_Gr7689810333322530600at_nat @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_192_image2__eqI,axiom,
% 7.78/3.91 ! [B: int,F: $o > int,X2: $o,C: int,G: $o > int,A4: set_o] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_o @ X2 @ A4 )
% 7.78/3.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr2943678036615987864nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_193_image2__eqI,axiom,
% 7.78/3.91 ! [B: int,F: nat > int,X2: nat,C: int,G: nat > int,A4: set_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr8315020014477690244nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_194_image2__eqI,axiom,
% 7.78/3.91 ! [B: int,F: int > int,X2: int,C: int,G: int > int,A4: set_int] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member_int @ X2 @ A4 )
% 7.78/3.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( bNF_Gr8686673574714534880nt_int @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_195_image2__eqI,axiom,
% 7.78/3.91 ! [B: nat,F: product_prod_nat_nat > nat,X2: product_prod_nat_nat,C: num,G: product_prod_nat_nat > num,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( B
% 7.78/3.91 = ( F @ X2 ) )
% 7.78/3.91 => ( ( C
% 7.78/3.91 = ( G @ X2 ) )
% 7.78/3.91 => ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 7.78/3.91 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ B @ C ) @ ( bNF_Gr5511461681843259283at_num @ A4 @ F @ G ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_196_lim__set,axiom,
% 7.78/3.91 ! [R: ref_a,V: a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.91 ( ( lim_Product_unit @ ( set_a @ R @ V @ H ) )
% 7.78/3.91 = ( lim_Product_unit @ H ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_197_prod_Osplit__sel__asm,axiom,
% 7.78/3.91 ! [P2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 7.78/3.91 = ( ~ ( ( Prod
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 7.78/3.91 & ~ ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_198_prod_Osplit__sel__asm,axiom,
% 7.78/3.91 ! [P2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 7.78/3.91 = ( ~ ( ( Prod
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 7.78/3.91 & ~ ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_199_prod_Osplit__sel__asm,axiom,
% 7.78/3.91 ! [P2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 7.78/3.91 = ( ~ ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_200_prod_Osplit__sel__asm,axiom,
% 7.78/3.91 ! [P2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 7.78/3.91 = ( ~ ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_201_prod_Osplit__sel__asm,axiom,
% 7.78/3.91 ! [P2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 7.78/3.91 = ( ~ ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 & ~ ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_202_prod_Osplit__sel,axiom,
% 7.78/3.91 ! [P2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ ( produc27273713700761075at_nat @ F @ Prod ) )
% 7.78/3.91 = ( ( Prod
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 7.78/3.91 => ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_203_prod_Osplit__sel,axiom,
% 7.78/3.91 ! [P2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 7.78/3.91 ( ( P2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 7.78/3.91 = ( ( Prod
% 7.78/3.91 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) )
% 7.78/3.91 => ( P2 @ ( F @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_204_prod_Osplit__sel,axiom,
% 7.78/3.91 ! [P2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 7.78/3.91 = ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_205_prod_Osplit__sel,axiom,
% 7.78/3.91 ! [P2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 7.78/3.91 = ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_206_prod_Osplit__sel,axiom,
% 7.78/3.91 ! [P2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 7.78/3.91 ( ( P2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 7.78/3.91 = ( ( Prod
% 7.78/3.91 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) )
% 7.78/3.91 => ( P2 @ ( F @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_207_ssubst__Pair__rhs,axiom,
% 7.78/3.91 ! [R: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat,S3: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ R @ S2 ) @ R3 )
% 7.78/3.91 => ( ( S3 = S2 )
% 7.78/3.91 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ R @ S3 ) @ R3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_208_ssubst__Pair__rhs,axiom,
% 7.78/3.91 ! [R: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,S3: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S2 ) @ R3 )
% 7.78/3.91 => ( ( S3 = S2 )
% 7.78/3.91 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S3 ) @ R3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_209_ssubst__Pair__rhs,axiom,
% 7.78/3.91 ! [R: nat,S2: num,R3: set_Pr6200539531224447659at_num,S3: num] :
% 7.78/3.91 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ R @ S2 ) @ R3 )
% 7.78/3.91 => ( ( S3 = S2 )
% 7.78/3.91 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ R @ S3 ) @ R3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_210_ssubst__Pair__rhs,axiom,
% 7.78/3.91 ! [R: nat,S2: nat,R3: set_Pr1261947904930325089at_nat,S3: nat] :
% 7.78/3.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S2 ) @ R3 )
% 7.78/3.91 => ( ( S3 = S2 )
% 7.78/3.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S3 ) @ R3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_211_ssubst__Pair__rhs,axiom,
% 7.78/3.91 ! [R: int,S2: int,R3: set_Pr958786334691620121nt_int,S3: int] :
% 7.78/3.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S2 ) @ R3 )
% 7.78/3.91 => ( ( S3 = S2 )
% 7.78/3.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S3 ) @ R3 ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_212_effect__raiseE,axiom,
% 7.78/3.91 ! [X2: literal,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.91 ~ ( heap_effect_ref_a @ ( heap_raise_ref_a @ X2 ) @ H @ H2 @ R ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_213_effect__updateE,axiom,
% 7.78/3.91 ! [R2: ref_a,V: a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: product_unit] :
% 7.78/3.91 ( ( heap_e2830298082929533060t_unit @ ( update_a @ R2 @ V ) @ H @ H2 @ R )
% 7.78/3.91 => ( H2
% 7.78/3.91 = ( set_a @ R2 @ V @ H ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_214_curryI,axiom,
% 7.78/3.91 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.91 ( ( F @ ( produc9060074326276436823at_nat @ A @ B ) )
% 7.78/3.91 => ( produc447603880154497357_nat_o @ F @ A @ B ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_215_curryI,axiom,
% 7.78/3.91 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.91 ( ( F @ ( produc2922128104949294807at_nat @ A @ B ) )
% 7.78/3.91 => ( produc7820828192191229133_nat_o @ F @ A @ B ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_216_curryI,axiom,
% 7.78/3.91 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 7.78/3.91 ( ( F @ ( product_Pair_nat_num @ A @ B ) )
% 7.78/3.91 => ( produc156083480235303841_num_o @ F @ A @ B ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_217_curryI,axiom,
% 7.78/3.91 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 7.78/3.91 ( ( F @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.91 => ( produc1310100445399344235_nat_o @ F @ A @ B ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_218_curryI,axiom,
% 7.78/3.91 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 7.78/3.91 ( ( F @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.91 => ( produc175634133007206835_int_o @ F @ A @ B ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_219_case__prod__curry,axiom,
% 7.78/3.91 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.91 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_220_case__prod__curry,axiom,
% 7.78/3.91 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.91 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_221_case__prod__curry,axiom,
% 7.78/3.91 ! [F: product_prod_int_int > product_prod_int_int] :
% 7.78/3.91 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_222_case__prod__curry,axiom,
% 7.78/3.91 ! [F: product_prod_int_int > $o] :
% 7.78/3.91 ( ( produc4947309494688390418_int_o @ ( produc175634133007206835_int_o @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_223_case__prod__curry,axiom,
% 7.78/3.91 ! [F: product_prod_int_int > int] :
% 7.78/3.91 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_224_curry__case__prod,axiom,
% 7.78/3.91 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.91 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_225_curry__case__prod,axiom,
% 7.78/3.91 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 7.78/3.91 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_226_curry__case__prod,axiom,
% 7.78/3.91 ! [F: int > int > product_prod_int_int] :
% 7.78/3.91 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_227_curry__case__prod,axiom,
% 7.78/3.91 ! [F: int > int > $o] :
% 7.78/3.91 ( ( produc175634133007206835_int_o @ ( produc4947309494688390418_int_o @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_228_curry__case__prod,axiom,
% 7.78/3.91 ! [F: int > int > int] :
% 7.78/3.91 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 7.78/3.91 = F ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_229_mem__case__prodE,axiom,
% 7.78/3.91 ! [Z2: $o,C: nat > num > set_o,P: product_prod_nat_num] :
% 7.78/3.91 ( ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ P ) )
% 7.78/3.91 => ~ ! [X: nat,Y: num] :
% 7.78/3.91 ( ( P
% 7.78/3.91 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.91 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.91
% 7.78/3.91 thf(fact_230_mem__case__prodE,axiom,
% 7.78/3.91 ! [Z2: nat,C: nat > num > set_nat,P: product_prod_nat_num] :
% 7.78/3.91 ( ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.92 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_231_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: int,C: nat > num > set_int,P: product_prod_nat_num] :
% 7.78/3.92 ( ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.92 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_232_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: $o,C: nat > nat > set_o,P: product_prod_nat_nat] :
% 7.78/3.92 ( ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.92 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_233_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: nat,C: nat > nat > set_nat,P: product_prod_nat_nat] :
% 7.78/3.92 ( ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.92 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_234_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: int,C: nat > nat > set_int,P: product_prod_nat_nat] :
% 7.78/3.92 ( ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.92 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_235_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: $o,C: int > int > set_o,P: product_prod_int_int] :
% 7.78/3.92 ( ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ P ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.92 => ~ ( member_o @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_236_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: nat,C: int > int > set_nat,P: product_prod_int_int] :
% 7.78/3.92 ( ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.92 => ~ ( member_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_237_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: int,C: int > int > set_int,P: product_prod_int_int] :
% 7.78/3.92 ( ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.92 => ~ ( member_int @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_238_mem__case__prodE,axiom,
% 7.78/3.92 ! [Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat,P: product_prod_nat_num] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.92 => ~ ( member8440522571783428010at_nat @ Z2 @ ( C @ X @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_239_old_Oprod_Ocase,axiom,
% 7.78/3.92 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 7.78/3.92 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 7.78/3.92 = ( F @ X1 @ X22 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_240_old_Oprod_Ocase,axiom,
% 7.78/3.92 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 7.78/3.92 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 7.78/3.92 = ( F @ X1 @ X22 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_241_old_Oprod_Ocase,axiom,
% 7.78/3.92 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 7.78/3.92 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 7.78/3.92 = ( F @ X1 @ X22 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_242_old_Oprod_Ocase,axiom,
% 7.78/3.92 ! [F: int > int > $o,X1: int,X22: int] :
% 7.78/3.92 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 7.78/3.92 = ( F @ X1 @ X22 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_243_old_Oprod_Ocase,axiom,
% 7.78/3.92 ! [F: int > int > int,X1: int,X22: int] :
% 7.78/3.92 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 7.78/3.92 = ( F @ X1 @ X22 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_244_curryD,axiom,
% 7.78/3.92 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( produc447603880154497357_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_245_curryD,axiom,
% 7.78/3.92 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( produc7820828192191229133_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_246_curryD,axiom,
% 7.78/3.92 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 7.78/3.92 ( ( produc156083480235303841_num_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_247_curryD,axiom,
% 7.78/3.92 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 7.78/3.92 ( ( produc1310100445399344235_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_248_curryD,axiom,
% 7.78/3.92 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 7.78/3.92 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_249_curryE,axiom,
% 7.78/3.92 ! [F: produc1319942482725812455at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( produc447603880154497357_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_250_curryE,axiom,
% 7.78/3.92 ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( produc7820828192191229133_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_251_curryE,axiom,
% 7.78/3.92 ! [F: product_prod_nat_num > $o,A: nat,B: num] :
% 7.78/3.92 ( ( produc156083480235303841_num_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_252_curryE,axiom,
% 7.78/3.92 ! [F: product_prod_nat_nat > $o,A: nat,B: nat] :
% 7.78/3.92 ( ( produc1310100445399344235_nat_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_253_curryE,axiom,
% 7.78/3.92 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 7.78/3.92 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 7.78/3.92 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_254_Product__Type_OCollect__case__prodD,axiom,
% 7.78/3.92 ! [X2: produc3843707927480180839at_nat,A4: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ X2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ A4 ) ) )
% 7.78/3.92 => ( A4 @ ( produc6011863565407846595at_nat @ X2 ) @ ( produc2937545259423399429at_nat @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_255_Product__Type_OCollect__case__prodD,axiom,
% 7.78/3.92 ! [X2: product_prod_nat_nat,A4: nat > nat > $o] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ X2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A4 ) ) )
% 7.78/3.92 => ( A4 @ ( product_fst_nat_nat @ X2 ) @ ( product_snd_nat_nat @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_256_Product__Type_OCollect__case__prodD,axiom,
% 7.78/3.92 ! [X2: produc7812382424243267045t_unit,A4: ref_a > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.92 ( ( member7849944260330398460t_unit @ X2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ A4 ) ) )
% 7.78/3.92 => ( A4 @ ( produc473321116828791851t_unit @ X2 ) @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_257_Product__Type_OCollect__case__prodD,axiom,
% 7.78/3.92 ! [X2: product_prod_int_int,A4: int > int > $o] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ X2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) )
% 7.78/3.92 => ( A4 @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_258_effect__returnI,axiom,
% 7.78/3.92 ! [H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,X2: ref_a] :
% 7.78/3.92 ( ( H = H2 )
% 7.78/3.92 => ( heap_effect_ref_a @ ( heap_return_ref_a @ X2 ) @ H @ H2 @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_259_effect__returnE,axiom,
% 7.78/3.92 ! [X2: ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.92 ( ( heap_effect_ref_a @ ( heap_return_ref_a @ X2 ) @ H @ H2 @ R )
% 7.78/3.92 => ~ ( ( R = X2 )
% 7.78/3.92 => ( H2 != H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_260_split__beta,axiom,
% 7.78/3.92 ( produc27273713700761075at_nat
% 7.78/3.92 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Prod3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod3 ) @ ( product_snd_nat_nat @ Prod3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_261_split__beta,axiom,
% 7.78/3.92 ( produc8739625826339149834_nat_o
% 7.78/3.92 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,Prod3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ Prod3 ) @ ( product_snd_nat_nat @ Prod3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_262_split__beta,axiom,
% 7.78/3.92 ( produc4245557441103728435nt_int
% 7.78/3.92 = ( ^ [F2: int > int > product_prod_int_int,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_263_split__beta,axiom,
% 7.78/3.92 ( produc4947309494688390418_int_o
% 7.78/3.92 = ( ^ [F2: int > int > $o,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_264_split__beta,axiom,
% 7.78/3.92 ( produc8211389475949308722nt_int
% 7.78/3.92 = ( ^ [F2: int > int > int,Prod3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ Prod3 ) @ ( product_snd_int_int @ Prod3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_265_case__prod__beta,axiom,
% 7.78/3.92 ( produc27273713700761075at_nat
% 7.78/3.92 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_266_case__prod__beta,axiom,
% 7.78/3.92 ( produc8739625826339149834_nat_o
% 7.78/3.92 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_267_case__prod__beta,axiom,
% 7.78/3.92 ( produc4245557441103728435nt_int
% 7.78/3.92 = ( ^ [F2: int > int > product_prod_int_int,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_268_case__prod__beta,axiom,
% 7.78/3.92 ( produc4947309494688390418_int_o
% 7.78/3.92 = ( ^ [F2: int > int > $o,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_269_case__prod__beta,axiom,
% 7.78/3.92 ( produc8211389475949308722nt_int
% 7.78/3.92 = ( ^ [F2: int > int > int,P3: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_270_internal__case__prod__def,axiom,
% 7.78/3.92 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 7.78/3.92
% 7.78/3.92 thf(fact_271_internal__case__prod__def,axiom,
% 7.78/3.92 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 7.78/3.92
% 7.78/3.92 thf(fact_272_internal__case__prod__def,axiom,
% 7.78/3.92 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 7.78/3.92
% 7.78/3.92 thf(fact_273_internal__case__prod__def,axiom,
% 7.78/3.92 produc8005341501107743676_int_o = produc4947309494688390418_int_o ).
% 7.78/3.92
% 7.78/3.92 thf(fact_274_internal__case__prod__def,axiom,
% 7.78/3.92 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 7.78/3.92
% 7.78/3.92 thf(fact_275_effect__updateI,axiom,
% 7.78/3.92 ! [H2: heap_e7401611519738050253t_unit,R: ref_a,V: a,H: heap_e7401611519738050253t_unit,X2: product_unit] :
% 7.78/3.92 ( ( H2
% 7.78/3.92 = ( set_a @ R @ V @ H ) )
% 7.78/3.92 => ( heap_e2830298082929533060t_unit @ ( update_a @ R @ V ) @ H @ H2 @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_276_split__cong,axiom,
% 7.78/3.92 ! [Q: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P: product_prod_nat_nat] :
% 7.78/3.92 ( ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( ( product_Pair_nat_nat @ X @ Y )
% 7.78/3.92 = Q )
% 7.78/3.92 => ( ( F @ X @ Y )
% 7.78/3.92 = ( G @ X @ Y ) ) )
% 7.78/3.92 => ( ( P = Q )
% 7.78/3.92 => ( ( produc27273713700761075at_nat @ F @ P )
% 7.78/3.92 = ( produc27273713700761075at_nat @ G @ Q ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_277_split__cong,axiom,
% 7.78/3.92 ! [Q: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 7.78/3.92 ( ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( ( product_Pair_nat_nat @ X @ Y )
% 7.78/3.92 = Q )
% 7.78/3.92 => ( ( F @ X @ Y )
% 7.78/3.92 = ( G @ X @ Y ) ) )
% 7.78/3.92 => ( ( P = Q )
% 7.78/3.92 => ( ( produc8739625826339149834_nat_o @ F @ P )
% 7.78/3.92 = ( produc8739625826339149834_nat_o @ G @ Q ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_278_split__cong,axiom,
% 7.78/3.92 ! [Q: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P: product_prod_int_int] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( ( product_Pair_int_int @ X @ Y )
% 7.78/3.92 = Q )
% 7.78/3.92 => ( ( F @ X @ Y )
% 7.78/3.92 = ( G @ X @ Y ) ) )
% 7.78/3.92 => ( ( P = Q )
% 7.78/3.92 => ( ( produc4245557441103728435nt_int @ F @ P )
% 7.78/3.92 = ( produc4245557441103728435nt_int @ G @ Q ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_279_split__cong,axiom,
% 7.78/3.92 ! [Q: product_prod_int_int,F: int > int > $o,G: int > int > $o,P: product_prod_int_int] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( ( product_Pair_int_int @ X @ Y )
% 7.78/3.92 = Q )
% 7.78/3.92 => ( ( F @ X @ Y )
% 7.78/3.92 = ( G @ X @ Y ) ) )
% 7.78/3.92 => ( ( P = Q )
% 7.78/3.92 => ( ( produc4947309494688390418_int_o @ F @ P )
% 7.78/3.92 = ( produc4947309494688390418_int_o @ G @ Q ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_280_split__cong,axiom,
% 7.78/3.92 ! [Q: product_prod_int_int,F: int > int > int,G: int > int > int,P: product_prod_int_int] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( ( product_Pair_int_int @ X @ Y )
% 7.78/3.92 = Q )
% 7.78/3.92 => ( ( F @ X @ Y )
% 7.78/3.92 = ( G @ X @ Y ) ) )
% 7.78/3.92 => ( ( P = Q )
% 7.78/3.92 => ( ( produc8211389475949308722nt_int @ F @ P )
% 7.78/3.92 = ( produc8211389475949308722nt_int @ G @ Q ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_281_csquare__fstOp__sndOp,axiom,
% 7.78/3.92 ! [F: ( product_prod_nat_nat > int > $o ) > produc4196048018000912732at_int > $o,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] : ( bNF_cs7194553038297458973at_int @ ( collec2851339944984316337at_int @ ( F @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) @ produc6408287024330202629at_nat @ produc4619704898428564714at_int @ ( bNF_fs6342258632037972510at_int @ P2 @ Q2 ) @ ( bNF_sn649997494946348640at_int @ P2 @ Q2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_282_csquare__fstOp__sndOp,axiom,
% 7.78/3.92 ! [F: ( int > code_integer > $o ) > produc2963269191615333738nteger > $o,P2: int > int > $o,Q2: int > code_integer > $o] : ( bNF_cs4943907971211754724nteger @ ( collec7215431352809750357nteger @ ( F @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) @ product_snd_int_int @ produc45500017171379470nteger @ ( bNF_fs4543836202474805097nteger @ P2 @ Q2 ) @ ( bNF_sn8000174127721201323nteger @ P2 @ Q2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_283_effect__tapI,axiom,
% 7.78/3.92 ! [H2: heap_e7401611519738050253t_unit,H: heap_e7401611519738050253t_unit,R: ref_a,F: heap_e7401611519738050253t_unit > ref_a] :
% 7.78/3.92 ( ( H2 = H )
% 7.78/3.92 => ( ( R
% 7.78/3.92 = ( F @ H ) )
% 7.78/3.92 => ( heap_effect_ref_a @ ( heap_tap_ref_a @ F ) @ H @ H2 @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_284_effect__tapE,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.92 ( ( heap_effect_ref_a @ ( heap_tap_ref_a @ F ) @ H @ H2 @ R )
% 7.78/3.92 => ~ ( ( H2 = H )
% 7.78/3.92 => ( R
% 7.78/3.92 != ( F @ H ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_285_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: num,X2: nat,A4: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ( member6570852975090897396um_nat @ ( product_Pair_num_nat @ Y3 @ X2 ) @ ( image_2347970371937200581um_nat @ product_swap_nat_num @ A4 ) )
% 7.78/3.92 = ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_286_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,A4: set_Pr7459493094073627847at_nat] :
% 7.78/3.92 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y3 @ X2 ) @ ( image_3313167189156628421at_nat @ produc5396952528824381687at_nat @ A4 ) )
% 7.78/3.92 = ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_287_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X2 ) @ ( image_960689587819713477at_nat @ produc3946833401584108663at_nat @ A4 ) )
% 7.78/3.92 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_288_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: nat,X2: num,A4: set_Pr3280342998896498603um_nat] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ Y3 @ X2 ) @ ( image_7762062833379733445at_num @ product_swap_num_nat @ A4 ) )
% 7.78/3.92 = ( member6570852975090897396um_nat @ ( product_Pair_num_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_289_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: nat,X2: nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ ( image_5168914502847457605at_nat @ product_swap_nat_nat @ A4 ) )
% 7.78/3.92 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_290_pair__in__swap__image,axiom,
% 7.78/3.92 ! [Y3: int,X2: int,A4: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ ( image_2653370878348428101nt_int @ product_swap_int_int @ A4 ) )
% 7.78/3.92 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_291_snd__sndOp,axiom,
% 7.78/3.92 ! [P2: ref_a > ref_a > $o,Q2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.92 ( produc1126150082675451753t_unit
% 7.78/3.92 = ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( bNF_sn8323453914685745821t_unit @ P2 @ Q2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_292_comp__cong,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > $o,X2: nat,F3: $o > $o,G2: nat > $o,X3: nat] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_o_o_nat @ F @ G @ X2 )
% 7.78/3.92 = ( comp_o_o_nat @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_293_comp__cong,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,X2: int,F3: nat > num,G2: int > nat,X3: int] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_nat_num_int @ F @ G @ X2 )
% 7.78/3.92 = ( comp_nat_num_int @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_294_comp__cong,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,X2: nat,F3: nat > nat,G2: nat > nat,X3: nat] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 7.78/3.92 = ( comp_nat_nat_nat @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_295_comp__cong,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,X2: nat,F3: int > nat,G2: int > int,X3: int] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 7.78/3.92 = ( comp_int_nat_int @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_296_comp__cong,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > int,X2: int,F3: nat > nat,G2: nat > nat,X3: nat] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 7.78/3.92 = ( comp_nat_nat_nat @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_297_comp__cong,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > int,X2: int,F3: int > nat,G2: int > int,X3: int] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 7.78/3.92 = ( comp_int_nat_int @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_298_comp__cong,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X3: code_integer] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( F3 @ ( G2 @ X3 ) ) )
% 7.78/3.92 => ( ( comp_C8797469213163452608nteger @ F @ G @ X2 )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ F3 @ G2 @ X3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_299_comp__apply__eq,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > $o,X2: nat,H: $o > $o,K: nat > $o] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( H @ ( K @ X2 ) ) )
% 7.78/3.92 => ( ( comp_o_o_nat @ F @ G @ X2 )
% 7.78/3.92 = ( comp_o_o_nat @ H @ K @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_300_comp__apply__eq,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,X2: int,H: nat > num,K: int > nat] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( H @ ( K @ X2 ) ) )
% 7.78/3.92 => ( ( comp_nat_num_int @ F @ G @ X2 )
% 7.78/3.92 = ( comp_nat_num_int @ H @ K @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_301_comp__apply__eq,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,X2: nat,H: nat > nat,K: nat > nat] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( H @ ( K @ X2 ) ) )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ F @ G @ X2 )
% 7.78/3.92 = ( comp_nat_nat_nat @ H @ K @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_302_comp__apply__eq,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > int,X2: int,H: int > nat,K: int > int] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( H @ ( K @ X2 ) ) )
% 7.78/3.92 => ( ( comp_int_nat_int @ F @ G @ X2 )
% 7.78/3.92 = ( comp_int_nat_int @ H @ K @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_303_comp__apply__eq,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,H: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( ( F @ ( G @ X2 ) )
% 7.78/3.92 = ( H @ ( K @ X2 ) ) )
% 7.78/3.92 => ( ( comp_C8797469213163452608nteger @ F @ G @ X2 )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ H @ K @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_304_pick__middlep,axiom,
% 7.78/3.92 ! [P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o,A: product_prod_nat_nat,C: int] :
% 7.78/3.92 ( ( relcom8911704206367525917at_int @ P2 @ Q2 @ A @ C )
% 7.78/3.92 => ( ( P2 @ A @ ( bNF_pi770922605693484880at_int @ P2 @ Q2 @ A @ C ) )
% 7.78/3.92 & ( Q2 @ ( bNF_pi770922605693484880at_int @ P2 @ Q2 @ A @ C ) @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_305_pick__middlep,axiom,
% 7.78/3.92 ! [P2: int > int > $o,Q2: int > code_integer > $o,A: int,C: code_integer] :
% 7.78/3.92 ( ( relcom967497705283160040nteger @ P2 @ Q2 @ A @ C )
% 7.78/3.92 => ( ( P2 @ A @ ( bNF_pi4515785505327359899nteger @ P2 @ Q2 @ A @ C ) )
% 7.78/3.92 & ( Q2 @ ( bNF_pi4515785505327359899nteger @ P2 @ Q2 @ A @ C ) @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_306_sndOp__in,axiom,
% 7.78/3.92 ! [Ac: produc3843707927480180839at_nat,P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Q2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ Ac @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( relcom8363394528208558896at_nat @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8757157785044589968at_nat @ ( bNF_sn1857951156667551021at_nat @ P2 @ Q2 @ Ac ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ Q2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_307_sndOp__in,axiom,
% 7.78/3.92 ! [Ac: product_prod_nat_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ Ac @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( bNF_sn8916957246138178918at_nat @ P2 @ Q2 @ Ac ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_308_sndOp__in,axiom,
% 7.78/3.92 ! [Ac: produc4196048018000912732at_int,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( ( member8394280151737582451at_int @ Ac @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8394280151737582451at_int @ ( bNF_sn649997494946348640at_int @ P2 @ Q2 @ Ac ) @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ Q2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_309_sndOp__in,axiom,
% 7.78/3.92 ! [Ac: produc2963269191615333738nteger,P2: int > int > $o,Q2: int > code_integer > $o] :
% 7.78/3.92 ( ( member4345257455949424659nteger @ Ac @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member4345257455949424659nteger @ ( bNF_sn8000174127721201323nteger @ P2 @ Q2 @ Ac ) @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ Q2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_310_sndOp__in,axiom,
% 7.78/3.92 ! [Ac: product_prod_int_int,P2: int > int > $o,Q2: int > int > $o] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ Ac @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( relcompp_int_int_int @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( bNF_sn1062102010912252026nt_int @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_311_fstOp__in,axiom,
% 7.78/3.92 ! [Ac: produc3843707927480180839at_nat,P2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,Q2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ Ac @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( relcom8363394528208558896at_nat @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8757157785044589968at_nat @ ( bNF_fs1946732770515719151at_nat @ P2 @ Q2 @ Ac ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ P2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_312_fstOp__in,axiom,
% 7.78/3.92 ! [Ac: product_prod_nat_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ Ac @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( bNF_fs6799373675401686564at_nat @ P2 @ Q2 @ Ac ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_313_fstOp__in,axiom,
% 7.78/3.92 ! [Ac: produc4196048018000912732at_int,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( ( member8394280151737582451at_int @ Ac @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ ( relcom8911704206367525917at_int @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member8206827879206165904at_nat @ ( bNF_fs6342258632037972510at_int @ P2 @ Q2 @ Ac ) @ ( collec7088162979684241874at_nat @ ( produc6590410687421337004_nat_o @ P2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_314_fstOp__in,axiom,
% 7.78/3.92 ! [Ac: produc2963269191615333738nteger,P2: int > int > $o,Q2: int > code_integer > $o] :
% 7.78/3.92 ( ( member4345257455949424659nteger @ Ac @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ ( relcom967497705283160040nteger @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( bNF_fs4543836202474805097nteger @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_315_fstOp__in,axiom,
% 7.78/3.92 ! [Ac: product_prod_int_int,P2: int > int > $o,Q2: int > int > $o] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ Ac @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( relcompp_int_int_int @ P2 @ Q2 ) ) ) )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( bNF_fs8167890477030535480nt_int @ P2 @ Q2 @ Ac ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_316_effect__bindE,axiom,
% 7.78/3.92 ! [F: heap_Heap_ref_a,G: ref_a > heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: ref_a] :
% 7.78/3.92 ( ( heap_effect_ref_a @ ( heap_b146640354529102224_ref_a @ F @ G ) @ H @ H3 @ R2 )
% 7.78/3.92 => ~ ! [H4: heap_e7401611519738050253t_unit,R4: ref_a] :
% 7.78/3.92 ( ( heap_effect_ref_a @ F @ H @ H4 @ R4 )
% 7.78/3.92 => ~ ( heap_effect_ref_a @ ( G @ R4 ) @ H4 @ H3 @ R2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_317_effect__bindI,axiom,
% 7.78/3.92 ! [F: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a,G: ref_a > heap_Heap_ref_a,H3: heap_e7401611519738050253t_unit,R2: ref_a] :
% 7.78/3.92 ( ( heap_effect_ref_a @ F @ H @ H2 @ R )
% 7.78/3.92 => ( ( heap_effect_ref_a @ ( G @ R ) @ H2 @ H3 @ R2 )
% 7.78/3.92 => ( heap_effect_ref_a @ ( heap_b146640354529102224_ref_a @ F @ G ) @ H @ H3 @ R2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_318_fst__fstOp,axiom,
% 7.78/3.92 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o,Q2: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.92 ( produc473321116828791851t_unit
% 7.78/3.92 = ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( bNF_fs409234558581511823t_unit @ P2 @ Q2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_319_comp__apply,axiom,
% 7.78/3.92 ( comp_o_o_nat
% 7.78/3.92 = ( ^ [F2: $o > $o,G3: nat > $o,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_320_comp__apply,axiom,
% 7.78/3.92 ( comp_nat_num_int
% 7.78/3.92 = ( ^ [F2: nat > num,G3: int > nat,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_321_comp__apply,axiom,
% 7.78/3.92 ( comp_nat_nat_nat
% 7.78/3.92 = ( ^ [F2: nat > nat,G3: nat > nat,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_322_comp__apply,axiom,
% 7.78/3.92 ( comp_int_nat_int
% 7.78/3.92 = ( ^ [F2: int > nat,G3: int > int,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_323_comp__apply,axiom,
% 7.78/3.92 ( comp_C8797469213163452608nteger
% 7.78/3.92 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X4: code_integer] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_324_image__eqI,axiom,
% 7.78/3.92 ! [B: $o,F: $o > $o,X2: $o,A4: set_o] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_325_image__eqI,axiom,
% 7.78/3.92 ! [B: nat,F: $o > nat,X2: $o,A4: set_o] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ B @ ( image_o_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_326_image__eqI,axiom,
% 7.78/3.92 ! [B: int,F: $o > int,X2: $o,A4: set_o] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ B @ ( image_o_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_327_image__eqI,axiom,
% 7.78/3.92 ! [B: rat,F: nat > rat,X2: nat,A4: set_nat] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_328_image__eqI,axiom,
% 7.78/3.92 ! [B: $o,F: nat > $o,X2: nat,A4: set_nat] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ B @ ( image_nat_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_329_image__eqI,axiom,
% 7.78/3.92 ! [B: nat,F: nat > nat,X2: nat,A4: set_nat] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_330_image__eqI,axiom,
% 7.78/3.92 ! [B: int,F: nat > int,X2: nat,A4: set_nat] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_331_image__eqI,axiom,
% 7.78/3.92 ! [B: $o,F: int > $o,X2: int,A4: set_int] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ B @ ( image_int_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_332_image__eqI,axiom,
% 7.78/3.92 ! [B: nat,F: int > nat,X2: int,A4: set_int] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ B @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_333_image__eqI,axiom,
% 7.78/3.92 ! [B: int,F: int > int,X2: int,A4: set_int] :
% 7.78/3.92 ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ B @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_334_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_335_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_rat > rat,G: rat > rat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_rat_rat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_rat @ ( comp_rat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_336_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_nat > nat,G: rat > nat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_337_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_int > int,G: rat > int,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_338_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_rat > rat,G: int > rat,F: nat > int,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_int_rat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_rat @ ( comp_int_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_339_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_num > num,G: nat > num,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Inf @ ( image_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_340_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_rat > rat,G: nat > rat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_nat_rat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_rat @ ( comp_nat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_341_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_rat > rat,G: nat > rat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Inf @ ( image_nat_rat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_int_rat @ ( comp_nat_rat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_342_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( Inf @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_343_Inf_OINF__image,axiom,
% 7.78/3.92 ! [Inf: set_nat > nat,G: nat > nat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Inf @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Inf @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_344_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_345_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_rat > rat,G: rat > rat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_rat_rat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_rat @ ( comp_rat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_346_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_nat > nat,G: rat > nat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_347_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_int > int,G: rat > int,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_348_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_rat > rat,G: int > rat,F: nat > int,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_int_rat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_rat @ ( comp_int_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_349_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_num > num,G: nat > num,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Sup @ ( image_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_350_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_rat > rat,G: nat > rat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_nat_rat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_rat @ ( comp_nat_rat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_351_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_rat > rat,G: nat > rat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Sup @ ( image_nat_rat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_int_rat @ ( comp_nat_rat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_352_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( Sup @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_353_Sup_OSUP__image,axiom,
% 7.78/3.92 ! [Sup: set_nat > nat,G: nat > nat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( Sup @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.92 = ( Sup @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_354_image__comp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > $o,R: set_nat] :
% 7.78/3.92 ( ( image_o_o @ F @ ( image_nat_o @ G @ R ) )
% 7.78/3.92 = ( image_nat_o @ ( comp_o_o_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_355_image__comp,axiom,
% 7.78/3.92 ! [F: rat > rat,G: nat > rat,R: set_nat] :
% 7.78/3.92 ( ( image_rat_rat @ F @ ( image_nat_rat @ G @ R ) )
% 7.78/3.92 = ( image_nat_rat @ ( comp_rat_rat_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_356_image__comp,axiom,
% 7.78/3.92 ! [F: rat > nat,G: nat > rat,R: set_nat] :
% 7.78/3.92 ( ( image_rat_nat @ F @ ( image_nat_rat @ G @ R ) )
% 7.78/3.92 = ( image_nat_nat @ ( comp_rat_nat_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_357_image__comp,axiom,
% 7.78/3.92 ! [F: rat > int,G: nat > rat,R: set_nat] :
% 7.78/3.92 ( ( image_rat_int @ F @ ( image_nat_rat @ G @ R ) )
% 7.78/3.92 = ( image_nat_int @ ( comp_rat_int_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_358_image__comp,axiom,
% 7.78/3.92 ! [F: int > rat,G: nat > int,R: set_nat] :
% 7.78/3.92 ( ( image_int_rat @ F @ ( image_nat_int @ G @ R ) )
% 7.78/3.92 = ( image_nat_rat @ ( comp_int_rat_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_359_image__comp,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,R: set_int] :
% 7.78/3.92 ( ( image_nat_num @ F @ ( image_int_nat @ G @ R ) )
% 7.78/3.92 = ( image_int_num @ ( comp_nat_num_int @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_360_image__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,G: nat > nat,R: set_nat] :
% 7.78/3.92 ( ( image_nat_rat @ F @ ( image_nat_nat @ G @ R ) )
% 7.78/3.92 = ( image_nat_rat @ ( comp_nat_rat_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_361_image__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,G: int > nat,R: set_int] :
% 7.78/3.92 ( ( image_nat_rat @ F @ ( image_int_nat @ G @ R ) )
% 7.78/3.92 = ( image_int_rat @ ( comp_nat_rat_int @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_362_image__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,R: set_nat] :
% 7.78/3.92 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ R ) )
% 7.78/3.92 = ( image_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_363_image__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: int > nat,R: set_int] :
% 7.78/3.92 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ R ) )
% 7.78/3.92 = ( image_int_nat @ ( comp_nat_nat_int @ F @ G ) @ R ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_364_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat,H: $o > $o] :
% 7.78/3.92 ( ( ( image_nat_o @ F @ A4 )
% 7.78/3.92 = ( image_nat_o @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_o @ ( comp_o_o_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_o @ ( comp_o_o_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_365_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: int > rat,A4: set_int,G: nat > rat,B5: set_nat,H: rat > nat] :
% 7.78/3.92 ( ( ( image_int_rat @ F @ A4 )
% 7.78/3.92 = ( image_nat_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_int_nat @ ( comp_rat_nat_int @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_nat @ ( comp_rat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_366_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: int > rat,A4: set_int,G: nat > rat,B5: set_nat,H: rat > int] :
% 7.78/3.92 ( ( ( image_int_rat @ F @ A4 )
% 7.78/3.92 = ( image_nat_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_int_int @ ( comp_rat_int_int @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_int @ ( comp_rat_int_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_367_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,G: int > rat,B5: set_int,H: rat > nat] :
% 7.78/3.92 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.92 = ( image_int_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_nat @ ( comp_rat_nat_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_int_nat @ ( comp_rat_nat_int @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_368_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,G: int > rat,B5: set_int,H: rat > int] :
% 7.78/3.92 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.92 = ( image_int_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_int @ ( comp_rat_int_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_int_int @ ( comp_rat_int_int @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_369_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > rat] :
% 7.78/3.92 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.92 = ( image_nat_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_rat @ ( comp_rat_rat_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_rat @ ( comp_rat_rat_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_370_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > nat] :
% 7.78/3.92 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.92 = ( image_nat_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_nat @ ( comp_rat_nat_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_nat @ ( comp_rat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_371_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat,H: rat > int] :
% 7.78/3.92 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.92 = ( image_nat_rat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_int @ ( comp_rat_int_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_int @ ( comp_rat_int_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_372_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > rat] :
% 7.78/3.92 ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.92 = ( image_nat_nat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_rat @ ( comp_nat_rat_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_rat @ ( comp_nat_rat_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_373_image__eq__imp__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > nat] :
% 7.78/3.92 ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.92 = ( image_nat_nat @ G @ B5 ) )
% 7.78/3.92 => ( ( image_nat_nat @ ( comp_nat_nat_nat @ H @ F ) @ A4 )
% 7.78/3.92 = ( image_nat_nat @ ( comp_nat_nat_nat @ H @ G ) @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_374_snd__comp__apsnd,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer] :
% 7.78/3.92 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F ) )
% 7.78/3.92 = ( comp_C1043215000170864188nteger @ F @ produc6174133586879617921nteger ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_375_snd__comp__apsnd,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc3038839249364385243_ref_a @ F ) )
% 7.78/3.92 = ( comp_h4837689053573563144t_unit @ F @ produc1126150082675451753t_unit ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_376_fst__comp__apfst,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a] :
% 7.78/3.92 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc4508741384315284437t_unit @ F ) )
% 7.78/3.92 = ( comp_r2143332150499412868t_unit @ F @ produc473321116828791851t_unit ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_377_Collect__case__prod__Grp__eqD,axiom,
% 7.78/3.92 ! [Z2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ Z2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ F ) ) ) )
% 7.78/3.92 => ( ( comp_s7355055891894327172at_nat @ F @ produc6011863565407846595at_nat @ Z2 )
% 7.78/3.92 = ( produc2937545259423399429at_nat @ Z2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_378_Collect__case__prod__Grp__eqD,axiom,
% 7.78/3.92 ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
% 7.78/3.92 => ( ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat @ Z2 )
% 7.78/3.92 = ( product_snd_nat_nat @ Z2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_379_Collect__case__prod__Grp__eqD,axiom,
% 7.78/3.92 ! [Z2: produc7812382424243267045t_unit,A4: set_ref_a,F: ref_a > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( member7849944260330398460t_unit @ Z2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_Gr6510375311308651680t_unit @ A4 @ F ) ) ) )
% 7.78/3.92 => ( ( comp_r3604920825623061426t_unit @ F @ produc473321116828791851t_unit @ Z2 )
% 7.78/3.92 = ( produc1126150082675451753t_unit @ Z2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_380_Collect__case__prod__Grp__eqD,axiom,
% 7.78/3.92 ! [Z2: product_prod_int_int,A4: set_int,F: int > int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ Z2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ F ) ) ) )
% 7.78/3.92 => ( ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int @ Z2 )
% 7.78/3.92 = ( product_snd_int_int @ Z2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_381_Collect__split__mono__strong,axiom,
% 7.78/3.92 ! [X5: set_nat,A4: set_Pr1261947904930325089at_nat,Y4: set_nat,P2: nat > nat > $o,Q2: nat > nat > $o] :
% 7.78/3.92 ( ( X5
% 7.78/3.92 = ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A4 ) )
% 7.78/3.92 => ( ( Y4
% 7.78/3.92 = ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A4 ) )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ X5 )
% 7.78/3.92 => ! [Xa: nat] :
% 7.78/3.92 ( ( member_nat @ Xa @ Y4 )
% 7.78/3.92 => ( ( P2 @ X @ Xa )
% 7.78/3.92 => ( Q2 @ X @ Xa ) ) ) )
% 7.78/3.92 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) )
% 7.78/3.92 => ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q2 ) ) ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_382_Collect__split__mono__strong,axiom,
% 7.78/3.92 ! [X5: set_ref_a,A4: set_Pr1133966238863718811t_unit,Y4: set_he8644174446132254637t_unit,P2: ref_a > heap_e7401611519738050253t_unit > $o,Q2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.92 ( ( X5
% 7.78/3.92 = ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ A4 ) )
% 7.78/3.92 => ( ( Y4
% 7.78/3.92 = ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ A4 ) )
% 7.78/3.92 => ( ! [X: ref_a] :
% 7.78/3.92 ( ( member_ref_a @ X @ X5 )
% 7.78/3.92 => ! [Xa: heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( member242389114213480694t_unit @ Xa @ Y4 )
% 7.78/3.92 => ( ( P2 @ X @ Xa )
% 7.78/3.92 => ( Q2 @ X @ Xa ) ) ) )
% 7.78/3.92 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ P2 ) ) )
% 7.78/3.92 => ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ Q2 ) ) ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_383_Collect__split__mono__strong,axiom,
% 7.78/3.92 ! [X5: set_int,A4: set_Pr958786334691620121nt_int,Y4: set_int,P2: int > int > $o,Q2: int > int > $o] :
% 7.78/3.92 ( ( X5
% 7.78/3.92 = ( image_5042161079198086560nt_int @ product_fst_int_int @ A4 ) )
% 7.78/3.92 => ( ( Y4
% 7.78/3.92 = ( image_5042161079198086560nt_int @ product_snd_int_int @ A4 ) )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ X5 )
% 7.78/3.92 => ! [Xa: int] :
% 7.78/3.92 ( ( member_int @ Xa @ Y4 )
% 7.78/3.92 => ( ( P2 @ X @ Xa )
% 7.78/3.92 => ( Q2 @ X @ Xa ) ) ) )
% 7.78/3.92 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ P2 ) ) )
% 7.78/3.92 => ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ Q2 ) ) ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_384_snd__comp__map__prod,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc3456481717235892722t_unit @ F @ G ) )
% 7.78/3.92 = ( comp_h4837689053573563144t_unit @ G @ produc1126150082675451753t_unit ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_385_fst__comp__map__prod,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc3456481717235892722t_unit @ F @ G ) )
% 7.78/3.92 = ( comp_r2143332150499412868t_unit @ F @ produc473321116828791851t_unit ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_386_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: num > num,A: nat,B: num] :
% 7.78/3.92 ( ( produc1665548884793878990um_num @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_387_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: num > nat,A: nat,B: num] :
% 7.78/3.92 ( ( produc5108217098638100356um_nat @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_388_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > int,G: num > int,A: nat,B: num] :
% 7.78/3.92 ( ( produc5477380188365894716um_int @ F @ G @ ( product_Pair_nat_num @ A @ B ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_389_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > num,A: nat,B: nat] :
% 7.78/3.92 ( ( produc3535218481486409604at_num @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_390_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,A: nat,B: nat] :
% 7.78/3.92 ( ( produc6977886695330630970at_nat @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_391_map__prod__simp,axiom,
% 7.78/3.92 ! [F: nat > int,G: nat > int,A: nat,B: nat] :
% 7.78/3.92 ( ( produc7347049785058425330at_int @ F @ G @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_392_map__prod__simp,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > num,A: int,B: int] :
% 7.78/3.92 ( ( produc2224754261294513212nt_num @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_393_map__prod__simp,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > nat,A: int,B: int] :
% 7.78/3.92 ( ( produc5667422475138734578nt_nat @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_394_map__prod__simp,axiom,
% 7.78/3.92 ! [F: int > int,G: int > int,A: int,B: int] :
% 7.78/3.92 ( ( produc6036585564866528938nt_int @ F @ G @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_395_map__prod__simp,axiom,
% 7.78/3.92 ! [F: set_Pr1261947904930325089at_nat > nat,G: set_Pr1261947904930325089at_nat > num,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( produc3932168101365401472at_num @ F @ G @ ( produc2922128104949294807at_nat @ A @ B ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_396_fst__map__prod,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc473321116828791851t_unit @ ( produc3456481717235892722t_unit @ F @ G @ X2 ) )
% 7.78/3.92 = ( F @ ( produc473321116828791851t_unit @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_397_snd__map__prod,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc1126150082675451753t_unit @ ( produc3456481717235892722t_unit @ F @ G @ X2 ) )
% 7.78/3.92 = ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_398_apfst__conv,axiom,
% 7.78/3.92 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( produc6529295065807390923at_nat @ F @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( produc9060074326276436823at_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_399_apfst__conv,axiom,
% 7.78/3.92 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( produc5380969780118646373at_nat @ F @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( produc2922128104949294807at_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_400_apfst__conv,axiom,
% 7.78/3.92 ! [F: nat > nat,X2: nat,Y3: num] :
% 7.78/3.92 ( ( produc6767424583952363640at_num @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ X2 ) @ Y3 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_401_apfst__conv,axiom,
% 7.78/3.92 ! [F: nat > nat,X2: nat,Y3: nat] :
% 7.78/3.92 ( ( produc986720760941809198at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ X2 ) @ Y3 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_402_apfst__conv,axiom,
% 7.78/3.92 ! [F: int > int,X2: int,Y3: int] :
% 7.78/3.92 ( ( produc2355237562570658114nt_int @ F @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ X2 ) @ Y3 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_403_apsnd__conv,axiom,
% 7.78/3.92 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( produc8057050257526108681at_nat @ F @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( produc9060074326276436823at_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_404_apsnd__conv,axiom,
% 7.78/3.92 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( produc6468969725218530979at_nat @ F @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( produc2922128104949294807at_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_405_apsnd__conv,axiom,
% 7.78/3.92 ! [F: num > num,X2: nat,Y3: num] :
% 7.78/3.92 ( ( produc8389275579088931588um_nat @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_num @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_406_apsnd__conv,axiom,
% 7.78/3.92 ! [F: num > nat,X2: nat,Y3: num] :
% 7.78/3.92 ( ( produc1035573138926686394at_nat @ F @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_407_apsnd__conv,axiom,
% 7.78/3.92 ! [F: nat > num,X2: nat,Y3: nat] :
% 7.78/3.92 ( ( produc1225095714263496890um_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_num @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_408_apsnd__conv,axiom,
% 7.78/3.92 ! [F: nat > nat,X2: nat,Y3: nat] :
% 7.78/3.92 ( ( produc3094765310956027504at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_409_apsnd__conv,axiom,
% 7.78/3.92 ! [F: int > int,X2: int,Y3: int] :
% 7.78/3.92 ( ( produc4463282112584876420nt_int @ F @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.92 = ( product_Pair_int_int @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_410_apsnd__conv,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,X2: code_integer,Y3: code_integer] :
% 7.78/3.92 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X2 @ Y3 ) )
% 7.78/3.92 = ( produc1086072967326762835nteger @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_411_fst__apfst,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc473321116828791851t_unit @ ( produc4508741384315284437t_unit @ F @ X2 ) )
% 7.78/3.92 = ( F @ ( produc473321116828791851t_unit @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_412_snd__apfst,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc1126150082675451753t_unit @ ( produc4508741384315284437t_unit @ F @ X2 ) )
% 7.78/3.92 = ( produc1126150082675451753t_unit @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_413_fst__apsnd,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 7.78/3.92 ( ( produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F @ X2 ) )
% 7.78/3.92 = ( produc8508995932063986495nteger @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_414_fst__apsnd,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc473321116828791851t_unit @ ( produc3038839249364385243_ref_a @ F @ X2 ) )
% 7.78/3.92 = ( produc473321116828791851t_unit @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_415_snd__apsnd,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 7.78/3.92 ( ( produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F @ X2 ) )
% 7.78/3.92 = ( F @ ( produc6174133586879617921nteger @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_416_snd__apsnd,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc1126150082675451753t_unit @ ( produc3038839249364385243_ref_a @ F @ X2 ) )
% 7.78/3.92 = ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_417_apsnd__eq__conv,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,X2: produc8923325533196201883nteger,G: code_integer > code_integer] :
% 7.78/3.92 ( ( ( produc6499014454317279255nteger @ F @ X2 )
% 7.78/3.92 = ( produc6499014454317279255nteger @ G @ X2 ) )
% 7.78/3.92 = ( ( F @ ( produc6174133586879617921nteger @ X2 ) )
% 7.78/3.92 = ( G @ ( produc6174133586879617921nteger @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_418_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > nat,G: num > num] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 7.78/3.92 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_4925883905578568901at_num @ ( produc1665548884793878990um_num @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_419_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > nat,G: num > nat] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_4217639968629731195at_nat @ ( produc5108217098638100356um_nat @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_420_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: num,R3: set_Pr6200539531224447659at_num,F: nat > int,G: num > int] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ R3 )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_1039142661021589043nt_int @ ( produc5477380188365894716um_int @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_421_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > nat,G: nat > num] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 7.78/3.92 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_5877158439796295311at_num @ ( produc3535218481486409604at_num @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_422_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > nat,G: nat > nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_423_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > int,G: nat > int] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_424_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > nat,G: int > num] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 7.78/3.92 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_6540112122905407959at_num @ ( produc2224754261294513212nt_num @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_425_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > nat,G: int > nat] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A ) @ ( G @ B ) ) @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_426_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > int,G: int > int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A ) @ ( G @ B ) ) @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_427_map__prod__imageI,axiom,
% 7.78/3.92 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > nat,G: set_Pr1261947904930325089at_nat > num] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R3 )
% 7.78/3.92 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ ( F @ A ) @ ( G @ B ) ) @ ( image_8033574621161215657at_num @ ( produc3932168101365401472at_num @ F @ G ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_428_snd__comp__apfst,axiom,
% 7.78/3.92 ! [F: ref_a > ref_a] :
% 7.78/3.92 ( ( comp_P8019343326919024234t_unit @ produc1126150082675451753t_unit @ ( produc4508741384315284437t_unit @ F ) )
% 7.78/3.92 = produc1126150082675451753t_unit ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_429_fst__comp__apsnd,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer] :
% 7.78/3.92 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F ) )
% 7.78/3.92 = produc8508995932063986495nteger ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_430_fst__comp__apsnd,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( comp_P4044372497395451596t_unit @ produc473321116828791851t_unit @ ( produc3038839249364385243_ref_a @ F ) )
% 7.78/3.92 = produc473321116828791851t_unit ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_431_apfst__apsnd,axiom,
% 7.78/3.92 ! [F: ref_a > set_Pr4329608150637261639at_nat,G: heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc2316621926130398489at_nat @ F @ ( produc5080965012319039829_ref_a @ G @ X2 ) )
% 7.78/3.92 = ( produc9060074326276436823at_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_432_apfst__apsnd,axiom,
% 7.78/3.92 ! [F: ref_a > set_Pr1261947904930325089at_nat,G: heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc4016808307611786905at_nat @ F @ ( produc2928627021203296111_ref_a @ G @ X2 ) )
% 7.78/3.92 = ( produc2922128104949294807at_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_433_apfst__apsnd,axiom,
% 7.78/3.92 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > num,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc1704413584773205829at_num @ F @ ( produc7633249859560231688_ref_a @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_434_apfst__apsnd,axiom,
% 7.78/3.92 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc5147081798617427195at_nat @ F @ ( produc8366372614399963582_ref_a @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_435_apfst__apsnd,axiom,
% 7.78/3.92 ! [F: ref_a > int,G: heap_e7401611519738050253t_unit > int,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc6143945040009431475nt_int @ F @ ( produc3558794870892339738_ref_a @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ ( produc473321116828791851t_unit @ X2 ) ) @ ( G @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_436_apsnd__apfst,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat,G: ref_a > set_Pr4329608150637261639at_nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc5990651871820846223at_nat @ F @ ( produc5988837738927868575t_unit @ G @ X2 ) )
% 7.78/3.92 = ( produc9060074326276436823at_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_437_apsnd__apfst,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat,G: ref_a > set_Pr1261947904930325089at_nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc8705118745468743695at_nat @ F @ ( produc5323809043756447493t_unit @ G @ X2 ) )
% 7.78/3.92 = ( produc2922128104949294807at_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_438_apsnd__apfst,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > num,G: ref_a > nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc3902377510303101371um_nat @ F @ ( produc6942186945380262242t_unit @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_nat_num @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_439_apsnd__apfst,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > nat,G: ref_a > nat,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc5772047106995631985at_nat @ F @ ( produc6942186945380262242t_unit @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_nat_nat @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_440_apsnd__apfst,axiom,
% 7.78/3.92 ! [F: heap_e7401611519738050253t_unit > int,G: ref_a > int,X2: produc7812382424243267045t_unit] :
% 7.78/3.92 ( ( produc6768910348387636265nt_int @ F @ ( produc5845103964736263686t_unit @ G @ X2 ) )
% 7.78/3.92 = ( product_Pair_int_int @ ( G @ ( produc473321116828791851t_unit @ X2 ) ) @ ( F @ ( produc1126150082675451753t_unit @ X2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_441_apsnd__apfst__commute,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,G: code_integer > code_integer,P: produc8923325533196201883nteger] :
% 7.78/3.92 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ P ) )
% 7.78/3.92 = ( produc3195571438000033749nteger @ G @ ( produc6499014454317279255nteger @ F @ P ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_442_subset__image__iff,axiom,
% 7.78/3.92 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 = ( ? [AA: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 7.78/3.92 & ( B5
% 7.78/3.92 = ( image_nat_rat @ F @ AA ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_443_subset__image__iff,axiom,
% 7.78/3.92 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 = ( ? [AA: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 7.78/3.92 & ( B5
% 7.78/3.92 = ( image_nat_nat @ F @ AA ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_444_subset__image__iff,axiom,
% 7.78/3.92 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 = ( ? [AA: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 7.78/3.92 & ( B5
% 7.78/3.92 = ( image_nat_int @ F @ AA ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_445_subset__image__iff,axiom,
% 7.78/3.92 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 = ( ? [AA: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ AA @ A4 )
% 7.78/3.92 & ( B5
% 7.78/3.92 = ( image_int_nat @ F @ AA ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_446_subset__image__iff,axiom,
% 7.78/3.92 ! [B5: set_int,F: int > int,A4: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 = ( ? [AA: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ AA @ A4 )
% 7.78/3.92 & ( B5
% 7.78/3.92 = ( image_int_int @ F @ AA ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_447_image__subset__iff,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.92 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.92 = ( ! [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 => ( member_rat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_448_image__subset__iff,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.92 = ( ! [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_449_image__subset__iff,axiom,
% 7.78/3.92 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.92 = ( ! [X4: int] :
% 7.78/3.92 ( ( member_int @ X4 @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_450_image__subset__iff,axiom,
% 7.78/3.92 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.92 = ( ! [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_451_image__subset__iff,axiom,
% 7.78/3.92 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.92 = ( ! [X4: int] :
% 7.78/3.92 ( ( member_int @ X4 @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X4 ) @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_452_subset__imageE,axiom,
% 7.78/3.92 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 => ~ ! [C2: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.92 => ( B5
% 7.78/3.92 != ( image_nat_rat @ F @ C2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_453_subset__imageE,axiom,
% 7.78/3.92 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 => ~ ! [C2: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.92 => ( B5
% 7.78/3.92 != ( image_nat_nat @ F @ C2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_454_subset__imageE,axiom,
% 7.78/3.92 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 => ~ ! [C2: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.92 => ( B5
% 7.78/3.92 != ( image_nat_int @ F @ C2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_455_subset__imageE,axiom,
% 7.78/3.92 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 => ~ ! [C2: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 7.78/3.92 => ( B5
% 7.78/3.92 != ( image_int_nat @ F @ C2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_456_subset__imageE,axiom,
% 7.78/3.92 ! [B5: set_int,F: int > int,A4: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 => ~ ! [C2: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 7.78/3.92 => ( B5
% 7.78/3.92 != ( image_int_int @ F @ C2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_457_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_o,F: $o > $o,B5: set_o] :
% 7.78/3.92 ( ! [X: $o] :
% 7.78/3.92 ( ( member_o @ X @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_458_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_o,F: $o > nat,B5: set_nat] :
% 7.78/3.92 ( ! [X: $o] :
% 7.78/3.92 ( ( member_o @ X @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_nat @ ( image_o_nat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_459_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_o,F: $o > int,B5: set_int] :
% 7.78/3.92 ( ! [X: $o] :
% 7.78/3.92 ( ( member_o @ X @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_int @ ( image_o_int @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_460_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_nat,F: nat > rat,B5: set_rat] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 => ( member_rat @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_461_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_nat,F: nat > $o,B5: set_o] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_462_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_463_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_nat,F: nat > int,B5: set_int] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_464_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_int,F: int > $o,B5: set_o] :
% 7.78/3.92 ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_o @ ( image_int_o @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_465_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_int,F: int > nat,B5: set_nat] :
% 7.78/3.92 ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_466_image__subsetI,axiom,
% 7.78/3.92 ! [A4: set_int,F: int > int,B5: set_int] :
% 7.78/3.92 ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.92 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_467_image__mono,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.92 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_468_image__mono,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.92 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_469_image__mono,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,F: nat > int] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.92 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_470_image__mono,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,F: int > nat] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.92 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_471_image__mono,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,F: int > int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.92 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_472_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,H: nat > $o,I: nat > $o] :
% 7.78/3.92 ( ( comp_P4785046977597218846at_nat @ ( produc1928436952130685430_o_o_o @ F @ G ) @ ( produc6957950696844810486_nat_o @ H @ I ) )
% 7.78/3.92 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_473_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > num,H: nat > $o,I: int > nat] :
% 7.78/3.92 ( ( comp_P9057111047297513408at_int @ ( produc3628557804203378146at_num @ F @ G ) @ ( produc8250590009387450446nt_nat @ H @ I ) )
% 7.78/3.92 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_474_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > nat,H: nat > $o,I: nat > nat] :
% 7.78/3.92 ( ( comp_P4962864564169660718at_nat @ ( produc7071226018047599512at_nat @ F @ G ) @ ( produc7251236297486395890at_nat @ H @ I ) )
% 7.78/3.92 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_475_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: int > nat,H: nat > $o,I: int > int] :
% 7.78/3.92 ( ( comp_P465755969289462830at_int @ ( produc8070579729948654068nt_nat @ F @ G ) @ ( produc8248099538878400170nt_int @ H @ I ) )
% 7.78/3.92 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_int_nat_int @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_476_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > num,G: $o > $o,H: int > nat,I: nat > $o] :
% 7.78/3.92 ( ( comp_P5807473265676440968nt_nat @ ( produc3264868786340801506um_o_o @ F @ G ) @ ( produc8298419091753553490_nat_o @ H @ I ) )
% 7.78/3.92 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_477_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > num,H: int > nat,I: int > nat] :
% 7.78/3.92 ( ( comp_P9218946435557410242nt_int @ ( produc1476026309457068494at_num @ F @ G ) @ ( produc5667422475138734578nt_nat @ H @ I ) )
% 7.78/3.92 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_478_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > nat,H: int > nat,I: nat > nat] :
% 7.78/3.92 ( ( comp_P5124699952429557552nt_nat @ ( produc4918694523301289860at_nat @ F @ G ) @ ( produc4668068763237680022at_nat @ H @ I ) )
% 7.78/3.92 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_479_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,H: int > nat,I: int > int] :
% 7.78/3.92 ( ( comp_P3772045228931366376nt_int @ ( produc5918048235202344416nt_nat @ F @ G ) @ ( produc5664932004629684302nt_int @ H @ I ) )
% 7.78/3.92 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_int_nat_int @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_480_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: $o > $o,H: nat > nat,I: nat > $o] :
% 7.78/3.92 ( ( comp_P8901546994122883554at_nat @ ( produc2001155298098703512at_o_o @ F @ G ) @ ( produc4787215299218314158_nat_o @ H @ I ) )
% 7.78/3.92 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_481_map__prod_Ocomp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > num,H: nat > nat,I: int > nat] :
% 7.78/3.92 ( ( comp_P6334688330072917552at_int @ ( produc3535218481486409604at_num @ F @ G ) @ ( produc7977240407231685526nt_nat @ H @ I ) )
% 7.78/3.92 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_482_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,H: nat > $o,I: nat > $o,Prod: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc1928436952130685430_o_o_o @ F @ G @ ( produc6957950696844810486_nat_o @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_483_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > num,H: nat > $o,I: int > nat,Prod: product_prod_nat_int] :
% 7.78/3.92 ( ( produc3628557804203378146at_num @ F @ G @ ( produc8250590009387450446nt_nat @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_484_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > nat,H: nat > $o,I: nat > nat,Prod: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc7071226018047599512at_nat @ F @ G @ ( produc7251236297486395890at_nat @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_485_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: $o > $o,G: int > nat,H: nat > $o,I: int > int,Prod: product_prod_nat_int] :
% 7.78/3.92 ( ( produc8070579729948654068nt_nat @ F @ G @ ( produc8248099538878400170nt_int @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F @ H ) @ ( comp_int_nat_int @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_486_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > num,G: $o > $o,H: int > nat,I: nat > $o,Prod: product_prod_int_nat] :
% 7.78/3.92 ( ( produc3264868786340801506um_o_o @ F @ G @ ( produc8298419091753553490_nat_o @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_487_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > num,H: int > nat,I: int > nat,Prod: product_prod_int_int] :
% 7.78/3.92 ( ( produc1476026309457068494at_num @ F @ G @ ( produc5667422475138734578nt_nat @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_488_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > nat,H: int > nat,I: nat > nat,Prod: product_prod_int_nat] :
% 7.78/3.92 ( ( produc4918694523301289860at_nat @ F @ G @ ( produc4668068763237680022at_nat @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_489_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,H: int > nat,I: int > int,Prod: product_prod_int_int] :
% 7.78/3.92 ( ( produc5918048235202344416nt_nat @ F @ G @ ( produc5664932004629684302nt_int @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F @ H ) @ ( comp_int_nat_int @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_490_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > nat,G: $o > $o,H: nat > nat,I: nat > $o,Prod: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc2001155298098703512at_o_o @ F @ G @ ( produc4787215299218314158_nat_o @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_o_o_nat @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_491_map__prod_Ocompositionality,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > num,H: nat > nat,I: int > nat,Prod: product_prod_nat_int] :
% 7.78/3.92 ( ( produc3535218481486409604at_num @ F @ G @ ( produc7977240407231685526nt_nat @ H @ I @ Prod ) )
% 7.78/3.92 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_num_int @ G @ I ) @ Prod ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_492_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: $o > $o,F22: nat > $o,G1: $o > $o,G22: nat > $o] :
% 7.78/3.92 ( ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P4785046977597218846at_nat @ ( produc1928436952130685430_o_o_o @ F1 @ G1 ) @ ( produc6957950696844810486_nat_o @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_493_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: $o > $o,F22: nat > $o,G1: nat > num,G22: int > nat] :
% 7.78/3.92 ( ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P9057111047297513408at_int @ ( produc3628557804203378146at_num @ F1 @ G1 ) @ ( produc8250590009387450446nt_nat @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_494_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: $o > $o,F22: nat > $o,G1: nat > nat,G22: nat > nat] :
% 7.78/3.92 ( ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_nat_nat_nat @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P4962864564169660718at_nat @ ( produc7071226018047599512at_nat @ F1 @ G1 ) @ ( produc7251236297486395890at_nat @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_495_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: $o > $o,F22: nat > $o,G1: int > nat,G22: int > int] :
% 7.78/3.92 ( ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ F1 @ F22 ) @ ( comp_int_nat_int @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P465755969289462830at_int @ ( produc8070579729948654068nt_nat @ F1 @ G1 ) @ ( produc8248099538878400170nt_int @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_496_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > num,F22: int > nat,G1: $o > $o,G22: nat > $o] :
% 7.78/3.92 ( ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P5807473265676440968nt_nat @ ( produc3264868786340801506um_o_o @ F1 @ G1 ) @ ( produc8298419091753553490_nat_o @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_497_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > num,F22: int > nat,G1: nat > num,G22: int > nat] :
% 7.78/3.92 ( ( produc165562089265172102nt_num @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P9218946435557410242nt_int @ ( produc1476026309457068494at_num @ F1 @ G1 ) @ ( produc5667422475138734578nt_nat @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_498_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > num,F22: int > nat,G1: nat > nat,G22: nat > nat] :
% 7.78/3.92 ( ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_nat_nat_nat @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P5124699952429557552nt_nat @ ( produc4918694523301289860at_nat @ F1 @ G1 ) @ ( produc4668068763237680022at_nat @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_499_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > num,F22: int > nat,G1: int > nat,G22: int > int] :
% 7.78/3.92 ( ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ F1 @ F22 ) @ ( comp_int_nat_int @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P3772045228931366376nt_int @ ( produc5918048235202344416nt_nat @ F1 @ G1 ) @ ( produc5664932004629684302nt_int @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_500_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > nat,F22: nat > nat,G1: $o > $o,G22: nat > $o] :
% 7.78/3.92 ( ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ F1 @ F22 ) @ ( comp_o_o_nat @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P8901546994122883554at_nat @ ( produc2001155298098703512at_o_o @ F1 @ G1 ) @ ( produc4787215299218314158_nat_o @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_501_map__prod__compose,axiom,
% 7.78/3.92 ! [F1: nat > nat,F22: nat > nat,G1: nat > num,G22: int > nat] :
% 7.78/3.92 ( ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ F1 @ F22 ) @ ( comp_nat_num_int @ G1 @ G22 ) )
% 7.78/3.92 = ( comp_P6334688330072917552at_int @ ( produc3535218481486409604at_num @ F1 @ G1 ) @ ( produc7977240407231685526nt_nat @ F22 @ G22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_502_apsnd__compose,axiom,
% 7.78/3.92 ! [F: code_integer > code_integer,G: code_integer > code_integer,X2: produc8923325533196201883nteger] :
% 7.78/3.92 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X2 ) )
% 7.78/3.92 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_503_Collect__case__prod__Grp__in,axiom,
% 7.78/3.92 ! [Z2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ Z2 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ F ) ) ) )
% 7.78/3.92 => ( member2643936169264416010at_nat @ ( produc6011863565407846595at_nat @ Z2 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_504_Collect__case__prod__Grp__in,axiom,
% 7.78/3.92 ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
% 7.78/3.92 => ( member_nat @ ( product_fst_nat_nat @ Z2 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_505_Collect__case__prod__Grp__in,axiom,
% 7.78/3.92 ! [Z2: produc7812382424243267045t_unit,A4: set_ref_a,F: ref_a > heap_e7401611519738050253t_unit] :
% 7.78/3.92 ( ( member7849944260330398460t_unit @ Z2 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_Gr6510375311308651680t_unit @ A4 @ F ) ) ) )
% 7.78/3.92 => ( member_ref_a @ ( produc473321116828791851t_unit @ Z2 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_506_Collect__case__prod__Grp__in,axiom,
% 7.78/3.92 ! [Z2: product_prod_int_int,A4: set_int,F: int > int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ Z2 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ F ) ) ) )
% 7.78/3.92 => ( member_int @ ( product_fst_int_int @ Z2 ) @ A4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_507_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_num,F: nat > nat,G: num > num,R3: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ C @ ( image_4925883905578568901at_num @ ( produc1665548884793878990um_num @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_508_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_num,F: nat > nat,G: nat > num,R3: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ C @ ( image_5877158439796295311at_num @ ( produc3535218481486409604at_num @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_509_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_num,F: int > nat,G: int > num,R3: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ C @ ( image_6540112122905407959at_num @ ( produc2224754261294513212nt_num @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_num @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_510_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_nat,F: nat > nat,G: num > nat,R3: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ C @ ( image_4217639968629731195at_nat @ ( produc5108217098638100356um_nat @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_511_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_nat,F: nat > nat,G: nat > nat,R3: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ C @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_512_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_nat_nat,F: int > nat,G: int > nat,R3: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ C @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_nat_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_513_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_int_int,F: nat > int,G: num > int,R3: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ C @ ( image_1039142661021589043nt_int @ ( produc5477380188365894716um_int @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_514_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_int_int,F: nat > int,G: nat > int,R3: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ C @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_515_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: product_prod_int_int,F: int > int,G: int > int,R3: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ C @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( product_Pair_int_int @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_516_prod__fun__imageE,axiom,
% 7.78/3.92 ! [C: produc3843707927480180839at_nat,F: nat > set_Pr1261947904930325089at_nat,G: num > set_Pr1261947904930325089at_nat,R3: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ C @ ( image_2708129733610033121at_nat @ ( produc170006858110003436at_nat @ F @ G ) @ R3 ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( C
% 7.78/3.92 = ( produc2922128104949294807at_nat @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ~ ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_517_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,B: $o,F: $o > $o] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_518_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,B: nat,F: $o > nat] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_nat @ B @ ( image_o_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_519_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,B: int,F: $o > int] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_int @ B @ ( image_o_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_520_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,B: rat,F: nat > rat] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_521_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,B: $o,F: nat > $o] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_o @ B @ ( image_nat_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_522_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,B: nat,F: nat > nat] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_523_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,B: int,F: nat > int] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_524_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,B: $o,F: int > $o] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_o @ B @ ( image_int_o @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_525_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,B: nat,F: int > nat] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_nat @ B @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_526_rev__image__eqI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,B: int,F: int > int] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( ( B
% 7.78/3.92 = ( F @ X2 ) )
% 7.78/3.92 => ( member_int @ B @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_527_ball__imageD,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 7.78/3.92 ( ! [X: rat] :
% 7.78/3.92 ( ( member_rat @ X @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ X ) )
% 7.78/3.92 => ! [X6: nat] :
% 7.78/3.92 ( ( member_nat @ X6 @ A4 )
% 7.78/3.92 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_528_ball__imageD,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ X ) )
% 7.78/3.92 => ! [X6: nat] :
% 7.78/3.92 ( ( member_nat @ X6 @ A4 )
% 7.78/3.92 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_529_ball__imageD,axiom,
% 7.78/3.92 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 7.78/3.92 ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ X ) )
% 7.78/3.92 => ! [X6: nat] :
% 7.78/3.92 ( ( member_nat @ X6 @ A4 )
% 7.78/3.92 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_530_ball__imageD,axiom,
% 7.78/3.92 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 7.78/3.92 ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ X ) )
% 7.78/3.92 => ! [X6: int] :
% 7.78/3.92 ( ( member_int @ X6 @ A4 )
% 7.78/3.92 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_531_ball__imageD,axiom,
% 7.78/3.92 ! [F: int > int,A4: set_int,P2: int > $o] :
% 7.78/3.92 ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ X ) )
% 7.78/3.92 => ! [X6: int] :
% 7.78/3.92 ( ( member_int @ X6 @ A4 )
% 7.78/3.92 => ( P2 @ ( F @ X6 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_532_image__cong,axiom,
% 7.78/3.92 ! [M: set_nat,N: set_nat,F: nat > rat,G: nat > rat] :
% 7.78/3.92 ( ( M = N )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ N )
% 7.78/3.92 => ( ( F @ X )
% 7.78/3.92 = ( G @ X ) ) )
% 7.78/3.92 => ( ( image_nat_rat @ F @ M )
% 7.78/3.92 = ( image_nat_rat @ G @ N ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_533_image__cong,axiom,
% 7.78/3.92 ! [M: set_nat,N: set_nat,F: nat > nat,G: nat > nat] :
% 7.78/3.92 ( ( M = N )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ N )
% 7.78/3.92 => ( ( F @ X )
% 7.78/3.92 = ( G @ X ) ) )
% 7.78/3.92 => ( ( image_nat_nat @ F @ M )
% 7.78/3.92 = ( image_nat_nat @ G @ N ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_534_image__cong,axiom,
% 7.78/3.92 ! [M: set_nat,N: set_nat,F: nat > int,G: nat > int] :
% 7.78/3.92 ( ( M = N )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ N )
% 7.78/3.92 => ( ( F @ X )
% 7.78/3.92 = ( G @ X ) ) )
% 7.78/3.92 => ( ( image_nat_int @ F @ M )
% 7.78/3.92 = ( image_nat_int @ G @ N ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_535_image__cong,axiom,
% 7.78/3.92 ! [M: set_int,N: set_int,F: int > nat,G: int > nat] :
% 7.78/3.92 ( ( M = N )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ N )
% 7.78/3.92 => ( ( F @ X )
% 7.78/3.92 = ( G @ X ) ) )
% 7.78/3.92 => ( ( image_int_nat @ F @ M )
% 7.78/3.92 = ( image_int_nat @ G @ N ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_536_image__cong,axiom,
% 7.78/3.92 ! [M: set_int,N: set_int,F: int > int,G: int > int] :
% 7.78/3.92 ( ( M = N )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ N )
% 7.78/3.92 => ( ( F @ X )
% 7.78/3.92 = ( G @ X ) ) )
% 7.78/3.92 => ( ( image_int_int @ F @ M )
% 7.78/3.92 = ( image_int_int @ G @ N ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_537_bex__imageD,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 7.78/3.92 ( ? [X6: rat] :
% 7.78/3.92 ( ( member_rat @ X6 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 & ( P2 @ X6 ) )
% 7.78/3.92 => ? [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 & ( P2 @ ( F @ X ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_538_bex__imageD,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 7.78/3.92 ( ? [X6: nat] :
% 7.78/3.92 ( ( member_nat @ X6 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 & ( P2 @ X6 ) )
% 7.78/3.92 => ? [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 & ( P2 @ ( F @ X ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_539_bex__imageD,axiom,
% 7.78/3.92 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 7.78/3.92 ( ? [X6: int] :
% 7.78/3.92 ( ( member_int @ X6 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 & ( P2 @ X6 ) )
% 7.78/3.92 => ? [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ A4 )
% 7.78/3.92 & ( P2 @ ( F @ X ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_540_bex__imageD,axiom,
% 7.78/3.92 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 7.78/3.92 ( ? [X6: nat] :
% 7.78/3.92 ( ( member_nat @ X6 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 & ( P2 @ X6 ) )
% 7.78/3.92 => ? [X: int] :
% 7.78/3.92 ( ( member_int @ X @ A4 )
% 7.78/3.92 & ( P2 @ ( F @ X ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_541_bex__imageD,axiom,
% 7.78/3.92 ! [F: int > int,A4: set_int,P2: int > $o] :
% 7.78/3.92 ( ? [X6: int] :
% 7.78/3.92 ( ( member_int @ X6 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 & ( P2 @ X6 ) )
% 7.78/3.92 => ? [X: int] :
% 7.78/3.92 ( ( member_int @ X @ A4 )
% 7.78/3.92 & ( P2 @ ( F @ X ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_542_image__iff,axiom,
% 7.78/3.92 ! [Z2: rat,F: nat > rat,A4: set_nat] :
% 7.78/3.92 ( ( member_rat @ Z2 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 = ( ? [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 & ( Z2
% 7.78/3.92 = ( F @ X4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_543_image__iff,axiom,
% 7.78/3.92 ! [Z2: nat,F: nat > nat,A4: set_nat] :
% 7.78/3.92 ( ( member_nat @ Z2 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 = ( ? [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 & ( Z2
% 7.78/3.92 = ( F @ X4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_544_image__iff,axiom,
% 7.78/3.92 ! [Z2: nat,F: int > nat,A4: set_int] :
% 7.78/3.92 ( ( member_nat @ Z2 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 = ( ? [X4: int] :
% 7.78/3.92 ( ( member_int @ X4 @ A4 )
% 7.78/3.92 & ( Z2
% 7.78/3.92 = ( F @ X4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_545_image__iff,axiom,
% 7.78/3.92 ! [Z2: int,F: nat > int,A4: set_nat] :
% 7.78/3.92 ( ( member_int @ Z2 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 = ( ? [X4: nat] :
% 7.78/3.92 ( ( member_nat @ X4 @ A4 )
% 7.78/3.92 & ( Z2
% 7.78/3.92 = ( F @ X4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_546_image__iff,axiom,
% 7.78/3.92 ! [Z2: int,F: int > int,A4: set_int] :
% 7.78/3.92 ( ( member_int @ Z2 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 = ( ? [X4: int] :
% 7.78/3.92 ( ( member_int @ X4 @ A4 )
% 7.78/3.92 & ( Z2
% 7.78/3.92 = ( F @ X4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_547_imageI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,F: $o > $o] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_548_imageI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,F: $o > nat] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X2 ) @ ( image_o_nat @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_549_imageI,axiom,
% 7.78/3.92 ! [X2: $o,A4: set_o,F: $o > int] :
% 7.78/3.92 ( ( member_o @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X2 ) @ ( image_o_int @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_550_imageI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,F: nat > rat] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_551_imageI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,F: nat > $o] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X2 ) @ ( image_nat_o @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_552_imageI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_553_imageI,axiom,
% 7.78/3.92 ! [X2: nat,A4: set_nat,F: nat > int] :
% 7.78/3.92 ( ( member_nat @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X2 ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_554_imageI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,F: int > $o] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_o @ ( F @ X2 ) @ ( image_int_o @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_555_imageI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,F: int > nat] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_nat @ ( F @ X2 ) @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_556_imageI,axiom,
% 7.78/3.92 ! [X2: int,A4: set_int,F: int > int] :
% 7.78/3.92 ( ( member_int @ X2 @ A4 )
% 7.78/3.92 => ( member_int @ ( F @ X2 ) @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_557_Sup_OSUP__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > rat,D: nat > rat,Sup: set_rat > rat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Sup @ ( image_nat_rat @ C3 @ A4 ) )
% 7.78/3.92 = ( Sup @ ( image_nat_rat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_558_Sup_OSUP__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Sup: set_nat > nat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Sup @ ( image_nat_nat @ C3 @ A4 ) )
% 7.78/3.92 = ( Sup @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_559_Sup_OSUP__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int,Sup: set_int > int] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Sup @ ( image_nat_int @ C3 @ A4 ) )
% 7.78/3.92 = ( Sup @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_560_Sup_OSUP__cong,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat,Sup: set_nat > nat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Sup @ ( image_int_nat @ C3 @ A4 ) )
% 7.78/3.92 = ( Sup @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_561_Sup_OSUP__cong,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int,Sup: set_int > int] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Sup @ ( image_int_int @ C3 @ A4 ) )
% 7.78/3.92 = ( Sup @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_562_Inf_OINF__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > rat,D: nat > rat,Inf: set_rat > rat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Inf @ ( image_nat_rat @ C3 @ A4 ) )
% 7.78/3.92 = ( Inf @ ( image_nat_rat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_563_Inf_OINF__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Inf: set_nat > nat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Inf @ ( image_nat_nat @ C3 @ A4 ) )
% 7.78/3.92 = ( Inf @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_564_Inf_OINF__cong,axiom,
% 7.78/3.92 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int,Inf: set_int > int] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: nat] :
% 7.78/3.92 ( ( member_nat @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Inf @ ( image_nat_int @ C3 @ A4 ) )
% 7.78/3.92 = ( Inf @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_565_Inf_OINF__cong,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat,Inf: set_nat > nat] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Inf @ ( image_int_nat @ C3 @ A4 ) )
% 7.78/3.92 = ( Inf @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_566_Inf_OINF__cong,axiom,
% 7.78/3.92 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int,Inf: set_int > int] :
% 7.78/3.92 ( ( A4 = B5 )
% 7.78/3.92 => ( ! [X: int] :
% 7.78/3.92 ( ( member_int @ X @ B5 )
% 7.78/3.92 => ( ( C3 @ X )
% 7.78/3.92 = ( D @ X ) ) )
% 7.78/3.92 => ( ( Inf @ ( image_int_int @ C3 @ A4 ) )
% 7.78/3.92 = ( Inf @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_567_comp__eq__dest__lhs,axiom,
% 7.78/3.92 ! [A: $o > $o,B: nat > $o,C: nat > $o,V: nat] :
% 7.78/3.92 ( ( ( comp_o_o_nat @ A @ B )
% 7.78/3.92 = C )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ V ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_568_comp__eq__dest__lhs,axiom,
% 7.78/3.92 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 7.78/3.92 ( ( ( comp_nat_num_int @ A @ B )
% 7.78/3.92 = C )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ V ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_569_comp__eq__dest__lhs,axiom,
% 7.78/3.92 ! [A: nat > nat,B: nat > nat,C: nat > nat,V: nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_nat @ A @ B )
% 7.78/3.92 = C )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ V ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_570_comp__eq__dest__lhs,axiom,
% 7.78/3.92 ! [A: int > nat,B: int > int,C: int > nat,V: int] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ A @ B )
% 7.78/3.92 = C )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ V ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_571_comp__eq__dest__lhs,axiom,
% 7.78/3.92 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 7.78/3.92 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 7.78/3.92 = C )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ V ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_572_comp__eq__elim,axiom,
% 7.78/3.92 ! [A: $o > $o,B: nat > $o,C: $o > $o,D2: nat > $o] :
% 7.78/3.92 ( ( ( comp_o_o_nat @ A @ B )
% 7.78/3.92 = ( comp_o_o_nat @ C @ D2 ) )
% 7.78/3.92 => ! [V4: nat] :
% 7.78/3.92 ( ( A @ ( B @ V4 ) )
% 7.78/3.92 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_573_comp__eq__elim,axiom,
% 7.78/3.92 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat] :
% 7.78/3.92 ( ( ( comp_nat_num_int @ A @ B )
% 7.78/3.92 = ( comp_nat_num_int @ C @ D2 ) )
% 7.78/3.92 => ! [V4: int] :
% 7.78/3.92 ( ( A @ ( B @ V4 ) )
% 7.78/3.92 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_574_comp__eq__elim,axiom,
% 7.78/3.92 ! [A: nat > nat,B: nat > nat,C: nat > nat,D2: nat > nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_nat @ A @ B )
% 7.78/3.92 = ( comp_nat_nat_nat @ C @ D2 ) )
% 7.78/3.92 => ! [V4: nat] :
% 7.78/3.92 ( ( A @ ( B @ V4 ) )
% 7.78/3.92 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_575_comp__eq__elim,axiom,
% 7.78/3.92 ! [A: int > nat,B: int > int,C: int > nat,D2: int > int] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ A @ B )
% 7.78/3.92 = ( comp_int_nat_int @ C @ D2 ) )
% 7.78/3.92 => ! [V4: int] :
% 7.78/3.92 ( ( A @ ( B @ V4 ) )
% 7.78/3.92 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_576_comp__eq__elim,axiom,
% 7.78/3.92 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 7.78/3.92 => ! [V4: code_integer] :
% 7.78/3.92 ( ( A @ ( B @ V4 ) )
% 7.78/3.92 = ( C @ ( D2 @ V4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_577_comp__eq__dest,axiom,
% 7.78/3.92 ! [A: $o > $o,B: nat > $o,C: $o > $o,D2: nat > $o,V: nat] :
% 7.78/3.92 ( ( ( comp_o_o_nat @ A @ B )
% 7.78/3.92 = ( comp_o_o_nat @ C @ D2 ) )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ ( D2 @ V ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_578_comp__eq__dest,axiom,
% 7.78/3.92 ! [A: nat > num,B: int > nat,C: nat > num,D2: int > nat,V: int] :
% 7.78/3.92 ( ( ( comp_nat_num_int @ A @ B )
% 7.78/3.92 = ( comp_nat_num_int @ C @ D2 ) )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ ( D2 @ V ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_579_comp__eq__dest,axiom,
% 7.78/3.92 ! [A: nat > nat,B: nat > nat,C: nat > nat,D2: nat > nat,V: nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_nat @ A @ B )
% 7.78/3.92 = ( comp_nat_nat_nat @ C @ D2 ) )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ ( D2 @ V ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_580_comp__eq__dest,axiom,
% 7.78/3.92 ! [A: int > nat,B: int > int,C: int > nat,D2: int > int,V: int] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ A @ B )
% 7.78/3.92 = ( comp_int_nat_int @ C @ D2 ) )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ ( D2 @ V ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_581_comp__eq__dest,axiom,
% 7.78/3.92 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,D2: code_integer > code_integer > code_integer,V: code_integer] :
% 7.78/3.92 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ C @ D2 ) )
% 7.78/3.92 => ( ( A @ ( B @ V ) )
% 7.78/3.92 = ( C @ ( D2 @ V ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_582_comp__assoc,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > $o,H: nat > nat] :
% 7.78/3.92 ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_o_nat @ F @ ( comp_nat_o_nat @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_583_comp__assoc,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,H: int > int] :
% 7.78/3.92 ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_584_comp__assoc,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,H: nat > $o] :
% 7.78/3.92 ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_585_comp__assoc,axiom,
% 7.78/3.92 ! [F: num > num,G: nat > num,H: int > nat] :
% 7.78/3.92 ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_586_comp__assoc,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > nat,H: int > nat] :
% 7.78/3.92 ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_587_comp__assoc,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,H: nat > nat] :
% 7.78/3.92 ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_588_comp__assoc,axiom,
% 7.78/3.92 ! [F: nat > nat,G: int > nat,H: int > int] :
% 7.78/3.92 ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_int @ F @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_589_comp__assoc,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > int,H: int > int] :
% 7.78/3.92 ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_nat_int @ F @ ( comp_int_int_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_590_comp__assoc,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,H: code_integer > code_integer] :
% 7.78/3.92 ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_591_comp__assoc,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,H: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_592_comp__def,axiom,
% 7.78/3.92 ( comp_o_o_nat
% 7.78/3.92 = ( ^ [F2: $o > $o,G3: nat > $o,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_593_comp__def,axiom,
% 7.78/3.92 ( comp_nat_num_int
% 7.78/3.92 = ( ^ [F2: nat > num,G3: int > nat,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_594_comp__def,axiom,
% 7.78/3.92 ( comp_nat_nat_nat
% 7.78/3.92 = ( ^ [F2: nat > nat,G3: nat > nat,X4: nat] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_595_comp__def,axiom,
% 7.78/3.92 ( comp_int_nat_int
% 7.78/3.92 = ( ^ [F2: int > nat,G3: int > int,X4: int] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_596_comp__def,axiom,
% 7.78/3.92 ( comp_C8797469213163452608nteger
% 7.78/3.92 = ( ^ [F2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G3: code_integer > code_integer > code_integer,X4: code_integer] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_597_apfst__convE,axiom,
% 7.78/3.92 ! [Q: produc1319942482725812455at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,P: produc1319942482725812455at_nat] :
% 7.78/3.92 ( ( Q
% 7.78/3.92 = ( produc6529295065807390923at_nat @ F @ P ) )
% 7.78/3.92 => ~ ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( produc9060074326276436823at_nat @ X @ Y ) )
% 7.78/3.92 => ( Q
% 7.78/3.92 != ( produc9060074326276436823at_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_598_apfst__convE,axiom,
% 7.78/3.92 ! [Q: produc3843707927480180839at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,P: produc3843707927480180839at_nat] :
% 7.78/3.92 ( ( Q
% 7.78/3.92 = ( produc5380969780118646373at_nat @ F @ P ) )
% 7.78/3.92 => ~ ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( produc2922128104949294807at_nat @ X @ Y ) )
% 7.78/3.92 => ( Q
% 7.78/3.92 != ( produc2922128104949294807at_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_599_apfst__convE,axiom,
% 7.78/3.92 ! [Q: product_prod_nat_num,F: nat > nat,P: product_prod_nat_num] :
% 7.78/3.92 ( ( Q
% 7.78/3.92 = ( produc6767424583952363640at_num @ F @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: num] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.92 => ( Q
% 7.78/3.92 != ( product_Pair_nat_num @ ( F @ X ) @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_600_apfst__convE,axiom,
% 7.78/3.92 ! [Q: product_prod_nat_nat,F: nat > nat,P: product_prod_nat_nat] :
% 7.78/3.92 ( ( Q
% 7.78/3.92 = ( produc986720760941809198at_nat @ F @ P ) )
% 7.78/3.92 => ~ ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.92 => ( Q
% 7.78/3.92 != ( product_Pair_nat_nat @ ( F @ X ) @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_601_apfst__convE,axiom,
% 7.78/3.92 ! [Q: product_prod_int_int,F: int > int,P: product_prod_int_int] :
% 7.78/3.92 ( ( Q
% 7.78/3.92 = ( produc2355237562570658114nt_int @ F @ P ) )
% 7.78/3.92 => ~ ! [X: int,Y: int] :
% 7.78/3.92 ( ( P
% 7.78/3.92 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.92 => ( Q
% 7.78/3.92 != ( product_Pair_int_int @ ( F @ X ) @ Y ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_602_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: $o > $o,G22: $o > $o,F1: nat > $o,F22: nat > $o,V: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc1928436952130685430_o_o_o @ G1 @ G22 @ ( produc6957950696844810486_nat_o @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc6957950696844810486_nat_o @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_603_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: $o > $o,G22: nat > num,F1: nat > $o,F22: int > nat,V: product_prod_nat_int] :
% 7.78/3.92 ( ( produc3628557804203378146at_num @ G1 @ G22 @ ( produc8250590009387450446nt_nat @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc4807921795543229080nt_num @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_604_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: $o > $o,G22: nat > nat,F1: nat > $o,F22: nat > nat,V: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc7071226018047599512at_nat @ G1 @ G22 @ ( produc7251236297486395890at_nat @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc7251236297486395890at_nat @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_nat_nat_nat @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_605_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: $o > $o,G22: int > nat,F1: nat > $o,F22: int > int,V: product_prod_nat_int] :
% 7.78/3.92 ( ( produc8070579729948654068nt_nat @ G1 @ G22 @ ( produc8248099538878400170nt_int @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc8250590009387450446nt_nat @ ( comp_o_o_nat @ G1 @ F1 ) @ ( comp_int_nat_int @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_606_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > num,G22: $o > $o,F1: int > nat,F22: nat > $o,V: product_prod_int_nat] :
% 7.78/3.92 ( ( produc3264868786340801506um_o_o @ G1 @ G22 @ ( produc8298419091753553490_nat_o @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc9074608839065728392_nat_o @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_607_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > num,G22: nat > num,F1: int > nat,F22: int > nat,V: product_prod_int_int] :
% 7.78/3.92 ( ( produc1476026309457068494at_num @ G1 @ G22 @ ( produc5667422475138734578nt_nat @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc165562089265172102nt_num @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_608_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > num,G22: nat > nat,F1: int > nat,F22: nat > nat,V: product_prod_int_nat] :
% 7.78/3.92 ( ( produc4918694523301289860at_nat @ G1 @ G22 @ ( produc4668068763237680022at_nat @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc2608876591208338912at_nat @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_nat_nat_nat @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_609_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > num,G22: int > nat,F1: int > nat,F22: int > int,V: product_prod_int_int] :
% 7.78/3.92 ( ( produc5918048235202344416nt_nat @ G1 @ G22 @ ( produc5664932004629684302nt_int @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc3608230303109393468nt_nat @ ( comp_nat_num_int @ G1 @ F1 ) @ ( comp_int_nat_int @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_610_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > nat,G22: $o > $o,F1: nat > nat,F22: nat > $o,V: product_prod_nat_nat] :
% 7.78/3.92 ( ( produc2001155298098703512at_o_o @ G1 @ G22 @ ( produc4787215299218314158_nat_o @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc4787215299218314158_nat_o @ ( comp_nat_nat_nat @ G1 @ F1 ) @ ( comp_o_o_nat @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_611_prod_Omap__comp,axiom,
% 7.78/3.92 ! [G1: nat > nat,G22: nat > num,F1: nat > nat,F22: int > nat,V: product_prod_nat_int] :
% 7.78/3.92 ( ( produc3535218481486409604at_num @ G1 @ G22 @ ( produc7977240407231685526nt_nat @ F1 @ F22 @ V ) )
% 7.78/3.92 = ( produc4534572193387464160nt_num @ ( comp_nat_nat_nat @ G1 @ F1 ) @ ( comp_nat_num_int @ G22 @ F22 ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_612_subrelI,axiom,
% 7.78/3.92 ! [R: set_Pr7459493094073627847at_nat,S2: set_Pr7459493094073627847at_nat] :
% 7.78/3.92 ( ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ R )
% 7.78/3.92 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ S2 ) )
% 7.78/3.92 => ( ord_le5997549366648089703at_nat @ R @ S2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_613_subrelI,axiom,
% 7.78/3.92 ! [R: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 7.78/3.92 ( ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
% 7.78/3.92 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ S2 ) )
% 7.78/3.92 => ( ord_le1268244103169919719at_nat @ R @ S2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_614_subrelI,axiom,
% 7.78/3.92 ! [R: set_Pr6200539531224447659at_num,S2: set_Pr6200539531224447659at_num] :
% 7.78/3.92 ( ! [X: nat,Y: num] :
% 7.78/3.92 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R )
% 7.78/3.92 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ S2 ) )
% 7.78/3.92 => ( ord_le8085105155179020875at_num @ R @ S2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_615_subrelI,axiom,
% 7.78/3.92 ! [R: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 7.78/3.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ S2 ) )
% 7.78/3.92 => ( ord_le3146513528884898305at_nat @ R @ S2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_616_subrelI,axiom,
% 7.78/3.92 ! [R: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 7.78/3.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ S2 ) )
% 7.78/3.92 => ( ord_le2843351958646193337nt_int @ R @ S2 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_617_all__subset__image,axiom,
% 7.78/3.92 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 7.78/3.92 ( ( ! [B6: set_rat] :
% 7.78/3.92 ( ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ B6 ) ) )
% 7.78/3.92 = ( ! [B6: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.92 => ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_618_all__subset__image,axiom,
% 7.78/3.92 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 7.78/3.92 ( ( ! [B6: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ B6 ) ) )
% 7.78/3.92 = ( ! [B6: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.92 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_619_all__subset__image,axiom,
% 7.78/3.92 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 7.78/3.92 ( ( ! [B6: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ B6 ) ) )
% 7.78/3.92 = ( ! [B6: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.92 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_620_all__subset__image,axiom,
% 7.78/3.92 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 7.78/3.92 ( ( ! [B6: set_nat] :
% 7.78/3.92 ( ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ B6 ) ) )
% 7.78/3.92 = ( ! [B6: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 7.78/3.92 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_621_all__subset__image,axiom,
% 7.78/3.92 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 7.78/3.92 ( ( ! [B6: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.92 => ( P2 @ B6 ) ) )
% 7.78/3.92 = ( ! [B6: set_int] :
% 7.78/3.92 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 7.78/3.92 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_622_rel__fun__Collect__case__prodD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 7.78/3.92 ( ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 7.78/3.92 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 7.78/3.92 => ( B5 @ ( comp_P8635049891247748876at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i5627883460353289149at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_623_rel__fun__Collect__case__prodD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 7.78/3.92 ( ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 7.78/3.92 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 7.78/3.92 => ( B5 @ ( comp_P4524073163769703009at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i4519014998770822500at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_624_rel__fun__Collect__case__prodD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,X5: set_Pr49084382684228242at_int,X2: produc4196048018000912732at_int] :
% 7.78/3.92 ( ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( ord_le4604737605482584818at_int @ X5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ A4 ) ) )
% 7.78/3.92 => ( ( member8394280151737582451at_int @ X2 @ X5 )
% 7.78/3.92 => ( B5 @ ( comp_P7900071416159368952at_int @ F @ produc4619704898428564714at_int @ X2 ) @ ( comp_i653165354545908656at_int @ G @ produc3064508320661873192at_int @ X2 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_625_rel__fun__Collect__case__prodD,axiom,
% 7.78/3.92 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num,X5: set_Pr8415741480598773322nteger,X2: produc2963269191615333738nteger] :
% 7.78/3.92 ( ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( ord_le2638047946463454698nteger @ X5 @ ( collec7215431352809750357nteger @ ( produc540600059291021473eger_o @ A4 ) ) )
% 7.78/3.92 => ( ( member4345257455949424659nteger @ X2 @ X5 )
% 7.78/3.92 => ( B5 @ ( comp_i3846818780818535807nteger @ F @ produc45500017171379470nteger @ X2 ) @ ( comp_C8580465762518603278nteger @ G @ produc2153544567185597776nteger @ X2 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_626_rel__fun__Collect__case__prodD,axiom,
% 7.78/3.92 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num,X5: set_Pr958786334691620121nt_int,X2: product_prod_int_int] :
% 7.78/3.92 ( ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) )
% 7.78/3.92 => ( ( member5262025264175285858nt_int @ X2 @ X5 )
% 7.78/3.92 => ( B5 @ ( comp_i7231038107349025742nt_int @ F @ product_fst_int_int @ X2 ) @ ( comp_i7231038107349025742nt_int @ G @ product_snd_int_int @ X2 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_627_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ ( bNF_co8276296344278409722at_nat @ ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat ) @ ( comp_n2711240574518091068at_nat @ G @ product_snd_nat_nat ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_vi6667456707345531737_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_628_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: ref_a > nat,G: heap_e7401611519738050253t_unit > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_4710180989675653397at_nat @ ( bNF_co5610825919353547504at_nat @ ( comp_r8155216869944865719t_unit @ F @ produc473321116828791851t_unit ) @ ( comp_h8354993580257045729t_unit @ G @ produc1126150082675451753t_unit ) ) @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_vi4623496019404053219_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_629_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: nat > int,G: nat > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_1990417195239315453nt_int @ ( bNF_co49787548815638194nt_int @ ( comp_n5749082658982224864at_nat @ F @ product_fst_nat_nat ) @ ( comp_n5749082658982224864at_nat @ G @ product_snd_nat_nat ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_vi8357618154448083105_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_630_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: ref_a > int,G: heap_e7401611519738050253t_unit > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_1531683682067511245nt_int @ ( bNF_co6607689160745551784nt_int @ ( comp_r7249815618783853587t_unit @ F @ produc473321116828791851t_unit ) @ ( comp_h7449592329096033597t_unit @ G @ produc1126150082675451753t_unit ) ) @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ ( bNF_vi7828673959370436579_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_631_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > nat,R3: nat > nat > $o] : ( ord_le3146513528884898305at_nat @ ( image_5831868185956570253at_nat @ ( bNF_co2751916026326257842at_nat @ ( comp_i1292779930663060120nt_int @ F @ product_fst_int_int ) @ ( comp_i1292779930663060120nt_int @ G @ product_snd_int_int ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_vi2193923016096921761_nat_o @ F @ G @ R3 ) ) ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_632_convol__image__vimage2p,axiom,
% 7.78/3.92 ! [F: int > int,G: int > int,R3: int > int > $o] : ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ ( bNF_co3748779267718262122nt_int @ ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) @ ( comp_i4330622015127193916nt_int @ G @ product_snd_int_int ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_vi3884084463199473129_int_o @ F @ G @ R3 ) ) ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_633_prod_Osize__gen__o__map,axiom,
% 7.78/3.92 ! [F: nat > nat,Fa: nat > nat,G: nat > nat,Ga: nat > nat] :
% 7.78/3.92 ( ( comp_P1567445206330693457at_nat @ ( basic_876126793109182934at_nat @ F @ Fa ) @ ( produc6977886695330630970at_nat @ G @ Ga ) )
% 7.78/3.92 = ( basic_876126793109182934at_nat @ ( comp_nat_nat_nat @ F @ G ) @ ( comp_nat_nat_nat @ Fa @ Ga ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_634_prod_Osize__gen__o__map,axiom,
% 7.78/3.92 ! [F: nat > nat,Fa: int > nat,G: nat > nat,Ga: int > int] :
% 7.78/3.92 ( ( comp_P397146161216181329at_int @ ( basic_873636322600132658at_int @ F @ Fa ) @ ( produc7974749936722635250nt_int @ G @ Ga ) )
% 7.78/3.92 = ( basic_873636322600132658at_int @ ( comp_nat_nat_nat @ F @ G ) @ ( comp_int_nat_int @ Fa @ Ga ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_635_prod_Osize__gen__o__map,axiom,
% 7.78/3.92 ! [F: int > nat,Fa: nat > nat,G: int > int,Ga: nat > nat] :
% 7.78/3.92 ( ( comp_P3488689526429045841nt_nat @ ( basic_1875480505010237490nt_nat @ F @ Fa ) @ ( produc5039722323474524658at_nat @ G @ Ga ) )
% 7.78/3.92 = ( basic_1875480505010237490nt_nat @ ( comp_int_nat_int @ F @ G ) @ ( comp_nat_nat_nat @ Fa @ Ga ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_636_prod_Osize__gen__o__map,axiom,
% 7.78/3.92 ! [F: int > nat,Fa: int > nat,G: int > int,Ga: int > int] :
% 7.78/3.92 ( ( comp_P2318390481314533713nt_int @ ( basic_1872990034501187214nt_int @ F @ Fa ) @ ( produc6036585564866528938nt_int @ G @ Ga ) )
% 7.78/3.92 = ( basic_1872990034501187214nt_int @ ( comp_int_nat_int @ F @ G ) @ ( comp_int_nat_int @ Fa @ Ga ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_637_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca968750328013420230at_nat
% 7.78/3.92 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > nat] :
% 7.78/3.92 ! [I2: nat,J: nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_638_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca1968104039914474786nt_nat
% 7.78/3.92 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > nat] :
% 7.78/3.92 ! [I2: int,J: int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_639_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca966259857504369954at_int
% 7.78/3.92 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > int] :
% 7.78/3.92 ! [I2: nat,J: nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_640_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca1965613569405424510nt_int
% 7.78/3.92 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > int] :
% 7.78/3.92 ! [I2: int,J: int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_641_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca333620267926924494at_rat
% 7.78/3.92 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > rat] :
% 7.78/3.92 ! [I2: nat,J: nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_rat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_642_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca1332973979827979050nt_rat
% 7.78/3.92 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > rat] :
% 7.78/3.92 ! [I2: int,J: int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_rat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_643_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca30959104405961555nteger
% 7.78/3.92 = ( ^ [R5: set_Pr1261947904930325089at_nat,As: nat > code_integer] :
% 7.78/3.92 ! [I2: nat,J: nat] :
% 7.78/3.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_le3102999989581377725nteger @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_644_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca402612664642806191nteger
% 7.78/3.92 = ( ^ [R5: set_Pr958786334691620121nt_int,As: int > code_integer] :
% 7.78/3.92 ! [I2: int,J: int] :
% 7.78/3.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_le3102999989581377725nteger @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_645_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca4949091444211332621at_nat
% 7.78/3.92 = ( ^ [R5: set_Pr4329608150637261639at_nat,As: set_Pr1261947904930325089at_nat > nat] :
% 7.78/3.92 ! [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_nat @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_646_relChain__def,axiom,
% 7.78/3.92 ( bNF_Ca4946600973702282345at_int
% 7.78/3.92 = ( ^ [R5: set_Pr4329608150637261639at_nat,As: set_Pr1261947904930325089at_nat > int] :
% 7.78/3.92 ! [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I2 @ J ) @ R5 )
% 7.78/3.92 => ( ord_less_eq_int @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_647_Collect__case__prod__in__rel__leI,axiom,
% 7.78/3.92 ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( ord_le3146513528884898305at_nat @ X5 @ Y4 )
% 7.78/3.92 => ( ord_le3146513528884898305at_nat @ X5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( fun_in_rel_nat_nat @ Y4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_648_Collect__case__prod__in__rel__leI,axiom,
% 7.78/3.92 ! [X5: set_Pr958786334691620121nt_int,Y4: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( ord_le2843351958646193337nt_int @ X5 @ Y4 )
% 7.78/3.92 => ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( fun_in_rel_int_int @ Y4 ) ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_649_Collect__case__prod__in__rel__leE,axiom,
% 7.78/3.92 ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 7.78/3.92 ( ( ord_le3146513528884898305at_nat @ X5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( fun_in_rel_nat_nat @ Y4 ) ) ) )
% 7.78/3.92 => ( ord_le3146513528884898305at_nat @ X5 @ Y4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_650_Collect__case__prod__in__rel__leE,axiom,
% 7.78/3.92 ! [X5: set_Pr958786334691620121nt_int,Y4: set_Pr958786334691620121nt_int] :
% 7.78/3.92 ( ( ord_le2843351958646193337nt_int @ X5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( fun_in_rel_int_int @ Y4 ) ) ) )
% 7.78/3.92 => ( ord_le2843351958646193337nt_int @ X5 @ Y4 ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_651_relcompp__assoc,axiom,
% 7.78/3.92 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,T2: int > int > $o] :
% 7.78/3.92 ( ( relcom2949942408940504938nt_int @ ( relcom8911704206367525917at_int @ R @ S2 ) @ T2 )
% 7.78/3.92 = ( relcom8911704206367525917at_int @ R @ ( relcom2949942408940504938nt_int @ S2 @ T2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_652_relcompp__assoc,axiom,
% 7.78/3.92 ! [R: int > int > $o,S2: int > code_integer > $o,T2: code_integer > code_integer > $o] :
% 7.78/3.92 ( ( relcom8320293257703906841nteger @ ( relcom967497705283160040nteger @ R @ S2 ) @ T2 )
% 7.78/3.92 = ( relcom967497705283160040nteger @ R @ ( relcom8320293257703906841nteger @ S2 @ T2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_653_relcompp__assoc,axiom,
% 7.78/3.92 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > product_prod_nat_nat > $o,T2: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( ( relcom8911704206367525917at_int @ ( relcom282571730187242960at_nat @ R @ S2 ) @ T2 )
% 7.78/3.92 = ( relcom8911704206367525917at_int @ R @ ( relcom8911704206367525917at_int @ S2 @ T2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_654_relcompp__assoc,axiom,
% 7.78/3.92 ! [R: int > int > $o,S2: int > int > $o,T2: int > code_integer > $o] :
% 7.78/3.92 ( ( relcom967497705283160040nteger @ ( relcompp_int_int_int @ R @ S2 ) @ T2 )
% 7.78/3.92 = ( relcom967497705283160040nteger @ R @ ( relcom967497705283160040nteger @ S2 @ T2 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_655_relcompp__apply,axiom,
% 7.78/3.92 ( relcom8911704206367525917at_int
% 7.78/3.92 = ( ^ [R6: product_prod_nat_nat > product_prod_nat_nat > $o,S4: product_prod_nat_nat > int > $o,A5: product_prod_nat_nat,C4: int] :
% 7.78/3.92 ? [B4: product_prod_nat_nat] :
% 7.78/3.92 ( ( R6 @ A5 @ B4 )
% 7.78/3.92 & ( S4 @ B4 @ C4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_656_relcompp__apply,axiom,
% 7.78/3.92 ( relcom967497705283160040nteger
% 7.78/3.92 = ( ^ [R6: int > int > $o,S4: int > code_integer > $o,A5: int,C4: code_integer] :
% 7.78/3.92 ? [B4: int] :
% 7.78/3.92 ( ( R6 @ A5 @ B4 )
% 7.78/3.92 & ( S4 @ B4 @ C4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_657_rel__funI,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_658_rel__funI,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_659_rel__funI,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_660_rel__funI,axiom,
% 7.78/3.92 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num] :
% 7.78/3.92 ( ! [X: int,Y: code_integer] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_661_rel__funI,axiom,
% 7.78/3.92 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ ( F @ X ) @ ( G @ Y ) ) )
% 7.78/3.92 => ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_662_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: $o > $o > $o,Sd: $o > $o > $o] :
% 7.78/3.92 ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re2697311982885662685_nat_o
% 7.78/3.92 @ ( bNF_re4705727531993890431at_o_o
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re4705727531993890431at_o_o
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_o_o_nat
% 7.78/3.92 @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_663_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: $o > nat > $o,Sd: $o > nat > $o] :
% 7.78/3.92 ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re2144779315220482269at_nat
% 7.78/3.92 @ ( bNF_re7523573913982466217_o_nat
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re7523573913982466217_o_nat
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_o_o_nat
% 7.78/3.92 @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_664_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: nat > int > $o,Sd: num > nat > $o] :
% 7.78/3.92 ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re3642433447925381491nt_nat
% 7.78/3.92 @ ( bNF_re3713166177374151349at_int
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re1845987051190671011um_nat
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_nat_num_int
% 7.78/3.92 @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_665_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: nat > $o > $o,Sd: nat > $o > $o] :
% 7.78/3.92 ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re7744223787735169245_nat_o
% 7.78/3.92 @ ( bNF_re1402873238235875719_nat_o
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re1402873238235875719_nat_o
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_nat_nat_nat
% 7.78/3.92 @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_666_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: nat > nat > $o,Sd: nat > nat > $o] :
% 7.78/3.92 ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re239970166668089693at_nat
% 7.78/3.92 @ ( bNF_re5653821019739307937at_nat
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re5653821019739307937at_nat
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_nat_nat_nat
% 7.78/3.92 @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_667_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: int > nat > $o,Sd: nat > num > $o] :
% 7.78/3.92 ( bNF_re4310571189260822741nt_num @ ( bNF_re9124706910656911431at_num @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re7492190849051111027nt_num
% 7.78/3.92 @ ( bNF_re4715010359784256181nt_nat
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re272988434038980259at_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_int_nat_int
% 7.78/3.92 @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_668_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: int > int > $o,Sd: nat > nat > $o] :
% 7.78/3.92 ( bNF_re6307232852808291833nt_nat @ ( bNF_re3715656647883201625at_nat @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re2034674868506727813nt_nat
% 7.78/3.92 @ ( bNF_re4712519889275205905nt_int
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re3715656647883201625at_nat
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_int_nat_int
% 7.78/3.92 @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_669_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: nat > nat > $o,Sd: num > num > $o] :
% 7.78/3.92 ( bNF_re3846787885862361009nt_num @ ( bNF_re341483209202555957um_num @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re9099949428469764705nt_num
% 7.78/3.92 @ ( bNF_re3715656647883201625at_nat
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_nat_num_int
% 7.78/3.92 @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_670_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: num > num > $o,Sd: num > num > $o] :
% 7.78/3.92 ( bNF_re5446066262214944985nt_num @ ( bNF_re4736500879113541833um_num @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re4768042542643474933nt_num
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_num_num_int
% 7.78/3.92 @ comp_num_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_671_fun_Omap__transfer,axiom,
% 7.78/3.92 ! [Rb: int > code_integer > $o,Sd: num > num > $o] :
% 7.78/3.92 ( bNF_re7839584876883444355nt_num @ ( bNF_re6718328864250387230um_num @ Rb @ Sd )
% 7.78/3.92 @ ( bNF_re2961086658867094474nt_num
% 7.78/3.92 @ ( bNF_re982302072995117890nteger
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Rb )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ Sd ) )
% 7.78/3.92 @ comp_int_num_int
% 7.78/3.92 @ comp_C2177396528461469320um_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_672_rel__fun__iff__leq__vimage2p,axiom,
% 7.78/3.92 ( bNF_re4555766996558763186at_nat
% 7.78/3.92 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: nat > nat > $o,F2: product_prod_nat_nat > nat,G3: int > nat] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi5493721401438417730_nat_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_673_rel__fun__iff__leq__vimage2p,axiom,
% 7.78/3.92 ( bNF_re7408651293131936558nt_int
% 7.78/3.92 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G3: int > int > int] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi8966365312794588230_int_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_674_rel__fun__iff__leq__vimage2p,axiom,
% 7.78/3.92 ( bNF_re717283939379294677_int_o
% 7.78/3.92 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > $o,G3: int > int > $o] : ( ord_le129227817499904167_int_o @ R6 @ ( bNF_vi5082502771524357669nt_o_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_675_rel__fun__iff__leq__vimage2p,axiom,
% 7.78/3.92 ( bNF_re6718328864250387230um_num
% 7.78/3.92 = ( ^ [R6: int > code_integer > $o,S4: num > num > $o,F2: int > num,G3: code_integer > num] : ( ord_le996066559646421213eger_o @ R6 @ ( bNF_vi2326032003723069084_num_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_676_rel__fun__iff__leq__vimage2p,axiom,
% 7.78/3.92 ( bNF_re7626690874201225453um_num
% 7.78/3.92 = ( ^ [R6: int > int > $o,S4: num > num > $o,F2: int > num,G3: int > num] : ( ord_le6741204236512500942_int_o @ R6 @ ( bNF_vi2107963681178519309_num_o @ F2 @ G3 @ S4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_677_rel__fun__mono_H,axiom,
% 7.78/3.92 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: nat > nat > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( ( bNF_re4555766996558763186at_nat @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( bNF_re4555766996558763186at_nat @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_678_rel__fun__mono_H,axiom,
% 7.78/3.92 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat > product_prod_nat_nat,Y: int > int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( ( bNF_re7408651293131936558nt_int @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( bNF_re7408651293131936558nt_int @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_679_rel__fun__mono_H,axiom,
% 7.78/3.92 ! [Y4: product_prod_nat_nat > int > $o,X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] :
% 7.78/3.92 ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat > $o,Y: int > $o] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( ( bNF_re717283939379294677_int_o @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( bNF_re717283939379294677_int_o @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_680_rel__fun__mono_H,axiom,
% 7.78/3.92 ! [Y4: int > code_integer > $o,X5: int > code_integer > $o,A4: num > num > $o,B5: num > num > $o,F: int > num,G: code_integer > num] :
% 7.78/3.92 ( ! [X: int,Y: code_integer] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: num,Y: num] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( ( bNF_re6718328864250387230um_num @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( bNF_re6718328864250387230um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_681_rel__fun__mono_H,axiom,
% 7.78/3.92 ! [Y4: int > int > $o,X5: int > int > $o,A4: num > num > $o,B5: num > num > $o,F: int > num,G: int > num] :
% 7.78/3.92 ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: num,Y: num] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( ( bNF_re7626690874201225453um_num @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( bNF_re7626690874201225453um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_682_rel__fun__mono,axiom,
% 7.78/3.92 ! [X5: product_prod_nat_nat > int > $o,A4: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,Y4: product_prod_nat_nat > int > $o,B5: nat > nat > $o] :
% 7.78/3.92 ( ( bNF_re4555766996558763186at_nat @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: nat,Y: nat] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( bNF_re4555766996558763186at_nat @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_683_rel__fun__mono,axiom,
% 7.78/3.92 ! [X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,Y4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o] :
% 7.78/3.92 ( ( bNF_re7408651293131936558nt_int @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat > product_prod_nat_nat,Y: int > int] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( bNF_re7408651293131936558nt_int @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_684_rel__fun__mono,axiom,
% 7.78/3.92 ! [X5: product_prod_nat_nat > int > $o,A4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,Y4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o] :
% 7.78/3.92 ( ( bNF_re717283939379294677_int_o @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: product_prod_nat_nat > $o,Y: int > $o] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( bNF_re717283939379294677_int_o @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_685_rel__fun__mono,axiom,
% 7.78/3.92 ! [X5: int > code_integer > $o,A4: num > num > $o,F: int > num,G: code_integer > num,Y4: int > code_integer > $o,B5: num > num > $o] :
% 7.78/3.92 ( ( bNF_re6718328864250387230um_num @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( ! [X: int,Y: code_integer] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: num,Y: num] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( bNF_re6718328864250387230um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_686_rel__fun__mono,axiom,
% 7.78/3.92 ! [X5: int > int > $o,A4: num > num > $o,F: int > num,G: int > num,Y4: int > int > $o,B5: num > num > $o] :
% 7.78/3.92 ( ( bNF_re7626690874201225453um_num @ X5 @ A4 @ F @ G )
% 7.78/3.92 => ( ! [X: int,Y: int] :
% 7.78/3.92 ( ( Y4 @ X @ Y )
% 7.78/3.92 => ( X5 @ X @ Y ) )
% 7.78/3.92 => ( ! [X: num,Y: num] :
% 7.78/3.92 ( ( A4 @ X @ Y )
% 7.78/3.92 => ( B5 @ X @ Y ) )
% 7.78/3.92 => ( bNF_re7626690874201225453um_num @ Y4 @ B5 @ F @ G ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_687_rel__funD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: nat > nat > $o,F: product_prod_nat_nat > nat,G: int > nat,X2: product_prod_nat_nat,Y3: int] :
% 7.78/3.92 ( ( bNF_re4555766996558763186at_nat @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( A4 @ X2 @ Y3 )
% 7.78/3.92 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_688_rel__funD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int,X2: product_prod_nat_nat,Y3: int] :
% 7.78/3.92 ( ( bNF_re7408651293131936558nt_int @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( A4 @ X2 @ Y3 )
% 7.78/3.92 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_689_rel__funD,axiom,
% 7.78/3.92 ! [A4: product_prod_nat_nat > int > $o,B5: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o,X2: product_prod_nat_nat,Y3: int] :
% 7.78/3.92 ( ( bNF_re717283939379294677_int_o @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( A4 @ X2 @ Y3 )
% 7.78/3.92 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_690_rel__funD,axiom,
% 7.78/3.92 ! [A4: int > code_integer > $o,B5: num > num > $o,F: int > num,G: code_integer > num,X2: int,Y3: code_integer] :
% 7.78/3.92 ( ( bNF_re6718328864250387230um_num @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( A4 @ X2 @ Y3 )
% 7.78/3.92 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_691_rel__funD,axiom,
% 7.78/3.92 ! [A4: int > int > $o,B5: num > num > $o,F: int > num,G: int > num,X2: int,Y3: int] :
% 7.78/3.92 ( ( bNF_re7626690874201225453um_num @ A4 @ B5 @ F @ G )
% 7.78/3.92 => ( ( A4 @ X2 @ Y3 )
% 7.78/3.92 => ( B5 @ ( F @ X2 ) @ ( G @ Y3 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_692_fun_Orel__compp,axiom,
% 7.78/3.92 ! [R3: num > num > $o,S5: num > num > $o] :
% 7.78/3.92 ( ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ ( relcompp_num_num_num @ R3 @ S5 ) )
% 7.78/3.92 = ( relcom9025577121137075810nt_num
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ R3 )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ S5 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_693_relcompp__mono,axiom,
% 7.78/3.92 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,S3: product_prod_nat_nat > int > $o,S2: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( ( ord_le5604493270027003598_nat_o @ R2 @ R )
% 7.78/3.92 => ( ( ord_le129227817499904167_int_o @ S3 @ S2 )
% 7.78/3.92 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R2 @ S3 ) @ ( relcom8911704206367525917at_int @ R @ S2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_694_relcompp__mono,axiom,
% 7.78/3.92 ! [R2: int > int > $o,R: int > int > $o,S3: int > code_integer > $o,S2: int > code_integer > $o] :
% 7.78/3.92 ( ( ord_le6741204236512500942_int_o @ R2 @ R )
% 7.78/3.92 => ( ( ord_le996066559646421213eger_o @ S3 @ S2 )
% 7.78/3.92 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R2 @ S3 ) @ ( relcom967497705283160040nteger @ R @ S2 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_695_in__rel__def,axiom,
% 7.78/3.92 ( fun_in6812141508599261570at_nat
% 7.78/3.92 = ( ^ [R6: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_696_in__rel__def,axiom,
% 7.78/3.92 ( fun_in8056734985859589634at_nat
% 7.78/3.92 = ( ^ [R6: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_697_in__rel__def,axiom,
% 7.78/3.92 ( fun_in_rel_nat_num
% 7.78/3.92 = ( ^ [R6: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_698_in__rel__def,axiom,
% 7.78/3.92 ( fun_in_rel_nat_nat
% 7.78/3.92 = ( ^ [R6: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_699_in__rel__def,axiom,
% 7.78/3.92 ( fun_in_rel_int_int
% 7.78/3.92 = ( ^ [R6: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_700_in__rel__Collect__case__prod__eq,axiom,
% 7.78/3.92 ! [X5: nat > nat > $o] :
% 7.78/3.92 ( ( fun_in_rel_nat_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ X5 ) ) )
% 7.78/3.92 = X5 ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_701_in__rel__Collect__case__prod__eq,axiom,
% 7.78/3.92 ! [X5: int > int > $o] :
% 7.78/3.92 ( ( fun_in_rel_int_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ X5 ) ) )
% 7.78/3.92 = X5 ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_702_Collect__case__prod__mono,axiom,
% 7.78/3.92 ! [A4: nat > nat > $o,B5: nat > nat > $o] :
% 7.78/3.92 ( ( ord_le2646555220125990790_nat_o @ A4 @ B5 )
% 7.78/3.92 => ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A4 ) ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_703_Collect__case__prod__mono,axiom,
% 7.78/3.92 ! [A4: int > int > $o,B5: int > int > $o] :
% 7.78/3.92 ( ( ord_le6741204236512500942_int_o @ A4 @ B5 )
% 7.78/3.92 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B5 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_704_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: num > num,F: nat > num,V: int > nat] :
% 7.78/3.92 ( ( comp_num_num_int @ G @ ( comp_nat_num_int @ F @ V ) )
% 7.78/3.92 = ( comp_nat_num_int @ ( comp_num_num_nat @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_705_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: nat > nat,F: int > nat,V: int > int] :
% 7.78/3.92 ( ( comp_nat_nat_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 7.78/3.92 = ( comp_int_nat_int @ ( comp_nat_nat_int @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_706_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: $o > $o,F: nat > $o,V: nat > nat] :
% 7.78/3.92 ( ( comp_o_o_nat @ G @ ( comp_nat_o_nat @ F @ V ) )
% 7.78/3.92 = ( comp_nat_o_nat @ ( comp_o_o_nat @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_707_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: $o > $o,F: $o > $o,V: nat > $o] :
% 7.78/3.92 ( ( comp_o_o_nat @ G @ ( comp_o_o_nat @ F @ V ) )
% 7.78/3.92 = ( comp_o_o_nat @ ( comp_o_o_o @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_708_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: nat > num,F: nat > nat,V: int > nat] :
% 7.78/3.92 ( ( comp_nat_num_int @ G @ ( comp_nat_nat_int @ F @ V ) )
% 7.78/3.92 = ( comp_nat_num_int @ ( comp_nat_num_nat @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_709_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: nat > num,F: int > nat,V: int > int] :
% 7.78/3.92 ( ( comp_nat_num_int @ G @ ( comp_int_nat_int @ F @ V ) )
% 7.78/3.92 = ( comp_int_num_int @ ( comp_nat_num_int @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_710_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: nat > nat,F: nat > nat,V: nat > nat] :
% 7.78/3.92 ( ( comp_nat_nat_nat @ G @ ( comp_nat_nat_nat @ F @ V ) )
% 7.78/3.92 = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_711_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: int > nat,F: int > int,V: int > int] :
% 7.78/3.92 ( ( comp_int_nat_int @ G @ ( comp_int_int_int @ F @ V ) )
% 7.78/3.92 = ( comp_int_nat_int @ ( comp_int_nat_int @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_712_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: code_integer > code_integer] :
% 7.78/3.92 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2931745410781319416nteger @ F @ V ) )
% 7.78/3.92 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_713_fun_Omap__comp,axiom,
% 7.78/3.92 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: ( code_integer > code_integer ) > code_integer > code_integer,V: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( comp_C8797469213163452608nteger @ G @ ( comp_C2822359487432382964nteger @ F @ V ) )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ G @ F ) @ V ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_714_relcompp_Ocases,axiom,
% 7.78/3.92 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,A1: product_prod_nat_nat,A22: int] :
% 7.78/3.92 ( ( relcom8911704206367525917at_int @ R @ S2 @ A1 @ A22 )
% 7.78/3.92 => ~ ! [B3: product_prod_nat_nat] :
% 7.78/3.92 ( ( R @ A1 @ B3 )
% 7.78/3.92 => ~ ( S2 @ B3 @ A22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_715_relcompp_Ocases,axiom,
% 7.78/3.92 ! [R: int > int > $o,S2: int > code_integer > $o,A1: int,A22: code_integer] :
% 7.78/3.92 ( ( relcom967497705283160040nteger @ R @ S2 @ A1 @ A22 )
% 7.78/3.92 => ~ ! [B3: int] :
% 7.78/3.92 ( ( R @ A1 @ B3 )
% 7.78/3.92 => ~ ( S2 @ B3 @ A22 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_716_relcompp_Osimps,axiom,
% 7.78/3.92 ( relcom8911704206367525917at_int
% 7.78/3.92 = ( ^ [R5: product_prod_nat_nat > product_prod_nat_nat > $o,S: product_prod_nat_nat > int > $o,A12: product_prod_nat_nat,A23: int] :
% 7.78/3.92 ? [A5: product_prod_nat_nat,B4: product_prod_nat_nat,C4: int] :
% 7.78/3.92 ( ( A12 = A5 )
% 7.78/3.92 & ( A23 = C4 )
% 7.78/3.92 & ( R5 @ A5 @ B4 )
% 7.78/3.92 & ( S @ B4 @ C4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_717_relcompp_Osimps,axiom,
% 7.78/3.92 ( relcom967497705283160040nteger
% 7.78/3.92 = ( ^ [R5: int > int > $o,S: int > code_integer > $o,A12: int,A23: code_integer] :
% 7.78/3.92 ? [A5: int,B4: int,C4: code_integer] :
% 7.78/3.92 ( ( A12 = A5 )
% 7.78/3.92 & ( A23 = C4 )
% 7.78/3.92 & ( R5 @ A5 @ B4 )
% 7.78/3.92 & ( S @ B4 @ C4 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_718_eq__OO,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( ( relcom8911704206367525917at_int
% 7.78/3.92 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z )
% 7.78/3.92 @ R3 )
% 7.78/3.92 = R3 ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_719_eq__OO,axiom,
% 7.78/3.92 ! [R3: int > code_integer > $o] :
% 7.78/3.92 ( ( relcom967497705283160040nteger
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.92 @ R3 )
% 7.78/3.92 = R3 ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_720_relcomppE,axiom,
% 7.78/3.92 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o,A: product_prod_nat_nat,C: int] :
% 7.78/3.92 ( ( relcom8911704206367525917at_int @ R @ S2 @ A @ C )
% 7.78/3.92 => ~ ! [B3: product_prod_nat_nat] :
% 7.78/3.92 ( ( R @ A @ B3 )
% 7.78/3.92 => ~ ( S2 @ B3 @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_721_relcomppE,axiom,
% 7.78/3.92 ! [R: int > int > $o,S2: int > code_integer > $o,A: int,C: code_integer] :
% 7.78/3.92 ( ( relcom967497705283160040nteger @ R @ S2 @ A @ C )
% 7.78/3.92 => ~ ! [B3: int] :
% 7.78/3.92 ( ( R @ A @ B3 )
% 7.78/3.92 => ~ ( S2 @ B3 @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_722_relcomppI,axiom,
% 7.78/3.92 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat,B: product_prod_nat_nat,S2: product_prod_nat_nat > int > $o,C: int] :
% 7.78/3.92 ( ( R @ A @ B )
% 7.78/3.92 => ( ( S2 @ B @ C )
% 7.78/3.92 => ( relcom8911704206367525917at_int @ R @ S2 @ A @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_723_relcomppI,axiom,
% 7.78/3.92 ! [R: int > int > $o,A: int,B: int,S2: int > code_integer > $o,C: code_integer] :
% 7.78/3.92 ( ( R @ A @ B )
% 7.78/3.92 => ( ( S2 @ B @ C )
% 7.78/3.92 => ( relcom967497705283160040nteger @ R @ S2 @ A @ C ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_724_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: $o > $o,H22: $o > $o,F: nat > $o,G: nat > $o] :
% 7.78/3.92 ( ( comp_P7034811116587396339_o_nat @ ( produc1928436952130685430_o_o_o @ H1 @ H22 ) @ ( bNF_convol_nat_o_o @ F @ G ) )
% 7.78/3.92 = ( bNF_convol_nat_o_o @ ( comp_o_o_nat @ H1 @ F ) @ ( comp_o_o_nat @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_725_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: $o > $o,H22: nat > nat,F: nat > $o,G: nat > nat] :
% 7.78/3.92 ( ( comp_P1391661485614827491at_nat @ ( produc7071226018047599512at_nat @ H1 @ H22 ) @ ( bNF_convol_nat_o_nat @ F @ G ) )
% 7.78/3.92 = ( bNF_convol_nat_o_nat @ ( comp_o_o_nat @ H1 @ F ) @ ( comp_nat_nat_nat @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_726_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: nat > num,H22: nat > num,F: int > nat,G: int > nat] :
% 7.78/3.92 ( ( comp_P7387482301570536291um_int @ ( produc1476026309457068494at_num @ H1 @ H22 ) @ ( bNF_co1177303703936631735at_nat @ F @ G ) )
% 7.78/3.92 = ( bNF_co5088337930254655563um_num @ ( comp_nat_num_int @ H1 @ F ) @ ( comp_nat_num_int @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_727_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: nat > num,H22: int > nat,F: int > nat,G: int > int] :
% 7.78/3.92 ( ( comp_P8376639181999047357at_int @ ( produc5918048235202344416nt_nat @ H1 @ H22 ) @ ( bNF_co1174813233427581459at_int @ F @ G ) )
% 7.78/3.92 = ( bNF_co8531006144098876929um_nat @ ( comp_nat_num_int @ H1 @ F ) @ ( comp_int_nat_int @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_728_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: nat > nat,H22: $o > $o,F: nat > nat,G: nat > $o] :
% 7.78/3.92 ( ( comp_P5799945282029801519_o_nat @ ( produc2001155298098703512at_o_o @ H1 @ H22 ) @ ( bNF_convol_nat_nat_o @ F @ G ) )
% 7.78/3.92 = ( bNF_convol_nat_nat_o @ ( comp_nat_nat_nat @ H1 @ F ) @ ( comp_o_o_nat @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_729_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: nat > nat,H22: nat > nat,F: nat > nat,G: nat > nat] :
% 7.78/3.92 ( ( comp_P7430769850142754163at_nat @ ( produc6977886695330630970at_nat @ H1 @ H22 ) @ ( bNF_co805650143699787099at_nat @ F @ G ) )
% 7.78/3.92 = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ H1 @ F ) @ ( comp_nat_nat_nat @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_730_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: int > nat,H22: nat > num,F: int > int,G: int > nat] :
% 7.78/3.92 ( ( comp_P1145193044942399421um_int @ ( produc1225400549393458656at_num @ H1 @ H22 ) @ ( bNF_co2176657415837686291nt_nat @ F @ G ) )
% 7.78/3.92 = ( bNF_co6958007526947186177at_num @ ( comp_int_nat_int @ H1 @ F ) @ ( comp_nat_num_int @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_731_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: int > nat,H22: int > nat,F: int > int,G: int > int] :
% 7.78/3.92 ( ( comp_P2134349925370910487at_int @ ( produc5667422475138734578nt_nat @ H1 @ H22 ) @ ( bNF_co2174166945328636015nt_int @ F @ G ) )
% 7.78/3.92 = ( bNF_co1177303703936631735at_nat @ ( comp_int_nat_int @ H1 @ F ) @ ( comp_int_nat_int @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_732_map__prod__o__convol,axiom,
% 7.78/3.92 ! [H1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,G: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( comp_P8564252314792299288nteger @ ( produc4724772261320961782nteger @ H1 @ H22 ) @ ( bNF_co6169604788974073338nteger @ F @ G ) )
% 7.78/3.92 = ( bNF_co3156833790671340178nteger @ ( comp_C8797469213163452608nteger @ H1 @ F ) @ ( comp_C8797469213163452608nteger @ H22 @ G ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_733_convol__o,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,H: nat > $o] :
% 7.78/3.92 ( ( comp_o7658611401268416066_o_nat @ ( bNF_convol_o_o_o @ F @ G ) @ H )
% 7.78/3.92 = ( bNF_convol_nat_o_o @ ( comp_o_o_nat @ F @ H ) @ ( comp_o_o_nat @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_734_convol__o,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > num,H: int > nat] :
% 7.78/3.92 ( ( comp_n8531277669757933902um_int @ ( bNF_co4716684370017810927um_num @ F @ G ) @ H )
% 7.78/3.92 = ( bNF_co5088337930254655563um_num @ ( comp_nat_num_int @ F @ H ) @ ( comp_nat_num_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_735_convol__o,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,H: nat > nat] :
% 7.78/3.92 ( ( comp_n8574565218330151774at_nat @ ( bNF_co805650143699787099at_nat @ F @ G ) @ H )
% 7.78/3.92 = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_736_convol__o,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > nat,H: int > int] :
% 7.78/3.92 ( ( comp_i1108739374719436894at_int @ ( bNF_co1177303703936631735at_nat @ F @ G ) @ H )
% 7.78/3.92 = ( bNF_co1177303703936631735at_nat @ ( comp_int_nat_int @ F @ H ) @ ( comp_int_nat_int @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_737_convol__o,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] :
% 7.78/3.92 ( ( comp_C6484513282182537548nteger @ ( bNF_co1764293801198077070nteger @ F @ G ) @ H )
% 7.78/3.92 = ( bNF_co3156833790671340178nteger @ ( comp_C8797469213163452608nteger @ F @ H ) @ ( comp_C8797469213163452608nteger @ G @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_738_vimage2p__relcompp__mono,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat,H: int > int] :
% 7.78/3.92 ( ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ T3 )
% 7.78/3.92 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ ( bNF_vi763171854521451549_nat_o @ F @ G @ R3 ) @ ( bNF_vi5426221348228882691_int_o @ G @ H @ S5 ) ) @ ( bNF_vi5426221348228882691_int_o @ F @ H @ T3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_739_vimage2p__relcompp__mono,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o,F: int > product_prod_nat_nat,G: int > product_prod_nat_nat,H: code_integer > int] :
% 7.78/3.92 ( ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ T3 )
% 7.78/3.92 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ ( bNF_vi1204582724742824157_nat_o @ F @ G @ R3 ) @ ( bNF_vi2881549544236934259_int_o @ G @ H @ S5 ) ) @ ( bNF_vi2881549544236934259_int_o @ F @ H @ T3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_740_vimage2p__relcompp__mono,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o,F: product_prod_nat_nat > int,G: product_prod_nat_nat > int,H: int > code_integer] :
% 7.78/3.92 ( ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ T3 )
% 7.78/3.92 => ( ord_le129227817499904167_int_o @ ( relcom8911704206367525917at_int @ ( bNF_vi2682369418337388893_int_o @ F @ G @ R3 ) @ ( bNF_vi33923956287962137eger_o @ G @ H @ S5 ) ) @ ( bNF_vi33923956287962137eger_o @ F @ H @ T3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_741_vimage2p__relcompp__mono,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o,F: int > int,G: int > int,H: code_integer > code_integer] :
% 7.78/3.92 ( ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ T3 )
% 7.78/3.92 => ( ord_le996066559646421213eger_o @ ( relcom967497705283160040nteger @ ( bNF_vi3884084463199473129_int_o @ F @ G @ R3 ) @ ( bNF_vi699694178825965831eger_o @ G @ H @ S5 ) ) @ ( bNF_vi699694178825965831eger_o @ F @ H @ T3 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_742_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > code_integer > $o,S5: num > num > $o,R7: code_integer > code_integer > $o,S6: num > num > $o] : ( ord_le6931201860925936491_num_o @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_743_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > code_integer > $o,S5: num > num > $o,R7: code_integer > int > $o,S6: num > num > $o] : ( ord_le4541714130423454556_num_o @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_744_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: num > num > $o,R7: int > int > $o,S6: num > num > $o] : ( ord_le4541714130423454556_num_o @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_745_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: num > num > $o,R7: int > code_integer > $o,S6: num > num > $o] : ( ord_le6931201860925936491_num_o @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_746_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: int > int > $o,R7: int > code_integer > $o,S6: int > code_integer > $o] : ( ord_le7522433683449569238eger_o @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_747_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > int > $o,S5: nat > nat > $o,R7: int > int > $o,S6: nat > nat > $o] : ( ord_le1714508135640884727_nat_o @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_748_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: nat > nat > $o,R7: product_prod_nat_nat > int > $o,S6: nat > nat > $o] : ( ord_le1714508135640884727_nat_o @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_749_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: int > int > $o,R7: product_prod_nat_nat > int > $o,S6: int > code_integer > $o] : ( ord_le6141271677531915726eger_o @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_750_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: int > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,R7: int > code_integer > $o,S6: product_prod_nat_nat > int > $o] : ( ord_le8615040745438789472_int_o @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_751_pos__fun__distr,axiom,
% 7.78/3.92 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S6: product_prod_nat_nat > int > $o] : ( ord_le2484784447047653514_int_o @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_752_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: nat > nat > $o] :
% 7.78/3.92 ( bNF_re6580757339198446453_nat_o
% 7.78/3.92 @ ^ [Y2: $o > $o,Z: $o > $o] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re2697311982885662685_nat_o
% 7.78/3.92 @ ( bNF_re4705727531993890431at_o_o @ R1
% 7.78/3.92 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re4705727531993890431at_o_o @ R1
% 7.78/3.92 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_o_o_nat
% 7.78/3.92 @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_753_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: nat > nat > $o] :
% 7.78/3.92 ( bNF_re3262823321055862553at_nat
% 7.78/3.92 @ ^ [Y2: nat > nat,Z: nat > nat] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re239970166668089693at_nat
% 7.78/3.92 @ ( bNF_re5653821019739307937at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re5653821019739307937at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_nat_nat_nat
% 7.78/3.92 @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_754_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: int > int > $o] :
% 7.78/3.92 ( bNF_re6307232852808291833nt_nat
% 7.78/3.92 @ ^ [Y2: int > nat,Z: int > nat] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re2034674868506727813nt_nat
% 7.78/3.92 @ ( bNF_re4712519889275205905nt_int @ R1
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re3715656647883201625at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_int_nat_int
% 7.78/3.92 @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_755_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: int > code_integer > $o] :
% 7.78/3.92 ( bNF_re2655444144887082515er_num
% 7.78/3.92 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re5502197115626545091er_num
% 7.78/3.92 @ ( bNF_re2807294637932363402at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re6718328864250387230um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_nat_num_int
% 7.78/3.92 @ comp_n2103536230552569900nteger ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_756_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: int > int > $o] :
% 7.78/3.92 ( bNF_re3846787885862361009nt_num
% 7.78/3.92 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re9099949428469764705nt_num
% 7.78/3.92 @ ( bNF_re3715656647883201625at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_nat_num_int
% 7.78/3.92 @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_757_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: int > code_integer > $o] :
% 7.78/3.92 ( bNF_re4105200416192800571er_num
% 7.78/3.92 @ ^ [Y2: num > num,Z: num > num] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re6292805115969292119er_num
% 7.78/3.92 @ ( bNF_re6718328864250387230um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re6718328864250387230um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_num_num_int
% 7.78/3.92 @ comp_n8557746072492896886nteger ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_758_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: int > int > $o] :
% 7.78/3.92 ( bNF_re5446066262214944985nt_num
% 7.78/3.92 @ ^ [Y2: num > num,Z: num > num] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re4768042542643474933nt_num
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re7626690874201225453um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_num_num_int
% 7.78/3.92 @ comp_num_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_759_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( bNF_re4099335476084980305nt_nat
% 7.78/3.92 @ ^ [Y2: int > nat,Z: int > nat] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re3284331099615978085nt_nat
% 7.78/3.92 @ ( bNF_re5552630237950767466nt_int @ R1
% 7.78/3.92 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re4555766996558763186at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_i4471277238271202272at_nat
% 7.78/3.92 @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_760_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( bNF_re2742285375668209089nt_num
% 7.78/3.92 @ ^ [Y2: nat > num,Z: nat > num] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re2682547871993127601nt_num
% 7.78/3.92 @ ( bNF_re4555766996558763186at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re8466801222876787014um_num @ R1
% 7.78/3.92 @ ^ [Y2: num,Z: num] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_n8649498751204056690at_nat
% 7.78/3.92 @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_761_o__rsp_I2_J,axiom,
% 7.78/3.92 ! [R1: product_prod_nat_nat > int > $o] :
% 7.78/3.92 ( bNF_re1160762158786734233nt_nat
% 7.78/3.92 @ ^ [Y2: nat > nat,Z: nat > nat] : ( Y2 = Z )
% 7.78/3.92 @ ( bNF_re8419181437172746013nt_nat
% 7.78/3.92 @ ( bNF_re4555766996558763186at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.92 @ ( bNF_re4555766996558763186at_nat @ R1
% 7.78/3.92 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
% 7.78/3.92 @ comp_n2711240574518091068at_nat
% 7.78/3.92 @ comp_nat_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_762_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: $o > $o > $o,R32: $o > $o > $o,R1: nat > nat > $o] : ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ R22 @ R32 ) @ ( bNF_re2697311982885662685_nat_o @ ( bNF_re4705727531993890431at_o_o @ R1 @ R22 ) @ ( bNF_re4705727531993890431at_o_o @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_763_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: $o > nat > $o,R32: $o > num > $o,R1: nat > int > $o] : ( bNF_re7387973359137000979nt_num @ ( bNF_re766437678722298023_o_num @ R22 @ R32 ) @ ( bNF_re4102725726183926567nt_num @ ( bNF_re8210149947023016781_o_nat @ R1 @ R22 ) @ ( bNF_re4767481733178795415_o_num @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_764_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: $o > nat > $o,R32: $o > nat > $o,R1: nat > nat > $o] : ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ R22 @ R32 ) @ ( bNF_re2144779315220482269at_nat @ ( bNF_re7523573913982466217_o_nat @ R1 @ R22 ) @ ( bNF_re7523573913982466217_o_nat @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_765_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: $o > int > $o,R32: $o > nat > $o,R1: nat > int > $o] : ( bNF_re7413876800493218871nt_nat @ ( bNF_re4895681925607069953_o_nat @ R22 @ R32 ) @ ( bNF_re1982657550219213441nt_nat @ ( bNF_re8207659476513966505_o_int @ R1 @ R22 ) @ ( bNF_re8210149947023016781_o_nat @ R1 @ R32 ) ) @ comp_o_o_nat @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_766_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > $o > $o,R32: num > $o > $o,R1: int > nat > $o] : ( bNF_re3931674169038344211_nat_o @ ( bNF_re8508505965575957011_num_o @ R22 @ R32 ) @ ( bNF_re7435575058205011731_nat_o @ ( bNF_re4914077030771115051_nat_o @ R1 @ R22 ) @ ( bNF_re3760060065607074657_num_o @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_767_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > nat > $o,R32: num > nat > $o,R1: int > nat > $o] : ( bNF_re6524732562925676389at_nat @ ( bNF_re3784151423046777323um_nat @ R22 @ R32 ) @ ( bNF_re717418264989850719at_nat @ ( bNF_re3344003087646356989at_nat @ R1 @ R22 ) @ ( bNF_re1474333490953826375um_nat @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_768_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > int > $o,R32: num > nat > $o,R1: int > int > $o] : ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ R22 @ R32 ) @ ( bNF_re3642433447925381491nt_nat @ ( bNF_re3713166177374151349at_int @ R1 @ R22 ) @ ( bNF_re1845987051190671011um_nat @ R1 @ R32 ) ) @ comp_nat_num_int @ comp_int_nat_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_769_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > $o > $o,R32: nat > $o > $o,R1: nat > nat > $o] : ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ R22 @ R32 ) @ ( bNF_re7744223787735169245_nat_o @ ( bNF_re1402873238235875719_nat_o @ R1 @ R22 ) @ ( bNF_re1402873238235875719_nat_o @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_o_o_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_770_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > nat > $o,R32: nat > num > $o,R1: nat > int > $o] : ( bNF_re584878643992547173nt_num @ ( bNF_re2211152805895086571at_num @ R22 @ R32 ) @ ( bNF_re8622501330148003679nt_num @ ( bNF_re6025474579976152573at_nat @ R1 @ R22 ) @ ( bNF_re2582806366131931207at_num @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_nat_num_int ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_771_o__rsp_I1_J,axiom,
% 7.78/3.92 ! [R22: nat > nat > $o,R32: nat > nat > $o,R1: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ R22 @ R32 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ R1 @ R22 ) @ ( bNF_re5653821019739307937at_nat @ R1 @ R32 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_772_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: int > int,H: nat > int,R12: nat > int,R23: nat > nat,F: int > nat,L: nat > nat] :
% 7.78/3.92 ( ( ( comp_int_int_nat @ G @ H )
% 7.78/3.92 = ( comp_nat_int_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_int_nat_nat @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_773_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: nat > int,H: nat > nat,R12: int > int,R23: nat > int,F: int > nat,L: int > nat] :
% 7.78/3.92 ( ( ( comp_nat_int_nat @ G @ H )
% 7.78/3.92 = ( comp_int_int_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_int_nat_int @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_nat_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_774_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: int > int,H: int > int,R12: int > int,R23: int > int,F: int > nat,L: int > nat] :
% 7.78/3.92 ( ( ( comp_int_int_int @ G @ H )
% 7.78/3.92 = ( comp_int_int_int @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_int_nat_int @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_nat_int @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_775_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: nat > $o,H: nat > nat,R12: $o > $o,R23: nat > $o,F: $o > $o,L: $o > $o] :
% 7.78/3.92 ( ( ( comp_nat_o_nat @ G @ H )
% 7.78/3.92 = ( comp_o_o_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_o_o_o @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_o_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_776_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: nat > $o,H: nat > nat,R12: $o > $o,R23: nat > $o,F: $o > nat,L: $o > nat] :
% 7.78/3.92 ( ( ( comp_nat_o_nat @ G @ H )
% 7.78/3.92 = ( comp_o_o_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_o_nat_o @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_nat_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_777_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: int > num,H: int > int,R12: nat > num,R23: int > nat,F: num > nat,L: nat > nat] :
% 7.78/3.92 ( ( ( comp_int_num_int @ G @ H )
% 7.78/3.92 = ( comp_nat_num_int @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_num_nat_nat @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_int_nat_int @ ( comp_num_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_int @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_778_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: int > nat,H: nat > int,R12: nat > nat,R23: nat > nat,F: nat > num,L: nat > num] :
% 7.78/3.92 ( ( ( comp_int_nat_nat @ G @ H )
% 7.78/3.92 = ( comp_nat_nat_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_nat_num_nat @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_int_num_nat @ ( comp_nat_num_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_num_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_779_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: $o > nat,H: nat > $o,R12: nat > nat,R23: nat > nat,F: nat > $o,L: nat > $o] :
% 7.78/3.92 ( ( ( comp_o_nat_nat @ G @ H )
% 7.78/3.92 = ( comp_nat_nat_nat @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_nat_o_nat @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_o_o_nat @ ( comp_nat_o_o @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_o_nat @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_780_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: nat > nat,H: int > nat,R12: int > nat,R23: int > int,F: nat > nat,L: int > nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_int @ G @ H )
% 7.78/3.92 = ( comp_int_nat_int @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_nat_nat_int @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_nat_int @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_781_rewriteR__comp__comp2,axiom,
% 7.78/3.92 ! [G: nat > nat,H: int > nat,R12: int > nat,R23: int > int,F: nat > num,L: int > num] :
% 7.78/3.92 ( ( ( comp_nat_nat_int @ G @ H )
% 7.78/3.92 = ( comp_int_nat_int @ R12 @ R23 ) )
% 7.78/3.92 => ( ( ( comp_nat_num_int @ F @ R12 )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_num_int @ L @ R23 ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_782_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: $o > nat,G: $o > $o,L1: nat > nat,L2: $o > nat,H: nat > $o,R: nat > nat] :
% 7.78/3.92 ( ( ( comp_o_nat_o @ F @ G )
% 7.78/3.92 = ( comp_nat_nat_o @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_o_nat_nat @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_o_nat_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 7.78/3.92 = ( comp_nat_nat_nat @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_783_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: num > num,G: nat > num,L1: nat > num,L2: nat > nat,H: int > nat,R: int > nat] :
% 7.78/3.92 ( ( ( comp_num_num_nat @ F @ G )
% 7.78/3.92 = ( comp_nat_num_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_nat_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 7.78/3.92 = ( comp_nat_num_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_784_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: num > nat,G: nat > num,L1: int > nat,L2: nat > int,H: int > nat,R: int > int] :
% 7.78/3.92 ( ( ( comp_num_nat_nat @ F @ G )
% 7.78/3.92 = ( comp_int_nat_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_int_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_num_nat_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 7.78/3.92 = ( comp_int_nat_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_785_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,L1: $o > $o,L2: $o > $o,H: nat > $o,R: nat > $o] :
% 7.78/3.92 ( ( ( comp_o_o_o @ F @ G )
% 7.78/3.92 = ( comp_o_o_o @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_o_o_nat @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 7.78/3.92 = ( comp_o_o_nat @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_786_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: nat > nat,G: $o > nat,L1: $o > nat,L2: $o > $o,H: nat > $o,R: nat > $o] :
% 7.78/3.92 ( ( ( comp_nat_nat_o @ F @ G )
% 7.78/3.92 = ( comp_o_nat_o @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_o_o_nat @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ F @ ( comp_o_nat_nat @ G @ H ) )
% 7.78/3.92 = ( comp_o_nat_nat @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_787_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > nat,L1: num > num,L2: nat > num,H: int > nat,R: int > num] :
% 7.78/3.92 ( ( ( comp_nat_num_nat @ F @ G )
% 7.78/3.92 = ( comp_num_num_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_num_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) )
% 7.78/3.92 = ( comp_num_num_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_788_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: int > nat,G: nat > int,L1: num > nat,L2: nat > num,H: int > nat,R: int > num] :
% 7.78/3.92 ( ( ( comp_int_nat_nat @ F @ G )
% 7.78/3.92 = ( comp_num_nat_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_num_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_int_nat_int @ F @ ( comp_nat_int_int @ G @ H ) )
% 7.78/3.92 = ( comp_num_nat_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_789_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: num > $o,G: nat > num,L1: $o > $o,L2: nat > $o,H: int > nat,R: int > $o] :
% 7.78/3.92 ( ( ( comp_num_o_nat @ F @ G )
% 7.78/3.92 = ( comp_o_o_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_o_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_num_o_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 7.78/3.92 = ( comp_o_o_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_790_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: nat > $o,G: nat > nat,L1: $o > $o,L2: nat > $o,H: nat > nat,R: nat > $o] :
% 7.78/3.92 ( ( ( comp_nat_o_nat @ F @ G )
% 7.78/3.92 = ( comp_o_o_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_o_nat @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_o_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
% 7.78/3.92 = ( comp_o_o_nat @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_791_rewriteL__comp__comp2,axiom,
% 7.78/3.92 ! [F: num > nat,G: nat > num,L1: nat > nat,L2: nat > nat,H: int > nat,R: int > nat] :
% 7.78/3.92 ( ( ( comp_num_nat_nat @ F @ G )
% 7.78/3.92 = ( comp_nat_nat_nat @ L1 @ L2 ) )
% 7.78/3.92 => ( ( ( comp_nat_nat_int @ L2 @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_num_nat_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 7.78/3.92 = ( comp_nat_nat_int @ L1 @ R ) ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_792_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: nat > $o,H: nat > nat,R: nat > $o,F: $o > $o] :
% 7.78/3.92 ( ( ( comp_nat_o_nat @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_o_nat @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_793_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: nat > nat,H: int > nat,R: int > nat,F: nat > num] :
% 7.78/3.92 ( ( ( comp_nat_nat_int @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_num_int @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_794_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: int > int,H: int > int,R: int > int,F: int > nat] :
% 7.78/3.92 ( ( ( comp_int_int_int @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_int_nat_int @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_795_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: $o > $o,H: nat > $o,R: nat > $o,F: $o > $o] :
% 7.78/3.92 ( ( ( comp_o_o_nat @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ G ) @ H )
% 7.78/3.92 = ( comp_o_o_nat @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_796_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: nat > num,H: int > nat,R: int > num,F: num > num] :
% 7.78/3.92 ( ( ( comp_nat_num_int @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_num_int @ ( comp_num_num_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_num_num_int @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_797_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: nat > nat,H: nat > nat,R: nat > nat,F: nat > nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_nat @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_nat @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_798_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: int > nat,H: int > int,R: int > nat,F: nat > num] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_num_int @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_799_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: int > nat,H: int > int,R: int > nat,F: nat > nat] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ G ) @ H )
% 7.78/3.92 = ( comp_nat_nat_int @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_800_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: code_integer > code_integer > code_integer,H: code_integer > code_integer,R: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.92 ( ( ( comp_C2931745410781319416nteger @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ H )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_801_rewriteR__comp__comp,axiom,
% 7.78/3.92 ! [G: ( code_integer > code_integer ) > code_integer > code_integer,H: code_integer > code_integer > code_integer,R: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.92 ( ( ( comp_C2822359487432382964nteger @ G @ H )
% 7.78/3.92 = R )
% 7.78/3.92 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ G ) @ H )
% 7.78/3.92 = ( comp_C8797469213163452608nteger @ F @ R ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_802_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: num > num,G: nat > num,L: nat > num,H: int > nat] :
% 7.78/3.92 ( ( ( comp_num_num_nat @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_num_num_int @ F @ ( comp_nat_num_int @ G @ H ) )
% 7.78/3.92 = ( comp_nat_num_int @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_803_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: int > nat,L: int > nat,H: int > int] :
% 7.78/3.92 ( ( ( comp_nat_nat_int @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_nat_int @ F @ ( comp_int_nat_int @ G @ H ) )
% 7.78/3.92 = ( comp_int_nat_int @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_804_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: $o > $o,L: $o > $o,H: nat > $o] :
% 7.78/3.92 ( ( ( comp_o_o_o @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_o_o_nat @ F @ ( comp_o_o_nat @ G @ H ) )
% 7.78/3.92 = ( comp_o_o_nat @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_805_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: nat > num,G: nat > nat,L: nat > num,H: int > nat] :
% 7.78/3.92 ( ( ( comp_nat_num_nat @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_num_int @ F @ ( comp_nat_nat_int @ G @ H ) )
% 7.78/3.92 = ( comp_nat_num_int @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_806_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: $o > $o,G: nat > $o,L: nat > $o,H: nat > nat] :
% 7.78/3.92 ( ( ( comp_o_o_nat @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_o_o_nat @ F @ ( comp_nat_o_nat @ G @ H ) )
% 7.78/3.92 = ( comp_nat_o_nat @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_807_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: nat > num,G: int > nat,L: int > num,H: int > int] :
% 7.78/3.92 ( ( ( comp_nat_num_int @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_num_int @ F @ ( comp_int_nat_int @ G @ H ) )
% 7.78/3.92 = ( comp_int_num_int @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_808_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: nat > nat,G: nat > nat,L: nat > nat,H: nat > nat] :
% 7.78/3.92 ( ( ( comp_nat_nat_nat @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
% 7.78/3.92 = ( comp_nat_nat_nat @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_809_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: int > nat,G: int > int,L: int > nat,H: int > int] :
% 7.78/3.92 ( ( ( comp_int_nat_int @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_int_nat_int @ F @ ( comp_int_int_int @ G @ H ) )
% 7.78/3.92 = ( comp_int_nat_int @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_810_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,L: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer] :
% 7.78/3.92 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 7.78/3.92 = L )
% 7.78/3.92 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2931745410781319416nteger @ G @ H ) )
% 7.78/3.92 = ( comp_C1593894019821074884nteger @ L @ H ) ) ) ).
% 7.78/3.92
% 7.78/3.92 thf(fact_811_rewriteL__comp__comp,axiom,
% 7.78/3.92 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > code_integer > code_integer,L: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > code_integer > code_integer] :
% 7.78/3.93 ( ( ( comp_C3983183376822107068nteger @ F @ G )
% 7.78/3.93 = L )
% 7.78/3.93 => ( ( comp_C8797469213163452608nteger @ F @ ( comp_C2822359487432382964nteger @ G @ H ) )
% 7.78/3.93 = ( comp_C8797469213163452608nteger @ L @ H ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_812_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: nat > $o,G: nat > nat,X2: nat,N: $o > $o,H: nat > $o,F: $o > $o] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_o_o_nat @ ( comp_o_o_o @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_813_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: int > nat,G: int > int,X2: int,N: nat > nat,H: int > nat,F: nat > num] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_int_num_int @ ( comp_nat_num_int @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_814_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: nat > nat,G: int > nat,X2: int,N: int > nat,H: int > int,F: nat > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_815_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: int > int,G: nat > int,X2: nat,N: nat > int,H: nat > nat,F: int > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_816_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: $o > $o,G: nat > $o,X2: nat,N: nat > $o,H: nat > nat,F: $o > $o] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_o_o_nat @ ( comp_o_o_o @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_817_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: nat > nat,G: int > nat,X2: int,N: int > nat,H: int > int,F: nat > num] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_nat_num_int @ ( comp_nat_num_nat @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_int_num_int @ ( comp_nat_num_int @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_818_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: nat > int,G: nat > nat,X2: nat,N: int > int,H: nat > int,F: int > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ ( comp_int_nat_nat @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_int_nat_nat @ ( comp_int_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_819_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: nat > nat,G: nat > nat,X2: nat,N: nat > nat,H: nat > nat,F: nat > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_820_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: int > nat,G: int > int,X2: int,N: nat > nat,H: int > nat,F: nat > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_int_nat_int @ ( comp_nat_nat_int @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_nat_nat_int @ ( comp_nat_nat_nat @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_821_type__copy__map__cong0,axiom,
% 7.78/3.93 ! [M: int > int,G: int > int,X2: int,N: int > int,H: int > int,F: int > nat] :
% 7.78/3.93 ( ( ( M @ ( G @ X2 ) )
% 7.78/3.93 = ( N @ ( H @ X2 ) ) )
% 7.78/3.93 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ M ) @ G @ X2 )
% 7.78/3.93 = ( comp_int_nat_int @ ( comp_int_nat_int @ F @ N ) @ H @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_822_comp__transfer,axiom,
% 7.78/3.93 ! [B5: $o > $o > $o,C3: $o > $o > $o,A4: nat > nat > $o] : ( bNF_re6580757339198446453_nat_o @ ( bNF_rel_fun_o_o_o_o @ B5 @ C3 ) @ ( bNF_re2697311982885662685_nat_o @ ( bNF_re4705727531993890431at_o_o @ A4 @ B5 ) @ ( bNF_re4705727531993890431at_o_o @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_o_o_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_823_comp__transfer,axiom,
% 7.78/3.93 ! [B5: $o > nat > $o,C3: $o > num > $o,A4: nat > int > $o] : ( bNF_re7387973359137000979nt_num @ ( bNF_re766437678722298023_o_num @ B5 @ C3 ) @ ( bNF_re4102725726183926567nt_num @ ( bNF_re8210149947023016781_o_nat @ A4 @ B5 ) @ ( bNF_re4767481733178795415_o_num @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_nat_num_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_824_comp__transfer,axiom,
% 7.78/3.93 ! [B5: $o > nat > $o,C3: $o > nat > $o,A4: nat > nat > $o] : ( bNF_re1515921786380824775at_nat @ ( bNF_re4209105892566519389_o_nat @ B5 @ C3 ) @ ( bNF_re2144779315220482269at_nat @ ( bNF_re7523573913982466217_o_nat @ A4 @ B5 ) @ ( bNF_re7523573913982466217_o_nat @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_nat_nat_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_825_comp__transfer,axiom,
% 7.78/3.93 ! [B5: $o > int > $o,C3: $o > nat > $o,A4: nat > int > $o] : ( bNF_re7413876800493218871nt_nat @ ( bNF_re4895681925607069953_o_nat @ B5 @ C3 ) @ ( bNF_re1982657550219213441nt_nat @ ( bNF_re8207659476513966505_o_int @ A4 @ B5 ) @ ( bNF_re8210149947023016781_o_nat @ A4 @ C3 ) ) @ comp_o_o_nat @ comp_int_nat_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_826_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > $o > $o,C3: num > $o > $o,A4: int > nat > $o] : ( bNF_re3931674169038344211_nat_o @ ( bNF_re8508505965575957011_num_o @ B5 @ C3 ) @ ( bNF_re7435575058205011731_nat_o @ ( bNF_re4914077030771115051_nat_o @ A4 @ B5 ) @ ( bNF_re3760060065607074657_num_o @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_o_o_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_827_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > nat > $o,C3: num > nat > $o,A4: int > nat > $o] : ( bNF_re6524732562925676389at_nat @ ( bNF_re3784151423046777323um_nat @ B5 @ C3 ) @ ( bNF_re717418264989850719at_nat @ ( bNF_re3344003087646356989at_nat @ A4 @ B5 ) @ ( bNF_re1474333490953826375um_nat @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_nat_nat_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_828_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > int > $o,C3: num > nat > $o,A4: int > int > $o] : ( bNF_re5843449549409830101nt_nat @ ( bNF_re4155804983283621959um_nat @ B5 @ C3 ) @ ( bNF_re3642433447925381491nt_nat @ ( bNF_re3713166177374151349at_int @ A4 @ B5 ) @ ( bNF_re1845987051190671011um_nat @ A4 @ C3 ) ) @ comp_nat_num_int @ comp_int_nat_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_829_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > $o > $o,C3: nat > $o > $o,A4: nat > nat > $o] : ( bNF_re3930744952143938759_nat_o @ ( bNF_re439150893885221597_nat_o @ B5 @ C3 ) @ ( bNF_re7744223787735169245_nat_o @ ( bNF_re1402873238235875719_nat_o @ A4 @ B5 ) @ ( bNF_re1402873238235875719_nat_o @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_o_o_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_830_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > nat > $o,C3: nat > num > $o,A4: nat > int > $o] : ( bNF_re584878643992547173nt_num @ ( bNF_re2211152805895086571at_num @ B5 @ C3 ) @ ( bNF_re8622501330148003679nt_num @ ( bNF_re6025474579976152573at_nat @ A4 @ B5 ) @ ( bNF_re2582806366131931207at_num @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_nat_num_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_831_comp__transfer,axiom,
% 7.78/3.93 ! [B5: nat > nat > $o,C3: nat > nat > $o,A4: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ B5 @ C3 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ A4 @ B5 ) @ ( bNF_re5653821019739307937at_nat @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_832_rel__fun__iff__geq__image2p,axiom,
% 7.78/3.93 ( bNF_re4555766996558763186at_nat
% 7.78/3.93 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: nat > nat > $o,F2: product_prod_nat_nat > nat,G3: int > nat] : ( ord_le2646555220125990790_nat_o @ ( bNF_Gr6955563364113978072nt_nat @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_833_rel__fun__iff__geq__image2p,axiom,
% 7.78/3.93 ( bNF_re7408651293131936558nt_int
% 7.78/3.93 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G3: int > int > int] : ( ord_le2484784447047653514_int_o @ ( bNF_Gr1354378531936274772nt_int @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_834_rel__fun__iff__geq__image2p,axiom,
% 7.78/3.93 ( bNF_re717283939379294677_int_o
% 7.78/3.93 = ( ^ [R6: product_prod_nat_nat > int > $o,S4: ( product_prod_nat_nat > $o ) > ( int > $o ) > $o,F2: product_prod_nat_nat > product_prod_nat_nat > $o,G3: int > int > $o] : ( ord_le2932013042137311317nt_o_o @ ( bNF_Gr364077372107685167_int_o @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_835_rel__fun__iff__geq__image2p,axiom,
% 7.78/3.93 ( bNF_re6718328864250387230um_num
% 7.78/3.93 = ( ^ [R6: int > code_integer > $o,S4: num > num > $o,F2: int > num,G3: code_integer > num] : ( ord_le6124364862034508274_num_o @ ( bNF_Gr166583433173494904er_num @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_836_rel__fun__iff__geq__image2p,axiom,
% 7.78/3.93 ( bNF_re7626690874201225453um_num
% 7.78/3.93 = ( ^ [R6: int > int > $o,S4: num > num > $o,F2: int > num,G3: int > num] : ( ord_le6124364862034508274_num_o @ ( bNF_Gr7020624548710275655nt_num @ F2 @ G3 @ R6 ) @ S4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_837_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: nat > num,G: nat > nat,X2: nat] :
% 7.78/3.93 ( ( comp_P5371577678113413053at_nat @ ( produc4918694523301289860at_nat @ F @ id_nat ) @ ( bNF_co805650143699787099at_nat @ id_nat @ G ) @ X2 )
% 7.78/3.93 = ( bNF_co8159352583862032293um_nat @ ( comp_num_num_nat @ id_num @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_838_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: $o > nat,G: $o > nat,X2: $o] :
% 7.78/3.93 ( ( comp_P196761593691424337_nat_o @ ( produc6587185857518356756at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_o_nat_nat @ ( comp_nat_nat_o @ id_nat @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_839_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: $o > $o,G: $o > nat,X2: $o] :
% 7.78/3.93 ( ( comp_P1422407636550552773_nat_o @ ( produc7071226018047599512at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_o_o_nat @ ( comp_o_o_o @ id_o @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_840_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: $o > num,G: $o > nat,X2: $o] :
% 7.78/3.93 ( ( comp_P972951341003599239_nat_o @ ( produc4527993685489015646at_nat @ F @ id_nat ) @ ( bNF_convol_o_o_nat @ id_o @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_o_num_nat @ ( comp_num_num_o @ id_num @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_841_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: num > nat,G: num > nat,X2: num] :
% 7.78/3.93 ( ( comp_P2539519431309506803at_num @ ( produc4208724500416182148at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 7.78/3.93 = ( bNF_co7969830008525221797at_nat @ ( comp_nat_nat_num @ id_nat @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_842_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: num > $o,G: num > nat,X2: num] :
% 7.78/3.93 ( ( comp_P3192427084145116251at_num @ ( produc8319293927732033832at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_num_o_nat @ ( comp_o_o_num @ id_o @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_843_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: num > num,G: num > nat,X2: num] :
% 7.78/3.93 ( ( comp_P480327259280165693at_num @ ( produc2149532328386841038at_nat @ F @ id_nat ) @ ( bNF_co6100160411832691183um_nat @ id_num @ G ) @ X2 )
% 7.78/3.93 = ( bNF_co6100160411832691183um_nat @ ( comp_num_num_num @ id_num @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_844_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: nat > num,G: nat > $o,X2: nat] :
% 7.78/3.93 ( ( comp_P6576135029341976421_o_nat @ ( produc3264868786340801506um_o_o @ F @ id_o ) @ ( bNF_convol_nat_nat_o @ id_nat @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_nat_num_o @ ( comp_num_num_nat @ id_num @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_845_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: $o > nat,G: $o > $o,X2: $o] :
% 7.78/3.93 ( ( comp_P1471321874221585045at_o_o @ ( produc9141321880750005618at_o_o @ F @ id_o ) @ ( bNF_convol_o_o_o @ id_o @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_o_nat_o @ ( comp_nat_nat_o @ id_nat @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_846_map__prod__o__convol__id,axiom,
% 7.78/3.93 ! [F: $o > $o,G: $o > $o,X2: $o] :
% 7.78/3.93 ( ( comp_P551574746845053877_o_o_o @ ( produc1928436952130685430_o_o_o @ F @ id_o ) @ ( bNF_convol_o_o_o @ id_o @ G ) @ X2 )
% 7.78/3.93 = ( bNF_convol_o_o_o @ ( comp_o_o_o @ id_o @ F ) @ G @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_847_image__Fpow__mono,axiom,
% 7.78/3.93 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.93 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le513522071413781156et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_rat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_848_image__Fpow__mono,axiom,
% 7.78/3.93 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_nat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_849_image__Fpow__mono,axiom,
% 7.78/3.93 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_int @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_850_image__Fpow__mono,axiom,
% 7.78/3.93 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_nat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_851_image__Fpow__mono,axiom,
% 7.78/3.93 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_int @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_852_convol__mem__GrpI,axiom,
% 7.78/3.93 ! [X2: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,G: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( member2643936169264416010at_nat @ X2 @ A4 )
% 7.78/3.93 => ( member8757157785044589968at_nat @ ( bNF_co147202357524637304at_nat @ id_set2334057505560298834at_nat @ G @ X2 ) @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( bNF_Gr6677838525845560078at_nat @ A4 @ G ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_853_convol__mem__GrpI,axiom,
% 7.78/3.93 ! [X2: nat,A4: set_nat,G: nat > nat] :
% 7.78/3.93 ( ( member_nat @ X2 @ A4 )
% 7.78/3.93 => ( member8440522571783428010at_nat @ ( bNF_co805650143699787099at_nat @ id_nat @ G @ X2 ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ G ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_854_convol__mem__GrpI,axiom,
% 7.78/3.93 ! [X2: int,A4: set_int,G: int > int] :
% 7.78/3.93 ( ( member_int @ X2 @ A4 )
% 7.78/3.93 => ( member5262025264175285858nt_int @ ( bNF_co2174166945328636015nt_int @ id_int @ G @ X2 ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( bNF_Grp_int_int @ A4 @ G ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_855_image__id,axiom,
% 7.78/3.93 ( ( image_o_o @ id_o )
% 7.78/3.93 = id_set_o ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_856_image__id,axiom,
% 7.78/3.93 ( ( image_num_num @ id_num )
% 7.78/3.93 = id_set_num ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_857_image__id,axiom,
% 7.78/3.93 ( ( image_nat_nat @ id_nat )
% 7.78/3.93 = id_set_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_858_image__id,axiom,
% 7.78/3.93 ( ( image_int_int @ id_int )
% 7.78/3.93 = id_set_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_859_fun_Omap__id,axiom,
% 7.78/3.93 ! [T2: nat > $o] :
% 7.78/3.93 ( ( comp_o_o_nat @ id_o @ T2 )
% 7.78/3.93 = T2 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_860_fun_Omap__id,axiom,
% 7.78/3.93 ! [T2: nat > nat] :
% 7.78/3.93 ( ( comp_nat_nat_nat @ id_nat @ T2 )
% 7.78/3.93 = T2 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_861_comp__id,axiom,
% 7.78/3.93 ! [F: nat > nat] :
% 7.78/3.93 ( ( comp_nat_nat_nat @ F @ id_nat )
% 7.78/3.93 = F ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_862_comp__id,axiom,
% 7.78/3.93 ! [F: int > nat] :
% 7.78/3.93 ( ( comp_int_nat_int @ F @ id_int )
% 7.78/3.93 = F ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_863_id__comp,axiom,
% 7.78/3.93 ! [G: nat > $o] :
% 7.78/3.93 ( ( comp_o_o_nat @ id_o @ G )
% 7.78/3.93 = G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_864_id__comp,axiom,
% 7.78/3.93 ! [G: nat > nat] :
% 7.78/3.93 ( ( comp_nat_nat_nat @ id_nat @ G )
% 7.78/3.93 = G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_865_case__prod__Pair,axiom,
% 7.78/3.93 ( ( produc5456455677105495163at_nat @ produc9060074326276436823at_nat )
% 7.78/3.93 = id_Pro6043886709289754456at_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_866_case__prod__Pair,axiom,
% 7.78/3.93 ( ( produc7548845685434208379at_nat @ produc2922128104949294807at_nat )
% 7.78/3.93 = id_Pro8722402698821300696at_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_867_case__prod__Pair,axiom,
% 7.78/3.93 ( ( produc49306077274653107at_num @ product_Pair_nat_num )
% 7.78/3.93 = id_Pro8267972854940751164at_num ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_868_case__prod__Pair,axiom,
% 7.78/3.93 ( ( produc2626176000494625587at_nat @ product_Pair_nat_nat )
% 7.78/3.93 = id_Pro7559728917991913458at_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_869_case__prod__Pair,axiom,
% 7.78/3.93 ( ( produc4245557441103728435nt_int @ product_Pair_int_int )
% 7.78/3.93 = id_Pro4381231610383771306nt_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_870_apsnd__id,axiom,
% 7.78/3.93 ( ( produc6499014454317279255nteger @ id_Code_integer )
% 7.78/3.93 = id_Pro2309048762231606924nteger ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_871_range__fst,axiom,
% 7.78/3.93 ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ top_to2503719809363509323t_unit )
% 7.78/3.93 = top_top_set_ref_a ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_872_range__snd,axiom,
% 7.78/3.93 ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ top_to2503719809363509323t_unit )
% 7.78/3.93 = top_to3956321331435058429t_unit ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_873_fun_Omap__id0,axiom,
% 7.78/3.93 ( ( comp_o_o_nat @ id_o )
% 7.78/3.93 = id_nat_o ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_874_fun_Omap__id0,axiom,
% 7.78/3.93 ( ( comp_nat_nat_nat @ id_nat )
% 7.78/3.93 = id_nat_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_875_surj__id,axiom,
% 7.78/3.93 ( ( image_o_o @ id_o @ top_top_set_o )
% 7.78/3.93 = top_top_set_o ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_876_surj__id,axiom,
% 7.78/3.93 ( ( image_num_num @ id_num @ top_top_set_num )
% 7.78/3.93 = top_top_set_num ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_877_surj__id,axiom,
% 7.78/3.93 ( ( image_char_char @ id_char @ top_top_set_char )
% 7.78/3.93 = top_top_set_char ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_878_surj__id,axiom,
% 7.78/3.93 ( ( image_7976474329151083847st_nat @ id_list_nat @ top_top_set_list_nat )
% 7.78/3.93 = top_top_set_list_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_879_surj__id,axiom,
% 7.78/3.93 ( ( image_rat_rat @ id_rat @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_880_surj__id,axiom,
% 7.78/3.93 ( ( image_nat_nat @ id_nat @ top_top_set_nat )
% 7.78/3.93 = top_top_set_nat ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_881_surj__id,axiom,
% 7.78/3.93 ( ( image_int_int @ id_int @ top_top_set_int )
% 7.78/3.93 = top_top_set_int ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_882_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: $o,Y3: $o] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_o_o @ top_top_set_o @ id_o @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_883_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: num,Y3: num] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_num_num @ top_top_set_num @ id_num @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_884_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: char,Y3: char] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_char_char @ top_top_set_char @ id_char @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_885_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: list_nat,Y3: list_nat] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ id_list_nat @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_886_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: rat,Y3: rat] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_rat_rat @ top_top_set_rat @ id_rat @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_887_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: nat,Y3: nat] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_888_Grp__UNIV__idI,axiom,
% 7.78/3.93 ! [X2: int,Y3: int] :
% 7.78/3.93 ( ( X2 = Y3 )
% 7.78/3.93 => ( bNF_Grp_int_int @ top_top_set_int @ id_int @ X2 @ Y3 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_889_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_o_o @ top_top_set_o @ id_o ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_890_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: num,Z: num] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_num_num @ top_top_set_num @ id_num ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_891_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: char,Z: char] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_char_char @ top_top_set_char @ id_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_892_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ id_list_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_893_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: rat,Z: rat] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_rat_rat @ top_top_set_rat @ id_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_894_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_895_eq__alt,axiom,
% 7.78/3.93 ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 7.78/3.93 = ( bNF_Grp_int_int @ top_top_set_int @ id_int ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_896_Inf_OINF__id__eq,axiom,
% 7.78/3.93 ! [Inf: set_o > $o,A4: set_o] :
% 7.78/3.93 ( ( Inf @ ( image_o_o @ id_o @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_897_Inf_OINF__id__eq,axiom,
% 7.78/3.93 ! [Inf: set_num > num,A4: set_num] :
% 7.78/3.93 ( ( Inf @ ( image_num_num @ id_num @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_898_Inf_OINF__id__eq,axiom,
% 7.78/3.93 ! [Inf: set_nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( Inf @ ( image_nat_nat @ id_nat @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_899_Inf_OINF__id__eq,axiom,
% 7.78/3.93 ! [Inf: set_int > int,A4: set_int] :
% 7.78/3.93 ( ( Inf @ ( image_int_int @ id_int @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_900_Sup_OSUP__id__eq,axiom,
% 7.78/3.93 ! [Sup: set_o > $o,A4: set_o] :
% 7.78/3.93 ( ( Sup @ ( image_o_o @ id_o @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_901_Sup_OSUP__id__eq,axiom,
% 7.78/3.93 ! [Sup: set_num > num,A4: set_num] :
% 7.78/3.93 ( ( Sup @ ( image_num_num @ id_num @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_902_Sup_OSUP__id__eq,axiom,
% 7.78/3.93 ! [Sup: set_nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( Sup @ ( image_nat_nat @ id_nat @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_903_Sup_OSUP__id__eq,axiom,
% 7.78/3.93 ! [Sup: set_int > int,A4: set_int] :
% 7.78/3.93 ( ( Sup @ ( image_int_int @ id_int @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_904_comp__eq__id__dest,axiom,
% 7.78/3.93 ! [A: $o > $o,B: nat > $o,C: nat > $o,V: nat] :
% 7.78/3.93 ( ( ( comp_o_o_nat @ A @ B )
% 7.78/3.93 = ( comp_o_o_nat @ id_o @ C ) )
% 7.78/3.93 => ( ( A @ ( B @ V ) )
% 7.78/3.93 = ( C @ V ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_905_comp__eq__id__dest,axiom,
% 7.78/3.93 ! [A: nat > num,B: int > nat,C: int > num,V: int] :
% 7.78/3.93 ( ( ( comp_nat_num_int @ A @ B )
% 7.78/3.93 = ( comp_num_num_int @ id_num @ C ) )
% 7.78/3.93 => ( ( A @ ( B @ V ) )
% 7.78/3.93 = ( C @ V ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_906_comp__eq__id__dest,axiom,
% 7.78/3.93 ! [A: nat > nat,B: nat > nat,C: nat > nat,V: nat] :
% 7.78/3.93 ( ( ( comp_nat_nat_nat @ A @ B )
% 7.78/3.93 = ( comp_nat_nat_nat @ id_nat @ C ) )
% 7.78/3.93 => ( ( A @ ( B @ V ) )
% 7.78/3.93 = ( C @ V ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_907_comp__eq__id__dest,axiom,
% 7.78/3.93 ! [A: int > nat,B: int > int,C: int > nat,V: int] :
% 7.78/3.93 ( ( ( comp_int_nat_int @ A @ B )
% 7.78/3.93 = ( comp_nat_nat_int @ id_nat @ C ) )
% 7.78/3.93 => ( ( A @ ( B @ V ) )
% 7.78/3.93 = ( C @ V ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_908_comp__eq__id__dest,axiom,
% 7.78/3.93 ! [A: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,B: code_integer > code_integer > code_integer,C: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,V: code_integer] :
% 7.78/3.93 ( ( ( comp_C8797469213163452608nteger @ A @ B )
% 7.78/3.93 = ( comp_P3928908779438215820nteger @ id_Pro496765588584934260nteger @ C ) )
% 7.78/3.93 => ( ( A @ ( B @ V ) )
% 7.78/3.93 = ( C @ V ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_909_pointfree__idE,axiom,
% 7.78/3.93 ! [F: nat > nat,G: nat > nat,X2: nat] :
% 7.78/3.93 ( ( ( comp_nat_nat_nat @ F @ G )
% 7.78/3.93 = id_nat )
% 7.78/3.93 => ( ( F @ ( G @ X2 ) )
% 7.78/3.93 = X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_910_surjD,axiom,
% 7.78/3.93 ! [F: char > char,Y3: char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ? [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_911_surjD,axiom,
% 7.78/3.93 ! [F: char > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ? [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_912_surjD,axiom,
% 7.78/3.93 ! [F: char > nat,Y3: nat] :
% 7.78/3.93 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ? [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_913_surjD,axiom,
% 7.78/3.93 ! [F: char > int,Y3: int] :
% 7.78/3.93 ( ( ( image_char_int @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ? [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_914_surjD,axiom,
% 7.78/3.93 ! [F: rat > char,Y3: char] :
% 7.78/3.93 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ? [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_915_surjD,axiom,
% 7.78/3.93 ! [F: rat > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ? [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_916_surjD,axiom,
% 7.78/3.93 ! [F: rat > nat,Y3: nat] :
% 7.78/3.93 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ? [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_917_surjD,axiom,
% 7.78/3.93 ! [F: rat > int,Y3: int] :
% 7.78/3.93 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ? [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_918_surjD,axiom,
% 7.78/3.93 ! [F: nat > char,Y3: char] :
% 7.78/3.93 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ? [X: nat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_919_surjD,axiom,
% 7.78/3.93 ! [F: nat > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ? [X: nat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 = ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_920_surjE,axiom,
% 7.78/3.93 ! [F: char > char,Y3: char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ~ ! [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_921_surjE,axiom,
% 7.78/3.93 ! [F: char > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ~ ! [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_922_surjE,axiom,
% 7.78/3.93 ! [F: char > nat,Y3: nat] :
% 7.78/3.93 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ~ ! [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_923_surjE,axiom,
% 7.78/3.93 ! [F: char > int,Y3: int] :
% 7.78/3.93 ( ( ( image_char_int @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ~ ! [X: char] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_924_surjE,axiom,
% 7.78/3.93 ! [F: rat > char,Y3: char] :
% 7.78/3.93 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ~ ! [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_925_surjE,axiom,
% 7.78/3.93 ! [F: rat > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ~ ! [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_926_surjE,axiom,
% 7.78/3.93 ! [F: rat > nat,Y3: nat] :
% 7.78/3.93 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ~ ! [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_927_surjE,axiom,
% 7.78/3.93 ! [F: rat > int,Y3: int] :
% 7.78/3.93 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ~ ! [X: rat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_928_surjE,axiom,
% 7.78/3.93 ! [F: nat > char,Y3: char] :
% 7.78/3.93 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_929_surjE,axiom,
% 7.78/3.93 ! [F: nat > rat,Y3: rat] :
% 7.78/3.93 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( Y3
% 7.78/3.93 != ( F @ X ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_930_surjI,axiom,
% 7.78/3.93 ! [G: char > char,F: char > char] :
% 7.78/3.93 ( ! [X: char] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_char_char @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_931_surjI,axiom,
% 7.78/3.93 ! [G: char > rat,F: rat > char] :
% 7.78/3.93 ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_char_rat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_932_surjI,axiom,
% 7.78/3.93 ! [G: char > nat,F: nat > char] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_char_nat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_933_surjI,axiom,
% 7.78/3.93 ! [G: char > int,F: int > char] :
% 7.78/3.93 ( ! [X: int] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_char_int @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_int ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_934_surjI,axiom,
% 7.78/3.93 ! [G: rat > char,F: char > rat] :
% 7.78/3.93 ( ! [X: char] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_rat_char @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_935_surjI,axiom,
% 7.78/3.93 ! [G: rat > rat,F: rat > rat] :
% 7.78/3.93 ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_rat_rat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_936_surjI,axiom,
% 7.78/3.93 ! [G: rat > nat,F: nat > rat] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_rat_nat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_937_surjI,axiom,
% 7.78/3.93 ! [G: rat > int,F: int > rat] :
% 7.78/3.93 ( ! [X: int] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_rat_int @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_938_surjI,axiom,
% 7.78/3.93 ! [G: nat > char,F: char > nat] :
% 7.78/3.93 ( ! [X: char] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_nat_char @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_939_surjI,axiom,
% 7.78/3.93 ! [G: nat > rat,F: rat > nat] :
% 7.78/3.93 ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( ( image_nat_rat @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_940_rangeI,axiom,
% 7.78/3.93 ! [F: char > $o,X2: char] : ( member_o @ ( F @ X2 ) @ ( image_char_o @ F @ top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_941_rangeI,axiom,
% 7.78/3.93 ! [F: char > nat,X2: char] : ( member_nat @ ( F @ X2 ) @ ( image_char_nat @ F @ top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_942_rangeI,axiom,
% 7.78/3.93 ! [F: char > int,X2: char] : ( member_int @ ( F @ X2 ) @ ( image_char_int @ F @ top_top_set_char ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_943_rangeI,axiom,
% 7.78/3.93 ! [F: rat > $o,X2: rat] : ( member_o @ ( F @ X2 ) @ ( image_rat_o @ F @ top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_944_rangeI,axiom,
% 7.78/3.93 ! [F: rat > nat,X2: rat] : ( member_nat @ ( F @ X2 ) @ ( image_rat_nat @ F @ top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_945_rangeI,axiom,
% 7.78/3.93 ! [F: rat > int,X2: rat] : ( member_int @ ( F @ X2 ) @ ( image_rat_int @ F @ top_top_set_rat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_946_rangeI,axiom,
% 7.78/3.93 ! [F: nat > rat,X2: nat] : ( member_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_947_rangeI,axiom,
% 7.78/3.93 ! [F: nat > $o,X2: nat] : ( member_o @ ( F @ X2 ) @ ( image_nat_o @ F @ top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_948_rangeI,axiom,
% 7.78/3.93 ! [F: nat > nat,X2: nat] : ( member_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_949_rangeI,axiom,
% 7.78/3.93 ! [F: nat > int,X2: nat] : ( member_int @ ( F @ X2 ) @ ( image_nat_int @ F @ top_top_set_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_950_surj__def,axiom,
% 7.78/3.93 ! [F: char > char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 = ( ! [Y5: char] :
% 7.78/3.93 ? [X4: char] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_951_surj__def,axiom,
% 7.78/3.93 ! [F: char > rat] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 = ( ! [Y5: rat] :
% 7.78/3.93 ? [X4: char] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_952_surj__def,axiom,
% 7.78/3.93 ! [F: char > nat] :
% 7.78/3.93 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 = ( ! [Y5: nat] :
% 7.78/3.93 ? [X4: char] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_953_surj__def,axiom,
% 7.78/3.93 ! [F: char > int] :
% 7.78/3.93 ( ( ( image_char_int @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 = ( ! [Y5: int] :
% 7.78/3.93 ? [X4: char] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_954_surj__def,axiom,
% 7.78/3.93 ! [F: rat > char] :
% 7.78/3.93 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 = ( ! [Y5: char] :
% 7.78/3.93 ? [X4: rat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_955_surj__def,axiom,
% 7.78/3.93 ! [F: rat > rat] :
% 7.78/3.93 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 = ( ! [Y5: rat] :
% 7.78/3.93 ? [X4: rat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_956_surj__def,axiom,
% 7.78/3.93 ! [F: rat > nat] :
% 7.78/3.93 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 = ( ! [Y5: nat] :
% 7.78/3.93 ? [X4: rat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_957_surj__def,axiom,
% 7.78/3.93 ! [F: rat > int] :
% 7.78/3.93 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 = ( ! [Y5: int] :
% 7.78/3.93 ? [X4: rat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_958_surj__def,axiom,
% 7.78/3.93 ! [F: nat > char] :
% 7.78/3.93 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 = ( ! [Y5: char] :
% 7.78/3.93 ? [X4: nat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_959_surj__def,axiom,
% 7.78/3.93 ! [F: nat > rat] :
% 7.78/3.93 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 = ( ! [Y5: rat] :
% 7.78/3.93 ? [X4: nat] :
% 7.78/3.93 ( Y5
% 7.78/3.93 = ( F @ X4 ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_960_range__eqI,axiom,
% 7.78/3.93 ! [B: $o,F: char > $o,X2: char] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_961_range__eqI,axiom,
% 7.78/3.93 ! [B: nat,F: char > nat,X2: char] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_962_range__eqI,axiom,
% 7.78/3.93 ! [B: int,F: char > int,X2: char] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_963_range__eqI,axiom,
% 7.78/3.93 ! [B: $o,F: rat > $o,X2: rat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_964_range__eqI,axiom,
% 7.78/3.93 ! [B: nat,F: rat > nat,X2: rat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_965_range__eqI,axiom,
% 7.78/3.93 ! [B: int,F: rat > int,X2: rat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_966_range__eqI,axiom,
% 7.78/3.93 ! [B: rat,F: nat > rat,X2: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_967_range__eqI,axiom,
% 7.78/3.93 ! [B: $o,F: nat > $o,X2: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_968_range__eqI,axiom,
% 7.78/3.93 ! [B: nat,F: nat > nat,X2: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_969_range__eqI,axiom,
% 7.78/3.93 ! [B: int,F: nat > int,X2: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X2 ) )
% 7.78/3.93 => ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_970_effect__success,axiom,
% 7.78/3.93 ! [C: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit,R: ref_a] :
% 7.78/3.93 ( ( heap_effect_ref_a @ C @ H @ H2 @ R )
% 7.78/3.93 => ( heap_success_ref_a @ C @ H ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_971_success__effectE,axiom,
% 7.78/3.93 ! [C: heap_Heap_ref_a,H: heap_e7401611519738050253t_unit] :
% 7.78/3.93 ( ( heap_success_ref_a @ C @ H )
% 7.78/3.93 => ~ ! [R4: ref_a,H4: heap_e7401611519738050253t_unit] :
% 7.78/3.93 ~ ( heap_effect_ref_a @ C @ H @ H4 @ R4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_972_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_char @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_7676512070627423941r_char @ ( produc7830753070125841726r_char @ F @ G ) @ top_to1235241553633177651r_char )
% 7.78/3.93 = top_to1235241553633177651r_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_973_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > rat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_rat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_7275072250160737868ar_rat @ ( produc5209943433214700613ar_rat @ F @ G ) @ top_to1235241553633177651r_char )
% 7.78/3.93 = top_to8437673547576850234ar_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_974_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > nat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_nat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( image_1559928771699358788ar_nat @ ( produc5845073493301196349ar_nat @ F @ G ) @ top_to1235241553633177651r_char )
% 7.78/3.93 = top_to5594287848199751986ar_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_975_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > int] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_int @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ( image_6605449789044937888ar_int @ ( produc5842583022792146073ar_int @ F @ G ) @ top_to1235241553633177651r_char )
% 7.78/3.93 = top_to3104204703268025230ar_int ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_976_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: rat > char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_rat_char @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_8036680598759533694r_char @ ( produc5432746246116964165t_char @ F @ G ) @ top_to8437673547576850234ar_rat )
% 7.78/3.93 = top_to1235241553633177651r_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_977_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: rat > rat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_rat_rat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_5644637116751559941ar_rat @ ( produc1230515432254573900at_rat @ F @ G ) @ top_to8437673547576850234ar_rat )
% 7.78/3.93 = top_to8437673547576850234ar_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_978_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: rat > nat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_rat_nat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( image_9152865675144956669ar_nat @ ( produc1865645492341069636at_nat @ F @ G ) @ top_to8437673547576850234ar_rat )
% 7.78/3.93 = top_to5594287848199751986ar_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_979_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: rat > int] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_rat_int @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ( image_4975014655635759961ar_int @ ( produc1863155021832019360at_int @ F @ G ) @ top_to8437673547576850234ar_rat )
% 7.78/3.93 = top_to3104204703268025230ar_int ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_980_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: nat > char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_nat_char @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_5973708714899544198r_char @ ( produc8759894717825771837t_char @ F @ G ) @ top_to5594287848199751986ar_nat )
% 7.78/3.93 = top_to1235241553633177651r_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_981_map__prod__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: nat > rat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_nat_rat @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_2699825501378146573ar_rat @ ( produc1547070076189439812at_rat @ F @ G ) @ top_to5594287848199751986ar_nat )
% 7.78/3.93 = top_to8437673547576850234ar_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_982_GrD1,axiom,
% 7.78/3.93 ! [X2: set_Pr4329608150637261639at_nat,Fx: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Fx ) @ ( bNF_Gr7888059597227825506at_nat @ A4 @ F ) )
% 7.78/3.93 => ( member6273874620674182256at_nat @ X2 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_983_GrD1,axiom,
% 7.78/3.93 ! [X2: set_Pr1261947904930325089at_nat,Fx: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Fx ) @ ( bNF_Gr1527221351080490466at_nat @ A4 @ F ) )
% 7.78/3.93 => ( member2643936169264416010at_nat @ X2 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_984_GrD1,axiom,
% 7.78/3.93 ! [X2: nat,Fx: num,A4: set_nat,F: nat > num] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Fx ) @ ( bNF_Gr_nat_num @ A4 @ F ) )
% 7.78/3.93 => ( member_nat @ X2 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_985_GrD1,axiom,
% 7.78/3.93 ! [X2: nat,Fx: nat,A4: set_nat,F: nat > nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Fx ) @ ( bNF_Gr_nat_nat @ A4 @ F ) )
% 7.78/3.93 => ( member_nat @ X2 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_986_GrD1,axiom,
% 7.78/3.93 ! [X2: int,Fx: int,A4: set_int,F: int > int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Fx ) @ ( bNF_Gr_int_int @ A4 @ F ) )
% 7.78/3.93 => ( member_int @ X2 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_987_GrD2,axiom,
% 7.78/3.93 ! [X2: set_Pr4329608150637261639at_nat,Fx: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Fx ) @ ( bNF_Gr7888059597227825506at_nat @ A4 @ F ) )
% 7.78/3.93 => ( ( F @ X2 )
% 7.78/3.93 = Fx ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_988_GrD2,axiom,
% 7.78/3.93 ! [X2: set_Pr1261947904930325089at_nat,Fx: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Fx ) @ ( bNF_Gr1527221351080490466at_nat @ A4 @ F ) )
% 7.78/3.93 => ( ( F @ X2 )
% 7.78/3.93 = Fx ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_989_GrD2,axiom,
% 7.78/3.93 ! [X2: nat,Fx: num,A4: set_nat,F: nat > num] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Fx ) @ ( bNF_Gr_nat_num @ A4 @ F ) )
% 7.78/3.93 => ( ( F @ X2 )
% 7.78/3.93 = Fx ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_990_GrD2,axiom,
% 7.78/3.93 ! [X2: nat,Fx: nat,A4: set_nat,F: nat > nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Fx ) @ ( bNF_Gr_nat_nat @ A4 @ F ) )
% 7.78/3.93 => ( ( F @ X2 )
% 7.78/3.93 = Fx ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_991_GrD2,axiom,
% 7.78/3.93 ! [X2: int,Fx: int,A4: set_int,F: int > int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Fx ) @ ( bNF_Gr_int_int @ A4 @ F ) )
% 7.78/3.93 => ( ( F @ X2 )
% 7.78/3.93 = Fx ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_992_success__refI,axiom,
% 7.78/3.93 ! [V: a,H: heap_e7401611519738050253t_unit] : ( heap_success_ref_a @ ( ref_a2 @ V ) @ H ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_993_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > $o,Ya: char > $o,Y3: char > $o,Xa2: char > $o,R3: $o > $o > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re1692451286490762625ar_o_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re1692451286490762625ar_o_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_994_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > $o,Ya: char > $o,Y3: char > nat,Xa2: char > nat,R3: $o > nat > $o,Ra: $o > nat > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: nat] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re4782998131235581479_o_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re4782998131235581479_o_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_995_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > $o,Ya: char > $o,Y3: char > int,Xa2: char > int,R3: $o > int > $o,Ra: $o > int > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: int] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re4780507660726531203_o_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re4780507660726531203_o_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_996_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > nat,Ya: char > nat,Y3: char > $o,Xa2: char > $o,R3: nat > $o > $o,Ra: nat > $o > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: $o] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re7885669492343766789_nat_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re7885669492343766789_nat_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_997_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > nat,Ya: char > nat,Y3: char > nat,Xa2: char > nat,R3: nat > nat > $o,Ra: nat > nat > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_998_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > nat,Ya: char > nat,Y3: char > int,Xa2: char > int,R3: nat > int > $o,Ra: nat > int > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: int] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re3731845416926587903at_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re3731845416926587903at_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_999_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > int,Ya: char > int,Y3: char > $o,Xa2: char > $o,R3: int > $o > $o,Ra: int > $o > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: int,Yb: $o] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re6064627146911078825_int_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re6064627146911078825_int_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1000_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > int,Ya: char > int,Y3: char > nat,Xa2: char > nat,R3: int > nat > $o,Ra: int > nat > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: int,Yb: nat] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re4733689599336692735nt_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re4733689599336692735nt_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1001_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: char > int,Ya: char > int,Y3: char > int,Xa2: char > int,R3: int > int > $o,Ra: int > int > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: int,Yb: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ Ya @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Xa2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1002_fun_Orel__cong,axiom,
% 7.78/3.93 ! [X2: rat > $o,Ya: rat > $o,Y3: rat > $o,Xa2: rat > $o,R3: $o > $o > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ( Y3 = Xa2 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_rat_o @ Ya @ top_top_set_rat ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_rat_o @ Xa2 @ top_top_set_rat ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 = ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( ( bNF_re1865807574169326223at_o_o
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 = ( bNF_re1865807574169326223at_o_o
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ Ya
% 7.78/3.93 @ Xa2 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1003_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: $o > $o > $o,X2: char > $o,Y3: char > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ( bNF_re1692451286490762625ar_o_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re1692451286490762625ar_o_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1004_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: $o > nat > $o,X2: char > $o,Y3: char > nat,Ra: $o > nat > $o] :
% 7.78/3.93 ( ( bNF_re4782998131235581479_o_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: nat] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re4782998131235581479_o_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1005_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: $o > int > $o,X2: char > $o,Y3: char > int,Ra: $o > int > $o] :
% 7.78/3.93 ( ( bNF_re4780507660726531203_o_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: int] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re4780507660726531203_o_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1006_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: nat > $o > $o,X2: char > nat,Y3: char > $o,Ra: nat > $o > $o] :
% 7.78/3.93 ( ( bNF_re7885669492343766789_nat_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: $o] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re7885669492343766789_nat_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1007_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,X2: char > nat,Y3: char > nat,Ra: nat > nat > $o] :
% 7.78/3.93 ( ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1008_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: nat > int > $o,X2: char > nat,Y3: char > int,Ra: nat > int > $o] :
% 7.78/3.93 ( ( bNF_re3731845416926587903at_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: nat,Yb: int] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re3731845416926587903at_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1009_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: int > $o > $o,X2: char > int,Y3: char > $o,Ra: int > $o > $o] :
% 7.78/3.93 ( ( bNF_re6064627146911078825_int_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: int,Yb: $o] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_char_o @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re6064627146911078825_int_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1010_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: int > nat > $o,X2: char > int,Y3: char > nat,Ra: int > nat > $o] :
% 7.78/3.93 ( ( bNF_re4733689599336692735nt_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: int,Yb: nat] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_nat @ Yb @ ( image_char_nat @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re4733689599336692735nt_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1011_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: int > int > $o,X2: char > int,Y3: char > int,Ra: int > int > $o] :
% 7.78/3.93 ( ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: int,Yb: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( ( member_int @ Yb @ ( image_char_int @ Y3 @ top_top_set_char ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1012_fun_Orel__mono__strong,axiom,
% 7.78/3.93 ! [R3: $o > $o > $o,X2: rat > $o,Y3: rat > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ( bNF_re1865807574169326223at_o_o
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 )
% 7.78/3.93 => ( ! [Z3: $o,Yb: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_rat_o @ X2 @ top_top_set_rat ) )
% 7.78/3.93 => ( ( member_o @ Yb @ ( image_rat_o @ Y3 @ top_top_set_rat ) )
% 7.78/3.93 => ( ( R3 @ Z3 @ Yb )
% 7.78/3.93 => ( Ra @ Z3 @ Yb ) ) ) )
% 7.78/3.93 => ( bNF_re1865807574169326223at_o_o
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ Y3 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1013_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: char > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ! [Z3: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_char_o @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re1692451286490762625ar_o_o
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1014_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: char > nat,Ra: nat > nat > $o] :
% 7.78/3.93 ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_char_nat @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1015_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: char > int,Ra: int > int > $o] :
% 7.78/3.93 ( ! [Z3: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_char_int @ X2 @ top_top_set_char ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1016_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: rat > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ! [Z3: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_rat_o @ X2 @ top_top_set_rat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re1865807574169326223at_o_o
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1017_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: rat > nat,Ra: nat > nat > $o] :
% 7.78/3.93 ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_rat_nat @ X2 @ top_top_set_rat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re6557955094579809201at_nat
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1018_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: rat > int,Ra: int > int > $o] :
% 7.78/3.93 ( ! [Z3: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_rat_int @ X2 @ top_top_set_rat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re7554818335971813481nt_int
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1019_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: nat > rat,Ra: rat > rat > $o] :
% 7.78/3.93 ( ! [Z3: rat] :
% 7.78/3.93 ( ( member_rat @ Z3 @ ( image_nat_rat @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re4702136315717946289at_rat
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1020_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: nat > $o,Ra: $o > $o > $o] :
% 7.78/3.93 ( ! [Z3: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re4705727531993890431at_o_o
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1021_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: nat > nat,Ra: nat > nat > $o] :
% 7.78/3.93 ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re5653821019739307937at_nat
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1022_fun_Orel__refl__strong,axiom,
% 7.78/3.93 ! [X2: nat > int,Ra: int > int > $o] :
% 7.78/3.93 ( ! [Z3: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_nat_int @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( Ra @ Z3 @ Z3 ) )
% 7.78/3.93 => ( bNF_re6650684261131312217nt_int
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ Ra
% 7.78/3.93 @ X2
% 7.78/3.93 @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1023_range__subsetD,axiom,
% 7.78/3.93 ! [F: char > $o,B5: set_o,I: char] :
% 7.78/3.93 ( ( ord_less_eq_set_o @ ( image_char_o @ F @ top_top_set_char ) @ B5 )
% 7.78/3.93 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1024_range__subsetD,axiom,
% 7.78/3.93 ! [F: char > nat,B5: set_nat,I: char] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_char_nat @ F @ top_top_set_char ) @ B5 )
% 7.78/3.93 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1025_range__subsetD,axiom,
% 7.78/3.93 ! [F: char > int,B5: set_int,I: char] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_char_int @ F @ top_top_set_char ) @ B5 )
% 7.78/3.93 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1026_range__subsetD,axiom,
% 7.78/3.93 ! [F: rat > $o,B5: set_o,I: rat] :
% 7.78/3.93 ( ( ord_less_eq_set_o @ ( image_rat_o @ F @ top_top_set_rat ) @ B5 )
% 7.78/3.93 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1027_range__subsetD,axiom,
% 7.78/3.93 ! [F: rat > nat,B5: set_nat,I: rat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_rat_nat @ F @ top_top_set_rat ) @ B5 )
% 7.78/3.93 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1028_range__subsetD,axiom,
% 7.78/3.93 ! [F: rat > int,B5: set_int,I: rat] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_rat_int @ F @ top_top_set_rat ) @ B5 )
% 7.78/3.93 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1029_range__subsetD,axiom,
% 7.78/3.93 ! [F: nat > rat,B5: set_rat,I: nat] :
% 7.78/3.93 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ top_top_set_nat ) @ B5 )
% 7.78/3.93 => ( member_rat @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1030_range__subsetD,axiom,
% 7.78/3.93 ! [F: nat > $o,B5: set_o,I: nat] :
% 7.78/3.93 ( ( ord_less_eq_set_o @ ( image_nat_o @ F @ top_top_set_nat ) @ B5 )
% 7.78/3.93 => ( member_o @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1031_range__subsetD,axiom,
% 7.78/3.93 ! [F: nat > nat,B5: set_nat,I: nat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ top_top_set_nat ) @ B5 )
% 7.78/3.93 => ( member_nat @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1032_range__subsetD,axiom,
% 7.78/3.93 ! [F: nat > int,B5: set_int,I: nat] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ top_top_set_nat ) @ B5 )
% 7.78/3.93 => ( member_int @ ( F @ I ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1033_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > rat,V: char > nat] :
% 7.78/3.93 ( ( image_char_rat @ ( comp_nat_rat_char @ F @ V ) @ top_top_set_char )
% 7.78/3.93 = ( image_nat_rat @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1034_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > nat,V: char > nat] :
% 7.78/3.93 ( ( image_char_nat @ ( comp_nat_nat_char @ F @ V ) @ top_top_set_char )
% 7.78/3.93 = ( image_nat_nat @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1035_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > int,V: char > nat] :
% 7.78/3.93 ( ( image_char_int @ ( comp_nat_int_char @ F @ V ) @ top_top_set_char )
% 7.78/3.93 = ( image_nat_int @ F @ ( image_char_nat @ V @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1036_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: int > nat,V: char > int] :
% 7.78/3.93 ( ( image_char_nat @ ( comp_int_nat_char @ F @ V ) @ top_top_set_char )
% 7.78/3.93 = ( image_int_nat @ F @ ( image_char_int @ V @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1037_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: int > int,V: char > int] :
% 7.78/3.93 ( ( image_char_int @ ( comp_int_int_char @ F @ V ) @ top_top_set_char )
% 7.78/3.93 = ( image_int_int @ F @ ( image_char_int @ V @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1038_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > rat,V: rat > nat] :
% 7.78/3.93 ( ( image_rat_rat @ ( comp_nat_rat_rat @ F @ V ) @ top_top_set_rat )
% 7.78/3.93 = ( image_nat_rat @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1039_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > nat,V: rat > nat] :
% 7.78/3.93 ( ( image_rat_nat @ ( comp_nat_nat_rat @ F @ V ) @ top_top_set_rat )
% 7.78/3.93 = ( image_nat_nat @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1040_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: nat > int,V: rat > nat] :
% 7.78/3.93 ( ( image_rat_int @ ( comp_nat_int_rat @ F @ V ) @ top_top_set_rat )
% 7.78/3.93 = ( image_nat_int @ F @ ( image_rat_nat @ V @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1041_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: int > nat,V: rat > int] :
% 7.78/3.93 ( ( image_rat_nat @ ( comp_int_nat_rat @ F @ V ) @ top_top_set_rat )
% 7.78/3.93 = ( image_int_nat @ F @ ( image_rat_int @ V @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1042_fun_Oset__map,axiom,
% 7.78/3.93 ! [F: int > int,V: rat > int] :
% 7.78/3.93 ( ( image_rat_int @ ( comp_int_int_rat @ F @ V ) @ top_top_set_rat )
% 7.78/3.93 = ( image_int_int @ F @ ( image_rat_int @ V @ top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1043_fun_Omap__cong,axiom,
% 7.78/3.93 ! [X2: code_integer > code_integer > code_integer,Ya: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ! [Z3: code_integer > code_integer] :
% 7.78/3.93 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ Ya @ top_to4645266643341252675nteger ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 7.78/3.93 = ( comp_C8797469213163452608nteger @ G @ Ya ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1044_fun_Omap__cong,axiom,
% 7.78/3.93 ! [X2: nat > $o,Ya: nat > $o,F: $o > $o,G: $o > $o] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ! [Z3: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_nat_o @ Ya @ top_top_set_nat ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_o_o_nat @ F @ X2 )
% 7.78/3.93 = ( comp_o_o_nat @ G @ Ya ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1045_fun_Omap__cong,axiom,
% 7.78/3.93 ! [X2: nat > nat,Ya: nat > nat,F: nat > nat,G: nat > nat] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_nat_nat @ Ya @ top_top_set_nat ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ F @ X2 )
% 7.78/3.93 = ( comp_nat_nat_nat @ G @ Ya ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1046_fun_Omap__cong,axiom,
% 7.78/3.93 ! [X2: int > nat,Ya: int > nat,F: nat > num,G: nat > num] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_int_nat @ Ya @ top_top_set_int ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_nat_num_int @ F @ X2 )
% 7.78/3.93 = ( comp_nat_num_int @ G @ Ya ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1047_fun_Omap__cong,axiom,
% 7.78/3.93 ! [X2: int > int,Ya: int > int,F: int > nat,G: int > nat] :
% 7.78/3.93 ( ( X2 = Ya )
% 7.78/3.93 => ( ! [Z3: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_int_int @ Ya @ top_top_set_int ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_int_nat_int @ F @ X2 )
% 7.78/3.93 = ( comp_int_nat_int @ G @ Ya ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1048_fun_Omap__cong0,axiom,
% 7.78/3.93 ! [X2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.93 ( ! [Z3: code_integer > code_integer] :
% 7.78/3.93 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X2 @ top_to4645266643341252675nteger ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 7.78/3.93 = ( comp_C8797469213163452608nteger @ G @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1049_fun_Omap__cong0,axiom,
% 7.78/3.93 ! [X2: nat > $o,F: $o > $o,G: $o > $o] :
% 7.78/3.93 ( ! [Z3: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_o_o_nat @ F @ X2 )
% 7.78/3.93 = ( comp_o_o_nat @ G @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1050_fun_Omap__cong0,axiom,
% 7.78/3.93 ! [X2: nat > nat,F: nat > nat,G: nat > nat] :
% 7.78/3.93 ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ F @ X2 )
% 7.78/3.93 = ( comp_nat_nat_nat @ G @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1051_fun_Omap__cong0,axiom,
% 7.78/3.93 ! [X2: int > nat,F: nat > num,G: nat > num] :
% 7.78/3.93 ( ! [Z3: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_int_nat @ X2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_nat_num_int @ F @ X2 )
% 7.78/3.93 = ( comp_nat_num_int @ G @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1052_fun_Omap__cong0,axiom,
% 7.78/3.93 ! [X2: int > int,F: int > nat,G: int > nat] :
% 7.78/3.93 ( ! [Z3: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_int_int @ X2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( F @ Z3 )
% 7.78/3.93 = ( G @ Z3 ) ) )
% 7.78/3.93 => ( ( comp_int_nat_int @ F @ X2 )
% 7.78/3.93 = ( comp_int_nat_int @ G @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1053_fun_Oinj__map__strong,axiom,
% 7.78/3.93 ! [X2: code_integer > code_integer > code_integer,Xa2: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Fa: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.93 ( ! [Z3: code_integer > code_integer,Za: code_integer > code_integer] :
% 7.78/3.93 ( ( member2790140394383616496nteger @ Z3 @ ( image_2177946750938214461nteger @ X2 @ top_to4645266643341252675nteger ) )
% 7.78/3.93 => ( ( member2790140394383616496nteger @ Za @ ( image_2177946750938214461nteger @ Xa2 @ top_to4645266643341252675nteger ) )
% 7.78/3.93 => ( ( ( F @ Z3 )
% 7.78/3.93 = ( Fa @ Za ) )
% 7.78/3.93 => ( Z3 = Za ) ) ) )
% 7.78/3.93 => ( ( ( comp_C8797469213163452608nteger @ F @ X2 )
% 7.78/3.93 = ( comp_C8797469213163452608nteger @ Fa @ Xa2 ) )
% 7.78/3.93 => ( X2 = Xa2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1054_fun_Oinj__map__strong,axiom,
% 7.78/3.93 ! [X2: nat > $o,Xa2: nat > $o,F: $o > $o,Fa: $o > $o] :
% 7.78/3.93 ( ! [Z3: $o,Za: $o] :
% 7.78/3.93 ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( member_o @ Za @ ( image_nat_o @ Xa2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( ( F @ Z3 )
% 7.78/3.93 = ( Fa @ Za ) )
% 7.78/3.93 => ( Z3 = Za ) ) ) )
% 7.78/3.93 => ( ( ( comp_o_o_nat @ F @ X2 )
% 7.78/3.93 = ( comp_o_o_nat @ Fa @ Xa2 ) )
% 7.78/3.93 => ( X2 = Xa2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1055_fun_Oinj__map__strong,axiom,
% 7.78/3.93 ! [X2: nat > nat,Xa2: nat > nat,F: nat > nat,Fa: nat > nat] :
% 7.78/3.93 ( ! [Z3: nat,Za: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( member_nat @ Za @ ( image_nat_nat @ Xa2 @ top_top_set_nat ) )
% 7.78/3.93 => ( ( ( F @ Z3 )
% 7.78/3.93 = ( Fa @ Za ) )
% 7.78/3.93 => ( Z3 = Za ) ) ) )
% 7.78/3.93 => ( ( ( comp_nat_nat_nat @ F @ X2 )
% 7.78/3.93 = ( comp_nat_nat_nat @ Fa @ Xa2 ) )
% 7.78/3.93 => ( X2 = Xa2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1056_fun_Oinj__map__strong,axiom,
% 7.78/3.93 ! [X2: int > nat,Xa2: int > nat,F: nat > num,Fa: nat > num] :
% 7.78/3.93 ( ! [Z3: nat,Za: nat] :
% 7.78/3.93 ( ( member_nat @ Z3 @ ( image_int_nat @ X2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( member_nat @ Za @ ( image_int_nat @ Xa2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( ( F @ Z3 )
% 7.78/3.93 = ( Fa @ Za ) )
% 7.78/3.93 => ( Z3 = Za ) ) ) )
% 7.78/3.93 => ( ( ( comp_nat_num_int @ F @ X2 )
% 7.78/3.93 = ( comp_nat_num_int @ Fa @ Xa2 ) )
% 7.78/3.93 => ( X2 = Xa2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1057_fun_Oinj__map__strong,axiom,
% 7.78/3.93 ! [X2: int > int,Xa2: int > int,F: int > nat,Fa: int > nat] :
% 7.78/3.93 ( ! [Z3: int,Za: int] :
% 7.78/3.93 ( ( member_int @ Z3 @ ( image_int_int @ X2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( member_int @ Za @ ( image_int_int @ Xa2 @ top_top_set_int ) )
% 7.78/3.93 => ( ( ( F @ Z3 )
% 7.78/3.93 = ( Fa @ Za ) )
% 7.78/3.93 => ( Z3 = Za ) ) ) )
% 7.78/3.93 => ( ( ( comp_int_nat_int @ F @ X2 )
% 7.78/3.93 = ( comp_int_nat_int @ Fa @ Xa2 ) )
% 7.78/3.93 => ( X2 = Xa2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1058_surj__fun__eq,axiom,
% 7.78/3.93 ! [F: nat > $o,X5: set_nat,G1: $o > $o,G22: $o > $o] :
% 7.78/3.93 ( ( ( image_nat_o @ F @ X5 )
% 7.78/3.93 = top_top_set_o )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( member_nat @ X @ X5 )
% 7.78/3.93 => ( ( comp_o_o_nat @ G1 @ F @ X )
% 7.78/3.93 = ( comp_o_o_nat @ G22 @ F @ X ) ) )
% 7.78/3.93 => ( G1 = G22 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1059_surj__fun__eq,axiom,
% 7.78/3.93 ! [F: code_integer > code_integer > code_integer,X5: set_Code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G22: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.93 ( ( ( image_2177946750938214461nteger @ F @ X5 )
% 7.78/3.93 = top_to3804862627464599871nteger )
% 7.78/3.93 => ( ! [X: code_integer] :
% 7.78/3.93 ( ( member_Code_integer @ X @ X5 )
% 7.78/3.93 => ( ( comp_C8797469213163452608nteger @ G1 @ F @ X )
% 7.78/3.93 = ( comp_C8797469213163452608nteger @ G22 @ F @ X ) ) )
% 7.78/3.93 => ( G1 = G22 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1060_surj__fun__eq,axiom,
% 7.78/3.93 ! [F: nat > nat,X5: set_nat,G1: nat > nat,G22: nat > nat] :
% 7.78/3.93 ( ( ( image_nat_nat @ F @ X5 )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( member_nat @ X @ X5 )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ G1 @ F @ X )
% 7.78/3.93 = ( comp_nat_nat_nat @ G22 @ F @ X ) ) )
% 7.78/3.93 => ( G1 = G22 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1061_surj__fun__eq,axiom,
% 7.78/3.93 ! [F: int > nat,X5: set_int,G1: nat > num,G22: nat > num] :
% 7.78/3.93 ( ( ( image_int_nat @ F @ X5 )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( member_int @ X @ X5 )
% 7.78/3.93 => ( ( comp_nat_num_int @ G1 @ F @ X )
% 7.78/3.93 = ( comp_nat_num_int @ G22 @ F @ X ) ) )
% 7.78/3.93 => ( G1 = G22 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1062_surj__fun__eq,axiom,
% 7.78/3.93 ! [F: int > int,X5: set_int,G1: int > nat,G22: int > nat] :
% 7.78/3.93 ( ( ( image_int_int @ F @ X5 )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( member_int @ X @ X5 )
% 7.78/3.93 => ( ( comp_int_nat_int @ G1 @ F @ X )
% 7.78/3.93 = ( comp_int_nat_int @ G22 @ F @ X ) ) )
% 7.78/3.93 => ( G1 = G22 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1063_comp__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > char] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_char @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_char_char @ ( comp_char_char_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1064_comp__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > rat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_rat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_char_rat @ ( comp_char_rat_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1065_comp__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > nat] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_nat @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( image_char_nat @ ( comp_char_nat_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1066_comp__surj,axiom,
% 7.78/3.93 ! [F: char > char,G: char > int] :
% 7.78/3.93 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( ( image_char_int @ G @ top_top_set_char )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ( image_char_int @ ( comp_char_int_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_int ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1067_comp__surj,axiom,
% 7.78/3.93 ! [F: char > rat,G: rat > char] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( ( image_rat_char @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_char_char @ ( comp_rat_char_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1068_comp__surj,axiom,
% 7.78/3.93 ! [F: char > rat,G: rat > rat] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( ( image_rat_rat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_char_rat @ ( comp_rat_rat_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1069_comp__surj,axiom,
% 7.78/3.93 ! [F: char > rat,G: rat > nat] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( ( image_rat_nat @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( image_char_nat @ ( comp_rat_nat_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1070_comp__surj,axiom,
% 7.78/3.93 ! [F: char > rat,G: rat > int] :
% 7.78/3.93 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( ( image_rat_int @ G @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ( image_char_int @ ( comp_rat_int_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_int ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1071_comp__surj,axiom,
% 7.78/3.93 ! [F: char > nat,G: nat > char] :
% 7.78/3.93 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( ( image_nat_char @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_char )
% 7.78/3.93 => ( ( image_char_char @ ( comp_nat_char_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1072_comp__surj,axiom,
% 7.78/3.93 ! [F: char > nat,G: nat > rat] :
% 7.78/3.93 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ( ( image_nat_rat @ G @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ( image_char_rat @ ( comp_nat_rat_char @ G @ F ) @ top_top_set_char )
% 7.78/3.93 = top_top_set_rat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1073_apsnd__def,axiom,
% 7.78/3.93 ( produc6499014454317279255nteger
% 7.78/3.93 = ( produc1802105962441033582nteger @ id_Code_integer ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1074_rel__fun__image2p,axiom,
% 7.78/3.93 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > nat,G: int > nat] : ( bNF_re4555766996558763186at_nat @ R3 @ ( bNF_Gr6955563364113978072nt_nat @ F @ G @ R3 ) @ F @ G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1075_rel__fun__image2p,axiom,
% 7.78/3.93 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,G: int > int > int] : ( bNF_re7408651293131936558nt_int @ R3 @ ( bNF_Gr1354378531936274772nt_int @ F @ G @ R3 ) @ F @ G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1076_rel__fun__image2p,axiom,
% 7.78/3.93 ! [R3: product_prod_nat_nat > int > $o,F: product_prod_nat_nat > product_prod_nat_nat > $o,G: int > int > $o] : ( bNF_re717283939379294677_int_o @ R3 @ ( bNF_Gr364077372107685167_int_o @ F @ G @ R3 ) @ F @ G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1077_rel__fun__image2p,axiom,
% 7.78/3.93 ! [R3: int > code_integer > $o,F: int > num,G: code_integer > num] : ( bNF_re6718328864250387230um_num @ R3 @ ( bNF_Gr166583433173494904er_num @ F @ G @ R3 ) @ F @ G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1078_rel__fun__image2p,axiom,
% 7.78/3.93 ! [R3: int > int > $o,F: int > num,G: int > num] : ( bNF_re7626690874201225453um_num @ R3 @ ( bNF_Gr7020624548710275655nt_num @ F @ G @ R3 ) @ F @ G ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1079_comp__fun__idem__on_Ocomp__comp__fun__idem__on,axiom,
% 7.78/3.93 ! [S5: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,R3: set_Code_integer] :
% 7.78/3.93 ( ( finite954763878425697269nteger @ S5 @ F )
% 7.78/3.93 => ( ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ G @ top_to4645266643341252675nteger ) @ S5 )
% 7.78/3.93 => ( finite917065715488314481nteger @ R3 @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1080_comp__fun__commute__on_Ocomp__comp__fun__commute__on,axiom,
% 7.78/3.93 ! [S5: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,R3: set_Code_integer] :
% 7.78/3.93 ( ( finite6756937295472016048nteger @ S5 @ F )
% 7.78/3.93 => ( ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ G @ top_to4645266643341252675nteger ) @ S5 )
% 7.78/3.93 => ( finite366418920864469932nteger @ R3 @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1081_image__Pow__mono,axiom,
% 7.78/3.93 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.93 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le513522071413781156et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_rat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1082_image__Pow__mono,axiom,
% 7.78/3.93 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_nat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1083_image__Pow__mono,axiom,
% 7.78/3.93 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) ) @ ( pow_int @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1084_image__Pow__mono,axiom,
% 7.78/3.93 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) ) @ ( pow_nat @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1085_image__Pow__mono,axiom,
% 7.78/3.93 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.93 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) ) @ ( pow_int @ B5 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1086_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi7262943168399475603_int_o
% 7.78/3.93 = ( ^ [F2: char > int,G3: code_integer > int,P4: int > int > $o] : ( relcom5819909836510906509nteger @ ( bNF_Grp_char_int @ top_top_set_char @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1087_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi508398028314858188_int_o
% 7.78/3.93 = ( ^ [F2: rat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom3409376902655092628nteger @ ( bNF_Grp_rat_int @ top_top_set_rat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1088_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi7331807916455492308_int_o
% 7.78/3.93 = ( ^ [F2: nat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom3277315637376110988nteger @ ( bNF_Grp_nat_int @ top_top_set_nat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1089_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi2125572119366604152_int_o
% 7.78/3.93 = ( ^ [F2: int > int,G3: code_integer > int,P4: int > int > $o] : ( relcom967497705283160040nteger @ ( bNF_Grp_int_int @ top_top_set_int @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1090_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi467646977814820164_int_o
% 7.78/3.93 = ( ^ [F2: list_nat > int,G3: code_integer > int,P4: int > int > $o] : ( relcom7887202796854296604nteger @ ( bNF_Grp_list_nat_int @ top_top_set_list_nat @ F2 ) @ ( relcom967497705283160040nteger @ P4 @ ( conver1462408618118490240er_int @ ( bNF_Gr6045950513751025625er_int @ top_to4645266643341252675nteger @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1091_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi728936465572800120_nat_o
% 7.78/3.93 = ( ^ [F2: char > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom7879471502873553579at_int @ ( bNF_Gr8982933507515605408at_nat @ top_top_set_char @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1092_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi2997284877290766385_nat_o
% 7.78/3.93 = ( ^ [F2: rat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom1211213461163567844at_int @ ( bNF_Gr6883301533820405721at_nat @ top_top_set_rat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1093_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi190728152058600505_nat_o
% 7.78/3.93 = ( ^ [F2: nat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom8569543703982574316at_int @ ( bNF_Gr3553472063123884001at_nat @ top_top_set_nat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1094_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi1204582724742824157_nat_o
% 7.78/3.93 = ( ^ [F2: int > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom1106208330880909712at_int @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1095_vimage2p__Grp,axiom,
% 7.78/3.93 ( bNF_vi5202502398764838569_nat_o
% 7.78/3.93 = ( ^ [F2: list_nat > product_prod_nat_nat,G3: int > product_prod_nat_nat,P4: product_prod_nat_nat > product_prod_nat_nat > $o] : ( relcom170568170053003356at_int @ ( bNF_Gr4119388860389678161at_nat @ top_top_set_list_nat @ F2 ) @ ( relcom8911704206367525917at_int @ P4 @ ( conver1866313717161370910at_nat @ ( bNF_Gr6591314147588017797at_nat @ top_top_set_int @ G3 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1096_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,A: char > nat,B: char > nat] :
% 7.78/3.93 ( ( bNF_re3734335887435638179at_nat
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: char > product_prod_nat_nat] :
% 7.78/3.93 ( ( member3295615932019376976at_nat @ Z4
% 7.78/3.93 @ ( collec1683818095804863890at_nat
% 7.78/3.93 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P1491501995297412481t_char @ product_fst_nat_nat @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P1491501995297412481t_char @ product_snd_nat_nat @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1097_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,A: rat > nat,B: rat > nat] :
% 7.78/3.93 ( ( bNF_re6557955094579809201at_nat
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: rat > product_prod_nat_nat] :
% 7.78/3.93 ( ( member849810989832120969at_nat @ Z4
% 7.78/3.93 @ ( collec2824469931397938891at_nat
% 7.78/3.93 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P1320480151300532104at_rat @ product_fst_nat_nat @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P1320480151300532104at_rat @ product_snd_nat_nat @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1098_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,A: nat > nat,B: nat > nat] :
% 7.78/3.93 ( ( bNF_re5653821019739307937at_nat
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: nat > product_prod_nat_nat] :
% 7.78/3.93 ( ( member6743353555990375057at_nat @ Z4
% 7.78/3.93 @ ( collec8718012497556192979at_nat
% 7.78/3.93 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1099_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,A: int > nat,B: int > nat] :
% 7.78/3.93 ( ( bNF_re3715656647883201625at_nat
% 7.78/3.93 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: int > product_prod_nat_nat] :
% 7.78/3.93 ( ( member557823603599733045at_nat @ Z4
% 7.78/3.93 @ ( collec2532482545165550967at_nat
% 7.78/3.93 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P1953119740877977564at_int @ product_fst_nat_nat @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P1953119740877977564at_int @ product_snd_nat_nat @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1100_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: num > num > $o,A: int > num,B: int > num] :
% 7.78/3.93 ( ( bNF_re7626690874201225453um_num
% 7.78/3.93 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: int > product_prod_num_num] :
% 7.78/3.93 ( ( member7514810323860029129um_num @ Z4
% 7.78/3.93 @ ( collec266097228571071243um_num
% 7.78/3.93 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P4305060815297604026um_int @ product_fst_num_num @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P4305060815297604026um_int @ product_snd_num_num @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1101_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: int > int > $o,A: char > int,B: char > int] :
% 7.78/3.93 ( ( bNF_re4731199128827642459nt_int
% 7.78/3.93 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: char > product_prod_int_int] :
% 7.78/3.93 ( ( member2992454361780672008nt_int @ Z4
% 7.78/3.93 @ ( collec1380656525566158922nt_int
% 7.78/3.93 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P4161745170962941589t_char @ product_fst_int_int @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P4161745170962941589t_char @ product_snd_int_int @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1102_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: int > int > $o,A: rat > int,B: rat > int] :
% 7.78/3.93 ( ( bNF_re7554818335971813481nt_int
% 7.78/3.93 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: rat > product_prod_int_int] :
% 7.78/3.93 ( ( member546649419593416001nt_int @ Z4
% 7.78/3.93 @ ( collec2521308361159233923nt_int
% 7.78/3.93 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P6018825582104210588nt_rat @ product_fst_int_int @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P6018825582104210588nt_rat @ product_snd_int_int @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1103_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: int > int > $o,A: nat > int,B: nat > int] :
% 7.78/3.93 ( ( bNF_re6650684261131312217nt_int
% 7.78/3.93 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: nat > product_prod_int_int] :
% 7.78/3.93 ( ( member6440191985751670089nt_int @ Z4
% 7.78/3.93 @ ( collec8414850927317488011nt_int
% 7.78/3.93 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P6653955642190706324nt_nat @ product_fst_int_int @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P6653955642190706324nt_nat @ product_snd_int_int @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1104_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: int > int > $o,A: int > int,B: int > int] :
% 7.78/3.93 ( ( bNF_re4712519889275205905nt_int
% 7.78/3.93 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: int > product_prod_int_int] :
% 7.78/3.93 ( ( member254662033361028077nt_int @ Z4
% 7.78/3.93 @ ( collec2229320974926845999nt_int
% 7.78/3.93 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P6651465171681656048nt_int @ product_fst_int_int @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P6651465171681656048nt_int @ product_snd_int_int @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1105_fun_Oin__rel,axiom,
% 7.78/3.93 ! [R3: nat > nat > $o,A: list_nat > nat,B: list_nat > nat] :
% 7.78/3.93 ( ( bNF_re4629543205785817921at_nat
% 7.78/3.93 @ ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z )
% 7.78/3.93 @ R3
% 7.78/3.93 @ A
% 7.78/3.93 @ B )
% 7.78/3.93 = ( ? [Z4: list_nat > product_prod_nat_nat] :
% 7.78/3.93 ( ( member3963856813518191233at_nat @ Z4
% 7.78/3.93 @ ( collec3092956710985254339at_nat
% 7.78/3.93 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) )
% 7.78/3.93 & ( ( comp_P5292260908303971472st_nat @ product_fst_nat_nat @ Z4 )
% 7.78/3.93 = A )
% 7.78/3.93 & ( ( comp_P5292260908303971472st_nat @ product_snd_nat_nat @ Z4 )
% 7.78/3.93 = B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1106_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: $o > $o] :
% 7.78/3.93 ( ( F = id_o )
% 7.78/3.93 => ( ( relcompp_o_o_o @ ( conversep_o_o @ ( bNF_Grp_o_o @ top_top_set_o @ F ) ) @ ( bNF_Grp_o_o @ top_top_set_o @ F ) )
% 7.78/3.93 = ( bNF_Grp_o_o @ top_top_set_o @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1107_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: num > num] :
% 7.78/3.93 ( ( F = id_num )
% 7.78/3.93 => ( ( relcompp_num_num_num @ ( conversep_num_num @ ( bNF_Grp_num_num @ top_top_set_num @ F ) ) @ ( bNF_Grp_num_num @ top_top_set_num @ F ) )
% 7.78/3.93 = ( bNF_Grp_num_num @ top_top_set_num @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1108_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: char > char] :
% 7.78/3.93 ( ( F = id_char )
% 7.78/3.93 => ( ( relcom5872928454965100966r_char @ ( conversep_char_char @ ( bNF_Grp_char_char @ top_top_set_char @ F ) ) @ ( bNF_Grp_char_char @ top_top_set_char @ F ) )
% 7.78/3.93 = ( bNF_Grp_char_char @ top_top_set_char @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1109_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: list_nat > list_nat] :
% 7.78/3.93 ( ( F = id_list_nat )
% 7.78/3.93 => ( ( relcom8030397737370142931st_nat @ ( conver909888920752868663st_nat @ ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) ) @ ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) )
% 7.78/3.93 = ( bNF_Gr600725020315365264st_nat @ top_top_set_list_nat @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1110_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: rat > rat] :
% 7.78/3.93 ( ( F = id_rat )
% 7.78/3.93 => ( ( relcompp_rat_rat_rat @ ( conversep_rat_rat @ ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) ) @ ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) )
% 7.78/3.93 = ( bNF_Grp_rat_rat @ top_top_set_rat @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1111_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: nat > nat] :
% 7.78/3.93 ( ( F = id_nat )
% 7.78/3.93 => ( ( relcompp_nat_nat_nat @ ( conversep_nat_nat @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) )
% 7.78/3.93 = ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1112_Grp__UNIV__id,axiom,
% 7.78/3.93 ! [F: int > int] :
% 7.78/3.93 ( ( F = id_int )
% 7.78/3.93 => ( ( relcompp_int_int_int @ ( conversep_int_int @ ( bNF_Grp_int_int @ top_top_set_int @ F ) ) @ ( bNF_Grp_int_int @ top_top_set_int @ F ) )
% 7.78/3.93 = ( bNF_Grp_int_int @ top_top_set_int @ F ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1113_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: rat > rat,G: rat > rat] :
% 7.78/3.93 ( ( order_4774338944571509483at_rat @ F )
% 7.78/3.93 => ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_4774338944571509483at_rat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1114_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: rat > nat,G: nat > rat] :
% 7.78/3.93 ( ( order_5409469004658005219at_nat @ F )
% 7.78/3.93 => ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_5090893588506375395at_rat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1115_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: rat > int,G: int > rat] :
% 7.78/3.93 ( ( order_5406978534148954943at_int @ F )
% 7.78/3.93 => ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ! [X: rat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_6090247300407429951nt_rat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1116_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: nat > rat,G: rat > nat] :
% 7.78/3.93 ( ( order_5090893588506375395at_rat @ F )
% 7.78/3.93 => ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_5409469004658005219at_nat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1117_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: nat > nat,G: nat > nat] :
% 7.78/3.93 ( ( order_5726023648592871131at_nat @ F )
% 7.78/3.93 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_5726023648592871131at_nat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1118_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: nat > int,G: int > nat] :
% 7.78/3.93 ( ( order_5723533178083820855at_int @ F )
% 7.78/3.93 => ( ( ( image_nat_int @ F @ top_top_set_nat )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_6725377360493925687nt_nat @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1119_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: int > rat,G: rat > int] :
% 7.78/3.93 ( ( order_6090247300407429951nt_rat @ F )
% 7.78/3.93 => ( ( ( image_int_rat @ F @ top_top_set_int )
% 7.78/3.93 = top_top_set_rat )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_5406978534148954943at_int @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1120_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: int > nat,G: nat > int] :
% 7.78/3.93 ( ( order_6725377360493925687nt_nat @ F )
% 7.78/3.93 => ( ( ( image_int_nat @ F @ top_top_set_int )
% 7.78/3.93 = top_top_set_nat )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_5723533178083820855at_int @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1121_strict__mono__inv,axiom,
% 7.78/3.93 ! [F: int > int,G: int > int] :
% 7.78/3.93 ( ( order_6722886889984875411nt_int @ F )
% 7.78/3.93 => ( ( ( image_int_int @ F @ top_top_set_int )
% 7.78/3.93 = top_top_set_int )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( G @ ( F @ X ) )
% 7.78/3.93 = X )
% 7.78/3.93 => ( order_6722886889984875411nt_int @ G ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1122_Id__on__Gr,axiom,
% 7.78/3.93 ( id_on_nat
% 7.78/3.93 = ( ^ [A6: set_nat] : ( bNF_Gr_nat_nat @ A6 @ id_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1123_Id__on__Gr,axiom,
% 7.78/3.93 ( id_on_o
% 7.78/3.93 = ( ^ [A6: set_o] : ( bNF_Gr_o_o @ A6 @ id_o ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1124_Id__on__Gr,axiom,
% 7.78/3.93 ( id_on_num
% 7.78/3.93 = ( ^ [A6: set_num] : ( bNF_Gr_num_num @ A6 @ id_num ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1125_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: nat > $o,Abs: $o > nat,M: $o > $o] :
% 7.78/3.93 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.93 => ( ( M = id_o )
% 7.78/3.93 => ( ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1126_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: $o > $o,Abs: $o > $o,M: $o > $o] :
% 7.78/3.93 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.93 => ( ( M = id_o )
% 7.78/3.93 => ( ( comp_o_o_o @ ( comp_o_o_o @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_o ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1127_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: num > $o,Abs: $o > num,M: $o > $o] :
% 7.78/3.93 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.93 => ( ( M = id_o )
% 7.78/3.93 => ( ( comp_o_num_num @ ( comp_o_num_o @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_num ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1128_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: nat > num,Abs: num > nat,M: num > num] :
% 7.78/3.93 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.93 => ( ( M = id_num )
% 7.78/3.93 => ( ( comp_num_nat_nat @ ( comp_num_nat_num @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1129_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: $o > num,Abs: num > $o,M: num > num] :
% 7.78/3.93 ( ( type_d3678713432601627782_o_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.93 => ( ( M = id_num )
% 7.78/3.93 => ( ( comp_num_o_o @ ( comp_num_o_num @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_o ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1130_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: num > num,Abs: num > num,M: num > num] :
% 7.78/3.93 ( ( type_d938156138240996706um_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.93 => ( ( M = id_num )
% 7.78/3.93 => ( ( comp_num_num_num @ ( comp_num_num_num @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_num ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1131_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: nat > char,Abs: char > nat,M: char > char] :
% 7.78/3.93 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( M = id_char )
% 7.78/3.93 => ( ( comp_char_nat_nat @ ( comp_char_nat_char @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1132_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: $o > char,Abs: char > $o,M: char > char] :
% 7.78/3.93 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( M = id_char )
% 7.78/3.93 => ( ( comp_char_o_o @ ( comp_char_o_char @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_o ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1133_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: num > char,Abs: char > num,M: char > char] :
% 7.78/3.93 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( M = id_char )
% 7.78/3.93 => ( ( comp_char_num_num @ ( comp_char_num_char @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_num ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1134_type__copy__map__id0,axiom,
% 7.78/3.93 ! [Rep: nat > rat,Abs: rat > nat,M: rat > rat] :
% 7.78/3.93 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.93 => ( ( M = id_rat )
% 7.78/3.93 => ( ( comp_rat_nat_nat @ ( comp_rat_nat_rat @ Abs @ M ) @ Rep )
% 7.78/3.93 = id_nat ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1135_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: nat > char,Abs: char > nat] :
% 7.78/3.93 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( comp_char_nat_nat @ Abs @ Rep )
% 7.78/3.93 = id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1136_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: $o > char,Abs: char > $o] :
% 7.78/3.93 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( comp_char_o_o @ Abs @ Rep )
% 7.78/3.93 = id_o ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1137_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: num > char,Abs: char > num] :
% 7.78/3.93 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.93 => ( ( comp_char_num_num @ Abs @ Rep )
% 7.78/3.93 = id_num ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1138_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: nat > rat,Abs: rat > nat] :
% 7.78/3.93 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.93 => ( ( comp_rat_nat_nat @ Abs @ Rep )
% 7.78/3.93 = id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1139_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: $o > rat,Abs: rat > $o] :
% 7.78/3.93 ( ( type_d6486251586359353412_o_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.93 => ( ( comp_rat_o_o @ Abs @ Rep )
% 7.78/3.93 = id_o ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1140_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: num > rat,Abs: rat > num] :
% 7.78/3.93 ( ( type_d3745694291998722336um_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.93 => ( ( comp_rat_num_num @ Abs @ Rep )
% 7.78/3.93 = id_num ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1141_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: $o > nat,Abs: nat > $o] :
% 7.78/3.93 ( ( type_d7121381646445849148_o_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.93 => ( ( comp_nat_o_o @ Abs @ Rep )
% 7.78/3.93 = id_o ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1142_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: num > nat,Abs: nat > num] :
% 7.78/3.93 ( ( type_d4380824352085218072um_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.93 => ( ( comp_nat_num_num @ Abs @ Rep )
% 7.78/3.93 = id_num ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1143_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: nat > nat,Abs: nat > nat] :
% 7.78/3.93 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ Abs @ Rep )
% 7.78/3.93 = id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1144_type__copy__Abs__o__Rep,axiom,
% 7.78/3.93 ! [Rep: nat > int,Abs: int > nat] :
% 7.78/3.93 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ top_top_set_int )
% 7.78/3.93 => ( ( comp_int_nat_nat @ Abs @ Rep )
% 7.78/3.93 = id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1145_type__copy__Rep__o__Abs,axiom,
% 7.78/3.93 ! [Rep: nat > nat,Abs: nat > nat] :
% 7.78/3.93 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.93 => ( ( comp_nat_nat_nat @ Rep @ Abs )
% 7.78/3.93 = id_nat ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1146_type__copy__Rep__o__Abs,axiom,
% 7.78/3.93 ! [Rep: product_unit > $o,Abs: $o > product_unit] :
% 7.78/3.93 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.93 => ( ( comp_P5156358013004227690it_o_o @ Rep @ Abs )
% 7.78/3.93 = id_o ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1147_case__prodI2_H,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 7.78/3.93 ( ! [A3: nat,B3: nat] :
% 7.78/3.93 ( ( ( product_Pair_nat_nat @ A3 @ B3 )
% 7.78/3.93 = P )
% 7.78/3.93 => ( C @ A3 @ B3 @ X2 ) )
% 7.78/3.93 => ( produc8739625826339149834_nat_o @ C @ P @ X2 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1148_image__ident,axiom,
% 7.78/3.93 ! [Y4: set_nat] :
% 7.78/3.93 ( ( image_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : X4
% 7.78/3.93 @ Y4 )
% 7.78/3.93 = Y4 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1149_image__ident,axiom,
% 7.78/3.93 ! [Y4: set_int] :
% 7.78/3.93 ( ( image_int_int
% 7.78/3.93 @ ^ [X4: int] : X4
% 7.78/3.93 @ Y4 )
% 7.78/3.93 = Y4 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1150_split__part,axiom,
% 7.78/3.93 ! [P2: $o,Q2: int > int > $o] :
% 7.78/3.93 ( ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [A5: int,B4: int] :
% 7.78/3.93 ( P2
% 7.78/3.93 & ( Q2 @ A5 @ B4 ) ) )
% 7.78/3.93 = ( ^ [Ab: product_prod_int_int] :
% 7.78/3.93 ( P2
% 7.78/3.93 & ( produc4947309494688390418_int_o @ Q2 @ Ab ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1151_Id__onI,axiom,
% 7.78/3.93 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.93 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ ( id_on_7869290023980668164at_nat @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1152_Id__onI,axiom,
% 7.78/3.93 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.93 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ ( id_on_2554058798563519774at_nat @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1153_Id__onI,axiom,
% 7.78/3.93 ! [A: $o,A4: set_o] :
% 7.78/3.93 ( ( member_o @ A @ A4 )
% 7.78/3.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ ( id_on_o @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1154_Id__onI,axiom,
% 7.78/3.93 ! [A: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 7.78/3.93 ( ( member6273874620674182256at_nat @ A @ A4 )
% 7.78/3.93 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ ( id_on_3275838214495744996at_nat @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1155_Id__onI,axiom,
% 7.78/3.93 ! [A: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 7.78/3.93 ( ( member2643936169264416010at_nat @ A @ A4 )
% 7.78/3.93 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ ( id_on_6713504163309144702at_nat @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1156_Id__onI,axiom,
% 7.78/3.93 ! [A: nat,A4: set_nat] :
% 7.78/3.93 ( ( member_nat @ A @ A4 )
% 7.78/3.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1157_Id__onI,axiom,
% 7.78/3.93 ! [A: int,A4: set_int] :
% 7.78/3.93 ( ( member_int @ A @ A4 )
% 7.78/3.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1158_case__prod__conv,axiom,
% 7.78/3.93 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 7.78/3.93 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.93 = ( F @ A @ B ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1159_case__prod__conv,axiom,
% 7.78/3.93 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 7.78/3.93 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.93 = ( F @ A @ B ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1160_case__prod__conv,axiom,
% 7.78/3.93 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 7.78/3.93 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.93 = ( F @ A @ B ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1161_case__prod__conv,axiom,
% 7.78/3.93 ! [F: int > int > $o,A: int,B: int] :
% 7.78/3.93 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.93 = ( F @ A @ B ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1162_case__prod__conv,axiom,
% 7.78/3.93 ! [F: int > int > int,A: int,B: int] :
% 7.78/3.93 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.93 = ( F @ A @ B ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1163_case__prodI,axiom,
% 7.78/3.93 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( F @ A @ B )
% 7.78/3.93 => ( produc9020218426428501292_nat_o @ F @ ( produc9060074326276436823at_nat @ A @ B ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1164_case__prodI,axiom,
% 7.78/3.93 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( F @ A @ B )
% 7.78/3.93 => ( produc410239310623530412_nat_o @ F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1165_case__prodI,axiom,
% 7.78/3.93 ! [F: nat > num > $o,A: nat,B: num] :
% 7.78/3.93 ( ( F @ A @ B )
% 7.78/3.93 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1166_case__prodI,axiom,
% 7.78/3.93 ! [F: nat > nat > $o,A: nat,B: nat] :
% 7.78/3.93 ( ( F @ A @ B )
% 7.78/3.93 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1167_case__prodI,axiom,
% 7.78/3.93 ! [F: int > int > $o,A: int,B: int] :
% 7.78/3.93 ( ( F @ A @ B )
% 7.78/3.93 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1168_case__prodI2,axiom,
% 7.78/3.93 ! [P: produc1319942482725812455at_nat,C: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o] :
% 7.78/3.93 ( ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( produc9060074326276436823at_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( C @ A3 @ B3 ) )
% 7.78/3.93 => ( produc9020218426428501292_nat_o @ C @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1169_case__prodI2,axiom,
% 7.78/3.93 ! [P: produc3843707927480180839at_nat,C: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.93 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( C @ A3 @ B3 ) )
% 7.78/3.93 => ( produc410239310623530412_nat_o @ C @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1170_case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num,C: nat > num > $o] :
% 7.78/3.93 ( ! [A3: nat,B3: num] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.93 => ( C @ A3 @ B3 ) )
% 7.78/3.93 => ( produc4927758841916487424_num_o @ C @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1171_case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat,C: nat > nat > $o] :
% 7.78/3.93 ( ! [A3: nat,B3: nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( C @ A3 @ B3 ) )
% 7.78/3.93 => ( produc6081775807080527818_nat_o @ C @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1172_case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_int_int,C: int > int > $o] :
% 7.78/3.93 ( ! [A3: int,B3: int] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_int_int @ A3 @ B3 ) )
% 7.78/3.93 => ( C @ A3 @ B3 ) )
% 7.78/3.93 => ( produc4947309494688390418_int_o @ C @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1173_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: $o,C: nat > num > set_o,A: nat,B: num] :
% 7.78/3.93 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1174_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: nat,C: nat > num > set_nat,A: nat,B: num] :
% 7.78/3.93 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1175_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: int,C: nat > num > set_int,A: nat,B: num] :
% 7.78/3.93 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1176_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: $o,C: nat > nat > set_o,A: nat,B: nat] :
% 7.78/3.93 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1177_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: nat,C: nat > nat > set_nat,A: nat,B: nat] :
% 7.78/3.93 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1178_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: int,C: nat > nat > set_int,A: nat,B: nat] :
% 7.78/3.93 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ ( product_Pair_nat_nat @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1179_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: $o,C: int > int > set_o,A: int,B: int] :
% 7.78/3.93 ( ( member_o @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1180_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: nat,C: int > int > set_nat,A: int,B: int] :
% 7.78/3.93 ( ( member_nat @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1181_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: int,C: int > int > set_int,A: int,B: int] :
% 7.78/3.93 ( ( member_int @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1182_mem__case__prodI,axiom,
% 7.78/3.93 ! [Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat,A: nat,B: num] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ Z2 @ ( C @ A @ B ) )
% 7.78/3.93 => ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1183_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num,Z2: $o,C: nat > num > set_o] :
% 7.78/3.93 ( ! [A3: nat,B3: num] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc836176033315069408_set_o @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1184_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num,Z2: nat,C: nat > num > set_nat] :
% 7.78/3.93 ( ! [A3: nat,B3: num] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc4130284055270567454et_nat @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1185_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num,Z2: int,C: nat > num > set_int] :
% 7.78/3.93 ( ! [A3: nat,B3: num] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc9175805072616146554et_int @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1186_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat,Z2: $o,C: nat > nat > set_o] :
% 7.78/3.93 ( ! [A3: nat,B3: nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc59986286002894506_set_o @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1187_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat,Z2: nat,C: nat > nat > set_nat] :
% 7.78/3.93 ( ! [A3: nat,B3: nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc6189476227299908564et_nat @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1188_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat,Z2: int,C: nat > nat > set_int] :
% 7.78/3.93 ( ! [A3: nat,B3: nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc2011625207790711856et_int @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1189_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_int_int,Z2: $o,C: int > int > set_o] :
% 7.78/3.93 ( ! [A3: int,B3: int] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_int_int @ A3 @ B3 ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_o @ Z2 @ ( produc4257766111578684402_set_o @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1190_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_int_int,Z2: nat,C: int > int > set_nat] :
% 7.78/3.93 ( ! [A3: int,B3: int] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_int_int @ A3 @ B3 ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_nat @ Z2 @ ( produc4251311855443802252et_nat @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1191_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_int_int,Z2: int,C: int > int > set_int] :
% 7.78/3.93 ( ! [A3: int,B3: int] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_int_int @ A3 @ B3 ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member_int @ Z2 @ ( produc73460835934605544et_int @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1192_mem__case__prodI2,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num,Z2: product_prod_nat_nat,C: nat > num > set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ! [A3: nat,B3: num] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 7.78/3.93 => ( member8440522571783428010at_nat @ Z2 @ ( C @ A3 @ B3 ) ) )
% 7.78/3.93 => ( member8440522571783428010at_nat @ Z2 @ ( produc859037500352796105at_nat @ C @ P ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1193_case__swap,axiom,
% 7.78/3.93 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P: product_prod_nat_nat] :
% 7.78/3.93 ( ( produc27273713700761075at_nat
% 7.78/3.93 @ ^ [Y5: nat,X4: nat] : ( F @ X4 @ Y5 )
% 7.78/3.93 @ ( product_swap_nat_nat @ P ) )
% 7.78/3.93 = ( produc27273713700761075at_nat @ F @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1194_case__swap,axiom,
% 7.78/3.93 ! [F: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 7.78/3.93 ( ( produc8739625826339149834_nat_o
% 7.78/3.93 @ ^ [Y5: nat,X4: nat] : ( F @ X4 @ Y5 )
% 7.78/3.93 @ ( product_swap_nat_nat @ P ) )
% 7.78/3.93 = ( produc8739625826339149834_nat_o @ F @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1195_case__swap,axiom,
% 7.78/3.93 ! [F: int > int > product_prod_int_int,P: product_prod_int_int] :
% 7.78/3.93 ( ( produc4245557441103728435nt_int
% 7.78/3.93 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 7.78/3.93 @ ( product_swap_int_int @ P ) )
% 7.78/3.93 = ( produc4245557441103728435nt_int @ F @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1196_case__swap,axiom,
% 7.78/3.93 ! [F: int > int > $o,P: product_prod_int_int] :
% 7.78/3.93 ( ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 7.78/3.93 @ ( product_swap_int_int @ P ) )
% 7.78/3.93 = ( produc4947309494688390418_int_o @ F @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1197_case__swap,axiom,
% 7.78/3.93 ! [F: int > int > int,P: product_prod_int_int] :
% 7.78/3.93 ( ( produc8211389475949308722nt_int
% 7.78/3.93 @ ^ [Y5: int,X4: int] : ( F @ X4 @ Y5 )
% 7.78/3.93 @ ( product_swap_int_int @ P ) )
% 7.78/3.93 = ( produc8211389475949308722nt_int @ F @ P ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1198_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > $o] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_o @ ( F @ A @ B ) @ ( image_4451812852358507538_num_o @ ( produc4927758841916487424_num_o @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1199_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > nat] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_nat @ ( F @ A @ B ) @ ( image_4504471508743443926um_nat @ ( produc4973203077627929192um_nat @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1200_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > int] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_int @ ( F @ A @ B ) @ ( image_4501981038234393650um_int @ ( produc4970712607118878916um_int @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1201_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > $o] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_o @ ( F @ A @ B ) @ ( image_3693632289388996572_nat_o @ ( produc6081775807080527818_nat_o @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1202_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_nat @ ( F @ A @ B ) @ ( image_2486076414777270412at_nat @ ( produc6842872674320459806at_nat @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1203_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: nat,A4: set_Pr1261947904930325089at_nat,F: nat > nat > int] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_int @ ( F @ A @ B ) @ ( image_2483585944268220136at_int @ ( produc6840382203811409530at_int @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1204_pair__imageI,axiom,
% 7.78/3.93 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > nat] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_nat @ ( F @ A @ B ) @ ( image_5044651549707136836nt_nat @ ( produc8213879946458358998nt_nat @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1205_pair__imageI,axiom,
% 7.78/3.93 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > $o] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_o @ ( F @ A @ B ) @ ( image_2135063354759101220_int_o @ ( produc4947309494688390418_int_o @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1206_pair__imageI,axiom,
% 7.78/3.93 ! [A: int,B: int,A4: set_Pr958786334691620121nt_int,F: int > int > int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A4 )
% 7.78/3.93 => ( member_int @ ( F @ A @ B ) @ ( image_5042161079198086560nt_int @ ( produc8211389475949308722nt_int @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1207_pair__imageI,axiom,
% 7.78/3.93 ! [A: nat,B: num,A4: set_Pr6200539531224447659at_num,F: nat > num > product_prod_nat_nat] :
% 7.78/3.93 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ A4 )
% 7.78/3.93 => ( member8440522571783428010at_nat @ ( F @ A @ B ) @ ( image_4217639968629731195at_nat @ ( produc8564434177180591209at_nat @ F ) @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1208_Inf_OINF__identity__eq,axiom,
% 7.78/3.93 ! [Inf: set_nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( Inf
% 7.78/3.93 @ ( image_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : X4
% 7.78/3.93 @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1209_Inf_OINF__identity__eq,axiom,
% 7.78/3.93 ! [Inf: set_int > int,A4: set_int] :
% 7.78/3.93 ( ( Inf
% 7.78/3.93 @ ( image_int_int
% 7.78/3.93 @ ^ [X4: int] : X4
% 7.78/3.93 @ A4 ) )
% 7.78/3.93 = ( Inf @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1210_Sup_OSUP__identity__eq,axiom,
% 7.78/3.93 ! [Sup: set_nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( Sup
% 7.78/3.93 @ ( image_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : X4
% 7.78/3.93 @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1211_Sup_OSUP__identity__eq,axiom,
% 7.78/3.93 ! [Sup: set_int > int,A4: set_int] :
% 7.78/3.93 ( ( Sup
% 7.78/3.93 @ ( image_int_int
% 7.78/3.93 @ ^ [X4: int] : X4
% 7.78/3.93 @ A4 ) )
% 7.78/3.93 = ( Sup @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1212_imageE,axiom,
% 7.78/3.93 ! [B: rat,F: nat > rat,A4: set_nat] :
% 7.78/3.93 ( ( member_rat @ B @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1213_imageE,axiom,
% 7.78/3.93 ! [B: $o,F: $o > $o,A4: set_o] :
% 7.78/3.93 ( ( member_o @ B @ ( image_o_o @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: $o] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_o @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1214_imageE,axiom,
% 7.78/3.93 ! [B: $o,F: nat > $o,A4: set_nat] :
% 7.78/3.93 ( ( member_o @ B @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1215_imageE,axiom,
% 7.78/3.93 ! [B: $o,F: int > $o,A4: set_int] :
% 7.78/3.93 ( ( member_o @ B @ ( image_int_o @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: int] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_int @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1216_imageE,axiom,
% 7.78/3.93 ! [B: nat,F: $o > nat,A4: set_o] :
% 7.78/3.93 ( ( member_nat @ B @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: $o] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_o @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1217_imageE,axiom,
% 7.78/3.93 ! [B: nat,F: nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1218_imageE,axiom,
% 7.78/3.93 ! [B: nat,F: int > nat,A4: set_int] :
% 7.78/3.93 ( ( member_nat @ B @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: int] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_int @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1219_imageE,axiom,
% 7.78/3.93 ! [B: int,F: $o > int,A4: set_o] :
% 7.78/3.93 ( ( member_int @ B @ ( image_o_int @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: $o] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_o @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1220_imageE,axiom,
% 7.78/3.93 ! [B: int,F: nat > int,A4: set_nat] :
% 7.78/3.93 ( ( member_int @ B @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: nat] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_nat @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1221_imageE,axiom,
% 7.78/3.93 ! [B: int,F: int > int,A4: set_int] :
% 7.78/3.93 ( ( member_int @ B @ ( image_int_int @ F @ A4 ) )
% 7.78/3.93 => ~ ! [X: int] :
% 7.78/3.93 ( ( B
% 7.78/3.93 = ( F @ X ) )
% 7.78/3.93 => ~ ( member_int @ X @ A4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1222_image__image,axiom,
% 7.78/3.93 ! [F: rat > rat,G: nat > rat,A4: set_nat] :
% 7.78/3.93 ( ( image_rat_rat @ F @ ( image_nat_rat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_rat
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1223_image__image,axiom,
% 7.78/3.93 ! [F: rat > nat,G: nat > rat,A4: set_nat] :
% 7.78/3.93 ( ( image_rat_nat @ F @ ( image_nat_rat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1224_image__image,axiom,
% 7.78/3.93 ! [F: rat > int,G: nat > rat,A4: set_nat] :
% 7.78/3.93 ( ( image_rat_int @ F @ ( image_nat_rat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_int
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1225_image__image,axiom,
% 7.78/3.93 ! [F: int > rat,G: nat > int,A4: set_nat] :
% 7.78/3.93 ( ( image_int_rat @ F @ ( image_nat_int @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_rat
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1226_image__image,axiom,
% 7.78/3.93 ! [F: nat > rat,G: nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( image_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_rat
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1227_image__image,axiom,
% 7.78/3.93 ! [F: nat > rat,G: int > nat,A4: set_int] :
% 7.78/3.93 ( ( image_nat_rat @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_int_rat
% 7.78/3.93 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1228_image__image,axiom,
% 7.78/3.93 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1229_image__image,axiom,
% 7.78/3.93 ! [F: nat > nat,G: int > nat,A4: set_int] :
% 7.78/3.93 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_int_nat
% 7.78/3.93 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1230_image__image,axiom,
% 7.78/3.93 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 7.78/3.93 ( ( image_nat_int @ F @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_nat_int
% 7.78/3.93 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1231_image__image,axiom,
% 7.78/3.93 ! [F: nat > int,G: int > nat,A4: set_int] :
% 7.78/3.93 ( ( image_nat_int @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.93 = ( image_int_int
% 7.78/3.93 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ A4 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1232_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: $o > $o,A4: set_o,P2: $o > $o] :
% 7.78/3.93 ( ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ ( image_o_o @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_o_o @ F
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1233_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: int > $o,A4: set_int,P2: $o > $o] :
% 7.78/3.93 ( ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ ( image_int_o @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_int_o @ F
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1234_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: $o > int,A4: set_o,P2: int > $o] :
% 7.78/3.93 ( ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ ( image_o_int @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_o_int @ F
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1235_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: int > int,A4: set_int,P2: int > $o] :
% 7.78/3.93 ( ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_int_int @ F
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1236_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: nat > rat,A4: set_nat,P2: rat > $o] :
% 7.78/3.93 ( ( collect_rat
% 7.78/3.93 @ ^ [X4: rat] :
% 7.78/3.93 ( ( member_rat @ X4 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_nat_rat @ F
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1237_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: nat > $o,A4: set_nat,P2: $o > $o] :
% 7.78/3.93 ( ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_nat_o @ F
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1238_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 7.78/3.93 ( ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_nat_int @ F
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1239_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: $o > nat,A4: set_o,P2: nat > $o] :
% 7.78/3.93 ( ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_o_nat @ F
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1240_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 7.78/3.93 ( ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_int_nat @ F
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1241_Compr__image__eq,axiom,
% 7.78/3.93 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 7.78/3.93 ( ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 = ( image_nat_nat @ F
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1242_Id__on__def_H,axiom,
% 7.78/3.93 ! [A4: product_prod_nat_nat > $o] :
% 7.78/3.93 ( ( id_on_2554058798563519774at_nat @ ( collec3392354462482085612at_nat @ A4 ) )
% 7.78/3.93 = ( collec7088162979684241874at_nat
% 7.78/3.93 @ ( produc6590410687421337004_nat_o
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 7.78/3.93 ( ( X4 = Y5 )
% 7.78/3.93 & ( A4 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1243_Id__on__def_H,axiom,
% 7.78/3.93 ! [A4: nat > $o] :
% 7.78/3.93 ( ( id_on_nat @ ( collect_nat @ A4 ) )
% 7.78/3.93 = ( collec3392354462482085612at_nat
% 7.78/3.93 @ ( produc6081775807080527818_nat_o
% 7.78/3.93 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.93 ( ( X4 = Y5 )
% 7.78/3.93 & ( A4 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1244_Id__on__def_H,axiom,
% 7.78/3.93 ! [A4: product_prod_int_int > $o] :
% 7.78/3.93 ( ( id_on_8598933527810153430nt_int @ ( collec213857154873943460nt_int @ A4 ) )
% 7.78/3.93 = ( collec7447955092554649554nt_int
% 7.78/3.93 @ ( produc1676490119946744748_int_o
% 7.78/3.93 @ ^ [X4: product_prod_int_int,Y5: product_prod_int_int] :
% 7.78/3.93 ( ( X4 = Y5 )
% 7.78/3.93 & ( A4 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1245_Id__on__def_H,axiom,
% 7.78/3.93 ! [A4: int > $o] :
% 7.78/3.93 ( ( id_on_int @ ( collect_int @ A4 ) )
% 7.78/3.93 = ( collec213857154873943460nt_int
% 7.78/3.93 @ ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [X4: int,Y5: int] :
% 7.78/3.93 ( ( X4 = Y5 )
% 7.78/3.93 & ( A4 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1246_pred__equals__eq2,axiom,
% 7.78/3.93 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 7.78/3.93 ( ( ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 ) )
% 7.78/3.93 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) ) )
% 7.78/3.93 = ( R3 = S5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1247_pred__equals__eq2,axiom,
% 7.78/3.93 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 7.78/3.93 ( ( ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 ) )
% 7.78/3.93 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) ) )
% 7.78/3.93 = ( R3 = S5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1248_pred__equals__eq2,axiom,
% 7.78/3.93 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 7.78/3.93 ( ( ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 ) )
% 7.78/3.93 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) ) )
% 7.78/3.93 = ( R3 = S5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1249_pred__equals__eq2,axiom,
% 7.78/3.93 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ( ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 ) )
% 7.78/3.93 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) ) )
% 7.78/3.93 = ( R3 = S5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1250_pred__equals__eq2,axiom,
% 7.78/3.93 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.93 ( ( ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 ) )
% 7.78/3.93 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) ) )
% 7.78/3.93 = ( R3 = S5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1251_case__prodE_H,axiom,
% 7.78/3.93 ! [C: nat > nat > product_prod_nat_nat > $o,P: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 7.78/3.93 ( ( produc8739625826339149834_nat_o @ C @ P @ Z2 )
% 7.78/3.93 => ~ ! [X: nat,Y: nat] :
% 7.78/3.93 ( ( P
% 7.78/3.93 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.93 => ~ ( C @ X @ Y @ Z2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1252_case__prodD_H,axiom,
% 7.78/3.93 ! [R3: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 7.78/3.93 ( ( produc8739625826339149834_nat_o @ R3 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 7.78/3.93 => ( R3 @ A @ B @ C ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1253_case__prod__Pair__iden,axiom,
% 7.78/3.93 ! [P: produc1319942482725812455at_nat] :
% 7.78/3.93 ( ( produc5456455677105495163at_nat @ produc9060074326276436823at_nat @ P )
% 7.78/3.93 = P ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1254_case__prod__Pair__iden,axiom,
% 7.78/3.93 ! [P: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( produc7548845685434208379at_nat @ produc2922128104949294807at_nat @ P )
% 7.78/3.93 = P ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1255_case__prod__Pair__iden,axiom,
% 7.78/3.93 ! [P: product_prod_nat_num] :
% 7.78/3.93 ( ( produc49306077274653107at_num @ product_Pair_nat_num @ P )
% 7.78/3.93 = P ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1256_case__prod__Pair__iden,axiom,
% 7.78/3.93 ! [P: product_prod_nat_nat] :
% 7.78/3.93 ( ( produc2626176000494625587at_nat @ product_Pair_nat_nat @ P )
% 7.78/3.93 = P ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1257_case__prod__Pair__iden,axiom,
% 7.78/3.93 ! [P: product_prod_int_int] :
% 7.78/3.93 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P )
% 7.78/3.93 = P ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1258_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,Q2: produc3843707927480180839at_nat > $o,P2: produc3843707927480180839at_nat > $o] :
% 7.78/3.93 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_le1268244103169919719at_nat
% 7.78/3.93 @ ( collec6321179662152712658at_nat
% 7.78/3.93 @ ^ [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collec6321179662152712658at_nat
% 7.78/3.93 @ ^ [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1259_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_o,A4: set_o,Q2: $o > $o,P2: $o > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: $o] :
% 7.78/3.93 ( ( member_o @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_less_eq_set_o
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1260_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_int,A4: set_int,Q2: int > $o,P2: int > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: int] :
% 7.78/3.93 ( ( member_int @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_less_eq_set_int
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1261_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,Q2: product_prod_nat_nat > $o,P2: product_prod_nat_nat > $o] :
% 7.78/3.93 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_le3146513528884898305at_nat
% 7.78/3.93 @ ( collec3392354462482085612at_nat
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collec3392354462482085612at_nat
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1262_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_nat,A4: set_nat,Q2: nat > $o,P2: nat > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: nat] :
% 7.78/3.93 ( ( member_nat @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_less_eq_set_nat
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1263_subset__CollectI,axiom,
% 7.78/3.93 ! [B5: set_Pr958786334691620121nt_int,A4: set_Pr958786334691620121nt_int,Q2: product_prod_int_int > $o,P2: product_prod_int_int > $o] :
% 7.78/3.93 ( ( ord_le2843351958646193337nt_int @ B5 @ A4 )
% 7.78/3.93 => ( ! [X: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X @ B5 )
% 7.78/3.93 => ( ( Q2 @ X )
% 7.78/3.93 => ( P2 @ X ) ) )
% 7.78/3.93 => ( ord_le2843351958646193337nt_int
% 7.78/3.93 @ ( collec213857154873943460nt_int
% 7.78/3.93 @ ^ [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ B5 )
% 7.78/3.93 & ( Q2 @ X4 ) ) )
% 7.78/3.93 @ ( collec213857154873943460nt_int
% 7.78/3.93 @ ^ [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1264_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 7.78/3.93 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_le1268244103169919719at_nat @ B5
% 7.78/3.93 @ ( collec6321179662152712658at_nat
% 7.78/3.93 @ ^ [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1265_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_o,A4: set_o,P2: $o > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_less_eq_set_o @ B5
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1266_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_int,A4: set_int,P2: int > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_less_eq_set_int @ B5
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1267_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 7.78/3.93 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_le3146513528884898305at_nat @ B5
% 7.78/3.93 @ ( collec3392354462482085612at_nat
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1268_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_nat,A4: set_nat,P2: nat > $o] :
% 7.78/3.93 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_less_eq_set_nat @ B5
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1269_subset__Collect__iff,axiom,
% 7.78/3.93 ! [B5: set_Pr958786334691620121nt_int,A4: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 7.78/3.93 ( ( ord_le2843351958646193337nt_int @ B5 @ A4 )
% 7.78/3.93 => ( ( ord_le2843351958646193337nt_int @ B5
% 7.78/3.93 @ ( collec213857154873943460nt_int
% 7.78/3.93 @ ^ [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ A4 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 = ( ! [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ B5 )
% 7.78/3.93 => ( P2 @ X4 ) ) ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1270_prop__restrict,axiom,
% 7.78/3.93 ! [X2: produc3843707927480180839at_nat,Z5: set_Pr4329608150637261639at_nat,X5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_le1268244103169919719at_nat @ Z5
% 7.78/3.93 @ ( collec6321179662152712658at_nat
% 7.78/3.93 @ ^ [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1271_prop__restrict,axiom,
% 7.78/3.93 ! [X2: $o,Z5: set_o,X5: set_o,P2: $o > $o] :
% 7.78/3.93 ( ( member_o @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_less_eq_set_o @ Z5
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1272_prop__restrict,axiom,
% 7.78/3.93 ! [X2: int,Z5: set_int,X5: set_int,P2: int > $o] :
% 7.78/3.93 ( ( member_int @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_less_eq_set_int @ Z5
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1273_prop__restrict,axiom,
% 7.78/3.93 ! [X2: product_prod_nat_nat,Z5: set_Pr1261947904930325089at_nat,X5: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_le3146513528884898305at_nat @ Z5
% 7.78/3.93 @ ( collec3392354462482085612at_nat
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1274_prop__restrict,axiom,
% 7.78/3.93 ! [X2: nat,Z5: set_nat,X5: set_nat,P2: nat > $o] :
% 7.78/3.93 ( ( member_nat @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_less_eq_set_nat @ Z5
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1275_prop__restrict,axiom,
% 7.78/3.93 ! [X2: product_prod_int_int,Z5: set_Pr958786334691620121nt_int,X5: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X2 @ Z5 )
% 7.78/3.93 => ( ( ord_le2843351958646193337nt_int @ Z5
% 7.78/3.93 @ ( collec213857154873943460nt_int
% 7.78/3.93 @ ^ [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) ) )
% 7.78/3.93 => ( P2 @ X2 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1276_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 7.78/3.93 ( ord_le1268244103169919719at_nat
% 7.78/3.93 @ ( collec6321179662152712658at_nat
% 7.78/3.93 @ ^ [X4: produc3843707927480180839at_nat] :
% 7.78/3.93 ( ( member8757157785044589968at_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1277_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_o,P2: $o > $o] :
% 7.78/3.93 ( ord_less_eq_set_o
% 7.78/3.93 @ ( collect_o
% 7.78/3.93 @ ^ [X4: $o] :
% 7.78/3.93 ( ( member_o @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1278_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_int,P2: int > $o] :
% 7.78/3.93 ( ord_less_eq_set_int
% 7.78/3.93 @ ( collect_int
% 7.78/3.93 @ ^ [X4: int] :
% 7.78/3.93 ( ( member_int @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1279_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 7.78/3.93 ( ord_le3146513528884898305at_nat
% 7.78/3.93 @ ( collec3392354462482085612at_nat
% 7.78/3.93 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.93 ( ( member8440522571783428010at_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1280_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_nat,P2: nat > $o] :
% 7.78/3.93 ( ord_less_eq_set_nat
% 7.78/3.93 @ ( collect_nat
% 7.78/3.93 @ ^ [X4: nat] :
% 7.78/3.93 ( ( member_nat @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1281_Collect__restrict,axiom,
% 7.78/3.93 ! [X5: set_Pr958786334691620121nt_int,P2: product_prod_int_int > $o] :
% 7.78/3.93 ( ord_le2843351958646193337nt_int
% 7.78/3.93 @ ( collec213857154873943460nt_int
% 7.78/3.93 @ ^ [X4: product_prod_int_int] :
% 7.78/3.93 ( ( member5262025264175285858nt_int @ X4 @ X5 )
% 7.78/3.93 & ( P2 @ X4 ) ) )
% 7.78/3.93 @ X5 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1282_fun_Omap__ident,axiom,
% 7.78/3.93 ! [T2: nat > $o] :
% 7.78/3.93 ( ( comp_o_o_nat
% 7.78/3.93 @ ^ [X4: $o] : X4
% 7.78/3.93 @ T2 )
% 7.78/3.93 = T2 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1283_fun_Omap__ident,axiom,
% 7.78/3.93 ! [T2: nat > nat] :
% 7.78/3.93 ( ( comp_nat_nat_nat
% 7.78/3.93 @ ^ [X4: nat] : X4
% 7.78/3.93 @ T2 )
% 7.78/3.93 = T2 ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1284_case__prod__app,axiom,
% 7.78/3.93 ( produc27273713700761075at_nat
% 7.78/3.93 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 7.78/3.93 ( produc2626176000494625587at_nat
% 7.78/3.93 @ ^ [L3: nat,R5: nat] : ( F2 @ L3 @ R5 @ Y5 )
% 7.78/3.93 @ X4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1285_case__prod__app,axiom,
% 7.78/3.93 ( produc8739625826339149834_nat_o
% 7.78/3.93 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 7.78/3.93 ( produc6081775807080527818_nat_o
% 7.78/3.93 @ ^ [L3: nat,R5: nat] : ( F2 @ L3 @ R5 @ Y5 )
% 7.78/3.93 @ X4 ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1286_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 7.78/3.93 = ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1287_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 7.78/3.93 = ( produc8211389475949308722nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1288_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1289_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc8211389475949308722nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1290_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1291_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc8211389475949308722nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1292_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 7.78/3.93 = ( produc4245557441103728435nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1293_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc4245557441103728435nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1294_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 7.78/3.93 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 7.78/3.93 = ( produc4245557441103728435nt_int
% 7.78/3.93 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1295_prod_Ocase__distrib,axiom,
% 7.78/3.93 ! [H: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 7.78/3.93 ( ( H @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 7.78/3.93 = ( produc8739625826339149834_nat_o
% 7.78/3.93 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 7.78/3.93 @ Prod ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1296_prod_Odisc__eq__case,axiom,
% 7.78/3.93 ! [Prod: product_prod_int_int] :
% 7.78/3.93 ( produc4947309494688390418_int_o
% 7.78/3.93 @ ^ [Uu: int,Uv: int] : $true
% 7.78/3.93 @ Prod ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1297_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: int > $o,F: int > nat,B5: set_nat] :
% 7.78/3.93 ( ! [X: int] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( collect_int @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1298_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: int > $o,F: int > int,B5: set_int] :
% 7.78/3.93 ( ! [X: int] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_int @ ( image_int_int @ F @ ( collect_int @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1299_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: nat > $o,F: nat > rat,B5: set_rat] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_rat @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1300_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: nat > $o,F: nat > $o,B5: set_o] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_o @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1301_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: nat > $o,F: nat > nat,B5: set_nat] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1302_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: nat > $o,F: nat > int,B5: set_int] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1303_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > $o,B5: set_o] :
% 7.78/3.93 ( ! [X: product_prod_nat_nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_o @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_o @ ( image_3693632289388996572_nat_o @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1304_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > nat,B5: set_nat] :
% 7.78/3.93 ( ! [X: product_prod_nat_nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1305_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > int,B5: set_int] :
% 7.78/3.93 ( ! [X: product_prod_nat_nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member_int @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_less_eq_set_int @ ( image_2483585944268220136at_int @ F @ ( collec3392354462482085612at_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1306_image__Collect__subsetI,axiom,
% 7.78/3.93 ! [P2: nat > $o,F: nat > product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.93 ( ! [X: nat] :
% 7.78/3.93 ( ( P2 @ X )
% 7.78/3.93 => ( member8440522571783428010at_nat @ ( F @ X ) @ B5 ) )
% 7.78/3.93 => ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ ( collect_nat @ P2 ) ) @ B5 ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1307_range__composition,axiom,
% 7.78/3.93 ! [F: nat > rat,G: char > nat] :
% 7.78/3.93 ( ( image_char_rat
% 7.78/3.93 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ top_top_set_char )
% 7.78/3.93 = ( image_nat_rat @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1308_range__composition,axiom,
% 7.78/3.93 ! [F: nat > nat,G: char > nat] :
% 7.78/3.93 ( ( image_char_nat
% 7.78/3.93 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ top_top_set_char )
% 7.78/3.93 = ( image_nat_nat @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1309_range__composition,axiom,
% 7.78/3.93 ! [F: nat > int,G: char > nat] :
% 7.78/3.93 ( ( image_char_int
% 7.78/3.93 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.93 @ top_top_set_char )
% 7.78/3.93 = ( image_nat_int @ F @ ( image_char_nat @ G @ top_top_set_char ) ) ) ).
% 7.78/3.93
% 7.78/3.93 thf(fact_1310_range__composition,axiom,
% 7.78/3.93 ! [F: int > nat,G: char > int] :
% 7.78/3.94 ( ( image_char_nat
% 7.78/3.94 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_char )
% 7.78/3.94 = ( image_int_nat @ F @ ( image_char_int @ G @ top_top_set_char ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1311_range__composition,axiom,
% 7.78/3.94 ! [F: int > int,G: char > int] :
% 7.78/3.94 ( ( image_char_int
% 7.78/3.94 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_char )
% 7.78/3.94 = ( image_int_int @ F @ ( image_char_int @ G @ top_top_set_char ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1312_range__composition,axiom,
% 7.78/3.94 ! [F: nat > rat,G: rat > nat] :
% 7.78/3.94 ( ( image_rat_rat
% 7.78/3.94 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_rat )
% 7.78/3.94 = ( image_nat_rat @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1313_range__composition,axiom,
% 7.78/3.94 ! [F: nat > nat,G: rat > nat] :
% 7.78/3.94 ( ( image_rat_nat
% 7.78/3.94 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_rat )
% 7.78/3.94 = ( image_nat_nat @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1314_range__composition,axiom,
% 7.78/3.94 ! [F: nat > int,G: rat > nat] :
% 7.78/3.94 ( ( image_rat_int
% 7.78/3.94 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_rat )
% 7.78/3.94 = ( image_nat_int @ F @ ( image_rat_nat @ G @ top_top_set_rat ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1315_range__composition,axiom,
% 7.78/3.94 ! [F: int > nat,G: rat > int] :
% 7.78/3.94 ( ( image_rat_nat
% 7.78/3.94 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_rat )
% 7.78/3.94 = ( image_int_nat @ F @ ( image_rat_int @ G @ top_top_set_rat ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1316_range__composition,axiom,
% 7.78/3.94 ! [F: int > int,G: rat > int] :
% 7.78/3.94 ( ( image_rat_int
% 7.78/3.94 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.94 @ top_top_set_rat )
% 7.78/3.94 = ( image_int_int @ F @ ( image_rat_int @ G @ top_top_set_rat ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1317_rangeE,axiom,
% 7.78/3.94 ! [B: $o,F: char > $o] :
% 7.78/3.94 ( ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) )
% 7.78/3.94 => ~ ! [X: char] :
% 7.78/3.94 ( B
% 7.78/3.94 = ( ~ ( F @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1318_rangeE,axiom,
% 7.78/3.94 ! [B: nat,F: char > nat] :
% 7.78/3.94 ( ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) )
% 7.78/3.94 => ~ ! [X: char] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1319_rangeE,axiom,
% 7.78/3.94 ! [B: int,F: char > int] :
% 7.78/3.94 ( ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) )
% 7.78/3.94 => ~ ! [X: char] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1320_rangeE,axiom,
% 7.78/3.94 ! [B: $o,F: rat > $o] :
% 7.78/3.94 ( ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) )
% 7.78/3.94 => ~ ! [X: rat] :
% 7.78/3.94 ( B
% 7.78/3.94 = ( ~ ( F @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1321_rangeE,axiom,
% 7.78/3.94 ! [B: nat,F: rat > nat] :
% 7.78/3.94 ( ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) )
% 7.78/3.94 => ~ ! [X: rat] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1322_rangeE,axiom,
% 7.78/3.94 ! [B: int,F: rat > int] :
% 7.78/3.94 ( ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) )
% 7.78/3.94 => ~ ! [X: rat] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1323_rangeE,axiom,
% 7.78/3.94 ! [B: rat,F: nat > rat] :
% 7.78/3.94 ( ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1324_rangeE,axiom,
% 7.78/3.94 ! [B: $o,F: nat > $o] :
% 7.78/3.94 ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( B
% 7.78/3.94 = ( ~ ( F @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1325_rangeE,axiom,
% 7.78/3.94 ! [B: nat,F: nat > nat] :
% 7.78/3.94 ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1326_rangeE,axiom,
% 7.78/3.94 ! [B: int,F: nat > int] :
% 7.78/3.94 ( ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( B
% 7.78/3.94 != ( F @ X ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1327_fun_Orel__map_I1_J,axiom,
% 7.78/3.94 ! [Sb: num > num > $o,I: nat > num,X2: int > nat,Y3: int > num] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ Sb
% 7.78/3.94 @ ( comp_nat_num_int @ I @ X2 )
% 7.78/3.94 @ Y3 )
% 7.78/3.94 = ( bNF_re272988434038980259at_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ^ [X4: nat] : ( Sb @ ( I @ X4 ) )
% 7.78/3.94 @ X2
% 7.78/3.94 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1328_fun_Orel__map_I1_J,axiom,
% 7.78/3.94 ! [Sb: num > num > $o,I: num > num,X2: int > num,Y3: int > num] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ Sb
% 7.78/3.94 @ ( comp_num_num_int @ I @ X2 )
% 7.78/3.94 @ Y3 )
% 7.78/3.94 = ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ^ [X4: num] : ( Sb @ ( I @ X4 ) )
% 7.78/3.94 @ X2
% 7.78/3.94 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1329_fun_Orel__map_I2_J,axiom,
% 7.78/3.94 ! [Sa: num > num > $o,X2: int > num,G: nat > num,Y3: int > nat] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ Sa
% 7.78/3.94 @ X2
% 7.78/3.94 @ ( comp_nat_num_int @ G @ Y3 ) )
% 7.78/3.94 = ( bNF_re1845987051190671011um_nat
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ^ [X4: num,Y5: nat] : ( Sa @ X4 @ ( G @ Y5 ) )
% 7.78/3.94 @ X2
% 7.78/3.94 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1330_fun_Orel__map_I2_J,axiom,
% 7.78/3.94 ! [Sa: num > num > $o,X2: int > num,G: num > num,Y3: int > num] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ Sa
% 7.78/3.94 @ X2
% 7.78/3.94 @ ( comp_num_num_int @ G @ Y3 ) )
% 7.78/3.94 = ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ^ [X4: num,Y5: num] : ( Sa @ X4 @ ( G @ Y5 ) )
% 7.78/3.94 @ X2
% 7.78/3.94 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1331_case__prodE2,axiom,
% 7.78/3.94 ! [Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 7.78/3.94 ( ( Q2 @ ( produc27273713700761075at_nat @ P2 @ Z2 ) )
% 7.78/3.94 => ~ ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( Z2
% 7.78/3.94 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.94 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1332_case__prodE2,axiom,
% 7.78/3.94 ! [Q2: ( product_prod_nat_nat > $o ) > $o,P2: nat > nat > product_prod_nat_nat > $o,Z2: product_prod_nat_nat] :
% 7.78/3.94 ( ( Q2 @ ( produc8739625826339149834_nat_o @ P2 @ Z2 ) )
% 7.78/3.94 => ~ ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( Z2
% 7.78/3.94 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.94 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1333_case__prodE2,axiom,
% 7.78/3.94 ! [Q2: product_prod_int_int > $o,P2: int > int > product_prod_int_int,Z2: product_prod_int_int] :
% 7.78/3.94 ( ( Q2 @ ( produc4245557441103728435nt_int @ P2 @ Z2 ) )
% 7.78/3.94 => ~ ! [X: int,Y: int] :
% 7.78/3.94 ( ( Z2
% 7.78/3.94 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.94 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1334_case__prodE2,axiom,
% 7.78/3.94 ! [Q2: $o > $o,P2: int > int > $o,Z2: product_prod_int_int] :
% 7.78/3.94 ( ( Q2 @ ( produc4947309494688390418_int_o @ P2 @ Z2 ) )
% 7.78/3.94 => ~ ! [X: int,Y: int] :
% 7.78/3.94 ( ( Z2
% 7.78/3.94 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.94 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1335_case__prodE2,axiom,
% 7.78/3.94 ! [Q2: int > $o,P2: int > int > int,Z2: product_prod_int_int] :
% 7.78/3.94 ( ( Q2 @ ( produc8211389475949308722nt_int @ P2 @ Z2 ) )
% 7.78/3.94 => ~ ! [X: int,Y: int] :
% 7.78/3.94 ( ( Z2
% 7.78/3.94 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.94 => ~ ( Q2 @ ( P2 @ X @ Y ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1336_case__prod__eta,axiom,
% 7.78/3.94 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.94 ( ( produc27273713700761075at_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 7.78/3.94 = F ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1337_case__prod__eta,axiom,
% 7.78/3.94 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( produc8739625826339149834_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y5 ) ) )
% 7.78/3.94 = F ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1338_case__prod__eta,axiom,
% 7.78/3.94 ! [F: product_prod_int_int > product_prod_int_int] :
% 7.78/3.94 ( ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 7.78/3.94 = F ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1339_case__prod__eta,axiom,
% 7.78/3.94 ! [F: product_prod_int_int > $o] :
% 7.78/3.94 ( ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 7.78/3.94 = F ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1340_case__prod__eta,axiom,
% 7.78/3.94 ! [F: product_prod_int_int > int] :
% 7.78/3.94 ( ( produc8211389475949308722nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( F @ ( product_Pair_int_int @ X4 @ Y5 ) ) )
% 7.78/3.94 = F ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1341_cond__case__prod__eta,axiom,
% 7.78/3.94 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.94 ( ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( F @ X @ Y )
% 7.78/3.94 = ( G @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 7.78/3.94 => ( ( produc27273713700761075at_nat @ F )
% 7.78/3.94 = G ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1342_cond__case__prod__eta,axiom,
% 7.78/3.94 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( F @ X @ Y )
% 7.78/3.94 = ( G @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 7.78/3.94 => ( ( produc8739625826339149834_nat_o @ F )
% 7.78/3.94 = G ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1343_cond__case__prod__eta,axiom,
% 7.78/3.94 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 7.78/3.94 ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( F @ X @ Y )
% 7.78/3.94 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 7.78/3.94 => ( ( produc4245557441103728435nt_int @ F )
% 7.78/3.94 = G ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1344_cond__case__prod__eta,axiom,
% 7.78/3.94 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 7.78/3.94 ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( F @ X @ Y )
% 7.78/3.94 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 7.78/3.94 => ( ( produc4947309494688390418_int_o @ F )
% 7.78/3.94 = G ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1345_cond__case__prod__eta,axiom,
% 7.78/3.94 ! [F: int > int > int,G: product_prod_int_int > int] :
% 7.78/3.94 ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( F @ X @ Y )
% 7.78/3.94 = ( G @ ( product_Pair_int_int @ X @ Y ) ) )
% 7.78/3.94 => ( ( produc8211389475949308722nt_int @ F )
% 7.78/3.94 = G ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1346_case__prodD,axiom,
% 7.78/3.94 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( produc9020218426428501292_nat_o @ F @ ( produc9060074326276436823at_nat @ A @ B ) )
% 7.78/3.94 => ( F @ A @ B ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1347_case__prodD,axiom,
% 7.78/3.94 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( produc410239310623530412_nat_o @ F @ ( produc2922128104949294807at_nat @ A @ B ) )
% 7.78/3.94 => ( F @ A @ B ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1348_case__prodD,axiom,
% 7.78/3.94 ! [F: nat > num > $o,A: nat,B: num] :
% 7.78/3.94 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 7.78/3.94 => ( F @ A @ B ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1349_case__prodD,axiom,
% 7.78/3.94 ! [F: nat > nat > $o,A: nat,B: nat] :
% 7.78/3.94 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 7.78/3.94 => ( F @ A @ B ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1350_case__prodD,axiom,
% 7.78/3.94 ! [F: int > int > $o,A: int,B: int] :
% 7.78/3.94 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 7.78/3.94 => ( F @ A @ B ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1351_case__prodE,axiom,
% 7.78/3.94 ! [C: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,P: produc1319942482725812455at_nat] :
% 7.78/3.94 ( ( produc9020218426428501292_nat_o @ C @ P )
% 7.78/3.94 => ~ ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( P
% 7.78/3.94 = ( produc9060074326276436823at_nat @ X @ Y ) )
% 7.78/3.94 => ~ ( C @ X @ Y ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1352_case__prodE,axiom,
% 7.78/3.94 ! [C: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,P: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( produc410239310623530412_nat_o @ C @ P )
% 7.78/3.94 => ~ ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( P
% 7.78/3.94 = ( produc2922128104949294807at_nat @ X @ Y ) )
% 7.78/3.94 => ~ ( C @ X @ Y ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1353_case__prodE,axiom,
% 7.78/3.94 ! [C: nat > num > $o,P: product_prod_nat_num] :
% 7.78/3.94 ( ( produc4927758841916487424_num_o @ C @ P )
% 7.78/3.94 => ~ ! [X: nat,Y: num] :
% 7.78/3.94 ( ( P
% 7.78/3.94 = ( product_Pair_nat_num @ X @ Y ) )
% 7.78/3.94 => ~ ( C @ X @ Y ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1354_case__prodE,axiom,
% 7.78/3.94 ! [C: nat > nat > $o,P: product_prod_nat_nat] :
% 7.78/3.94 ( ( produc6081775807080527818_nat_o @ C @ P )
% 7.78/3.94 => ~ ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( P
% 7.78/3.94 = ( product_Pair_nat_nat @ X @ Y ) )
% 7.78/3.94 => ~ ( C @ X @ Y ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1355_case__prodE,axiom,
% 7.78/3.94 ! [C: int > int > $o,P: product_prod_int_int] :
% 7.78/3.94 ( ( produc4947309494688390418_int_o @ C @ P )
% 7.78/3.94 => ~ ! [X: int,Y: int] :
% 7.78/3.94 ( ( P
% 7.78/3.94 = ( product_Pair_int_int @ X @ Y ) )
% 7.78/3.94 => ~ ( C @ X @ Y ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1356_fst__def,axiom,
% 7.78/3.94 ( produc473321116828791851t_unit
% 7.78/3.94 = ( produc4846201513286513633_ref_a
% 7.78/3.94 @ ^ [X12: ref_a,X23: heap_e7401611519738050253t_unit] : X12 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1357_fst__def,axiom,
% 7.78/3.94 ( product_fst_int_int
% 7.78/3.94 = ( produc8211389475949308722nt_int
% 7.78/3.94 @ ^ [X12: int,X23: int] : X12 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1358_snd__def,axiom,
% 7.78/3.94 ( produc1126150082675451753t_unit
% 7.78/3.94 = ( produc2552614499379209865t_unit
% 7.78/3.94 @ ^ [X12: ref_a,X23: heap_e7401611519738050253t_unit] : X23 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1359_snd__def,axiom,
% 7.78/3.94 ( product_snd_int_int
% 7.78/3.94 = ( produc8211389475949308722nt_int
% 7.78/3.94 @ ^ [X12: int,X23: int] : X23 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1360_map__prod__def,axiom,
% 7.78/3.94 ( produc6036585564866528938nt_int
% 7.78/3.94 = ( ^ [F2: int > int,G3: int > int] :
% 7.78/3.94 ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ ( F2 @ X4 ) @ ( G3 @ Y5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1361_case__prod__map__prod,axiom,
% 7.78/3.94 ! [H: nat > nat > product_prod_nat_nat > product_prod_nat_nat,F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
% 7.78/3.94 ( ( produc27273713700761075at_nat @ H @ ( produc6977886695330630970at_nat @ F @ G @ X2 ) )
% 7.78/3.94 = ( produc27273713700761075at_nat
% 7.78/3.94 @ ^ [L3: nat,R5: nat] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 7.78/3.94 @ X2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1362_case__prod__map__prod,axiom,
% 7.78/3.94 ! [H: nat > nat > product_prod_nat_nat > $o,F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
% 7.78/3.94 ( ( produc8739625826339149834_nat_o @ H @ ( produc6977886695330630970at_nat @ F @ G @ X2 ) )
% 7.78/3.94 = ( produc8739625826339149834_nat_o
% 7.78/3.94 @ ^ [L3: nat,R5: nat] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 7.78/3.94 @ X2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1363_case__prod__map__prod,axiom,
% 7.78/3.94 ! [H: int > int > product_prod_int_int,F: int > int,G: int > int,X2: product_prod_int_int] :
% 7.78/3.94 ( ( produc4245557441103728435nt_int @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 7.78/3.94 = ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 7.78/3.94 @ X2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1364_case__prod__map__prod,axiom,
% 7.78/3.94 ! [H: int > int > $o,F: int > int,G: int > int,X2: product_prod_int_int] :
% 7.78/3.94 ( ( produc4947309494688390418_int_o @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 7.78/3.94 = ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 7.78/3.94 @ X2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1365_case__prod__map__prod,axiom,
% 7.78/3.94 ! [H: int > int > int,F: int > int,G: int > int,X2: product_prod_int_int] :
% 7.78/3.94 ( ( produc8211389475949308722nt_int @ H @ ( produc6036585564866528938nt_int @ F @ G @ X2 ) )
% 7.78/3.94 = ( produc8211389475949308722nt_int
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( H @ ( F @ L3 ) @ ( G @ R5 ) )
% 7.78/3.94 @ X2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1366_converse__relcompp,axiom,
% 7.78/3.94 ! [R: int > product_prod_nat_nat > $o,S2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( conver1866313717161370910at_nat @ ( relcom716700242784427165at_nat @ R @ S2 ) )
% 7.78/3.94 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ S2 ) @ ( conver1866313717161370910at_nat @ R ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1367_converse__relcompp,axiom,
% 7.78/3.94 ! [R: code_integer > int > $o,S2: int > int > $o] :
% 7.78/3.94 ( ( conver1462408618118490240er_int @ ( relcom3789353511612409832nt_int @ R @ S2 ) )
% 7.78/3.94 = ( relcom967497705283160040nteger @ ( conversep_int_int @ S2 ) @ ( conver1462408618118490240er_int @ R ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1368_converse__relcompp,axiom,
% 7.78/3.94 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S2: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( conver4689305806000247544at_int @ ( relcom8911704206367525917at_int @ R @ S2 ) )
% 7.78/3.94 = ( relcom716700242784427165at_nat @ ( conver4689305806000247544at_int @ S2 ) @ ( conver6965824823119931701at_nat @ R ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1369_converse__relcompp,axiom,
% 7.78/3.94 ! [R: int > int > $o,S2: int > code_integer > $o] :
% 7.78/3.94 ( ( conver2101108097643427968nteger @ ( relcom967497705283160040nteger @ R @ S2 ) )
% 7.78/3.94 = ( relcom3789353511612409832nt_int @ ( conver2101108097643427968nteger @ S2 ) @ ( conversep_int_int @ R ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1370_flip__pred,axiom,
% 7.78/3.94 ! [A4: set_Pr7459493094073627847at_nat,R3: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o] :
% 7.78/3.94 ( ( ord_le5997549366648089703at_nat @ A4 @ ( collec7872792499061297490at_nat @ ( produc9020218426428501292_nat_o @ ( conver9095369822871743413at_nat @ R3 ) ) ) )
% 7.78/3.94 => ( ord_le5997549366648089703at_nat
% 7.78/3.94 @ ( image_3313167189156628421at_nat
% 7.78/3.94 @ ( produc5456455677105495163at_nat
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) )
% 7.78/3.94 @ A4 )
% 7.78/3.94 @ ( collec7872792499061297490at_nat @ ( produc9020218426428501292_nat_o @ R3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1371_flip__pred,axiom,
% 7.78/3.94 ! [A4: set_Pr4329608150637261639at_nat,R3: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.94 ( ( ord_le1268244103169919719at_nat @ A4 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ ( conver5243090411617913141at_nat @ R3 ) ) ) )
% 7.78/3.94 => ( ord_le1268244103169919719at_nat
% 7.78/3.94 @ ( image_960689587819713477at_nat
% 7.78/3.94 @ ( produc7548845685434208379at_nat
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) )
% 7.78/3.94 @ A4 )
% 7.78/3.94 @ ( collec6321179662152712658at_nat @ ( produc410239310623530412_nat_o @ R3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1372_flip__pred,axiom,
% 7.78/3.94 ! [A4: set_Pr3280342998896498603um_nat,R3: nat > num > $o] :
% 7.78/3.94 ( ( ord_le5164908622851071819um_nat @ A4 @ ( collec1522684865789554998um_nat @ ( produc6857965554392702720_nat_o @ ( conversep_nat_num @ R3 ) ) ) )
% 7.78/3.94 => ( ord_le8085105155179020875at_num
% 7.78/3.94 @ ( image_7762062833379733445at_num
% 7.78/3.94 @ ( produc5219324331026901427at_num
% 7.78/3.94 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) )
% 7.78/3.94 @ A4 )
% 7.78/3.94 @ ( collec4100598399430923318at_num @ ( produc4927758841916487424_num_o @ R3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1373_flip__pred,axiom,
% 7.78/3.94 ! [A4: set_Pr1261947904930325089at_nat,R3: nat > nat > $o] :
% 7.78/3.94 ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( conversep_nat_nat @ R3 ) ) ) )
% 7.78/3.94 => ( ord_le3146513528884898305at_nat
% 7.78/3.94 @ ( image_5168914502847457605at_nat
% 7.78/3.94 @ ( produc2626176000494625587at_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 7.78/3.94 @ A4 )
% 7.78/3.94 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1374_flip__pred,axiom,
% 7.78/3.94 ! [A4: set_Pr958786334691620121nt_int,R3: int > int > $o] :
% 7.78/3.94 ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ ( conversep_int_int @ R3 ) ) ) )
% 7.78/3.94 => ( ord_le2843351958646193337nt_int
% 7.78/3.94 @ ( image_2653370878348428101nt_int
% 7.78/3.94 @ ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) )
% 7.78/3.94 @ A4 )
% 7.78/3.94 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1375_type__copy__wit,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: produc3843707927480180839at_nat,S5: $o > set_Pr4329608150637261639at_nat,Y3: $o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ X2 @ ( comp_o4913564575355137019t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 7.78/3.94 => ( member8757157785044589968at_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1376_type__copy__wit,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: product_prod_nat_nat,S5: $o > set_Pr1261947904930325089at_nat,Y3: $o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ X2 @ ( comp_o2254869825208929t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 7.78/3.94 => ( member8440522571783428010at_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1377_type__copy__wit,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: $o,S5: $o > set_o,Y3: $o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( member_o @ X2 @ ( comp_o6895741221744486154t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 7.78/3.94 => ( member_o @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1378_type__copy__wit,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: nat,S5: $o > set_nat,Y3: $o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( member_nat @ X2 @ ( comp_o9190160103024335696t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 7.78/3.94 => ( member_nat @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1379_type__copy__wit,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,X2: int,S5: $o > set_int,Y3: $o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( member_int @ X2 @ ( comp_o1521574261646630388t_unit @ S5 @ Rep @ ( Abs @ Y3 ) ) )
% 7.78/3.94 => ( member_int @ X2 @ ( S5 @ Y3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1380_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,F: nat > nat,P2: nat > $o,H: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( bNF_vi6818137723729380987_o_o_o @ F @ Rep @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1381_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,F: int > int,P2: int > $o,H: int > char] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( bNF_vi9149698133064535136char_o @ F @ Rep @ ( bNF_Grp_int_char @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_nat
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1382_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: $o > char,Abs: char > $o,F: nat > $o,P2: $o > $o,H: $o > char] :
% 7.78/3.94 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( bNF_vi8816436626763797690char_o @ F @ Rep @ ( bNF_Grp_o_char @ ( collect_o @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1383_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: num > char,Abs: char > num,F: int > nat,P2: nat > $o,H: nat > char] :
% 7.78/3.94 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( bNF_vi1300075849944819442char_o @ F @ Rep @ ( bNF_Grp_nat_char @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_num
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1384_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,F: nat > nat,P2: nat > $o,H: nat > char] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( bNF_vi8943400373106913048char_o @ F @ Rep @ ( bNF_Grp_nat_char @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_nat
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1385_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: nat > rat,Abs: rat > nat,F: int > int,P2: int > $o,H: int > rat] :
% 7.78/3.94 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.94 => ( ( bNF_vi1281217848275042457_rat_o @ F @ Rep @ ( bNF_Grp_int_rat @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_nat
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_nat_int @ ( comp_rat_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1386_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: $o > rat,Abs: rat > $o,F: nat > $o,P2: $o > $o,H: $o > rat] :
% 7.78/3.94 ( ( type_d6486251586359353412_o_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.94 => ( ( bNF_vi3868162310295888627_rat_o @ F @ Rep @ ( bNF_Grp_o_rat @ ( collect_o @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_o_o_nat @ ( comp_rat_o_o @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1387_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: num > rat,Abs: rat > num,F: int > nat,P2: nat > $o,H: nat > rat] :
% 7.78/3.94 ( ( type_d3745694291998722336um_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.94 => ( ( bNF_vi7769575839906753835_rat_o @ F @ Rep @ ( bNF_Grp_nat_rat @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_num
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_num_int @ ( comp_rat_num_nat @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1388_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: nat > rat,Abs: rat > nat,F: nat > nat,P2: nat > $o,H: nat > rat] :
% 7.78/3.94 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ top_top_set_rat )
% 7.78/3.94 => ( ( bNF_vi2930123780028963665_rat_o @ F @ Rep @ ( bNF_Grp_nat_rat @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_nat
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_nat_nat @ ( comp_rat_nat_nat @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1389_type__copy__vimage2p__Grp__Rep,axiom,
% 7.78/3.94 ! [Rep: nat > nat,Abs: nat > nat,F: int > int,P2: int > $o,H: int > nat] :
% 7.78/3.94 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.94 => ( ( bNF_vi5018550775591610529_nat_o @ F @ Rep @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_nat
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( F @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_nat_int @ ( comp_nat_nat_int @ Abs @ H ) @ F ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1390_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: nat > num,Abs: num > nat,G: nat > int,P2: int > $o,H: int > nat] :
% 7.78/3.94 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.94 => ( ( bNF_vi1731478210338170163_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_num
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_num_nat @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1391_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,G: nat > nat,P2: nat > $o,H: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( bNF_vi6818137723729380987_o_o_o @ G @ Abs @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1392_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: int > nat,Abs: nat > int,G: int > int,P2: int > $o,H: int > int] :
% 7.78/3.94 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.94 => ( ( bNF_vi3197508430158922565_int_o @ G @ Abs @ ( bNF_Grp_int_int @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_int_nat
% 7.78/3.94 @ ( collect_int
% 7.78/3.94 @ ^ [X4: int] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_nat_int @ ( comp_int_nat_int @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1393_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: int > nat,Abs: nat > int,G: nat > int,P2: int > $o,H: int > int] :
% 7.78/3.94 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.94 => ( ( bNF_vi8357618154448083105_int_o @ G @ Abs @ ( bNF_Grp_int_int @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_nat
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_int_nat_nat @ ( comp_int_nat_int @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1394_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: nat > nat,Abs: nat > nat,G: nat > nat,P2: nat > $o,H: nat > nat] :
% 7.78/3.94 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ top_top_set_nat )
% 7.78/3.94 => ( ( bNF_vi6667456707345531737_nat_o @ G @ Abs @ ( bNF_Grp_nat_nat @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_nat
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1395_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,G: nat > $o,P2: $o > $o,H: $o > product_unit] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( bNF_vi5856767400800367702unit_o @ G @ Abs @ ( bNF_Gr395642070819736771t_unit @ ( collect_o @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_o_o_nat @ ( comp_P5156358013004227690it_o_o @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1396_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,G: nat > nat,P2: nat > $o,H: nat > product_unit] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( bNF_vi1443435967014148806unit_o @ G @ Abs @ ( bNF_Gr1993012052113314029t_unit @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Grp_nat_o
% 7.78/3.94 @ ( collect_nat
% 7.78/3.94 @ ^ [X4: nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_nat_o_nat @ ( comp_P4985893458130756478_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1397_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: nat > num,Abs: num > nat,G: product_prod_nat_nat > int,P2: int > $o,H: int > nat] :
% 7.78/3.94 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.94 => ( ( bNF_vi9094538908245281400_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Gr5974128493091723341at_num
% 7.78/3.94 @ ( collec3392354462482085612at_nat
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_i1186163378102392086at_nat @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1398_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: nat > num,Abs: num > nat,G: product_prod_int_int > int,P2: int > $o,H: int > nat] :
% 7.78/3.94 ( ( type_d2807825734933527320at_num @ Rep @ Abs @ top_top_set_num )
% 7.78/3.94 => ( ( bNF_vi1633389952966819264_nat_o @ G @ Abs @ ( bNF_Grp_int_nat @ ( collect_int @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Gr8532703628021589765nt_num
% 7.78/3.94 @ ( collec213857154873943460nt_int
% 7.78/3.94 @ ^ [X4: product_prod_int_int] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_i7231038107349025742nt_int @ ( comp_nat_num_int @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1399_type__copy__vimage2p__Grp__Abs,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,G: product_prod_nat_nat > nat,P2: nat > $o,H: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( bNF_vi9025507403824386624_o_o_o @ G @ Abs @ ( bNF_Grp_nat_o @ ( collect_nat @ P2 ) @ H ) )
% 7.78/3.94 = ( bNF_Gr8859634586176591525_nat_o
% 7.78/3.94 @ ( collec3392354462482085612at_nat
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat] : ( P2 @ ( G @ X4 ) ) )
% 7.78/3.94 @ ( comp_n1662990198670838940at_nat @ ( comp_o_o_nat @ Rep @ H ) @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1400_exE__realizer,axiom,
% 7.78/3.94 ! [P2: nat > nat > $o,P: product_prod_nat_nat,Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ ( product_snd_nat_nat @ P ) @ ( product_fst_nat_nat @ P ) )
% 7.78/3.94 => ( ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( P2 @ Y @ X )
% 7.78/3.94 => ( Q2 @ ( F @ X @ Y ) ) )
% 7.78/3.94 => ( Q2 @ ( produc27273713700761075at_nat @ F @ P ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1401_exE__realizer,axiom,
% 7.78/3.94 ! [P2: nat > nat > $o,P: product_prod_nat_nat,Q2: ( product_prod_nat_nat > $o ) > $o,F: nat > nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( P2 @ ( product_snd_nat_nat @ P ) @ ( product_fst_nat_nat @ P ) )
% 7.78/3.94 => ( ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( P2 @ Y @ X )
% 7.78/3.94 => ( Q2 @ ( F @ X @ Y ) ) )
% 7.78/3.94 => ( Q2 @ ( produc8739625826339149834_nat_o @ F @ P ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1402_exE__realizer,axiom,
% 7.78/3.94 ! [P2: int > int > $o,P: product_prod_int_int,Q2: product_prod_int_int > $o,F: int > int > product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 7.78/3.94 => ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( P2 @ Y @ X )
% 7.78/3.94 => ( Q2 @ ( F @ X @ Y ) ) )
% 7.78/3.94 => ( Q2 @ ( produc4245557441103728435nt_int @ F @ P ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1403_exE__realizer,axiom,
% 7.78/3.94 ! [P2: int > int > $o,P: product_prod_int_int,Q2: $o > $o,F: int > int > $o] :
% 7.78/3.94 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 7.78/3.94 => ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( P2 @ Y @ X )
% 7.78/3.94 => ( Q2 @ ( F @ X @ Y ) ) )
% 7.78/3.94 => ( Q2 @ ( produc4947309494688390418_int_o @ F @ P ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1404_exE__realizer,axiom,
% 7.78/3.94 ! [P2: int > int > $o,P: product_prod_int_int,Q2: int > $o,F: int > int > int] :
% 7.78/3.94 ( ( P2 @ ( product_snd_int_int @ P ) @ ( product_fst_int_int @ P ) )
% 7.78/3.94 => ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( P2 @ Y @ X )
% 7.78/3.94 => ( Q2 @ ( F @ X @ Y ) ) )
% 7.78/3.94 => ( Q2 @ ( produc8211389475949308722nt_int @ F @ P ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1405_case__prod__beta_H,axiom,
% 7.78/3.94 ( produc27273713700761075at_nat
% 7.78/3.94 = ( ^ [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X4 ) @ ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1406_case__prod__beta_H,axiom,
% 7.78/3.94 ( produc8739625826339149834_nat_o
% 7.78/3.94 = ( ^ [F2: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat] : ( F2 @ ( product_fst_nat_nat @ X4 ) @ ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1407_case__prod__beta_H,axiom,
% 7.78/3.94 ( produc4245557441103728435nt_int
% 7.78/3.94 = ( ^ [F2: int > int > product_prod_int_int,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1408_case__prod__beta_H,axiom,
% 7.78/3.94 ( produc4947309494688390418_int_o
% 7.78/3.94 = ( ^ [F2: int > int > $o,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1409_case__prod__beta_H,axiom,
% 7.78/3.94 ( produc8211389475949308722nt_int
% 7.78/3.94 = ( ^ [F2: int > int > int,X4: product_prod_int_int] : ( F2 @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1410_case__prod__unfold,axiom,
% 7.78/3.94 ( produc27273713700761075at_nat
% 7.78/3.94 = ( ^ [C4: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P3: product_prod_nat_nat] : ( C4 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1411_case__prod__unfold,axiom,
% 7.78/3.94 ( produc8739625826339149834_nat_o
% 7.78/3.94 = ( ^ [C4: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat] : ( C4 @ ( product_fst_nat_nat @ P3 ) @ ( product_snd_nat_nat @ P3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1412_case__prod__unfold,axiom,
% 7.78/3.94 ( produc4245557441103728435nt_int
% 7.78/3.94 = ( ^ [C4: int > int > product_prod_int_int,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1413_case__prod__unfold,axiom,
% 7.78/3.94 ( produc4947309494688390418_int_o
% 7.78/3.94 = ( ^ [C4: int > int > $o,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1414_case__prod__unfold,axiom,
% 7.78/3.94 ( produc8211389475949308722nt_int
% 7.78/3.94 = ( ^ [C4: int > int > int,P3: product_prod_int_int] : ( C4 @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1415_pred__subset__eq2,axiom,
% 7.78/3.94 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 7.78/3.94 ( ( ord_le3072208448688395470_nat_o
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.94 = ( ord_le5997549366648089703at_nat @ R3 @ S5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1416_pred__subset__eq2,axiom,
% 7.78/3.94 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( ord_le3935385432712749774_nat_o
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.94 = ( ord_le1268244103169919719at_nat @ R3 @ S5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1417_pred__subset__eq2,axiom,
% 7.78/3.94 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 7.78/3.94 ( ( ord_le3404735783095501756_num_o
% 7.78/3.94 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 7.78/3.94 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.94 = ( ord_le8085105155179020875at_num @ R3 @ S5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1418_pred__subset__eq2,axiom,
% 7.78/3.94 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( ord_le2646555220125990790_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.94 = ( ord_le3146513528884898305at_nat @ R3 @ S5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1419_pred__subset__eq2,axiom,
% 7.78/3.94 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.94 ( ( ord_le6741204236512500942_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.94 = ( ord_le2843351958646193337nt_int @ R3 @ S5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1420_comp__fun__commute__on__def,axiom,
% 7.78/3.94 ( finite8619596206551965927at_nat
% 7.78/3.94 = ( ^ [S4: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat > nat] :
% 7.78/3.94 ! [X4: produc3843707927480180839at_nat,Y5: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ X4 @ S4 )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ Y5 @ S4 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1421_comp__fun__commute__on__def,axiom,
% 7.78/3.94 ( finite2110315540964234241at_nat
% 7.78/3.94 = ( ^ [S4: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat > nat] :
% 7.78/3.94 ! [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ X4 @ S4 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ Y5 @ S4 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1422_comp__fun__commute__on__def,axiom,
% 7.78/3.94 ( finite4703585013658510744_o_nat
% 7.78/3.94 = ( ^ [S4: set_o,F2: $o > nat > nat] :
% 7.78/3.94 ! [X4: $o,Y5: $o] :
% 7.78/3.94 ( ( member_o @ X4 @ S4 )
% 7.78/3.94 => ( ( member_o @ Y5 @ S4 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1423_comp__fun__commute__on__def,axiom,
% 7.78/3.94 ( finite3582905537739598962at_nat
% 7.78/3.94 = ( ^ [S4: set_nat,F2: nat > nat > nat] :
% 7.78/3.94 ! [X4: nat,Y5: nat] :
% 7.78/3.94 ( ( member_nat @ X4 @ S4 )
% 7.78/3.94 => ( ( member_nat @ Y5 @ S4 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1424_comp__fun__commute__on__def,axiom,
% 7.78/3.94 ( finite4582259249640653518nt_nat
% 7.78/3.94 = ( ^ [S4: set_int,F2: int > nat > nat] :
% 7.78/3.94 ! [X4: int,Y5: int] :
% 7.78/3.94 ( ( member_int @ X4 @ S4 )
% 7.78/3.94 => ( ( member_int @ Y5 @ S4 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F2 @ Y5 ) @ ( F2 @ X4 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1425_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 7.78/3.94 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( finite8619596206551965927at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1426_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 7.78/3.94 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.78/3.94 ( ( finite2110315540964234241at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1427_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 7.78/3.94 ! [S5: set_o,F: $o > nat > nat,X2: $o,Y3: $o] :
% 7.78/3.94 ( ( finite4703585013658510744_o_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_o @ X2 @ S5 )
% 7.78/3.94 => ( ( member_o @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1428_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 7.78/3.94 ! [S5: set_nat,F: nat > nat > nat,X2: nat,Y3: nat] :
% 7.78/3.94 ( ( finite3582905537739598962at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1429_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
% 7.78/3.94 ! [S5: set_int,F: int > nat > nat,X2: int,Y3: int] :
% 7.78/3.94 ( ( finite4582259249640653518nt_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_int @ X2 @ S5 )
% 7.78/3.94 => ( ( member_int @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1430_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > $o > $o,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,G: nat > $o] :
% 7.78/3.94 ( ( finite2818816984019561153_nat_o @ S5 @ F )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1431_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,G: nat > nat] :
% 7.78/3.94 ( ( finite8619596206551965927at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1432_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > $o > $o,X2: product_prod_nat_nat,Y3: product_prod_nat_nat,G: nat > $o] :
% 7.78/3.94 ( ( finite1496024664758132007_nat_o @ S5 @ F )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1433_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat,G: nat > nat] :
% 7.78/3.94 ( ( finite2110315540964234241at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1434_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_o,F: $o > $o > $o,X2: $o,Y3: $o,G: nat > $o] :
% 7.78/3.94 ( ( finite7905178416053733328on_o_o @ S5 @ F )
% 7.78/3.94 => ( ( member_o @ X2 @ S5 )
% 7.78/3.94 => ( ( member_o @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1435_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_o,F: $o > nat > nat,X2: $o,Y3: $o,G: nat > nat] :
% 7.78/3.94 ( ( finite4703585013658510744_o_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_o @ X2 @ S5 )
% 7.78/3.94 => ( ( member_o @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1436_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_nat,F: nat > $o > $o,X2: nat,Y3: nat,G: nat > $o] :
% 7.78/3.94 ( ( finite7806256374766696054_nat_o @ S5 @ F )
% 7.78/3.94 => ( ( member_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1437_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_nat,F: nat > nat > nat,X2: nat,Y3: nat,G: nat > nat] :
% 7.78/3.94 ( ( finite3582905537739598962at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( member_nat @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1438_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_int,F: int > $o > $o,X2: int,Y3: int,G: nat > $o] :
% 7.78/3.94 ( ( finite5985214029334008090_int_o @ S5 @ F )
% 7.78/3.94 => ( ( member_int @ X2 @ S5 )
% 7.78/3.94 => ( ( member_int @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_o_o_nat @ ( F @ Y3 ) @ ( comp_o_o_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_o_o_nat @ ( F @ X2 ) @ ( comp_o_o_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1439_comp__fun__commute__on_Ocommute__left__comp,axiom,
% 7.78/3.94 ! [S5: set_int,F: int > nat > nat,X2: int,Y3: int,G: nat > nat] :
% 7.78/3.94 ( ( finite4582259249640653518nt_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_int @ X2 @ S5 )
% 7.78/3.94 => ( ( member_int @ Y3 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1440_comp__fun__commute__on_Ointro,axiom,
% 7.78/3.94 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat] :
% 7.78/3.94 ( ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ X @ S5 )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ Y @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 7.78/3.94 => ( finite8619596206551965927at_nat @ S5 @ F ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1441_comp__fun__commute__on_Ointro,axiom,
% 7.78/3.94 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat] :
% 7.78/3.94 ( ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ X @ S5 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ Y @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 7.78/3.94 => ( finite2110315540964234241at_nat @ S5 @ F ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1442_comp__fun__commute__on_Ointro,axiom,
% 7.78/3.94 ! [S5: set_o,F: $o > nat > nat] :
% 7.78/3.94 ( ! [X: $o,Y: $o] :
% 7.78/3.94 ( ( member_o @ X @ S5 )
% 7.78/3.94 => ( ( member_o @ Y @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 7.78/3.94 => ( finite4703585013658510744_o_nat @ S5 @ F ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1443_comp__fun__commute__on_Ointro,axiom,
% 7.78/3.94 ! [S5: set_nat,F: nat > nat > nat] :
% 7.78/3.94 ( ! [X: nat,Y: nat] :
% 7.78/3.94 ( ( member_nat @ X @ S5 )
% 7.78/3.94 => ( ( member_nat @ Y @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 7.78/3.94 => ( finite3582905537739598962at_nat @ S5 @ F ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1444_comp__fun__commute__on_Ointro,axiom,
% 7.78/3.94 ! [S5: set_int,F: int > nat > nat] :
% 7.78/3.94 ( ! [X: int,Y: int] :
% 7.78/3.94 ( ( member_int @ X @ S5 )
% 7.78/3.94 => ( ( member_int @ Y @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
% 7.78/3.94 => ( finite4582259249640653518nt_nat @ S5 @ F ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1445_case__prod__o__map__prod,axiom,
% 7.78/3.94 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G1: nat > nat,G22: nat > nat] :
% 7.78/3.94 ( ( comp_P3913276677246710332at_nat @ ( produc27273713700761075at_nat @ F ) @ ( produc6977886695330630970at_nat @ G1 @ G22 ) )
% 7.78/3.94 = ( produc27273713700761075at_nat
% 7.78/3.94 @ ^ [L3: nat,R5: nat] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1446_case__prod__o__map__prod,axiom,
% 7.78/3.94 ! [F: nat > nat > product_prod_nat_nat > $o,G1: nat > nat,G22: nat > nat] :
% 7.78/3.94 ( ( comp_P2002127591014248037at_nat @ ( produc8739625826339149834_nat_o @ F ) @ ( produc6977886695330630970at_nat @ G1 @ G22 ) )
% 7.78/3.94 = ( produc8739625826339149834_nat_o
% 7.78/3.94 @ ^ [L3: nat,R5: nat] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1447_case__prod__o__map__prod,axiom,
% 7.78/3.94 ! [F: int > int > product_prod_int_int,G1: int > int,G22: int > int] :
% 7.78/3.94 ( ( comp_P2788356708182965334nt_int @ ( produc4245557441103728435nt_int @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 7.78/3.94 = ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1448_case__prod__o__map__prod,axiom,
% 7.78/3.94 ! [F: int > int > $o,G1: int > int,G22: int > int] :
% 7.78/3.94 ( ( comp_P9034173210191959223nt_int @ ( produc4947309494688390418_int_o @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 7.78/3.94 = ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1449_case__prod__o__map__prod,axiom,
% 7.78/3.94 ! [F: int > int > int,G1: int > int,G22: int > int] :
% 7.78/3.94 ( ( comp_P5356232565778667509nt_int @ ( produc8211389475949308722nt_int @ F ) @ ( produc6036585564866528938nt_int @ G1 @ G22 ) )
% 7.78/3.94 = ( produc8211389475949308722nt_int
% 7.78/3.94 @ ^ [L3: int,R5: int] : ( F @ ( G1 @ L3 ) @ ( G22 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1450_vimage2p__relcompp__converse,axiom,
% 7.78/3.94 ! [Rep: product_prod_nat_nat > product_prod_nat_nat,Abs: product_prod_nat_nat > product_prod_nat_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: int > int,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( type_d281131942595027436at_nat @ Rep @ Abs @ top_to4669805908274784177at_nat )
% 7.78/3.94 => ( ( bNF_vi5426221348228882691_int_o @ F @ G @ ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ R3 ) @ S5 ) )
% 7.78/3.94 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_vi763171854521451549_nat_o @ Rep @ F @ R3 ) ) @ ( bNF_vi5426221348228882691_int_o @ Rep @ G @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1451_vimage2p__relcompp__converse,axiom,
% 7.78/3.94 ! [Rep: int > product_prod_nat_nat,Abs: product_prod_nat_nat > int,F: int > product_prod_nat_nat,G: code_integer > int,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( type_d7732240953928457511at_nat @ Rep @ Abs @ top_to4669805908274784177at_nat )
% 7.78/3.94 => ( ( bNF_vi2881549544236934259_int_o @ F @ G @ ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ R3 ) @ S5 ) )
% 7.78/3.94 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_vi1204582724742824157_nat_o @ Rep @ F @ R3 ) ) @ ( bNF_vi2881549544236934259_int_o @ Rep @ G @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1452_vimage2p__relcompp__converse,axiom,
% 7.78/3.94 ! [Rep: product_prod_nat_nat > int,Abs: int > product_prod_nat_nat,F: product_prod_nat_nat > int,G: int > code_integer,R3: int > int > $o,S5: int > code_integer > $o] :
% 7.78/3.94 ( ( type_d1331861005912558337at_int @ Rep @ Abs @ top_top_set_int )
% 7.78/3.94 => ( ( bNF_vi33923956287962137eger_o @ F @ G @ ( relcom967497705283160040nteger @ ( conversep_int_int @ R3 ) @ S5 ) )
% 7.78/3.94 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_vi2682369418337388893_int_o @ Rep @ F @ R3 ) ) @ ( bNF_vi33923956287962137eger_o @ Rep @ G @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1453_vimage2p__relcompp__converse,axiom,
% 7.78/3.94 ! [Rep: int > int,Abs: int > int,F: int > int,G: code_integer > code_integer,R3: int > int > $o,S5: int > code_integer > $o] :
% 7.78/3.94 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ top_top_set_int )
% 7.78/3.94 => ( ( bNF_vi699694178825965831eger_o @ F @ G @ ( relcom967497705283160040nteger @ ( conversep_int_int @ R3 ) @ S5 ) )
% 7.78/3.94 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_vi3884084463199473129_int_o @ Rep @ F @ R3 ) ) @ ( bNF_vi699694178825965831eger_o @ Rep @ G @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1454_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ ( id_on_7869290023980668164at_nat @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member8757157785044589968at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1455_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ ( id_on_2554058798563519774at_nat @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member8440522571783428010at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1456_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: $o,Y3: $o,A4: set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ ( id_on_o @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member_o @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1457_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ ( id_on_3275838214495744996at_nat @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member6273874620674182256at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1458_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( id_on_6713504163309144702at_nat @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member2643936169264416010at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1459_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: nat,Y3: nat,A4: set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( id_on_nat @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1460_Id__on__iff,axiom,
% 7.78/3.94 ! [X2: int,Y3: int,A4: set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( id_on_int @ A4 ) )
% 7.78/3.94 = ( ( X2 = Y3 )
% 7.78/3.94 & ( member_int @ X2 @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1461_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.94 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ ( id_on_7869290023980668164at_nat @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1462_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.94 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( id_on_2554058798563519774at_nat @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1463_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: $o,B: $o,A4: set_o] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member_o @ A @ A4 )
% 7.78/3.94 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( id_on_o @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1464_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 7.78/3.94 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( id_on_3275838214495744996at_nat @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1465_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 7.78/3.94 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( id_on_6713504163309144702at_nat @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1466_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: nat,B: nat,A4: set_nat] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1467_Id__on__eqI,axiom,
% 7.78/3.94 ! [A: int,B: int,A4: set_int] :
% 7.78/3.94 ( ( A = B )
% 7.78/3.94 => ( ( member_int @ A @ A4 )
% 7.78/3.94 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1468_Id__onE,axiom,
% 7.78/3.94 ! [C: produc1906917888121415911at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( member6009668390874684176at_nat @ C @ ( id_on_7869290023980668164at_nat @ A4 ) )
% 7.78/3.94 => ~ ! [X: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( produc2335810615602371415at_nat @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1469_Id__onE,axiom,
% 7.78/3.94 ! [C: produc859450856879609959at_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member8206827879206165904at_nat @ C @ ( id_on_2554058798563519774at_nat @ A4 ) )
% 7.78/3.94 => ~ ! [X: product_prod_nat_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( produc6161850002892822231at_nat @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1470_Id__onE,axiom,
% 7.78/3.94 ! [C: product_prod_o_o,A4: set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ C @ ( id_on_o @ A4 ) )
% 7.78/3.94 => ~ ! [X: $o] :
% 7.78/3.94 ( ( member_o @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_o_o @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1471_Id__onE,axiom,
% 7.78/3.94 ! [C: produc1319942482725812455at_nat,A4: set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( member1466754251312161552at_nat @ C @ ( id_on_3275838214495744996at_nat @ A4 ) )
% 7.78/3.94 => ~ ! [X: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( member6273874620674182256at_nat @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( produc9060074326276436823at_nat @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1472_Id__onE,axiom,
% 7.78/3.94 ! [C: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ C @ ( id_on_6713504163309144702at_nat @ A4 ) )
% 7.78/3.94 => ~ ! [X: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member2643936169264416010at_nat @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( produc2922128104949294807at_nat @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1473_Id__onE,axiom,
% 7.78/3.94 ! [C: product_prod_nat_nat,A4: set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A4 ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_nat_nat @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1474_Id__onE,axiom,
% 7.78/3.94 ! [C: product_prod_int_int,A4: set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A4 ) )
% 7.78/3.94 => ~ ! [X: int] :
% 7.78/3.94 ( ( member_int @ X @ A4 )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_int_int @ X @ X ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1475_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,R22: nat > nat > $o,P2: nat > nat > $o,Q2: nat > nat > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( bNF_re578469030762574527_nat_o @ R1
% 7.78/3.94 @ ( bNF_re4705727531993890431at_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_fst_nat_nat @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1476_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,R22: int > int > $o,P2: nat > int > $o,Q2: nat > int > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 7.78/3.94 ( ( bNF_re605504016728627135_int_o @ R1
% 7.78/3.94 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_fst_int_int @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1477_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: int > int > $o,R22: nat > nat > $o,P2: int > nat > $o,Q2: int > nat > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( bNF_re3376528473927230327_nat_o @ R1
% 7.78/3.94 @ ( bNF_re4705727531993890431at_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( product_fst_nat_nat @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_int_int @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1478_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: int > int > $o,R22: int > int > $o,P2: int > int > $o,Q2: int > int > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 7.78/3.94 ( ( bNF_re3403563459893282935_int_o @ R1
% 7.78/3.94 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( product_fst_int_int @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_int_int @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1479_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: nat > ref_a > $o,Q2: nat > heap_e7401611519738050253t_unit > $o,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 7.78/3.94 ( ( bNF_re5655699643857186083unit_o @ R1
% 7.78/3.94 @ ( bNF_re1850668159662942673it_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_nat_nat @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_nat_nat @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1480_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: nat > nat > $o,P2: ref_a > nat > $o,Q2: heap_e7401611519738050253t_unit > nat > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( bNF_re9202112420002600977_nat_o @ R1
% 7.78/3.94 @ ( bNF_re4705727531993890431at_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ B @ B5 )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( product_fst_nat_nat @ B ) )
% 7.78/3.94 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( product_snd_nat_nat @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1481_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: int > int > $o,P2: ref_a > int > $o,Q2: heap_e7401611519738050253t_unit > int > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 7.78/3.94 ( ( bNF_re5775369113877777_int_o @ R1
% 7.78/3.94 @ ( bNF_re5089333283451836215nt_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ B @ B5 )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ B5 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( product_fst_int_int @ B ) )
% 7.78/3.94 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( product_snd_int_int @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1482_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: int > int > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: int > ref_a > $o,Q2: int > heap_e7401611519738050253t_unit > $o,A: product_prod_int_int,A4: set_Pr958786334691620121nt_int,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 7.78/3.94 ( ( bNF_re5404797796594736747unit_o @ R1
% 7.78/3.94 @ ( bNF_re1850668159662942673it_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member5262025264175285858nt_int @ A @ A4 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 7.78/3.94 => ( ( ord_le2843351958646193337nt_int @ A4 @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( product_fst_int_int @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 7.78/3.94 = ( Q2 @ ( product_snd_int_int @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1483_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: product_prod_nat_nat > int > $o,R22: product_prod_nat_nat > int > $o,P2: product_prod_nat_nat > product_prod_nat_nat > $o,Q2: int > int > $o,A: produc4196048018000912732at_int,A4: set_Pr49084382684228242at_int,B: produc4196048018000912732at_int,B5: set_Pr49084382684228242at_int] :
% 7.78/3.94 ( ( bNF_re717283939379294677_int_o @ R1
% 7.78/3.94 @ ( bNF_re6644619430987730960nt_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member8394280151737582451at_int @ A @ A4 )
% 7.78/3.94 => ( ( member8394280151737582451at_int @ B @ B5 )
% 7.78/3.94 => ( ( ord_le4604737605482584818at_int @ A4 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le4604737605482584818at_int @ B5 @ ( collec2851339944984316337at_int @ ( produc6937227050501860053_int_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( produc4619704898428564714at_int @ A ) @ ( produc4619704898428564714at_int @ B ) )
% 7.78/3.94 = ( Q2 @ ( produc3064508320661873192at_int @ A ) @ ( produc3064508320661873192at_int @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1484_predicate2__transferD,axiom,
% 7.78/3.94 ! [R1: ref_a > heap_e7401611519738050253t_unit > $o,R22: ref_a > heap_e7401611519738050253t_unit > $o,P2: ref_a > ref_a > $o,Q2: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o,A: produc7812382424243267045t_unit,A4: set_Pr1133966238863718811t_unit,B: produc7812382424243267045t_unit,B5: set_Pr1133966238863718811t_unit] :
% 7.78/3.94 ( ( bNF_re1366391616432607057unit_o @ R1
% 7.78/3.94 @ ( bNF_re1850668159662942673it_o_o @ R22
% 7.78/3.94 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.94 @ P2
% 7.78/3.94 @ Q2 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ A @ A4 )
% 7.78/3.94 => ( ( member7849944260330398460t_unit @ B @ B5 )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ A4 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R1 ) ) )
% 7.78/3.94 => ( ( ord_le5525191956872776187t_unit @ B5 @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R22 ) ) )
% 7.78/3.94 => ( ( P2 @ ( produc473321116828791851t_unit @ A ) @ ( produc473321116828791851t_unit @ B ) )
% 7.78/3.94 = ( Q2 @ ( produc1126150082675451753t_unit @ A ) @ ( produc1126150082675451753t_unit @ B ) ) ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1485_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: $o] :
% 7.78/3.94 ( ( comp_P2137996956111167876_o_o_o @ product_fst_o_o
% 7.78/3.94 @ ^ [X4: $o] : ( product_Pair_o_o @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_o @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1486_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: num] :
% 7.78/3.94 ( ( comp_P864883071962432936um_num @ product_fst_num_num
% 7.78/3.94 @ ^ [X4: num] : ( product_Pair_num_num @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_num @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1487_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( comp_P8235817900121468292at_nat @ produc4486455499028916547at_nat
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_set7849613212452405432at_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1488_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( comp_P4528037747288561284at_nat @ produc6011863565407846595at_nat
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_set2334057505560298834at_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1489_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: nat] :
% 7.78/3.94 ( ( comp_P1955610211387027840at_nat @ product_fst_nat_nat
% 7.78/3.94 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1490_fst__diag__id,axiom,
% 7.78/3.94 ! [Z2: int] :
% 7.78/3.94 ( ( comp_P6651465171681656048nt_int @ product_fst_int_int
% 7.78/3.94 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_int @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1491_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: $o] :
% 7.78/3.94 ( ( comp_P2137996956111167876_o_o_o @ product_snd_o_o
% 7.78/3.94 @ ^ [X4: $o] : ( product_Pair_o_o @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_o @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1492_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: num] :
% 7.78/3.94 ( ( comp_P864883071962432936um_num @ product_snd_num_num
% 7.78/3.94 @ ^ [X4: num] : ( product_Pair_num_num @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_num @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1493_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( comp_P8235817900121468292at_nat @ produc826222791318859909at_nat
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_set7849613212452405432at_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1494_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( comp_P4528037747288561284at_nat @ produc2937545259423399429at_nat
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_set2334057505560298834at_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1495_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: nat] :
% 7.78/3.94 ( ( comp_P1955610211387027840at_nat @ product_snd_nat_nat
% 7.78/3.94 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_nat @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1496_snd__diag__id,axiom,
% 7.78/3.94 ! [Z2: int] :
% 7.78/3.94 ( ( comp_P6651465171681656048nt_int @ product_snd_int_int
% 7.78/3.94 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ X4 )
% 7.78/3.94 @ Z2 )
% 7.78/3.94 = ( id_int @ Z2 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1497_case__prod__comp,axiom,
% 7.78/3.94 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: produc3346328345660746739nteger] :
% 7.78/3.94 ( ( produc4281629032016041417nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X2 )
% 7.78/3.94 = ( F @ ( G @ ( produc1861665112190112313nteger @ X2 ) ) @ ( produc7955729907432593271nteger @ X2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1498_lookup__def,axiom,
% 7.78/3.94 ( lookup_a
% 7.78/3.94 = ( ^ [R5: ref_a] :
% 7.78/3.94 ( heap_tap_a
% 7.78/3.94 @ ^ [H5: heap_e7401611519738050253t_unit] : ( get_a @ H5 @ R5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1499_fst__snd__flip,axiom,
% 7.78/3.94 ( produc4486455499028916547at_nat
% 7.78/3.94 = ( comp_P3728553842126764068at_nat @ produc826222791318859909at_nat
% 7.78/3.94 @ ( produc5456455677105495163at_nat
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1500_fst__snd__flip,axiom,
% 7.78/3.94 ( produc6011863565407846595at_nat
% 7.78/3.94 = ( comp_P4974406650942564362at_nat @ produc2937545259423399429at_nat
% 7.78/3.94 @ ( produc7548845685434208379at_nat
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1501_fst__snd__flip,axiom,
% 7.78/3.94 ( product_fst_num_nat
% 7.78/3.94 = ( comp_P5051845089628979463um_nat @ product_snd_nat_num
% 7.78/3.94 @ ( produc5219324331026901427at_num
% 7.78/3.94 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1502_fst__snd__flip,axiom,
% 7.78/3.94 ( product_fst_nat_nat
% 7.78/3.94 = ( comp_P1567445206330693457at_nat @ product_snd_nat_nat
% 7.78/3.94 @ ( produc2626176000494625587at_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1503_fst__snd__flip,axiom,
% 7.78/3.94 ( produc473321116828791851t_unit
% 7.78/3.94 = ( comp_P1287623958910499840t_unit @ produc6369869760173755749_ref_a
% 7.78/3.94 @ ( produc2058451029528183389_ref_a
% 7.78/3.94 @ ^ [X4: ref_a,Y5: heap_e7401611519738050253t_unit] : ( produc2564672488694626579_ref_a @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1504_fst__snd__flip,axiom,
% 7.78/3.94 ( produc5717040794327095847_ref_a
% 7.78/3.94 = ( comp_P2006160480335490974_ref_a @ produc1126150082675451753t_unit
% 7.78/3.94 @ ( produc4426278547552487717t_unit
% 7.78/3.94 @ ^ [X4: heap_e7401611519738050253t_unit,Y5: ref_a] : ( produc6544324848051098391t_unit @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1505_fst__snd__flip,axiom,
% 7.78/3.94 ( product_fst_int_int
% 7.78/3.94 = ( comp_P5356232565778667509nt_int @ product_snd_int_int
% 7.78/3.94 @ ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1506_snd__fst__flip,axiom,
% 7.78/3.94 ( produc826222791318859909at_nat
% 7.78/3.94 = ( comp_P3728553842126764068at_nat @ produc4486455499028916547at_nat
% 7.78/3.94 @ ( produc5456455677105495163at_nat
% 7.78/3.94 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1507_snd__fst__flip,axiom,
% 7.78/3.94 ( produc2937545259423399429at_nat
% 7.78/3.94 = ( comp_P4974406650942564362at_nat @ produc6011863565407846595at_nat
% 7.78/3.94 @ ( produc7548845685434208379at_nat
% 7.78/3.94 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1508_snd__fst__flip,axiom,
% 7.78/3.94 ( product_snd_num_nat
% 7.78/3.94 = ( comp_P8336958949797789649um_nat @ product_fst_nat_num
% 7.78/3.94 @ ( produc5219324331026901427at_num
% 7.78/3.94 @ ^ [X4: num,Y5: nat] : ( product_Pair_nat_num @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1509_snd__fst__flip,axiom,
% 7.78/3.94 ( product_snd_nat_nat
% 7.78/3.94 = ( comp_P1567445206330693457at_nat @ product_fst_nat_nat
% 7.78/3.94 @ ( produc2626176000494625587at_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1510_snd__fst__flip,axiom,
% 7.78/3.94 ( produc6369869760173755749_ref_a
% 7.78/3.94 = ( comp_P7254561687666694144_ref_a @ produc473321116828791851t_unit
% 7.78/3.94 @ ( produc4426278547552487717t_unit
% 7.78/3.94 @ ^ [X4: heap_e7401611519738050253t_unit,Y5: ref_a] : ( produc6544324848051098391t_unit @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1511_snd__fst__flip,axiom,
% 7.78/3.94 ( produc1126150082675451753t_unit
% 7.78/3.94 = ( comp_P3239167524078694454t_unit @ produc5717040794327095847_ref_a
% 7.78/3.94 @ ( produc2058451029528183389_ref_a
% 7.78/3.94 @ ^ [X4: ref_a,Y5: heap_e7401611519738050253t_unit] : ( produc2564672488694626579_ref_a @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1512_snd__fst__flip,axiom,
% 7.78/3.94 ( product_snd_int_int
% 7.78/3.94 = ( comp_P5356232565778667509nt_int @ product_fst_int_int
% 7.78/3.94 @ ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_int_int @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1513_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 7.78/3.94 ! [S5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat > nat,X2: produc3843707927480180839at_nat] :
% 7.78/3.94 ( ( finite352855791390415404at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8757157785044589968at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( F @ X2 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1514_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 7.78/3.94 ! [S5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat > nat,X2: product_prod_nat_nat] :
% 7.78/3.94 ( ( finite5150387867909132486at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member8440522571783428010at_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( F @ X2 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1515_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 7.78/3.94 ! [S5: set_o,F: $o > nat > nat,X2: $o] :
% 7.78/3.94 ( ( finite2426395113773319005_o_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_o @ X2 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( F @ X2 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1516_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 7.78/3.94 ! [S5: set_nat,F: nat > nat > nat,X2: nat] :
% 7.78/3.94 ( ( finite7982400111564556781at_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_nat @ X2 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( F @ X2 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1517_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
% 7.78/3.94 ! [S5: set_int,F: int > nat > nat,X2: int] :
% 7.78/3.94 ( ( finite8981753823465611337nt_nat @ S5 @ F )
% 7.78/3.94 => ( ( member_int @ X2 @ S5 )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
% 7.78/3.94 = ( F @ X2 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1518_OO__Grp__cong,axiom,
% 7.78/3.94 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > int] :
% 7.78/3.94 ( ( A4 = B5 )
% 7.78/3.94 => ( ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_Gr7275288873855648526at_nat @ A4 @ F ) ) @ ( bNF_Gr190934199572118623at_int @ A4 @ G ) )
% 7.78/3.94 = ( relcom8911704206367525917at_int @ ( conver6965824823119931701at_nat @ ( bNF_Gr7275288873855648526at_nat @ B5 @ F ) ) @ ( bNF_Gr190934199572118623at_int @ B5 @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1519_OO__Grp__cong,axiom,
% 7.78/3.94 ! [A4: set_int,B5: set_int,F: int > int,G: int > code_integer] :
% 7.78/3.94 ( ( A4 = B5 )
% 7.78/3.94 => ( ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_Grp_int_int @ A4 @ F ) ) @ ( bNF_Gr6684649993275963353nteger @ A4 @ G ) )
% 7.78/3.94 = ( relcom967497705283160040nteger @ ( conversep_int_int @ ( bNF_Grp_int_int @ B5 @ F ) ) @ ( bNF_Gr6684649993275963353nteger @ B5 @ G ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1520_fst__diag__fst,axiom,
% 7.78/3.94 ( ( comp_P9134237804721252988t_unit @ produc6942380573175061695_ref_a
% 7.78/3.94 @ ( comp_r6154141770783548544t_unit
% 7.78/3.94 @ ^ [X4: ref_a] : ( produc1340070678782110931_ref_a @ X4 @ X4 )
% 7.78/3.94 @ produc473321116828791851t_unit ) )
% 7.78/3.94 = produc473321116828791851t_unit ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1521_snd__diag__snd,axiom,
% 7.78/3.94 ( ( comp_P8237986404257982958t_unit @ produc1692618790031806469t_unit
% 7.78/3.94 @ ( comp_h5940001671827863714t_unit
% 7.78/3.94 @ ^ [X4: heap_e7401611519738050253t_unit] : ( produc8256076736985659095t_unit @ X4 @ X4 )
% 7.78/3.94 @ produc1126150082675451753t_unit ) )
% 7.78/3.94 = produc1126150082675451753t_unit ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1522_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,M: nat > nat,M1: $o > nat,M2: nat > $o,F: nat > nat,G: nat > nat] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_nat_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_nat_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1523_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: int > $o,Abs: $o > int,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: int > nat] :
% 7.78/3.94 ( ( type_d8403010662121346494_int_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_nat_int @ ( comp_o_nat_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_int_nat_int @ ( comp_o_nat_int @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_int_int @ ( comp_o_int_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1524_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: num > $o,Abs: $o > num,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: int > nat] :
% 7.78/3.94 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_o_int @ ( comp_o_o_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_num_o_int @ ( comp_o_o_num @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1525_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: nat > nat] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1526_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > $o,G: nat > nat] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_o_nat @ ( comp_o_o_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_o_o_nat @ ( comp_o_o_o @ ( comp_o_o_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1527_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_o_num_int @ ( comp_o_num_o @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_int @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1528_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: num > $o,Abs: $o > num,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 7.78/3.94 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_num_num_int @ ( comp_o_num_num @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1529_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > num,G: int > nat] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_num_int @ ( comp_o_num_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_nat_num_int @ ( comp_o_num_nat @ ( comp_o_num_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1530_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: nat > nat] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1531_type__copy__map__comp0,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,M: nat > $o,M1: $o > $o,M2: nat > $o,F: $o > nat,G: nat > nat] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( M
% 7.78/3.94 = ( comp_o_o_nat @ M1 @ M2 ) )
% 7.78/3.94 => ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ F @ M ) @ G )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( comp_o_nat_nat @ ( comp_o_nat_o @ F @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1532_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: int > $o,Abs: $o > int,Rep2: nat > $o,Abs2: $o > nat,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d8403010662121346494_int_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_int_nat_int @ ( comp_o_nat_int @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_int_int @ ( comp_o_int_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1533_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: num > $o,Abs: $o > num,Rep2: $o > $o,Abs2: $o > $o,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_o_int @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_num_o_int @ ( comp_o_o_num @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1534_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,Rep2: $o > $o,Abs2: $o > $o,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1535_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,Rep2: $o > $o,Abs2: $o > $o,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_definition_o_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_o_o_nat @ ( comp_o_o_o @ ( comp_o_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1536_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_o_num_int @ ( comp_o_num_o @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_int @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1537_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: num > $o,Abs: $o > num,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d9070036042389994064_num_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_num_num_int @ ( comp_o_num_num @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_num_int @ ( comp_o_num_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1538_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,Rep2: num > $o,Abs2: $o > num,Rep3: int > nat,Abs3: nat > int,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d9070036042389994064_num_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d7249847660678803242nt_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_num_int @ ( comp_o_num_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_nat_num_int @ ( comp_o_num_nat @ ( comp_o_num_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_int @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1539_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: $o > $o,Abs: $o > $o,Rep2: nat > $o,Abs2: $o > nat,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_definition_o_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_o_nat_nat @ ( comp_o_nat_o @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_o_nat @ ( comp_o_o_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1540_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,Rep2: nat > $o,Abs2: $o > nat,Rep3: nat > nat,Abs3: nat > nat,M: nat > $o,M1: $o > $o,M2: nat > $o] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d1000680970699258650_nat_o @ Rep2 @ Abs2 @ top_top_set_o )
% 7.78/3.94 => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 7.78/3.94 => ( ( ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_nat_nat_nat @ ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_nat_nat_nat @ ( comp_o_nat_nat @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_o_nat @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1541_type__copy__map__comp0__undo,axiom,
% 7.78/3.94 ! [Rep: nat > $o,Abs: $o > nat,Rep2: $o > char,Abs2: char > $o,Rep3: nat > $o,Abs3: $o > nat,M: $o > char,M1: $o > char,M2: $o > $o] :
% 7.78/3.94 ( ( type_d1000680970699258650_nat_o @ Rep @ Abs @ top_top_set_o )
% 7.78/3.94 => ( ( type_d9076672964931703357o_char @ Rep2 @ Abs2 @ top_top_set_char )
% 7.78/3.94 => ( ( type_d1000680970699258650_nat_o @ Rep3 @ Abs3 @ top_top_set_o )
% 7.78/3.94 => ( ( ( comp_o_o_nat @ ( comp_char_o_o @ Abs2 @ M ) @ Rep3 )
% 7.78/3.94 = ( comp_nat_o_nat @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs2 @ M1 ) @ Rep ) @ ( comp_o_nat_nat @ ( comp_o_nat_o @ Abs @ M2 ) @ Rep3 ) ) )
% 7.78/3.94 => ( ( comp_o_char_o @ M1 @ M2 )
% 7.78/3.94 = M ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1542_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( bNF_re3734335887435638179at_nat
% 7.78/3.94 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom8141925468094106422ar_nat
% 7.78/3.94 @ ( conver5210974729819302706ar_nat
% 7.78/3.94 @ ( bNF_Gr1779741795384719769ar_nat
% 7.78/3.94 @ ( collec1683818095804863890at_nat
% 7.78/3.94 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1491501995297412481t_char @ product_fst_nat_nat ) ) )
% 7.78/3.94 @ ( bNF_Gr1779741795384719769ar_nat
% 7.78/3.94 @ ( collec1683818095804863890at_nat
% 7.78/3.94 @ ^ [X4: char > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8382823969816519465at_nat @ X4 @ top_top_set_char ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1491501995297412481t_char @ product_snd_nat_nat ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1543_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( bNF_re6557955094579809201at_nat
% 7.78/3.94 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom7707146719550107439at_nat
% 7.78/3.94 @ ( conver7478146827351332082at_nat
% 7.78/3.94 @ ( bNF_Gr7368557922277781849at_nat
% 7.78/3.94 @ ( collec2824469931397938891at_nat
% 7.78/3.94 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1320480151300532104at_rat @ product_fst_nat_nat ) ) )
% 7.78/3.94 @ ( bNF_Gr7368557922277781849at_nat
% 7.78/3.94 @ ( collec2824469931397938891at_nat
% 7.78/3.94 @ ^ [X4: rat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_9175953278516507234at_nat @ X4 @ top_top_set_rat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1320480151300532104at_rat @ product_snd_nat_nat ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1544_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( bNF_re5653821019739307937at_nat
% 7.78/3.94 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom8186637903969514807at_nat
% 7.78/3.94 @ ( conver3498139987538047730at_nat
% 7.78/3.94 @ ( bNF_Gr3388551082464497497at_nat
% 7.78/3.94 @ ( collec8718012497556192979at_nat
% 7.78/3.94 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1955610211387027840at_nat @ product_fst_nat_nat ) ) )
% 7.78/3.94 @ ( bNF_Gr3388551082464497497at_nat
% 7.78/3.94 @ ( collec8718012497556192979at_nat
% 7.78/3.94 @ ^ [X4: nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ X4 @ top_top_set_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1955610211387027840at_nat @ product_snd_nat_nat ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1545_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( bNF_re3715656647883201625at_nat
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom2406850561174050523nt_nat
% 7.78/3.94 @ ( conver1572571282669976050nt_nat
% 7.78/3.94 @ ( bNF_Gr1462982377596425817nt_nat
% 7.78/3.94 @ ( collec2532482545165550967at_nat
% 7.78/3.94 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1953119740877977564at_int @ product_fst_nat_nat ) ) )
% 7.78/3.94 @ ( bNF_Gr1462982377596425817nt_nat
% 7.78/3.94 @ ( collec2532482545165550967at_nat
% 7.78/3.94 @ ^ [X4: int > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_8883965892284119310at_nat @ X4 @ top_top_set_int ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P1953119740877977564at_int @ product_snd_nat_nat ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1546_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: num > num > $o] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom1697847500783689711nt_num
% 7.78/3.94 @ ( conver5699786650113435344nt_num
% 7.78/3.94 @ ( bNF_Gr5590197745039885111nt_num
% 7.78/3.94 @ ( collec266097228571071243um_num
% 7.78/3.94 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P4305060815297604026um_int @ product_fst_num_num ) ) )
% 7.78/3.94 @ ( bNF_Gr5590197745039885111nt_num
% 7.78/3.94 @ ( collec266097228571071243um_num
% 7.78/3.94 @ ^ [X4: int > product_prod_num_num] : ( ord_le880128212290418581um_num @ ( image_7722540232540426402um_num @ X4 @ top_top_set_int ) @ ( collec2230928802738392704um_num @ ( produc5703948589228662326_num_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P4305060815297604026um_int @ product_snd_num_num ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1547_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: int > int > $o] :
% 7.78/3.94 ( ( bNF_re4731199128827642459nt_int
% 7.78/3.94 @ ^ [Y2: char,Z: char] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom4417706183330134766ar_int
% 7.78/3.94 @ ( conver1155128050257070662ar_int
% 7.78/3.94 @ ( bNF_Gr6947267152677263533ar_int
% 7.78/3.94 @ ( collec1380656525566158922nt_int
% 7.78/3.94 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P4161745170962941589t_char @ product_fst_int_int ) ) )
% 7.78/3.94 @ ( bNF_Gr6947267152677263533ar_int
% 7.78/3.94 @ ( collec1380656525566158922nt_int
% 7.78/3.94 @ ^ [X4: char > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5204326662208377313nt_int @ X4 @ top_top_set_char ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P4161745170962941589t_char @ product_snd_int_int ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1548_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: int > int > $o] :
% 7.78/3.94 ( ( bNF_re7554818335971813481nt_int
% 7.78/3.94 @ ^ [Y2: rat,Z: rat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom2810802720173317863at_int
% 7.78/3.94 @ ( conver6967689361887734790at_int
% 7.78/3.94 @ ( bNF_Gr6858100456814184557at_int
% 7.78/3.94 @ ( collec2521308361159233923nt_int
% 7.78/3.94 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6018825582104210588nt_rat @ product_fst_int_int ) ) )
% 7.78/3.94 @ ( bNF_Gr6858100456814184557at_int
% 7.78/3.94 @ ( collec2521308361159233923nt_int
% 7.78/3.94 @ ^ [X4: rat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5997455970908365082nt_int @ X4 @ top_top_set_rat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6018825582104210588nt_rat @ product_snd_int_int ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1549_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: int > int > $o] :
% 7.78/3.94 ( ( bNF_re6650684261131312217nt_int
% 7.78/3.94 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom3290293904592725231at_int
% 7.78/3.94 @ ( conver2987682522074450438at_int
% 7.78/3.94 @ ( bNF_Gr2878093617000900205at_int
% 7.78/3.94 @ ( collec8414850927317488011nt_int
% 7.78/3.94 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6653955642190706324nt_nat @ product_fst_int_int ) ) )
% 7.78/3.94 @ ( bNF_Gr2878093617000900205at_int
% 7.78/3.94 @ ( collec8414850927317488011nt_int
% 7.78/3.94 @ ^ [X4: nat > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_2667626500211843362nt_int @ X4 @ top_top_set_nat ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6653955642190706324nt_nat @ product_snd_int_int ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1550_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: int > int > $o] :
% 7.78/3.94 ( ( bNF_re4712519889275205905nt_int
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom6733878598652036755nt_int
% 7.78/3.94 @ ( conver1062113817206378758nt_int
% 7.78/3.94 @ ( bNF_Gr952524912132828525nt_int
% 7.78/3.94 @ ( collec2229320974926845999nt_int
% 7.78/3.94 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6651465171681656048nt_int @ product_fst_int_int ) ) )
% 7.78/3.94 @ ( bNF_Gr952524912132828525nt_int
% 7.78/3.94 @ ( collec2229320974926845999nt_int
% 7.78/3.94 @ ^ [X4: int > product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( image_5705468584675977158nt_int @ X4 @ top_top_set_int ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P6651465171681656048nt_int @ product_snd_int_int ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1551_fun_Orel__compp__Grp,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( bNF_re4629543205785817921at_nat
% 7.78/3.94 @ ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 = ( relcom5920149085449455271at_nat
% 7.78/3.94 @ ( conver6066198818478722162at_nat
% 7.78/3.94 @ ( bNF_Gr1532745923208276441at_nat
% 7.78/3.94 @ ( collec3092956710985254339at_nat
% 7.78/3.94 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P5292260908303971472st_nat @ product_fst_nat_nat ) ) )
% 7.78/3.94 @ ( bNF_Gr1532745923208276441at_nat
% 7.78/3.94 @ ( collec3092956710985254339at_nat
% 7.78/3.94 @ ^ [X4: list_nat > product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( image_2795870212791037530at_nat @ X4 @ top_top_set_list_nat ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) ) )
% 7.78/3.94 @ ( comp_P5292260908303971472st_nat @ product_snd_nat_nat ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1552_image__Pow__surj,axiom,
% 7.78/3.94 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.94 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.94 = B5 )
% 7.78/3.94 => ( ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) )
% 7.78/3.94 = ( pow_rat @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1553_image__Pow__surj,axiom,
% 7.78/3.94 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.94 = B5 )
% 7.78/3.94 => ( ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) )
% 7.78/3.94 = ( pow_nat @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1554_image__Pow__surj,axiom,
% 7.78/3.94 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.94 = B5 )
% 7.78/3.94 => ( ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) )
% 7.78/3.94 = ( pow_int @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1555_image__Pow__surj,axiom,
% 7.78/3.94 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.94 = B5 )
% 7.78/3.94 => ( ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) )
% 7.78/3.94 = ( pow_nat @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1556_image__Pow__surj,axiom,
% 7.78/3.94 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.94 ( ( ( image_int_int @ F @ A4 )
% 7.78/3.94 = B5 )
% 7.78/3.94 => ( ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) )
% 7.78/3.94 = ( pow_int @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1557_fst__diag__snd,axiom,
% 7.78/3.94 ( ( comp_P8237986404257982958t_unit @ produc2762368996035445955t_unit
% 7.78/3.94 @ ( comp_h5940001671827863714t_unit
% 7.78/3.94 @ ^ [X4: heap_e7401611519738050253t_unit] : ( produc8256076736985659095t_unit @ X4 @ X4 )
% 7.78/3.94 @ produc1126150082675451753t_unit ) )
% 7.78/3.94 = produc1126150082675451753t_unit ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1558_snd__diag__fst,axiom,
% 7.78/3.94 ( ( comp_P9134237804721252988t_unit @ produc8185483580310833921_ref_a
% 7.78/3.94 @ ( comp_r6154141770783548544t_unit
% 7.78/3.94 @ ^ [X4: ref_a] : ( produc1340070678782110931_ref_a @ X4 @ X4 )
% 7.78/3.94 @ produc473321116828791851t_unit ) )
% 7.78/3.94 = produc473321116828791851t_unit ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1559_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_Co726186806682698383nteger,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.94 ( ( bNF_re1181178334029315097nteger
% 7.78/3.94 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Gr4092539093814444494nteger @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Gr1453458339979195462nteger
% 7.78/3.94 @ ( collec5651646645946169514nteger
% 7.78/3.94 @ ^ [X4: code_integer > code_integer > code_integer] : ( ord_le348599935723844335nteger @ ( image_2177946750938214461nteger @ X4 @ top_to4645266643341252675nteger ) @ A4 ) )
% 7.78/3.94 @ ( comp_C8797469213163452608nteger @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1560_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_o,F: $o > $o] :
% 7.78/3.94 ( ( bNF_re4705727531993890431at_o_o
% 7.78/3.94 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Grp_o_o @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Grp_nat_o_nat_o
% 7.78/3.94 @ ( collect_nat_o
% 7.78/3.94 @ ^ [X4: nat > $o] : ( ord_less_eq_set_o @ ( image_nat_o @ X4 @ top_top_set_nat ) @ A4 ) )
% 7.78/3.94 @ ( comp_o_o_nat @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1561_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.94 ( ( bNF_re5653821019739307937at_nat
% 7.78/3.94 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Grp_nat_nat @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Gr3847987472475283150at_nat
% 7.78/3.94 @ ( collect_nat_nat
% 7.78/3.94 @ ^ [X4: nat > nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ X4 @ top_top_set_nat ) @ A4 ) )
% 7.78/3.94 @ ( comp_nat_nat_nat @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1562_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_nat,F: nat > num] :
% 7.78/3.94 ( ( bNF_re272988434038980259at_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Grp_nat_num @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Gr6763702254253555408nt_num
% 7.78/3.94 @ ( collect_int_nat
% 7.78/3.94 @ ^ [X4: int > nat] : ( ord_less_eq_set_nat @ ( image_int_nat @ X4 @ top_top_set_int ) @ A4 ) )
% 7.78/3.94 @ ( comp_nat_num_int @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1563_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_int,F: int > nat] :
% 7.78/3.94 ( ( bNF_re4715010359784256181nt_nat
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Grp_int_nat @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Gr2243168462153404386nt_nat
% 7.78/3.94 @ ( collect_int_int
% 7.78/3.94 @ ^ [X4: int > int] : ( ord_less_eq_set_int @ ( image_int_int @ X4 @ top_top_set_int ) @ A4 ) )
% 7.78/3.94 @ ( comp_int_nat_int @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1564_fun_Orel__Grp,axiom,
% 7.78/3.94 ! [A4: set_num,F: num > num] :
% 7.78/3.94 ( ( bNF_re7626690874201225453um_num
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ( bNF_Grp_num_num @ A4 @ F ) )
% 7.78/3.94 = ( bNF_Gr318824752125099290nt_num
% 7.78/3.94 @ ( collect_int_num
% 7.78/3.94 @ ^ [X4: int > num] : ( ord_less_eq_set_num @ ( image_int_num @ X4 @ top_top_set_int ) @ A4 ) )
% 7.78/3.94 @ ( comp_num_num_int @ F ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1565_Grp__fst__snd,axiom,
% 7.78/3.94 ! [R3: nat > nat > $o] :
% 7.78/3.94 ( ( relcom8572034174491624592at_nat @ ( conver4691796276509297820at_nat @ ( bNF_Gr193424670081168899at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) @ product_fst_nat_nat ) ) @ ( bNF_Gr193424670081168899at_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R3 ) ) @ product_snd_nat_nat ) )
% 7.78/3.94 = R3 ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1566_Grp__fst__snd,axiom,
% 7.78/3.94 ! [R3: ref_a > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.94 ( ( relcom3136146828236442456t_unit @ ( conver4368408235330554745_ref_a @ ( bNF_Gr5964920315653434322_ref_a @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R3 ) ) @ produc473321116828791851t_unit ) ) @ ( bNF_Gr5237703264515865432t_unit @ ( collec3252306575900995386t_unit @ ( produc4924168586796184916unit_o @ R3 ) ) @ produc1126150082675451753t_unit ) )
% 7.78/3.94 = R3 ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1567_Grp__fst__snd,axiom,
% 7.78/3.94 ! [R3: int > int > $o] :
% 7.78/3.94 ( ( relcom3664783465810776136nt_int @ ( conver7247880940930113968nt_int @ ( bNF_Gr2749509334501985047nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) @ product_fst_int_int ) ) @ ( bNF_Gr2749509334501985047nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R3 ) ) @ product_snd_int_int ) )
% 7.78/3.94 = R3 ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1568_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: $o > char,Abs: char > $o,S5: char > set_rat,M: $o > char,F: nat > rat,S6: $o > set_nat,G: nat > $o] :
% 7.78/3.94 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_char_set_rat_o @ S5 @ M )
% 7.78/3.94 = ( comp_s8507027185284273247_rat_o @ ( image_nat_rat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_o_set_rat_nat @ ( comp_char_set_rat_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1569_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: num > char,Abs: char > num,S5: char > set_rat,M: nat > char,F: nat > rat,S6: nat > set_nat,G: int > nat] :
% 7.78/3.94 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c5738158305436223508at_nat @ S5 @ M )
% 7.78/3.94 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_num_set_rat_int @ ( comp_c2295490091592002142at_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1570_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,S5: char > set_rat,M: nat > char,F: nat > rat,S6: nat > set_nat,G: nat > nat] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c5738158305436223508at_nat @ S5 @ M )
% 7.78/3.94 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_nat_set_rat_nat @ ( comp_c5738158305436223508at_nat @ S5 @ Rep ) @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s8255929034757298889at_nat @ ( image_nat_rat @ F ) @ ( comp_nat_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1571_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,S5: char > set_rat,M: int > char,F: nat > rat,S6: int > set_nat,G: int > int] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c5735667834927173232at_int @ S5 @ M )
% 7.78/3.94 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_nat_set_rat_int @ ( comp_c5738158305436223508at_nat @ S5 @ Rep ) @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s8253438564248248613at_int @ ( image_nat_rat @ F ) @ ( comp_int_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1572_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: $o > char,Abs: char > $o,S5: char > set_nat,M: $o > char,F: nat > nat,S6: $o > set_nat,G: nat > $o] :
% 7.78/3.94 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_char_set_nat_o @ S5 @ M )
% 7.78/3.94 = ( comp_s33089643564333159_nat_o @ ( image_nat_nat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_o_set_nat_nat @ ( comp_char_set_nat_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1573_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: num > char,Abs: char > num,S5: char > set_nat,M: nat > char,F: nat > nat,S6: nat > set_nat,G: int > nat] :
% 7.78/3.94 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c915470459090449932at_nat @ S5 @ M )
% 7.78/3.94 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_num_set_nat_int @ ( comp_c6696174282101004374at_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1574_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,S5: char > set_nat,M: nat > char,F: nat > nat,S6: nat > set_nat,G: nat > nat] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c915470459090449932at_nat @ S5 @ M )
% 7.78/3.94 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_nat_set_nat_nat @ ( comp_c915470459090449932at_nat @ S5 @ Rep ) @ ( comp_nat_nat_nat @ ( comp_char_nat_nat @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s3433241188411525313at_nat @ ( image_nat_nat @ F ) @ ( comp_nat_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1575_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: nat > char,Abs: char > nat,S5: char > set_nat,M: int > char,F: nat > nat,S6: int > set_nat,G: int > int] :
% 7.78/3.94 ( ( type_d5945782884131516111t_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c912979988581399656at_int @ S5 @ M )
% 7.78/3.94 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_nat_set_nat_int @ ( comp_c915470459090449932at_nat @ S5 @ Rep ) @ ( comp_int_nat_int @ ( comp_char_nat_int @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s3430750717902475037at_int @ ( image_nat_nat @ F ) @ ( comp_int_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1576_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: $o > char,Abs: char > $o,S5: char > set_int,M: $o > char,F: nat > int,S6: $o > set_nat,G: nat > $o] :
% 7.78/3.94 ( ( type_d9076672964931703357o_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_char_set_int_o @ S5 @ M )
% 7.78/3.94 = ( comp_s7011316712748663051_int_o @ ( image_nat_int @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_o_set_int_nat @ ( comp_char_set_int_o @ S5 @ Rep ) @ ( comp_o_o_nat @ ( comp_char_o_o @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s5620162763104547101nt_nat @ ( image_nat_int @ F ) @ ( comp_o_set_nat_nat @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1577_type__copy__set__map0,axiom,
% 7.78/3.94 ! [Rep: num > char,Abs: char > num,S5: char > set_int,M: nat > char,F: nat > int,S6: nat > set_nat,G: int > nat] :
% 7.78/3.94 ( ( type_d4396077731765706521m_char @ Rep @ Abs @ top_top_set_char )
% 7.78/3.94 => ( ( ( comp_c3102392033783471720nt_nat @ S5 @ M )
% 7.78/3.94 = ( comp_s5620162763104547101nt_nat @ ( image_nat_int @ F ) @ S6 ) )
% 7.78/3.94 => ( ( comp_num_set_int_int @ ( comp_c8883095856794026162nt_num @ S5 @ Rep ) @ ( comp_nat_num_int @ ( comp_char_num_nat @ Abs @ M ) @ G ) )
% 7.78/3.94 = ( comp_s5617672292595496825nt_int @ ( image_nat_int @ F ) @ ( comp_nat_set_nat_int @ S6 @ G ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1578_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: nat > rat,Abs: rat > nat,A4: set_rat] :
% 7.78/3.94 ( ( type_d5615363888691252950at_rat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_rat @ Rep @ top_top_set_nat )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1579_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: nat > nat,Abs: nat > nat,A4: set_nat] :
% 7.78/3.94 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_nat @ Rep @ top_top_set_nat )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1580_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: nat > int,Abs: int > nat,A4: set_int] :
% 7.78/3.94 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_int @ Rep @ top_top_set_nat )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1581_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: int > nat,Abs: nat > int,A4: set_nat] :
% 7.78/3.94 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_int_nat @ Rep @ top_top_set_int )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1582_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: int > int,Abs: int > int,A4: set_int] :
% 7.78/3.94 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_int_int @ Rep @ top_top_set_int )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1583_type__definition_ORep__range,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,A4: set_o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_Product_unit_o @ Rep @ top_to1996260823553986621t_unit )
% 7.78/3.94 = A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1584_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: rat > nat,Abs: nat > rat,A4: set_nat] :
% 7.78/3.94 ( ( type_d5933939304842882774at_nat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_rat @ Abs @ A4 )
% 7.78/3.94 = top_top_set_rat ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1585_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: nat > nat,Abs: nat > nat,A4: set_nat] :
% 7.78/3.94 ( ( type_d6250493948777748686at_nat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_nat @ Abs @ A4 )
% 7.78/3.94 = top_top_set_nat ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1586_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: nat > int,Abs: int > nat,A4: set_int] :
% 7.78/3.94 ( ( type_d6248003478268698410at_int @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_int_nat @ Abs @ A4 )
% 7.78/3.94 = top_top_set_nat ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1587_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: int > nat,Abs: nat > int,A4: set_nat] :
% 7.78/3.94 ( ( type_d7249847660678803242nt_nat @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_nat_int @ Abs @ A4 )
% 7.78/3.94 = top_top_set_int ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1588_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: int > int,Abs: int > int,A4: set_int] :
% 7.78/3.94 ( ( type_d7247357190169752966nt_int @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_int_int @ Abs @ A4 )
% 7.78/3.94 = top_top_set_int ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1589_type__definition_OAbs__image,axiom,
% 7.78/3.94 ! [Rep: product_unit > $o,Abs: $o > product_unit,A4: set_o] :
% 7.78/3.94 ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A4 )
% 7.78/3.94 => ( ( image_o_Product_unit @ Abs @ A4 )
% 7.78/3.94 = top_to1996260823553986621t_unit ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1590_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_char_char
% 7.78/3.94 = ( ^ [R6: char > char > $o,Abs4: char > char,Rep4: char > char,T4: char > char > $o] :
% 7.78/3.94 ( ( ord_le2540245887939449860char_o @ T4 @ ( bNF_Grp_char_char @ top_top_set_char @ Abs4 ) )
% 7.78/3.94 & ( ord_le2540245887939449860char_o @ ( bNF_Grp_char_char @ top_top_set_char @ Rep4 ) @ ( conversep_char_char @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom5872928454965100966r_char @ T4 @ ( conversep_char_char @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1591_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_char_rat
% 7.78/3.94 = ( ^ [R6: char > char > $o,Abs4: char > rat,Rep4: rat > char,T4: char > rat > $o] :
% 7.78/3.94 ( ( ord_le4891902658761385405_rat_o @ T4 @ ( bNF_Grp_char_rat @ top_top_set_char @ Abs4 ) )
% 7.78/3.94 & ( ord_le6546876390139131069char_o @ ( bNF_Grp_rat_char @ top_top_set_rat @ Rep4 ) @ ( conversep_char_rat @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom3428143170894750637t_char @ T4 @ ( conversep_char_rat @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1592_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_char_nat
% 7.78/3.94 = ( ^ [R6: char > char > $o,Abs4: char > nat,Rep4: nat > char,T4: char > nat > $o] :
% 7.78/3.94 ( ( ord_le5641337153896221125_nat_o @ T4 @ ( bNF_Grp_char_nat @ top_top_set_char @ Abs4 ) )
% 7.78/3.94 & ( ord_le4878496333587278021char_o @ ( bNF_Grp_nat_char @ top_top_set_nat @ Rep4 ) @ ( conversep_char_nat @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom6755291642603558309t_char @ T4 @ ( conversep_char_nat @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1593_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_char_int
% 7.78/3.94 = ( ^ [R6: char > char > $o,Abs4: char > int,Rep4: int > char,T4: char > int > $o] :
% 7.78/3.94 ( ( ord_le3396192186225775209_int_o @ T4 @ ( bNF_Grp_char_int @ top_top_set_char @ Abs4 ) )
% 7.78/3.94 & ( ord_le7608100903186094441char_o @ ( bNF_Grp_int_char @ top_top_set_int @ Rep4 ) @ ( conversep_char_int @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom750623199913152513t_char @ T4 @ ( conversep_char_int @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1594_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_rat_char
% 7.78/3.94 = ( ^ [R6: rat > rat > $o,Abs4: rat > char,Rep4: char > rat,T4: rat > char > $o] :
% 7.78/3.94 ( ( ord_le6546876390139131069char_o @ T4 @ ( bNF_Grp_rat_char @ top_top_set_rat @ Abs4 ) )
% 7.78/3.94 & ( ord_le4891902658761385405_rat_o @ ( bNF_Grp_char_rat @ top_top_set_char @ Rep4 ) @ ( conversep_rat_char @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom1505247221262953652ar_rat @ T4 @ ( conversep_rat_char @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1595_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_rat_rat
% 7.78/3.94 = ( ^ [R6: rat > rat > $o,Abs4: rat > rat,Rep4: rat > rat,T4: rat > rat > $o] :
% 7.78/3.94 ( ( ord_le4717968354871517046_rat_o @ T4 @ ( bNF_Grp_rat_rat @ top_top_set_rat @ Abs4 ) )
% 7.78/3.94 & ( ord_le4717968354871517046_rat_o @ ( bNF_Grp_rat_rat @ top_top_set_rat @ Rep4 ) @ ( conversep_rat_rat @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcompp_rat_rat_rat @ T4 @ ( conversep_rat_rat @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1596_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_rat_nat
% 7.78/3.94 = ( ^ [R6: rat > rat > $o,Abs4: rat > nat,Rep4: nat > rat,T4: rat > nat > $o] :
% 7.78/3.94 ( ( ord_le5467402850006352766_nat_o @ T4 @ ( bNF_Grp_rat_nat @ top_top_set_rat @ Abs4 ) )
% 7.78/3.94 & ( ord_le1897120724991155070_rat_o @ ( bNF_Grp_nat_rat @ top_top_set_nat @ Rep4 ) @ ( conversep_rat_nat @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcompp_rat_nat_rat @ T4 @ ( conversep_rat_nat @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1597_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_rat_int
% 7.78/3.94 = ( ^ [R6: rat > rat > $o,Abs4: rat > int,Rep4: int > rat,T4: rat > int > $o] :
% 7.78/3.94 ( ( ord_le3222257882335906850_int_o @ T4 @ ( bNF_Grp_rat_int @ top_top_set_rat @ Abs4 ) )
% 7.78/3.94 & ( ord_le8236914709048111138_rat_o @ ( bNF_Grp_int_rat @ top_top_set_int @ Rep4 ) @ ( conversep_rat_int @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcompp_rat_int_rat @ T4 @ ( conversep_rat_int @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1598_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_nat_char
% 7.78/3.94 = ( ^ [R6: nat > nat > $o,Abs4: nat > char,Rep4: char > nat,T4: nat > char > $o] :
% 7.78/3.94 ( ( ord_le4878496333587278021char_o @ T4 @ ( bNF_Grp_nat_char @ top_top_set_nat @ Abs4 ) )
% 7.78/3.94 & ( ord_le5641337153896221125_nat_o @ ( bNF_Grp_char_nat @ top_top_set_char @ Rep4 ) @ ( conversep_nat_char @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcom8112501251453913252ar_nat @ T4 @ ( conversep_nat_char @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1599_Quotient__alt__def5,axiom,
% 7.78/3.94 ( quotient_nat_rat
% 7.78/3.94 = ( ^ [R6: nat > nat > $o,Abs4: nat > rat,Rep4: rat > nat,T4: nat > rat > $o] :
% 7.78/3.94 ( ( ord_le1897120724991155070_rat_o @ T4 @ ( bNF_Grp_nat_rat @ top_top_set_nat @ Abs4 ) )
% 7.78/3.94 & ( ord_le5467402850006352766_nat_o @ ( bNF_Grp_rat_nat @ top_top_set_rat @ Rep4 ) @ ( conversep_nat_rat @ T4 ) )
% 7.78/3.94 & ( R6
% 7.78/3.94 = ( relcompp_nat_rat_nat @ T4 @ ( conversep_nat_rat @ T4 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1600_K__record__comp,axiom,
% 7.78/3.94 ! [C: $o,F: nat > $o] :
% 7.78/3.94 ( ( comp_o_o_nat
% 7.78/3.94 @ ^ [X4: $o] : C
% 7.78/3.94 @ F )
% 7.78/3.94 = ( ^ [X4: nat] : C ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1601_K__record__comp,axiom,
% 7.78/3.94 ! [C: num,F: int > nat] :
% 7.78/3.94 ( ( comp_nat_num_int
% 7.78/3.94 @ ^ [X4: nat] : C
% 7.78/3.94 @ F )
% 7.78/3.94 = ( ^ [X4: int] : C ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1602_K__record__comp,axiom,
% 7.78/3.94 ! [C: nat,F: nat > nat] :
% 7.78/3.94 ( ( comp_nat_nat_nat
% 7.78/3.94 @ ^ [X4: nat] : C
% 7.78/3.94 @ F )
% 7.78/3.94 = ( ^ [X4: nat] : C ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1603_K__record__comp,axiom,
% 7.78/3.94 ! [C: nat,F: int > int] :
% 7.78/3.94 ( ( comp_int_nat_int
% 7.78/3.94 @ ^ [X4: int] : C
% 7.78/3.94 @ F )
% 7.78/3.94 = ( ^ [X4: int] : C ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1604_K__record__comp,axiom,
% 7.78/3.94 ! [C: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 7.78/3.94 ( ( comp_C8797469213163452608nteger
% 7.78/3.94 @ ^ [X4: code_integer > code_integer] : C
% 7.78/3.94 @ F )
% 7.78/3.94 = ( ^ [X4: code_integer] : C ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1605_image__paired__Times,axiom,
% 7.78/3.94 ! [F: nat > rat,G: int > nat,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( image_3755276878268593137at_nat
% 7.78/3.94 @ ( produc5347463441023893471at_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: int] : ( product_Pair_rat_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc140472662868866674at_nat @ ( image_nat_rat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: rat] : ( image_int_nat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1606_image__paired__Times,axiom,
% 7.78/3.94 ! [F: nat > rat,G: int > int,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( image_8800797895614172237at_int
% 7.78/3.94 @ ( produc1169612421514696763at_int
% 7.78/3.94 @ ^ [X4: nat,Y5: int] : ( product_Pair_rat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc137982192359816398at_int @ ( image_nat_rat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: rat] : ( image_int_int @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1607_image__paired__Times,axiom,
% 7.78/3.94 ! [F: nat > nat,G: int > int,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( image_9117352539549038149at_int
% 7.78/3.94 @ ( produc1486167065449562675at_int
% 7.78/3.94 @ ^ [X4: nat,Y5: int] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ ( image_nat_nat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1608_image__paired__Times,axiom,
% 7.78/3.94 ! [F: nat > int,G: int > nat,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( image_5071185234104513605nt_nat
% 7.78/3.94 @ ( produc6663371796859813939nt_nat
% 7.78/3.94 @ ^ [X4: nat,Y5: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: int] : ( image_int_nat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1609_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > nat,G: nat > rat,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( image_3420722608207172081at_rat
% 7.78/3.94 @ ( produc877984105854340063at_rat
% 7.78/3.94 @ ^ [X4: int,Y5: nat] : ( product_Pair_nat_rat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc9045269283572012658at_rat @ ( image_int_nat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: nat] : ( image_nat_rat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1610_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > nat,G: nat > int,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( image_2751100147091372101at_int
% 7.78/3.94 @ ( produc208361644738540083at_int
% 7.78/3.94 @ ^ [X4: int,Y5: nat] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ ( image_int_nat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: nat] : ( image_nat_int @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1611_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > nat,G: int > int,A4: set_int,B5: set_int] :
% 7.78/3.94 ( ( image_1654017166447373545at_int
% 7.78/3.94 @ ( produc3246203729202673879at_int
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_nat_int @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ ( image_int_nat @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: nat] : ( image_int_int @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1612_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > int,G: nat > rat,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( image_4420076320108226637nt_rat
% 7.78/3.94 @ ( produc1877337817755394619nt_rat
% 7.78/3.94 @ ^ [X4: int,Y5: nat] : ( product_Pair_int_rat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc821250958618291406nt_rat @ ( image_int_int @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: int] : ( image_nat_rat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1613_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > int,G: nat > nat,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( image_7928304878501623365nt_nat
% 7.78/3.94 @ ( produc5385566376148791347nt_nat
% 7.78/3.94 @ ^ [X4: int,Y5: nat] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: int] : ( image_nat_nat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1614_image__paired__Times,axiom,
% 7.78/3.94 ! [F: int > int,G: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.94 ( ( image_6831221897857624809nt_nat
% 7.78/3.94 @ ( produc8423408460612925143nt_nat
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ Y5 ) ) )
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 7.78/3.94 @ ^ [Uu: int] : ( image_int_nat @ G @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1615_Gr__incl,axiom,
% 7.78/3.94 ! [A4: set_nat,F: nat > rat,B5: set_rat] :
% 7.78/3.94 ( ( ord_le5989899228261996553at_rat @ ( bNF_Gr_nat_rat @ A4 @ F )
% 7.78/3.94 @ ( produc9045269283572012658at_rat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1616_Gr__incl,axiom,
% 7.78/3.94 ! [A4: set_nat,F: nat > int,B5: set_int] :
% 7.78/3.94 ( ( ord_le656430383953171549at_int @ ( bNF_Gr_nat_int @ A4 @ F )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1617_Gr__incl,axiom,
% 7.78/3.94 ! [A4: set_int,F: int > nat,B5: set_nat] :
% 7.78/3.94 ( ( ord_le5333435103577920093nt_nat @ ( bNF_Gr_int_nat @ A4 @ F )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1618_Gr__incl,axiom,
% 7.78/3.94 ! [A4: set_int,F: int > int,B5: set_int] :
% 7.78/3.94 ( ( ord_le2843351958646193337nt_int @ ( bNF_Gr_int_int @ A4 @ F )
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1619_Gr__incl,axiom,
% 7.78/3.94 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 7.78/3.94 ( ( ord_le3146513528884898305at_nat @ ( bNF_Gr_nat_nat @ A4 @ F )
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1620_subset__fst__snd,axiom,
% 7.78/3.94 ! [A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ord_le3146513528884898305at_nat @ A4
% 7.78/3.94 @ ( produc457027306803732586at_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A4 )
% 7.78/3.94 @ ^ [Uu: nat] : ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1621_subset__fst__snd,axiom,
% 7.78/3.94 ! [A4: set_Pr1133966238863718811t_unit] :
% 7.78/3.94 ( ord_le5525191956872776187t_unit @ A4
% 7.78/3.94 @ ( produc3946373962484743846t_unit @ ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ A4 )
% 7.78/3.94 @ ^ [Uu: ref_a] : ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ A4 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1622_inv__image__def,axiom,
% 7.78/3.94 ( inv_im2903009620893676101at_nat
% 7.78/3.94 = ( ^ [R5: set_Pr7459493094073627847at_nat,F2: nat > set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1623_inv__image__def,axiom,
% 7.78/3.94 ( inv_im4437241714082187487at_nat
% 7.78/3.94 = ( ^ [R5: set_Pr4329608150637261639at_nat,F2: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1624_inv__image__def,axiom,
% 7.78/3.94 ( inv_image_nat_nat
% 7.78/3.94 = ( ^ [R5: set_Pr1261947904930325089at_nat,F2: nat > nat] :
% 7.78/3.94 ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1625_inv__image__def,axiom,
% 7.78/3.94 ( inv_image_int_nat
% 7.78/3.94 = ( ^ [R5: set_Pr958786334691620121nt_int,F2: nat > int] :
% 7.78/3.94 ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1626_inv__image__def,axiom,
% 7.78/3.94 ( inv_im2900519150384625825at_int
% 7.78/3.94 = ( ^ [R5: set_Pr7459493094073627847at_nat,F2: int > set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1627_inv__image__def,axiom,
% 7.78/3.94 ( inv_im4434751243573137211at_int
% 7.78/3.94 = ( ^ [R5: set_Pr4329608150637261639at_nat,F2: int > set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1628_inv__image__def,axiom,
% 7.78/3.94 ( inv_image_nat_int
% 7.78/3.94 = ( ^ [R5: set_Pr1261947904930325089at_nat,F2: int > nat] :
% 7.78/3.94 ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1629_inv__image__def,axiom,
% 7.78/3.94 ( inv_image_int_int
% 7.78/3.94 = ( ^ [R5: set_Pr958786334691620121nt_int,F2: int > int] :
% 7.78/3.94 ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F2 @ X4 ) @ ( F2 @ Y5 ) ) @ R5 ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1630_The__case__prod,axiom,
% 7.78/3.94 ! [P2: ref_a > heap_e7401611519738050253t_unit > $o] :
% 7.78/3.94 ( ( the_Pr5012129486825234846t_unit @ ( produc4924168586796184916unit_o @ P2 ) )
% 7.78/3.94 = ( the_Pr5012129486825234846t_unit
% 7.78/3.94 @ ^ [Xy: produc7812382424243267045t_unit] : ( P2 @ ( produc473321116828791851t_unit @ Xy ) @ ( produc1126150082675451753t_unit @ Xy ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1631_The__case__prod,axiom,
% 7.78/3.94 ! [P2: int > int > $o] :
% 7.78/3.94 ( ( the_Pr4378521158711661632nt_int @ ( produc4947309494688390418_int_o @ P2 ) )
% 7.78/3.94 = ( the_Pr4378521158711661632nt_int
% 7.78/3.94 @ ^ [Xy: product_prod_int_int] : ( P2 @ ( product_fst_int_int @ Xy ) @ ( product_snd_int_int @ Xy ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1632_Quotient__composition__ge__eq,axiom,
% 7.78/3.94 ! [T3: int > product_prod_nat_nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( left_t8261381459436684205at_nat @ T3 )
% 7.78/3.94 => ( ( ord_le5604493270027003598_nat_o
% 7.78/3.94 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 => ( ord_le6741204236512500942_int_o
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ ( relcom1106208330880909712at_int @ T3 @ ( relcom8911704206367525917at_int @ R3 @ ( conver1866313717161370910at_nat @ T3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1633_Quotient__composition__ge__eq,axiom,
% 7.78/3.94 ! [T3: code_integer > int > $o,R3: int > int > $o] :
% 7.78/3.94 ( ( left_t1735413524555719857er_int @ T3 )
% 7.78/3.94 => ( ( ord_le6741204236512500942_int_o
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.94 @ R3 )
% 7.78/3.94 => ( ord_le3602516367967493612eger_o
% 7.78/3.94 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z )
% 7.78/3.94 @ ( relcom692387321444912665nteger @ T3 @ ( relcom967497705283160040nteger @ R3 @ ( conver1462408618118490240er_int @ T3 ) ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1634_Quotient__composition__le__eq,axiom,
% 7.78/3.94 ! [T3: int > product_prod_nat_nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( left_u1182257597767569412at_nat @ T3 )
% 7.78/3.94 => ( ( ord_le5604493270027003598_nat_o @ R3
% 7.78/3.94 @ ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z ) )
% 7.78/3.94 => ( ord_le6741204236512500942_int_o @ ( relcom1106208330880909712at_int @ T3 @ ( relcom8911704206367525917at_int @ R3 @ ( conver1866313717161370910at_nat @ T3 ) ) )
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1635_Quotient__composition__le__eq,axiom,
% 7.78/3.94 ! [T3: code_integer > int > $o,R3: int > int > $o] :
% 7.78/3.94 ( ( left_u6156896403773009178er_int @ T3 )
% 7.78/3.94 => ( ( ord_le6741204236512500942_int_o @ R3
% 7.78/3.94 @ ^ [Y2: int,Z: int] : ( Y2 = Z ) )
% 7.78/3.94 => ( ord_le3602516367967493612eger_o @ ( relcom692387321444912665nteger @ T3 @ ( relcom967497705283160040nteger @ R3 @ ( conver1462408618118490240er_int @ T3 ) ) )
% 7.78/3.94 @ ^ [Y2: code_integer,Z: code_integer] : ( Y2 = Z ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1636_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_o @ A @ A4 )
% 7.78/3.94 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1637_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: $o,B: nat,A4: set_o,B5: $o > set_nat] :
% 7.78/3.94 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_o @ A @ A4 )
% 7.78/3.94 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1638_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: $o,B: int,A4: set_o,B5: $o > set_int] :
% 7.78/3.94 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_o @ A @ A4 )
% 7.78/3.94 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1639_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: nat,B: $o,A4: set_nat,B5: nat > set_o] :
% 7.78/3.94 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_nat @ A @ A4 )
% 7.78/3.94 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1640_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: nat,B: int,A4: set_nat,B5: nat > set_int] :
% 7.78/3.94 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_nat @ A @ A4 )
% 7.78/3.94 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1641_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: int,B: $o,A4: set_int,B5: int > set_o] :
% 7.78/3.94 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_int @ A @ A4 )
% 7.78/3.94 & ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1642_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: int,B: nat,A4: set_int,B5: int > set_nat] :
% 7.78/3.94 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_int @ A @ A4 )
% 7.78/3.94 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1643_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 7.78/3.94 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_nat @ A @ A4 )
% 7.78/3.94 & ( member_num @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1644_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_int @ A @ A4 )
% 7.78/3.94 & ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1645_mem__Sigma__iff,axiom,
% 7.78/3.94 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.94 = ( ( member_nat @ A @ A4 )
% 7.78/3.94 & ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1646_SigmaI,axiom,
% 7.78/3.94 ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
% 7.78/3.94 ( ( member_o @ A @ A4 )
% 7.78/3.94 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1647_SigmaI,axiom,
% 7.78/3.94 ! [A: $o,A4: set_o,B: nat,B5: $o > set_nat] :
% 7.78/3.94 ( ( member_o @ A @ A4 )
% 7.78/3.94 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1648_SigmaI,axiom,
% 7.78/3.94 ! [A: $o,A4: set_o,B: int,B5: $o > set_int] :
% 7.78/3.94 ( ( member_o @ A @ A4 )
% 7.78/3.94 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1649_SigmaI,axiom,
% 7.78/3.94 ! [A: nat,A4: set_nat,B: $o,B5: nat > set_o] :
% 7.78/3.94 ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1650_SigmaI,axiom,
% 7.78/3.94 ! [A: nat,A4: set_nat,B: int,B5: nat > set_int] :
% 7.78/3.94 ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1651_SigmaI,axiom,
% 7.78/3.94 ! [A: int,A4: set_int,B: $o,B5: int > set_o] :
% 7.78/3.94 ( ( member_int @ A @ A4 )
% 7.78/3.94 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1652_SigmaI,axiom,
% 7.78/3.94 ! [A: int,A4: set_int,B: nat,B5: int > set_nat] :
% 7.78/3.94 ( ( member_int @ A @ A4 )
% 7.78/3.94 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1653_SigmaI,axiom,
% 7.78/3.94 ! [A: nat,A4: set_nat,B: num,B5: nat > set_num] :
% 7.78/3.94 ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ( ( member_num @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1654_SigmaI,axiom,
% 7.78/3.94 ! [A: int,A4: set_int,B: int,B5: int > set_int] :
% 7.78/3.94 ( ( member_int @ A @ A4 )
% 7.78/3.94 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1655_SigmaI,axiom,
% 7.78/3.94 ! [A: nat,A4: set_nat,B: nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.94 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1656_in__inv__image,axiom,
% 7.78/3.94 ! [X2: nat,Y3: nat,R: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_image_nat_nat @ R @ F ) )
% 7.78/3.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1657_in__inv__image,axiom,
% 7.78/3.94 ! [X2: nat,Y3: nat,R: set_Pr958786334691620121nt_int,F: nat > int] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_image_int_nat @ R @ F ) )
% 7.78/3.94 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1658_in__inv__image,axiom,
% 7.78/3.94 ! [X2: int,Y3: int,R: set_Pr1261947904930325089at_nat,F: int > nat] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_image_nat_int @ R @ F ) )
% 7.78/3.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1659_in__inv__image,axiom,
% 7.78/3.94 ! [X2: int,Y3: int,R: set_Pr958786334691620121nt_int,F: int > int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_image_int_int @ R @ F ) )
% 7.78/3.94 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1660_in__inv__image,axiom,
% 7.78/3.94 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im6750873321330482877at_nat @ R @ F ) )
% 7.78/3.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1661_in__inv__image,axiom,
% 7.78/3.94 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr958786334691620121nt_int,F: set_Pr1261947904930325089at_nat > int] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im8510909985083594081at_nat @ R @ F ) )
% 7.78/3.94 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1662_in__inv__image,axiom,
% 7.78/3.94 ! [X2: nat,Y3: nat,R: set_Pr4329608150637261639at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( inv_im4437241714082187487at_nat @ R @ F ) )
% 7.78/3.94 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1663_in__inv__image,axiom,
% 7.78/3.94 ! [X2: int,Y3: int,R: set_Pr4329608150637261639at_nat,F: int > set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( inv_im4434751243573137211at_int @ R @ F ) )
% 7.78/3.94 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1664_in__inv__image,axiom,
% 7.78/3.94 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( inv_im7023619800666061458at_nat @ R @ F ) )
% 7.78/3.94 = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1665_in__inv__image,axiom,
% 7.78/3.94 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,R: set_Pr1261947904930325089at_nat,F: set_Pr4329608150637261639at_nat > nat] :
% 7.78/3.94 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ ( inv_im2354225701593503139at_nat @ R @ F ) )
% 7.78/3.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) @ R ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1666_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec7088162979684241874at_nat
% 7.78/3.94 @ ( produc6590410687421337004_nat_o
% 7.78/3.94 @ ^ [A5: product_prod_nat_nat,B4: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc2761391749766926216at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_nat_nat] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1667_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: nat > $o] :
% 7.78/3.94 ( ( collec7029190964493513045at_nat
% 7.78/3.94 @ ( produc8758269395934548017_nat_o
% 7.78/3.94 @ ^ [A5: product_prod_nat_nat,B4: nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc7672662199629908489at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_nat_nat] : ( collect_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1668_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec6785001409445536906nt_int
% 7.78/3.94 @ ( produc5031841752791441652_int_o
% 7.78/3.94 @ ^ [A5: product_prod_nat_nat,B4: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc8806266479013559872nt_int @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_nat_nat] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1669_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec5903703980526211963at_nat
% 7.78/3.94 @ ( produc5864757623865647827_nat_o
% 7.78/3.94 @ ^ [A5: nat,B4: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc1809337555817847783at_nat @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: nat] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1670_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec5600542410287506995nt_int
% 7.78/3.94 @ ( produc4306188689235752475_int_o
% 7.78/3.94 @ ^ [A5: nat,B4: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc7854212285064481439nt_int @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: nat] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1671_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec7751116662793354522at_nat
% 7.78/3.94 @ ( produc3235059054576640100_nat_o
% 7.78/3.94 @ ^ [A5: product_prod_int_int,B4: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc3424345432876038864at_nat @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_int_int] : ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1672_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: nat > $o] :
% 7.78/3.94 ( ( collec364394062568603661nt_nat
% 7.78/3.94 @ ( produc5441891513209881465_nat_o
% 7.78/3.94 @ ^ [A5: product_prod_int_int,B4: nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc1007865297704999105nt_nat @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_int_int] : ( collect_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1673_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec7447955092554649554nt_int
% 7.78/3.94 @ ( produc1676490119946744748_int_o
% 7.78/3.94 @ ^ [A5: product_prod_int_int,B4: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc245848125267896712nt_int @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [Uu: product_prod_int_int] : ( collec213857154873943460nt_int @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1674_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: nat > $o] :
% 7.78/3.94 ( ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [A5: nat,B4: nat] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc457027306803732586at_nat @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [Uu: nat] : ( collect_nat @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1675_Collect__case__prod,axiom,
% 7.78/3.94 ! [P2: int > $o,Q2: int > $o] :
% 7.78/3.94 ( ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [A5: int,B4: int] :
% 7.78/3.94 ( ( P2 @ A5 )
% 7.78/3.94 & ( Q2 @ B4 ) ) ) )
% 7.78/3.94 = ( produc1453890548195736866nt_int @ ( collect_int @ P2 )
% 7.78/3.94 @ ^ [Uu: int] : ( collect_int @ Q2 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1676_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc2936396906406871148r_char @ top_top_set_char
% 7.78/3.94 @ ^ [Uu: char] : top_top_set_char )
% 7.78/3.94 = top_to1235241553633177651r_char ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1677_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc1204236661673008499ar_rat @ top_top_set_char
% 7.78/3.94 @ ^ [Uu: char] : top_top_set_rat )
% 7.78/3.94 = top_to8437673547576850234ar_rat ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1678_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc1839366721759504235ar_nat @ top_top_set_char
% 7.78/3.94 @ ^ [Uu: char] : top_top_set_nat )
% 7.78/3.94 = top_to5594287848199751986ar_nat ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1679_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc1836876251250453959ar_int @ top_top_set_char
% 7.78/3.94 @ ^ [Uu: char] : top_top_set_int )
% 7.78/3.94 = top_to3104204703268025230ar_int ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1680_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc1427039474575272051t_char @ top_top_set_rat
% 7.78/3.94 @ ^ [Uu: rat] : top_top_set_char )
% 7.78/3.94 = top_to3221206985699244474t_char ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1681_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc8728714639637146746at_rat @ top_top_set_rat
% 7.78/3.94 @ ^ [Uu: rat] : top_top_set_rat )
% 7.78/3.94 = top_to3112507417142880193at_rat ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1682_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc140472662868866674at_nat @ top_top_set_rat
% 7.78/3.94 @ ^ [Uu: rat] : top_top_set_nat )
% 7.78/3.94 = top_to269121717765781945at_nat ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1683_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc137982192359816398at_int @ top_top_set_rat
% 7.78/3.94 @ ^ [Uu: rat] : top_top_set_int )
% 7.78/3.94 = top_to7002410609688830997at_int ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1684_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc4754187946284079723t_char @ top_top_set_nat
% 7.78/3.94 @ ^ [Uu: nat] : top_top_set_char )
% 7.78/3.94 = top_to7107842681480589234t_char ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1685_UNIV__Times__UNIV,axiom,
% 7.78/3.94 ( ( produc9045269283572012658at_rat @ top_top_set_nat
% 7.78/3.94 @ ^ [Uu: nat] : top_top_set_rat )
% 7.78/3.94 = top_to7513191607651882425at_rat ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1686_The__split__eq,axiom,
% 7.78/3.94 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( the_Pr4877703158196064750at_nat
% 7.78/3.94 @ ( produc9020218426428501292_nat_o
% 7.78/3.94 @ ^ [X7: set_Pr4329608150637261639at_nat,Y6: set_Pr4329608150637261639at_nat] :
% 7.78/3.94 ( ( X2 = X7 )
% 7.78/3.94 & ( Y3 = Y6 ) ) ) )
% 7.78/3.94 = ( produc9060074326276436823at_nat @ X2 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1687_The__split__eq,axiom,
% 7.78/3.94 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( the_Pr4604535484834969198at_nat
% 7.78/3.94 @ ( produc410239310623530412_nat_o
% 7.78/3.94 @ ^ [X7: set_Pr1261947904930325089at_nat,Y6: set_Pr1261947904930325089at_nat] :
% 7.78/3.94 ( ( X2 = X7 )
% 7.78/3.94 & ( Y3 = Y6 ) ) ) )
% 7.78/3.94 = ( produc2922128104949294807at_nat @ X2 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1688_The__split__eq,axiom,
% 7.78/3.94 ! [X2: nat,Y3: num] :
% 7.78/3.94 ( ( the_Pr8265262403268641490at_num
% 7.78/3.94 @ ( produc4927758841916487424_num_o
% 7.78/3.94 @ ^ [X7: nat,Y6: num] :
% 7.78/3.94 ( ( X2 = X7 )
% 7.78/3.94 & ( Y3 = Y6 ) ) ) )
% 7.78/3.94 = ( product_Pair_nat_num @ X2 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1689_The__split__eq,axiom,
% 7.78/3.94 ! [X2: nat,Y3: nat] :
% 7.78/3.94 ( ( the_Pr7557018466319803784at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X7: nat,Y6: nat] :
% 7.78/3.94 ( ( X2 = X7 )
% 7.78/3.94 & ( Y3 = Y6 ) ) ) )
% 7.78/3.94 = ( product_Pair_nat_nat @ X2 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1690_The__split__eq,axiom,
% 7.78/3.94 ! [X2: int,Y3: int] :
% 7.78/3.94 ( ( the_Pr4378521158711661632nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X7: int,Y6: int] :
% 7.78/3.94 ( ( X2 = X7 )
% 7.78/3.94 & ( Y3 = Y6 ) ) ) )
% 7.78/3.94 = ( product_Pair_int_int @ X2 @ Y3 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1691_Times__eq__cancel2,axiom,
% 7.78/3.94 ! [X2: nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( member_nat @ X2 @ C3 )
% 7.78/3.94 => ( ( ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : C3 )
% 7.78/3.94 = ( produc457027306803732586at_nat @ B5
% 7.78/3.94 @ ^ [Uu: nat] : C3 ) )
% 7.78/3.94 = ( A4 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1692_Sigma__cong,axiom,
% 7.78/3.94 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 7.78/3.94 ( ( A4 = B5 )
% 7.78/3.94 => ( ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ B5 )
% 7.78/3.94 => ( ( C3 @ X )
% 7.78/3.94 = ( D @ X ) ) )
% 7.78/3.94 => ( ( produc457027306803732586at_nat @ A4 @ C3 )
% 7.78/3.94 = ( produc457027306803732586at_nat @ B5 @ D ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1693_SigmaE2,axiom,
% 7.78/3.94 ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_o @ A @ A4 )
% 7.78/3.94 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1694_SigmaE2,axiom,
% 7.78/3.94 ! [A: $o,B: nat,A4: set_o,B5: $o > set_nat] :
% 7.78/3.94 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A @ B ) @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_o @ A @ A4 )
% 7.78/3.94 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1695_SigmaE2,axiom,
% 7.78/3.94 ! [A: $o,B: int,A4: set_o,B5: $o > set_int] :
% 7.78/3.94 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A @ B ) @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_o @ A @ A4 )
% 7.78/3.94 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1696_SigmaE2,axiom,
% 7.78/3.94 ! [A: nat,B: $o,A4: set_nat,B5: nat > set_o] :
% 7.78/3.94 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A @ B ) @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1697_SigmaE2,axiom,
% 7.78/3.94 ! [A: nat,B: int,A4: set_nat,B5: nat > set_int] :
% 7.78/3.94 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A @ B ) @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1698_SigmaE2,axiom,
% 7.78/3.94 ! [A: int,B: $o,A4: set_int,B5: int > set_o] :
% 7.78/3.94 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A @ B ) @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_int @ A @ A4 )
% 7.78/3.94 => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1699_SigmaE2,axiom,
% 7.78/3.94 ! [A: int,B: nat,A4: set_int,B5: int > set_nat] :
% 7.78/3.94 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A @ B ) @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_int @ A @ A4 )
% 7.78/3.94 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1700_SigmaE2,axiom,
% 7.78/3.94 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 7.78/3.94 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ~ ( member_num @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1701_SigmaE2,axiom,
% 7.78/3.94 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_int @ A @ A4 )
% 7.78/3.94 => ~ ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1702_SigmaE2,axiom,
% 7.78/3.94 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ( ( member_nat @ A @ A4 )
% 7.78/3.94 => ~ ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1703_SigmaD2,axiom,
% 7.78/3.94 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,B5: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( produc6258361011560675592at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member6273874620674182256at_nat @ B @ ( B5 @ A ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1704_SigmaD2,axiom,
% 7.78/3.94 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member2643936169264416010at_nat @ B @ ( B5 @ A ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1705_SigmaD2,axiom,
% 7.78/3.94 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 7.78/3.94 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 7.78/3.94 => ( member_num @ B @ ( B5 @ A ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1706_SigmaD2,axiom,
% 7.78/3.94 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 7.78/3.94 => ( member_int @ B @ ( B5 @ A ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1707_SigmaD2,axiom,
% 7.78/3.94 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member_nat @ B @ ( B5 @ A ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1708_SigmaD1,axiom,
% 7.78/3.94 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A4: set_se5479201105039950375at_nat,B5: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ ( produc6258361011560675592at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member6273874620674182256at_nat @ A @ A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1709_SigmaD1,axiom,
% 7.78/3.94 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc7726050920695093128at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member2643936169264416010at_nat @ A @ A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1710_SigmaD1,axiom,
% 7.78/3.94 ! [A: nat,B: num,A4: set_nat,B5: nat > set_num] :
% 7.78/3.94 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ A @ B ) @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 7.78/3.94 => ( member_nat @ A @ A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1711_SigmaD1,axiom,
% 7.78/3.94 ! [A: int,B: int,A4: set_int,B5: int > set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 7.78/3.94 => ( member_int @ A @ A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1712_SigmaD1,axiom,
% 7.78/3.94 ! [A: nat,B: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ( member_nat @ A @ A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1713_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_o_o,A4: set_o,B5: $o > set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ C @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: $o] :
% 7.78/3.94 ( ( member_o @ X @ A4 )
% 7.78/3.94 => ! [Y: $o] :
% 7.78/3.94 ( ( member_o @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_o_o @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1714_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_o_nat,A4: set_o,B5: $o > set_nat] :
% 7.78/3.94 ( ( member2802428098988154798_o_nat @ C @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: $o] :
% 7.78/3.94 ( ( member_o @ X @ A4 )
% 7.78/3.94 => ! [Y: nat] :
% 7.78/3.94 ( ( member_nat @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_o_nat @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1715_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_o_int,A4: set_o,B5: $o > set_int] :
% 7.78/3.94 ( ( member7847949116333733898_o_int @ C @ ( product_Sigma_o_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: $o] :
% 7.78/3.94 ( ( member_o @ X @ A4 )
% 7.78/3.94 => ! [Y: int] :
% 7.78/3.94 ( ( member_int @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_o_int @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1716_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_nat_o,A4: set_nat,B5: nat > set_o] :
% 7.78/3.94 ( ( member6310962623043647828_nat_o @ C @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ! [Y: $o] :
% 7.78/3.94 ( ( member_o @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_nat_o @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1717_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_nat_int,A4: set_nat,B5: nat > set_int] :
% 7.78/3.94 ( ( member4262671552274231302at_int @ C @ ( produc454536836294682310at_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ! [Y: int] :
% 7.78/3.94 ( ( member_int @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_nat_int @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1718_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_int_o,A4: set_int,B5: int > set_o] :
% 7.78/3.94 ( ( member4489920277610959864_int_o @ C @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: int] :
% 7.78/3.94 ( ( member_int @ X @ A4 )
% 7.78/3.94 => ! [Y: $o] :
% 7.78/3.94 ( ( member_o @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_int_o @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1719_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_int_nat,A4: set_int,B5: int > set_nat] :
% 7.78/3.94 ( ( member216504246829706758nt_nat @ C @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: int] :
% 7.78/3.94 ( ( member_int @ X @ A4 )
% 7.78/3.94 => ! [Y: nat] :
% 7.78/3.94 ( ( member_nat @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_int_nat @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1720_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_nat_num,A4: set_nat,B5: nat > set_num] :
% 7.78/3.94 ( ( member9148766508732265716at_num @ C @ ( produc6237731129814287028at_num @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ! [Y: num] :
% 7.78/3.94 ( ( member_num @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_nat_num @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1721_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_int_int,A4: set_int,B5: int > set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ C @ ( produc1453890548195736866nt_int @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: int] :
% 7.78/3.94 ( ( member_int @ X @ A4 )
% 7.78/3.94 => ! [Y: int] :
% 7.78/3.94 ( ( member_int @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_int_int @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1722_SigmaE,axiom,
% 7.78/3.94 ! [C: product_prod_nat_nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ C @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.94 => ~ ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ! [Y: nat] :
% 7.78/3.94 ( ( member_nat @ Y @ ( B5 @ X ) )
% 7.78/3.94 => ( C
% 7.78/3.94 != ( product_Pair_nat_nat @ X @ Y ) ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1723_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec7088162979684241874at_nat
% 7.78/3.94 @ ( produc6590410687421337004_nat_o
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc2761391749766926216at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1724_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > nat > $o] :
% 7.78/3.94 ( ( collec7029190964493513045at_nat
% 7.78/3.94 @ ( produc8758269395934548017_nat_o
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat,Y5: nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc7672662199629908489at_nat @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1725_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec6785001409445536906nt_int
% 7.78/3.94 @ ( produc5031841752791441652_int_o
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc8806266479013559872nt_int @ ( collec3392354462482085612at_nat @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_nat_nat] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1726_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: nat > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec5903703980526211963at_nat
% 7.78/3.94 @ ( produc5864757623865647827_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc1809337555817847783at_nat @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [X4: nat] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1727_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: nat > product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec5600542410287506995nt_int
% 7.78/3.94 @ ( produc4306188689235752475_int_o
% 7.78/3.94 @ ^ [X4: nat,Y5: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc7854212285064481439nt_int @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [X4: nat] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1728_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > product_prod_nat_nat > $o] :
% 7.78/3.94 ( ( collec7751116662793354522at_nat
% 7.78/3.94 @ ( produc3235059054576640100_nat_o
% 7.78/3.94 @ ^ [X4: product_prod_int_int,Y5: product_prod_nat_nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc3424345432876038864at_nat @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_int_int] : ( collec3392354462482085612at_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1729_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > nat > $o] :
% 7.78/3.94 ( ( collec364394062568603661nt_nat
% 7.78/3.94 @ ( produc5441891513209881465_nat_o
% 7.78/3.94 @ ^ [X4: product_prod_int_int,Y5: nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc1007865297704999105nt_nat @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_int_int] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1730_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: product_prod_int_int > $o,Q2: product_prod_int_int > product_prod_int_int > $o] :
% 7.78/3.94 ( ( collec7447955092554649554nt_int
% 7.78/3.94 @ ( produc1676490119946744748_int_o
% 7.78/3.94 @ ^ [X4: product_prod_int_int,Y5: product_prod_int_int] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc245848125267896712nt_int @ ( collec213857154873943460nt_int @ P2 )
% 7.78/3.94 @ ^ [X4: product_prod_int_int] : ( collec213857154873943460nt_int @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1731_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: nat > $o,Q2: nat > nat > $o] :
% 7.78/3.94 ( ( collec3392354462482085612at_nat
% 7.78/3.94 @ ( produc6081775807080527818_nat_o
% 7.78/3.94 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc457027306803732586at_nat @ ( collect_nat @ P2 )
% 7.78/3.94 @ ^ [X4: nat] : ( collect_nat @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1732_Collect__case__prod__Sigma,axiom,
% 7.78/3.94 ! [P2: int > $o,Q2: int > int > $o] :
% 7.78/3.94 ( ( collec213857154873943460nt_int
% 7.78/3.94 @ ( produc4947309494688390418_int_o
% 7.78/3.94 @ ^ [X4: int,Y5: int] :
% 7.78/3.94 ( ( P2 @ X4 )
% 7.78/3.94 & ( Q2 @ X4 @ Y5 ) ) ) )
% 7.78/3.94 = ( produc1453890548195736866nt_int @ ( collect_int @ P2 )
% 7.78/3.94 @ ^ [X4: int] : ( collect_int @ ( Q2 @ X4 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1733_Sigma__mono,axiom,
% 7.78/3.94 ! [A4: set_nat,C3: set_nat,B5: nat > set_nat,D: nat > set_nat] :
% 7.78/3.94 ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.94 => ( ! [X: nat] :
% 7.78/3.94 ( ( member_nat @ X @ A4 )
% 7.78/3.94 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ ( D @ X ) ) )
% 7.78/3.94 => ( ord_le3146513528884898305at_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) @ ( produc457027306803732586at_nat @ C3 @ D ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1734_Times__subset__cancel2,axiom,
% 7.78/3.94 ! [X2: nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( member_nat @ X2 @ C3 )
% 7.78/3.94 => ( ( ord_le3146513528884898305at_nat
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : C3 )
% 7.78/3.94 @ ( produc457027306803732586at_nat @ B5
% 7.78/3.94 @ ^ [Uu: nat] : C3 ) )
% 7.78/3.94 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1735_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_o_o,A4: set_o,B5: set_o] :
% 7.78/3.94 ( ( member7466972457876170832od_o_o @ X2
% 7.78/3.94 @ ( product_Sigma_o_o @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = ( ( member_o @ ( product_fst_o_o @ X2 ) @ A4 )
% 7.78/3.94 & ( member_o @ ( product_snd_o_o @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1736_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_o_nat,A4: set_o,B5: set_nat] :
% 7.78/3.94 ( ( member2802428098988154798_o_nat @ X2
% 7.78/3.94 @ ( product_Sigma_o_nat @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = ( ( member_o @ ( product_fst_o_nat @ X2 ) @ A4 )
% 7.78/3.94 & ( member_nat @ ( product_snd_o_nat @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1737_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_o_int,A4: set_o,B5: set_int] :
% 7.78/3.94 ( ( member7847949116333733898_o_int @ X2
% 7.78/3.94 @ ( product_Sigma_o_int @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = ( ( member_o @ ( product_fst_o_int @ X2 ) @ A4 )
% 7.78/3.94 & ( member_int @ ( product_snd_o_int @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1738_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_nat_o,A4: set_nat,B5: set_o] :
% 7.78/3.94 ( ( member6310962623043647828_nat_o @ X2
% 7.78/3.94 @ ( product_Sigma_nat_o @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ( member_nat @ ( product_fst_nat_o @ X2 ) @ A4 )
% 7.78/3.94 & ( member_o @ ( product_snd_nat_o @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1739_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_nat_int,A4: set_nat,B5: set_int] :
% 7.78/3.94 ( ( member4262671552274231302at_int @ X2
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ( member_nat @ ( product_fst_nat_int @ X2 ) @ A4 )
% 7.78/3.94 & ( member_int @ ( product_snd_nat_int @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1740_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_int_o,A4: set_int,B5: set_o] :
% 7.78/3.94 ( ( member4489920277610959864_int_o @ X2
% 7.78/3.94 @ ( product_Sigma_int_o @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( ( member_int @ ( product_fst_int_o @ X2 ) @ A4 )
% 7.78/3.94 & ( member_o @ ( product_snd_int_o @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1741_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_int_nat,A4: set_int,B5: set_nat] :
% 7.78/3.94 ( ( member216504246829706758nt_nat @ X2
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( ( member_int @ ( product_fst_int_nat @ X2 ) @ A4 )
% 7.78/3.94 & ( member_nat @ ( product_snd_int_nat @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1742_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_int_int,A4: set_int,B5: set_int] :
% 7.78/3.94 ( ( member5262025264175285858nt_int @ X2
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( ( member_int @ ( product_fst_int_int @ X2 ) @ A4 )
% 7.78/3.94 & ( member_int @ ( product_snd_int_int @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1743_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ X2
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( ( member_nat @ ( product_fst_nat_nat @ X2 ) @ A4 )
% 7.78/3.94 & ( member_nat @ ( product_snd_nat_nat @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1744_mem__Times__iff,axiom,
% 7.78/3.94 ! [X2: produc652263959640188542_nat_o,A4: set_Pr1261947904930325089at_nat,B5: set_o] :
% 7.78/3.94 ( ( member2200362271989506215_nat_o @ X2
% 7.78/3.94 @ ( produc203973861852599583_nat_o @ A4
% 7.78/3.94 @ ^ [Uu: product_prod_nat_nat] : B5 ) )
% 7.78/3.94 = ( ( member8440522571783428010at_nat @ ( produc6435950281062462810_nat_o @ X2 ) @ A4 )
% 7.78/3.94 & ( member_o @ ( produc668916169454083228_nat_o @ X2 ) @ B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1745_product__swap,axiom,
% 7.78/3.94 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( image_5168914502847457605at_nat @ product_swap_nat_nat
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc457027306803732586at_nat @ B5
% 7.78/3.94 @ ^ [Uu: nat] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1746_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: $o > $o > $o,Abs1: $o > $o,Rep1: $o > $o,T1: $o > $o > $o,R22: $o > $o > $o,Abs22: $o > nat,Rep22: nat > $o,T22: $o > nat > $o] :
% 7.78/3.94 ( ( quotient_o_o @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_o_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_o_nat @ ( relcompp_o_o_o @ T1 @ ( relcompp_o_o_o @ R22 @ ( conversep_o_o @ T1 ) ) ) @ ( comp_o_nat_o @ Abs22 @ Abs1 ) @ ( comp_o_o_nat @ Rep1 @ Rep22 ) @ ( relcompp_o_o_nat @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1747_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: num > num > $o,Abs1: num > nat,Rep1: nat > num,T1: num > nat > $o,R22: nat > nat > $o,Abs22: nat > int,Rep22: int > nat,T22: nat > int > $o] :
% 7.78/3.94 ( ( quotient_num_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_nat_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_num_int @ ( relcompp_num_nat_num @ T1 @ ( relcompp_nat_nat_num @ R22 @ ( conversep_num_nat @ T1 ) ) ) @ ( comp_nat_int_num @ Abs22 @ Abs1 ) @ ( comp_nat_num_int @ Rep1 @ Rep22 ) @ ( relcompp_num_nat_int @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1748_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,Abs1: nat > int,Rep1: int > nat,T1: nat > int > $o,R22: int > int > $o,Abs22: int > int,Rep22: int > int,T22: int > int > $o] :
% 7.78/3.94 ( ( quotient_nat_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_int_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_nat_int @ ( relcompp_nat_int_nat @ T1 @ ( relcompp_int_int_nat @ R22 @ ( conversep_nat_int @ T1 ) ) ) @ ( comp_int_int_nat @ Abs22 @ Abs1 ) @ ( comp_int_nat_int @ Rep1 @ Rep22 ) @ ( relcompp_nat_int_int @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1749_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,Abs1: nat > $o,Rep1: $o > nat,T1: nat > $o > $o,R22: $o > $o > $o,Abs22: $o > $o,Rep22: $o > $o,T22: $o > $o > $o] :
% 7.78/3.94 ( ( quotient_nat_o @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_o_o @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_nat_o @ ( relcompp_nat_o_nat @ T1 @ ( relcompp_o_o_nat @ R22 @ ( conversep_nat_o @ T1 ) ) ) @ ( comp_o_o_nat @ Abs22 @ Abs1 ) @ ( comp_o_nat_o @ Rep1 @ Rep22 ) @ ( relcompp_nat_o_o @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1750_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: int > int > $o,Abs1: int > nat,Rep1: nat > int,T1: int > nat > $o,R22: nat > nat > $o,Abs22: nat > num,Rep22: num > nat,T22: nat > num > $o] :
% 7.78/3.94 ( ( quotient_int_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_nat_num @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_int_num @ ( relcompp_int_nat_int @ T1 @ ( relcompp_nat_nat_int @ R22 @ ( conversep_int_nat @ T1 ) ) ) @ ( comp_nat_num_int @ Abs22 @ Abs1 ) @ ( comp_nat_int_num @ Rep1 @ Rep22 ) @ ( relcompp_int_nat_num @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1751_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: nat > nat > $o,Abs1: nat > nat,Rep1: nat > nat,T1: nat > nat > $o,R22: nat > nat > $o,Abs22: nat > nat,Rep22: nat > nat,T22: nat > nat > $o] :
% 7.78/3.94 ( ( quotient_nat_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_nat_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_nat_nat @ ( relcompp_nat_nat_nat @ T1 @ ( relcompp_nat_nat_nat @ R22 @ ( conversep_nat_nat @ T1 ) ) ) @ ( comp_nat_nat_nat @ Abs22 @ Abs1 ) @ ( comp_nat_nat_nat @ Rep1 @ Rep22 ) @ ( relcompp_nat_nat_nat @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1752_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: int > int > $o,Abs1: int > int,Rep1: int > int,T1: int > int > $o,R22: int > int > $o,Abs22: int > nat,Rep22: nat > int,T22: int > nat > $o] :
% 7.78/3.94 ( ( quotient_int_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotient_int_nat @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotient_int_nat @ ( relcompp_int_int_int @ T1 @ ( relcompp_int_int_int @ R22 @ ( conversep_int_int @ T1 ) ) ) @ ( comp_int_nat_int @ Abs22 @ Abs1 ) @ ( comp_int_int_nat @ Rep1 @ Rep22 ) @ ( relcompp_int_int_nat @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1753_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: int > int > $o,Abs1: int > int,Rep1: int > int,T1: int > int > $o,R22: int > int > $o,Abs22: int > code_integer,Rep22: code_integer > int,T22: int > code_integer > $o] :
% 7.78/3.94 ( ( quotient_int_int @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotie2291698863146621601nteger @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotie2291698863146621601nteger @ ( relcompp_int_int_int @ T1 @ ( relcompp_int_int_int @ R22 @ ( conversep_int_int @ T1 ) ) ) @ ( comp_i1585864551200866970er_int @ Abs22 @ Abs1 ) @ ( comp_i2224564030725804698nteger @ Rep1 @ Rep22 ) @ ( relcom967497705283160040nteger @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1754_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,Abs1: product_prod_nat_nat > product_prod_nat_nat,Rep1: product_prod_nat_nat > product_prod_nat_nat,T1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o,Abs22: product_prod_nat_nat > int,Rep22: int > product_prod_nat_nat,T22: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( quotie4166942682936818134at_nat @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotie1194848508323700631at_int @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotie1194848508323700631at_int @ ( relcom282571730187242960at_nat @ T1 @ ( relcom282571730187242960at_nat @ R22 @ ( conver6965824823119931701at_nat @ T1 ) ) ) @ ( comp_P4605287290794827253at_nat @ Abs22 @ Abs1 ) @ ( comp_P7428279379633703887at_int @ Rep1 @ Rep22 ) @ ( relcom8911704206367525917at_int @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1755_Quotient__compose,axiom,
% 7.78/3.94 ! [R1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,Abs1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > code_integer,Rep1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,T1: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > $o,R22: ( code_integer > code_integer ) > ( code_integer > code_integer ) > $o,Abs22: ( code_integer > code_integer ) > code_integer,Rep22: code_integer > code_integer > code_integer,T22: ( code_integer > code_integer ) > code_integer > $o] :
% 7.78/3.94 ( ( quotie8207154290130328982nteger @ R1 @ Abs1 @ Rep1 @ T1 )
% 7.78/3.94 => ( ( quotie9062115205763428814nteger @ R22 @ Abs22 @ Rep22 @ T22 )
% 7.78/3.94 => ( quotie8803226531959296410nteger @ ( relcom458776940982682326nteger @ T1 @ ( relcom1820845089908643850nteger @ R22 @ ( conver3229387634306789365nteger @ T1 ) ) ) @ ( comp_C7826480081638475456nteger @ Abs22 @ Abs1 ) @ ( comp_C8797469213163452608nteger @ Rep1 @ Rep22 ) @ ( relcom4829277440228594702nteger @ T1 @ T22 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1756_swap__product,axiom,
% 7.78/3.94 ! [A4: set_se5479201105039950375at_nat,B5: set_se5479201105039950375at_nat] :
% 7.78/3.94 ( ( image_3313167189156628421at_nat
% 7.78/3.94 @ ( produc5456455677105495163at_nat
% 7.78/3.94 @ ^ [I2: set_Pr4329608150637261639at_nat,J: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ J @ I2 ) )
% 7.78/3.94 @ ( produc6258361011560675592at_nat @ A4
% 7.78/3.94 @ ^ [Uu: set_Pr4329608150637261639at_nat] : B5 ) )
% 7.78/3.94 = ( produc6258361011560675592at_nat @ B5
% 7.78/3.94 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1757_swap__product,axiom,
% 7.78/3.94 ! [A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( image_960689587819713477at_nat
% 7.78/3.94 @ ( produc7548845685434208379at_nat
% 7.78/3.94 @ ^ [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ J @ I2 ) )
% 7.78/3.94 @ ( produc7726050920695093128at_nat @ A4
% 7.78/3.94 @ ^ [Uu: set_Pr1261947904930325089at_nat] : B5 ) )
% 7.78/3.94 = ( produc7726050920695093128at_nat @ B5
% 7.78/3.94 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1758_swap__product,axiom,
% 7.78/3.94 ! [A4: set_num,B5: set_nat] :
% 7.78/3.94 ( ( image_7762062833379733445at_num
% 7.78/3.94 @ ( produc5219324331026901427at_num
% 7.78/3.94 @ ^ [I2: num,J: nat] : ( product_Pair_nat_num @ J @ I2 ) )
% 7.78/3.94 @ ( produc7810729746965977780um_nat @ A4
% 7.78/3.94 @ ^ [Uu: num] : B5 ) )
% 7.78/3.94 = ( produc6237731129814287028at_num @ B5
% 7.78/3.94 @ ^ [Uu: nat] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1759_swap__product,axiom,
% 7.78/3.94 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( image_5168914502847457605at_nat
% 7.78/3.94 @ ( produc2626176000494625587at_nat
% 7.78/3.94 @ ^ [I2: nat,J: nat] : ( product_Pair_nat_nat @ J @ I2 ) )
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc457027306803732586at_nat @ B5
% 7.78/3.94 @ ^ [Uu: nat] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1760_swap__product,axiom,
% 7.78/3.94 ! [A4: set_int,B5: set_int] :
% 7.78/3.94 ( ( image_2653370878348428101nt_int
% 7.78/3.94 @ ( produc4245557441103728435nt_int
% 7.78/3.94 @ ^ [I2: int,J: int] : ( product_Pair_int_int @ J @ I2 ) )
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc1453890548195736866nt_int @ B5
% 7.78/3.94 @ ^ [Uu: int] : A4 ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1761_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: nat > rat,A4: set_nat,A7: set_rat,G: int > nat,B5: set_int,B7: set_nat] :
% 7.78/3.94 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_nat @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_3755276878268593137at_nat @ ( produc8749313216793205150nt_nat @ F @ G )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc140472662868866674at_nat @ A7
% 7.78/3.94 @ ^ [Uu: rat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1762_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: nat > rat,A4: set_nat,A7: set_rat,G: int > int,B5: set_int,B7: set_int] :
% 7.78/3.94 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_int @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_8800797895614172237at_int @ ( produc8746822746284154874nt_int @ F @ G )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc137982192359816398at_int @ A7
% 7.78/3.94 @ ^ [Uu: rat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1763_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: nat > nat,A4: set_nat,A7: set_nat,G: int > int,B5: set_int,B7: set_int] :
% 7.78/3.94 ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_int @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_9117352539549038149at_int @ ( produc7974749936722635250nt_int @ F @ G )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ A7
% 7.78/3.94 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1764_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: nat > int,A4: set_nat,A7: set_int,G: int > nat,B5: set_int,B7: set_nat] :
% 7.78/3.94 ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_nat @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_5071185234104513605nt_nat @ ( produc8348893967468530162nt_nat @ F @ G )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc1456381018704787142nt_nat @ A7
% 7.78/3.94 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1765_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: nat > int,A4: set_nat,A7: set_int,G: int > int,B5: set_int,B7: set_int] :
% 7.78/3.94 ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_int @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_893334214595316897nt_int @ ( produc8346403496959479886nt_int @ F @ G )
% 7.78/3.94 @ ( produc454536836294682310at_int @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = ( produc1453890548195736866nt_int @ A7
% 7.78/3.94 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1766_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: int > nat,A4: set_int,A7: set_nat,G: nat > rat,B5: set_nat,B7: set_rat] :
% 7.78/3.94 ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_nat_rat @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_3420722608207172081at_rat @ ( produc4032938703151184286at_rat @ F @ G )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc9045269283572012658at_rat @ A7
% 7.78/3.94 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1767_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: int > nat,A4: set_int,A7: set_nat,G: nat > int,B5: set_nat,B7: set_int] :
% 7.78/3.94 ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_nat_int @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_2751100147091372101at_int @ ( produc4665578292728629746at_int @ F @ G )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ A7
% 7.78/3.94 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1768_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: int > nat,A4: set_int,A7: set_nat,G: int > int,B5: set_int,B7: set_int] :
% 7.78/3.94 ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_int_int @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_1654017166447373545at_int @ ( produc5664932004629684302nt_int @ F @ G )
% 7.78/3.94 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc454536836294682310at_int @ A7
% 7.78/3.94 @ ^ [Uu: nat] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1769_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: int > int,A4: set_int,A7: set_int,G: nat > rat,B5: set_nat,B7: set_rat] :
% 7.78/3.94 ( ( ( image_int_int @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_nat_rat @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_4420076320108226637nt_rat @ ( produc4404592263388028922at_rat @ F @ G )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc821250958618291406nt_rat @ A7
% 7.78/3.94 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1770_map__prod__surj__on,axiom,
% 7.78/3.94 ! [F: int > int,A4: set_int,A7: set_int,G: nat > nat,B5: set_nat,B7: set_nat] :
% 7.78/3.94 ( ( ( image_int_int @ F @ A4 )
% 7.78/3.94 = A7 )
% 7.78/3.94 => ( ( ( image_nat_nat @ G @ B5 )
% 7.78/3.94 = B7 )
% 7.78/3.94 => ( ( image_7928304878501623365nt_nat @ ( produc5039722323474524658at_nat @ F @ G )
% 7.78/3.94 @ ( produc1456381018704787142nt_nat @ A4
% 7.78/3.94 @ ^ [Uu: int] : B5 ) )
% 7.78/3.94 = ( produc1456381018704787142nt_nat @ A7
% 7.78/3.94 @ ^ [Uu: int] : B7 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1771_left__total__OO,axiom,
% 7.78/3.94 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( left_t5646938096895998950at_nat @ R3 )
% 7.78/3.94 => ( ( left_t1861001511420785031at_int @ S5 )
% 7.78/3.94 => ( left_t1861001511420785031at_int @ ( relcom8911704206367525917at_int @ R3 @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1772_left__total__OO,axiom,
% 7.78/3.94 ! [R3: int > int > $o,S5: int > code_integer > $o] :
% 7.78/3.94 ( ( left_total_int_int @ R3 )
% 7.78/3.94 => ( ( left_t2374113004080657585nteger @ S5 )
% 7.78/3.94 => ( left_t2374113004080657585nteger @ ( relcom967497705283160040nteger @ R3 @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1773_left__unique__OO,axiom,
% 7.78/3.94 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o] :
% 7.78/3.94 ( ( left_u7296345956935681743at_nat @ R3 )
% 7.78/3.94 => ( ( left_u4005249686606446046at_int @ S5 )
% 7.78/3.94 => ( left_u4005249686606446046at_int @ ( relcom8911704206367525917at_int @ R3 @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1774_left__unique__OO,axiom,
% 7.78/3.94 ! [R3: int > int > $o,S5: int > code_integer > $o] :
% 7.78/3.94 ( ( left_unique_int_int @ R3 )
% 7.78/3.94 => ( ( left_u6795595883297946906nteger @ S5 )
% 7.78/3.94 => ( left_u6795595883297946906nteger @ ( relcom967497705283160040nteger @ R3 @ S5 ) ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1775_Product__Type_Oproduct__def,axiom,
% 7.78/3.94 ( produc929334515565554804at_nat
% 7.78/3.94 = ( ^ [A6: set_nat,B6: set_nat] :
% 7.78/3.94 ( produc457027306803732586at_nat @ A6
% 7.78/3.94 @ ^ [Uu: nat] : B6 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1776_member__product,axiom,
% 7.78/3.94 ! [X2: produc3843707927480180839at_nat,A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat] :
% 7.78/3.94 ( ( member8757157785044589968at_nat @ X2 @ ( produc3241716407206042770at_nat @ A4 @ B5 ) )
% 7.78/3.94 = ( member8757157785044589968at_nat @ X2
% 7.78/3.94 @ ( produc7726050920695093128at_nat @ A4
% 7.78/3.94 @ ^ [Uu: set_Pr1261947904930325089at_nat] : B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1777_member__product,axiom,
% 7.78/3.94 ! [X2: product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.94 ( ( member8440522571783428010at_nat @ X2 @ ( produc929334515565554804at_nat @ A4 @ B5 ) )
% 7.78/3.94 = ( member8440522571783428010at_nat @ X2
% 7.78/3.94 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1778_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_Product_unit,B5: set_Product_unit] :
% 7.78/3.94 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_262127665112854123t_unit @ produc6786084904866402309t_unit
% 7.78/3.94 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.94 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_262127665112854123t_unit @ produc6786084904866402309t_unit
% 7.78/3.94 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1779_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_Product_unit,B5: set_o] :
% 7.78/3.94 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_1801747192096393899it_o_o @ produc7461459235754980752unit_o
% 7.78/3.94 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = bot_bot_set_o ) )
% 7.78/3.94 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_1801747192096393899it_o_o @ produc7461459235754980752unit_o
% 7.78/3.94 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1780_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_Product_unit,B5: set_nat] :
% 7.78/3.94 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_6725568594985674851at_nat @ produc996414825743149016it_nat
% 7.78/3.94 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = bot_bot_set_nat ) )
% 7.78/3.94 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.94 => ( ( image_6725568594985674851at_nat @ produc996414825743149016it_nat
% 7.78/3.94 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.94 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1781_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_o,B5: set_Product_unit] :
% 7.78/3.94 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.94 => ( ( image_4419268941131634678t_unit @ produc2875488738488844090t_unit
% 7.78/3.94 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.94 & ( ( A4 != bot_bot_set_o )
% 7.78/3.94 => ( ( image_4419268941131634678t_unit @ produc2875488738488844090t_unit
% 7.78/3.94 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1782_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_o,B5: set_o] :
% 7.78/3.94 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.94 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 7.78/3.94 @ ( product_Sigma_o_o @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = bot_bot_set_o ) )
% 7.78/3.94 & ( ( A4 != bot_bot_set_o )
% 7.78/3.94 => ( ( image_7896445794123959606_o_o_o @ product_snd_o_o
% 7.78/3.94 @ ( product_Sigma_o_o @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1783_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_o,B5: set_nat] :
% 7.78/3.94 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.94 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 7.78/3.94 @ ( product_Sigma_o_nat @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = bot_bot_set_nat ) )
% 7.78/3.94 & ( ( A4 != bot_bot_set_o )
% 7.78/3.94 => ( ( image_4888532181312399726at_nat @ product_snd_o_nat
% 7.78/3.94 @ ( product_Sigma_o_nat @ A4
% 7.78/3.94 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1784_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_nat,B5: set_Product_unit] :
% 7.78/3.94 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.94 => ( ( image_5511522805742971924t_unit @ produc8850949007409916470t_unit
% 7.78/3.94 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.94 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.94 => ( ( image_5511522805742971924t_unit @ produc8850949007409916470t_unit
% 7.78/3.94 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = B5 ) ) ) ).
% 7.78/3.94
% 7.78/3.94 thf(fact_1785_snd__image__times,axiom,
% 7.78/3.94 ! [A4: set_nat,B5: set_o] :
% 7.78/3.94 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.94 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 7.78/3.94 @ ( product_Sigma_nat_o @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.94 = bot_bot_set_o ) )
% 7.78/3.94 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.94 => ( ( image_7478392465989118804at_o_o @ product_snd_nat_o
% 7.78/3.94 @ ( product_Sigma_nat_o @ A4
% 7.78/3.94 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1786_snd__image__times,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( image_2486076414777270412at_nat @ product_snd_nat_nat
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1787_snd__image__times,axiom,
% 7.78/3.95 ! [A4: set_ref_a,B5: set_he8644174446132254637t_unit] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_ref_a )
% 7.78/3.95 => ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit
% 7.78/3.95 @ ( produc3946373962484743846t_unit @ A4
% 7.78/3.95 @ ^ [Uu: ref_a] : B5 ) )
% 7.78/3.95 = bot_bo3686245532977126937t_unit ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_ref_a )
% 7.78/3.95 => ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit
% 7.78/3.95 @ ( produc3946373962484743846t_unit @ A4
% 7.78/3.95 @ ^ [Uu: ref_a] : B5 ) )
% 7.78/3.95 = B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1788_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_Product_unit,A4: set_Product_unit] :
% 7.78/3.95 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_262127665112854123t_unit @ produc6963936691090040003t_unit
% 7.78/3.95 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_262127665112854123t_unit @ produc6963936691090040003t_unit
% 7.78/3.95 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1789_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_Product_unit,A4: set_o] :
% 7.78/3.95 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit
% 7.78/3.95 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit
% 7.78/3.95 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1790_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_Product_unit,A4: set_nat] :
% 7.78/3.95 ( ( ( B5 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit
% 7.78/3.95 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit
% 7.78/3.95 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1791_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_o,A4: set_Product_unit] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_o )
% 7.78/3.95 => ( ( image_4246157487713968288t_unit @ produc582253812616888142unit_o
% 7.78/3.95 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_o )
% 7.78/3.95 => ( ( image_4246157487713968288t_unit @ produc582253812616888142unit_o
% 7.78/3.95 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1792_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_o,A4: set_o] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_o )
% 7.78/3.95 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 7.78/3.95 @ ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_o )
% 7.78/3.95 => ( ( image_7896445794123959606_o_o_o @ product_fst_o_o
% 7.78/3.95 @ ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1793_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_o,A4: set_nat] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_o )
% 7.78/3.95 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 7.78/3.95 @ ( product_Sigma_nat_o @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_o )
% 7.78/3.95 => ( ( image_8629803608462650132_o_nat @ product_fst_nat_o
% 7.78/3.95 @ ( product_Sigma_nat_o @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1794_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_nat,A4: set_Product_unit] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_nat )
% 7.78/3.95 => ( ( image_7474191388529947450t_unit @ produc5169466786534984090it_nat
% 7.78/3.95 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_nat )
% 7.78/3.95 => ( ( image_7474191388529947450t_unit @ produc5169466786534984090it_nat
% 7.78/3.95 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1795_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_nat,A4: set_o] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_nat )
% 7.78/3.95 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 7.78/3.95 @ ( product_Sigma_o_nat @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_nat )
% 7.78/3.95 => ( ( image_8105710389281276538_nat_o @ product_fst_o_nat
% 7.78/3.95 @ ( product_Sigma_o_nat @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1796_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_nat,A4: set_nat] :
% 7.78/3.95 ( ( ( B5 = bot_bot_set_nat )
% 7.78/3.95 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( B5 != bot_bot_set_nat )
% 7.78/3.95 => ( ( image_2486076414777270412at_nat @ product_fst_nat_nat
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1797_fst__image__times,axiom,
% 7.78/3.95 ! [B5: set_he8644174446132254637t_unit,A4: set_ref_a] :
% 7.78/3.95 ( ( ( B5 = bot_bo3686245532977126937t_unit )
% 7.78/3.95 => ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit
% 7.78/3.95 @ ( produc3946373962484743846t_unit @ A4
% 7.78/3.95 @ ^ [Uu: ref_a] : B5 ) )
% 7.78/3.95 = bot_bot_set_ref_a ) )
% 7.78/3.95 & ( ( B5 != bot_bo3686245532977126937t_unit )
% 7.78/3.95 => ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit
% 7.78/3.95 @ ( produc3946373962484743846t_unit @ A4
% 7.78/3.95 @ ^ [Uu: ref_a] : B5 ) )
% 7.78/3.95 = A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1798_image__is__empty,axiom,
% 7.78/3.95 ! [F: int > int,A4: set_int] :
% 7.78/3.95 ( ( ( image_int_int @ F @ A4 )
% 7.78/3.95 = bot_bot_set_int )
% 7.78/3.95 = ( A4 = bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1799_image__is__empty,axiom,
% 7.78/3.95 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.95 ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.95 = bot_bot_set_rat )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1800_image__is__empty,axiom,
% 7.78/3.95 ! [F: nat > int,A4: set_nat] :
% 7.78/3.95 ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.95 = bot_bot_set_int )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1801_image__is__empty,axiom,
% 7.78/3.95 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 7.78/3.95 ( ( ( image_405062704495631173t_unit @ F @ A4 )
% 7.78/3.95 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1802_image__is__empty,axiom,
% 7.78/3.95 ! [F: $o > product_unit,A4: set_o] :
% 7.78/3.95 ( ( ( image_o_Product_unit @ F @ A4 )
% 7.78/3.95 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 = ( A4 = bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1803_image__is__empty,axiom,
% 7.78/3.95 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.95 ( ( ( image_8730104196221521654t_unit @ F @ A4 )
% 7.78/3.95 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1804_image__is__empty,axiom,
% 7.78/3.95 ! [F: product_unit > $o,A4: set_Product_unit] :
% 7.78/3.95 ( ( ( image_Product_unit_o @ F @ A4 )
% 7.78/3.95 = bot_bot_set_o )
% 7.78/3.95 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1805_image__is__empty,axiom,
% 7.78/3.95 ! [F: $o > $o,A4: set_o] :
% 7.78/3.95 ( ( ( image_o_o @ F @ A4 )
% 7.78/3.95 = bot_bot_set_o )
% 7.78/3.95 = ( A4 = bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1806_image__is__empty,axiom,
% 7.78/3.95 ! [F: nat > $o,A4: set_nat] :
% 7.78/3.95 ( ( ( image_nat_o @ F @ A4 )
% 7.78/3.95 = bot_bot_set_o )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1807_image__is__empty,axiom,
% 7.78/3.95 ! [F: int > nat,A4: set_int] :
% 7.78/3.95 ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.95 = bot_bot_set_nat )
% 7.78/3.95 = ( A4 = bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1808_empty__is__image,axiom,
% 7.78/3.95 ! [F: int > int,A4: set_int] :
% 7.78/3.95 ( ( bot_bot_set_int
% 7.78/3.95 = ( image_int_int @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1809_empty__is__image,axiom,
% 7.78/3.95 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.95 ( ( bot_bot_set_rat
% 7.78/3.95 = ( image_nat_rat @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1810_empty__is__image,axiom,
% 7.78/3.95 ! [F: nat > int,A4: set_nat] :
% 7.78/3.95 ( ( bot_bot_set_int
% 7.78/3.95 = ( image_nat_int @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1811_empty__is__image,axiom,
% 7.78/3.95 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 7.78/3.95 ( ( bot_bo3957492148770167129t_unit
% 7.78/3.95 = ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1812_empty__is__image,axiom,
% 7.78/3.95 ! [F: $o > product_unit,A4: set_o] :
% 7.78/3.95 ( ( bot_bo3957492148770167129t_unit
% 7.78/3.95 = ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1813_empty__is__image,axiom,
% 7.78/3.95 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.95 ( ( bot_bo3957492148770167129t_unit
% 7.78/3.95 = ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1814_empty__is__image,axiom,
% 7.78/3.95 ! [F: product_unit > $o,A4: set_Product_unit] :
% 7.78/3.95 ( ( bot_bot_set_o
% 7.78/3.95 = ( image_Product_unit_o @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1815_empty__is__image,axiom,
% 7.78/3.95 ! [F: $o > $o,A4: set_o] :
% 7.78/3.95 ( ( bot_bot_set_o
% 7.78/3.95 = ( image_o_o @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1816_empty__is__image,axiom,
% 7.78/3.95 ! [F: nat > $o,A4: set_nat] :
% 7.78/3.95 ( ( bot_bot_set_o
% 7.78/3.95 = ( image_nat_o @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1817_empty__is__image,axiom,
% 7.78/3.95 ! [F: int > nat,A4: set_int] :
% 7.78/3.95 ( ( bot_bot_set_nat
% 7.78/3.95 = ( image_int_nat @ F @ A4 ) )
% 7.78/3.95 = ( A4 = bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1818_image__empty,axiom,
% 7.78/3.95 ! [F: int > int] :
% 7.78/3.95 ( ( image_int_int @ F @ bot_bot_set_int )
% 7.78/3.95 = bot_bot_set_int ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1819_image__empty,axiom,
% 7.78/3.95 ! [F: int > nat] :
% 7.78/3.95 ( ( image_int_nat @ F @ bot_bot_set_int )
% 7.78/3.95 = bot_bot_set_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1820_image__empty,axiom,
% 7.78/3.95 ! [F: product_unit > product_unit] :
% 7.78/3.95 ( ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1821_image__empty,axiom,
% 7.78/3.95 ! [F: product_unit > $o] :
% 7.78/3.95 ( ( image_Product_unit_o @ F @ bot_bo3957492148770167129t_unit )
% 7.78/3.95 = bot_bot_set_o ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1822_image__empty,axiom,
% 7.78/3.95 ! [F: product_unit > nat] :
% 7.78/3.95 ( ( image_875570014554754200it_nat @ F @ bot_bo3957492148770167129t_unit )
% 7.78/3.95 = bot_bot_set_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1823_image__empty,axiom,
% 7.78/3.95 ! [F: $o > product_unit] :
% 7.78/3.95 ( ( image_o_Product_unit @ F @ bot_bot_set_o )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1824_image__empty,axiom,
% 7.78/3.95 ! [F: $o > $o] :
% 7.78/3.95 ( ( image_o_o @ F @ bot_bot_set_o )
% 7.78/3.95 = bot_bot_set_o ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1825_image__empty,axiom,
% 7.78/3.95 ! [F: $o > nat] :
% 7.78/3.95 ( ( image_o_nat @ F @ bot_bot_set_o )
% 7.78/3.95 = bot_bot_set_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1826_image__empty,axiom,
% 7.78/3.95 ! [F: nat > rat] :
% 7.78/3.95 ( ( image_nat_rat @ F @ bot_bot_set_nat )
% 7.78/3.95 = bot_bot_set_rat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1827_image__empty,axiom,
% 7.78/3.95 ! [F: nat > int] :
% 7.78/3.95 ( ( image_nat_int @ F @ bot_bot_set_nat )
% 7.78/3.95 = bot_bot_set_int ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1828_Sigma__empty1,axiom,
% 7.78/3.95 ! [B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.95 ( ( produc7726050920695093128at_nat @ bot_bo3083307316010499117at_nat @ B5 )
% 7.78/3.95 = bot_bo228742789529271731at_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1829_Sigma__empty1,axiom,
% 7.78/3.95 ! [B5: nat > set_nat] :
% 7.78/3.95 ( ( produc457027306803732586at_nat @ bot_bot_set_nat @ B5 )
% 7.78/3.95 = bot_bo2099793752762293965at_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1830_Sigma__empty2,axiom,
% 7.78/3.95 ! [A4: set_se7855581050983116737at_nat] :
% 7.78/3.95 ( ( produc7726050920695093128at_nat @ A4
% 7.78/3.95 @ ^ [Uu: set_Pr1261947904930325089at_nat] : bot_bo3083307316010499117at_nat )
% 7.78/3.95 = bot_bo228742789529271731at_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1831_Sigma__empty2,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : bot_bot_set_nat )
% 7.78/3.95 = bot_bo2099793752762293965at_nat ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1832_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_Product_unit] :
% 7.78/3.95 ( ( ( produc6121607364029222536t_unit @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = bot_bo1654022762305692595t_unit )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1833_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_o] :
% 7.78/3.95 ( ( ( produc4996980317674386579unit_o @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = bot_bo3195362268743713342unit_o )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1834_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_nat] :
% 7.78/3.95 ( ( ( produc6875377002296012693it_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = bot_bo2472676621365177558it_nat )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1835_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_Product_unit] :
% 7.78/3.95 ( ( ( produc411009820408249917t_unit @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = bot_bo4402188677660116584t_unit )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1836_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o] :
% 7.78/3.95 ( ( ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = bot_bo7073875226086086771od_o_o )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1837_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_nat] :
% 7.78/3.95 ( ( ( product_Sigma_o_nat @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = bot_bo66526543525301729_o_nat )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1838_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_Product_unit] :
% 7.78/3.95 ( ( ( produc5506539147108004339t_unit @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = bot_bo5043309098482578556t_unit )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1839_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_o] :
% 7.78/3.95 ( ( ( product_Sigma_nat_o @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = bot_bo1114129665703605383_nat_o )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1840_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.95 ( ( ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = bot_bo2099793752762293965at_nat )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1841_Times__empty,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ( produc3904733337175673596at_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = bot_bo6659885642593197735at_nat )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bo2099793752762293965at_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1842_Collect__const__case__prod,axiom,
% 7.78/3.95 ! [P2: $o] :
% 7.78/3.95 ( ( P2
% 7.78/3.95 => ( ( collec6321179662152712658at_nat
% 7.78/3.95 @ ( produc410239310623530412_nat_o
% 7.78/3.95 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P2 ) )
% 7.78/3.95 = top_to6833984726390702231at_nat ) )
% 7.78/3.95 & ( ~ P2
% 7.78/3.95 => ( ( collec6321179662152712658at_nat
% 7.78/3.95 @ ( produc410239310623530412_nat_o
% 7.78/3.95 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : P2 ) )
% 7.78/3.95 = bot_bo228742789529271731at_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1843_Collect__const__case__prod,axiom,
% 7.78/3.95 ! [P2: $o] :
% 7.78/3.95 ( ( P2
% 7.78/3.95 => ( ( collec3392354462482085612at_nat
% 7.78/3.95 @ ( produc6081775807080527818_nat_o
% 7.78/3.95 @ ^ [A5: nat,B4: nat] : P2 ) )
% 7.78/3.95 = top_to4669805908274784177at_nat ) )
% 7.78/3.95 & ( ~ P2
% 7.78/3.95 => ( ( collec3392354462482085612at_nat
% 7.78/3.95 @ ( produc6081775807080527818_nat_o
% 7.78/3.95 @ ^ [A5: nat,B4: nat] : P2 ) )
% 7.78/3.95 = bot_bo2099793752762293965at_nat ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1844_Collect__const__case__prod,axiom,
% 7.78/3.95 ! [P2: $o] :
% 7.78/3.95 ( ( P2
% 7.78/3.95 => ( ( collec213857154873943460nt_int
% 7.78/3.95 @ ( produc4947309494688390418_int_o
% 7.78/3.95 @ ^ [A5: int,B4: int] : P2 ) )
% 7.78/3.95 = top_to4366644338036079209nt_int ) )
% 7.78/3.95 & ( ~ P2
% 7.78/3.95 => ( ( collec213857154873943460nt_int
% 7.78/3.95 @ ( produc4947309494688390418_int_o
% 7.78/3.95 @ ^ [A5: int,B4: int] : P2 ) )
% 7.78/3.95 = bot_bo1796632182523588997nt_int ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1845_Sigma__empty__iff,axiom,
% 7.78/3.95 ! [I3: set_se7855581050983116737at_nat,X5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.95 ( ( ( produc7726050920695093128at_nat @ I3 @ X5 )
% 7.78/3.95 = bot_bo228742789529271731at_nat )
% 7.78/3.95 = ( ! [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( member2643936169264416010at_nat @ X4 @ I3 )
% 7.78/3.95 => ( ( X5 @ X4 )
% 7.78/3.95 = bot_bo3083307316010499117at_nat ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1846_Sigma__empty__iff,axiom,
% 7.78/3.95 ! [I3: set_nat,X5: nat > set_nat] :
% 7.78/3.95 ( ( ( produc457027306803732586at_nat @ I3 @ X5 )
% 7.78/3.95 = bot_bo2099793752762293965at_nat )
% 7.78/3.95 = ( ! [X4: nat] :
% 7.78/3.95 ( ( member_nat @ X4 @ I3 )
% 7.78/3.95 => ( ( X5 @ X4 )
% 7.78/3.95 = bot_bot_set_nat ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1847_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_int] :
% 7.78/3.95 ( ! [X: int] :
% 7.78/3.95 ~ ( member_int @ X @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_int @ A4 @ bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1848_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ! [X: product_unit] :
% 7.78/3.95 ~ ( member_Product_unit @ X @ A4 )
% 7.78/3.95 => ( ord_le3507040750410214029t_unit @ A4 @ bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1849_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.95 ~ ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.95 => ( ord_le1268244103169919719at_nat @ A4 @ bot_bo228742789529271731at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1850_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ! [X: product_prod_nat_nat] :
% 7.78/3.95 ~ ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.95 => ( ord_le3146513528884898305at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1851_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_o] :
% 7.78/3.95 ( ! [X: $o] :
% 7.78/3.95 ~ ( member_o @ X @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1852_subset__emptyI,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ! [X: nat] :
% 7.78/3.95 ~ ( member_nat @ X @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1853_less__by__empty,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( A4 = bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1854_less__by__empty,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( A4 = bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1855_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_Product_unit,C3: set_Product_unit,D: set_Product_unit] :
% 7.78/3.95 ( ( ( produc6121607364029222536t_unit @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = ( produc6121607364029222536t_unit @ C3
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1856_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_o,C3: set_Product_unit,D: set_o] :
% 7.78/3.95 ( ( ( produc4996980317674386579unit_o @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = ( produc4996980317674386579unit_o @ C3
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1857_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_nat,C3: set_Product_unit,D: set_nat] :
% 7.78/3.95 ( ( ( produc6875377002296012693it_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = ( produc6875377002296012693it_nat @ C3
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1858_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_Product_unit,C3: set_o,D: set_Product_unit] :
% 7.78/3.95 ( ( ( produc411009820408249917t_unit @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = ( produc411009820408249917t_unit @ C3
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1859_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: set_o,D: set_o] :
% 7.78/3.95 ( ( ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = ( product_Sigma_o_o @ C3
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1860_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_nat,C3: set_o,D: set_nat] :
% 7.78/3.95 ( ( ( product_Sigma_o_nat @ A4
% 7.78/3.95 @ ^ [Uu: $o] : B5 )
% 7.78/3.95 = ( product_Sigma_o_nat @ C3
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1861_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_Product_unit,C3: set_nat,D: set_Product_unit] :
% 7.78/3.95 ( ( ( produc5506539147108004339t_unit @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = ( produc5506539147108004339t_unit @ C3
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( D = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1862_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_o,C3: set_nat,D: set_o] :
% 7.78/3.95 ( ( ( product_Sigma_nat_o @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = ( product_Sigma_nat_o @ C3
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( D = bot_bot_set_o ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1863_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: set_nat,D: set_nat] :
% 7.78/3.95 ( ( ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 )
% 7.78/3.95 = ( produc457027306803732586at_nat @ C3
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( B5 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( D = bot_bot_set_nat ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1864_times__eq__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,B5: set_Pr1261947904930325089at_nat,C3: set_Product_unit,D: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ( produc3904733337175673596at_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : B5 )
% 7.78/3.95 = ( produc3904733337175673596at_nat @ C3
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( ( A4 = C3 )
% 7.78/3.95 & ( B5 = D ) )
% 7.78/3.95 | ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( B5 = bot_bo2099793752762293965at_nat ) )
% 7.78/3.95 & ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( D = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1865_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C3: set_Product_unit,B5: set_Product_unit,D: set_Product_unit] :
% 7.78/3.95 ( ( ord_le930853871177014503t_unit
% 7.78/3.95 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : C3 )
% 7.78/3.95 @ ( produc6121607364029222536t_unit @ B5
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.95 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1866_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C3: set_o,B5: set_Product_unit,D: set_o] :
% 7.78/3.95 ( ( ord_le8534741403851954546unit_o
% 7.78/3.95 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : C3 )
% 7.78/3.95 @ ( produc4996980317674386579unit_o @ B5
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1867_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C3: set_nat,B5: set_Product_unit,D: set_nat] :
% 7.78/3.95 ( ( ord_le8121013740822022818it_nat
% 7.78/3.95 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : C3 )
% 7.78/3.95 @ ( produc6875377002296012693it_nat @ B5
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1868_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_o,C3: set_Product_unit,B5: set_o,D: set_Product_unit] :
% 7.78/3.95 ( ( ord_le518195775913581980t_unit
% 7.78/3.95 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.95 @ ^ [Uu: $o] : C3 )
% 7.78/3.95 @ ( produc411009820408249917t_unit @ B5
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.95 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1869_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_o,C3: set_o,B5: set_o,D: set_o] :
% 7.78/3.95 ( ( ord_le192195778054999463od_o_o
% 7.78/3.95 @ ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : C3 )
% 7.78/3.95 @ ( product_Sigma_o_o @ B5
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1870_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_o,C3: set_nat,B5: set_o,D: set_nat] :
% 7.78/3.95 ( ( ord_le6472378536984071597_o_nat
% 7.78/3.95 @ ( product_Sigma_o_nat @ A4
% 7.78/3.95 @ ^ [Uu: $o] : C3 )
% 7.78/3.95 @ ( product_Sigma_o_nat @ B5
% 7.78/3.95 @ ^ [Uu: $o] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_o )
% 7.78/3.95 | ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1871_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,C3: set_Product_unit,B5: set_nat,D: set_Product_unit] :
% 7.78/3.95 ( ( ord_le1468274181084648008t_unit
% 7.78/3.95 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.95 @ ^ [Uu: nat] : C3 )
% 7.78/3.95 @ ( produc5506539147108004339t_unit @ B5
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.95 & ( ord_le3507040750410214029t_unit @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1872_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,C3: set_o,B5: set_nat,D: set_o] :
% 7.78/3.95 ( ( ord_le7519981659162375251_nat_o
% 7.78/3.95 @ ( product_Sigma_nat_o @ A4
% 7.78/3.95 @ ^ [Uu: nat] : C3 )
% 7.78/3.95 @ ( product_Sigma_nat_o @ B5
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( C3 = bot_bot_set_o )
% 7.78/3.95 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_o @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1873_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_nat,C3: set_nat,B5: set_nat,D: set_nat] :
% 7.78/3.95 ( ( ord_le3146513528884898305at_nat
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : C3 )
% 7.78/3.95 @ ( produc457027306803732586at_nat @ B5
% 7.78/3.95 @ ^ [Uu: nat] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 | ( C3 = bot_bot_set_nat )
% 7.78/3.95 | ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1874_times__subset__iff,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C3: set_Pr1261947904930325089at_nat,B5: set_Product_unit,D: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ord_le8681960759543468507at_nat
% 7.78/3.95 @ ( produc3904733337175673596at_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_unit] : C3 )
% 7.78/3.95 @ ( produc3904733337175673596at_nat @ B5
% 7.78/3.95 @ ^ [Uu: product_unit] : D ) )
% 7.78/3.95 = ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 | ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.95 | ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.95 & ( ord_le3146513528884898305at_nat @ C3 @ D ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1875_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_o,B5: $o > set_Product_unit] :
% 7.78/3.95 ( ( image_8742399529945250561unit_o @ produc5219655352205527288t_unit @ ( produc411009820408249917t_unit @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_o
% 7.78/3.95 @ ^ [X4: $o] :
% 7.78/3.95 ( ( member_o @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1876_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_int,B5: int > set_Product_unit] :
% 7.78/3.95 ( ( image_7716461468295075337it_int @ produc917050878549155996t_unit @ ( produc2622961094310184599t_unit @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_int
% 7.78/3.95 @ ^ [X4: int] :
% 7.78/3.95 ( ( member_int @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1877_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: nat > set_Product_unit] :
% 7.78/3.95 ( ( image_3884712837920099081it_nat @ produc3800628931346975736t_unit @ ( produc5506539147108004339t_unit @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_nat
% 7.78/3.95 @ ^ [X4: nat] :
% 7.78/3.95 ( ( member_nat @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bo3957492148770167129t_unit ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1878_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_o,B5: $o > set_o] :
% 7.78/3.95 ( ( image_7896445794123959606_o_o_o @ product_fst_o_o @ ( product_Sigma_o_o @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_o
% 7.78/3.95 @ ^ [X4: $o] :
% 7.78/3.95 ( ( member_o @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_o ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1879_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_int,B5: int > set_o] :
% 7.78/3.95 ( ( image_90517134139374612_o_int @ product_fst_int_o @ ( product_Sigma_int_o @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_int
% 7.78/3.95 @ ^ [X4: int] :
% 7.78/3.95 ( ( member_int @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_o ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1880_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: nat > set_o] :
% 7.78/3.95 ( ( image_8629803608462650132_o_nat @ product_fst_nat_o @ ( product_Sigma_nat_o @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_nat
% 7.78/3.95 @ ^ [X4: nat] :
% 7.78/3.95 ( ( member_nat @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_o ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1881_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_o,B5: $o > set_nat] :
% 7.78/3.95 ( ( image_8105710389281276538_nat_o @ product_fst_o_nat @ ( product_Sigma_o_nat @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_o
% 7.78/3.95 @ ^ [X4: $o] :
% 7.78/3.95 ( ( member_o @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_nat ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1882_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_int,B5: int > set_nat] :
% 7.78/3.95 ( ( image_2855239504505064772at_int @ product_fst_int_nat @ ( produc1456381018704787142nt_nat @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_int
% 7.78/3.95 @ ^ [X4: int] :
% 7.78/3.95 ( ( member_int @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_nat ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1883_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( image_2486076414777270412at_nat @ product_fst_nat_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_nat
% 7.78/3.95 @ ^ [X4: nat] :
% 7.78/3.95 ( ( member_nat @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bot_set_nat ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1884_fst__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_ref_a,B5: ref_a > set_he8644174446132254637t_unit] :
% 7.78/3.95 ( ( image_7136766188234240905_ref_a @ produc473321116828791851t_unit @ ( produc3946373962484743846t_unit @ A4 @ B5 ) )
% 7.78/3.95 = ( collect_ref_a
% 7.78/3.95 @ ^ [X4: ref_a] :
% 7.78/3.95 ( ( member_ref_a @ X4 @ A4 )
% 7.78/3.95 & ( ( B5 @ X4 )
% 7.78/3.95 != bot_bo3686245532977126937t_unit ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1885_rp__inv__image__rp,axiom,
% 7.78/3.95 ! [P2: produc1319942482725812455at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( fun_re2478310338295953701at_nat @ P2 )
% 7.78/3.95 => ( fun_re2478310338295953701at_nat @ ( fun_rp8445993449185644698at_nat @ P2 @ F ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1886_the__elem__image__unique,axiom,
% 7.78/3.95 ! [A4: set_int,F: int > nat,X2: int] :
% 7.78/3.95 ( ( A4 != bot_bot_set_int )
% 7.78/3.95 => ( ! [Y: int] :
% 7.78/3.95 ( ( member_int @ Y @ A4 )
% 7.78/3.95 => ( ( F @ Y )
% 7.78/3.95 = ( F @ X2 ) ) )
% 7.78/3.95 => ( ( the_elem_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.95 = ( F @ X2 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1887_the__elem__image__unique,axiom,
% 7.78/3.95 ! [A4: set_int,F: int > int,X2: int] :
% 7.78/3.95 ( ( A4 != bot_bot_set_int )
% 7.78/3.95 => ( ! [Y: int] :
% 7.78/3.95 ( ( member_int @ Y @ A4 )
% 7.78/3.95 => ( ( F @ Y )
% 7.78/3.95 = ( F @ X2 ) ) )
% 7.78/3.95 => ( ( the_elem_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.95 = ( F @ X2 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1888_the__elem__image__unique,axiom,
% 7.78/3.95 ! [A4: set_nat,F: nat > rat,X2: nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ! [Y: nat] :
% 7.78/3.95 ( ( member_nat @ Y @ A4 )
% 7.78/3.95 => ( ( F @ Y )
% 7.78/3.95 = ( F @ X2 ) ) )
% 7.78/3.95 => ( ( the_elem_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.95 = ( F @ X2 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1889_the__elem__image__unique,axiom,
% 7.78/3.95 ! [A4: set_nat,F: nat > nat,X2: nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ! [Y: nat] :
% 7.78/3.95 ( ( member_nat @ Y @ A4 )
% 7.78/3.95 => ( ( F @ Y )
% 7.78/3.95 = ( F @ X2 ) ) )
% 7.78/3.95 => ( ( the_elem_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.95 = ( F @ X2 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1890_the__elem__image__unique,axiom,
% 7.78/3.95 ! [A4: set_nat,F: nat > int,X2: nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ! [Y: nat] :
% 7.78/3.95 ( ( member_nat @ Y @ A4 )
% 7.78/3.95 => ( ( F @ Y )
% 7.78/3.95 = ( F @ X2 ) ) )
% 7.78/3.95 => ( ( the_elem_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.95 = ( F @ X2 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1891_snd__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_ref_a,B5: ref_a > set_he8644174446132254637t_unit] :
% 7.78/3.95 ( ( image_17660834435998945t_unit @ produc1126150082675451753t_unit @ ( produc3946373962484743846t_unit @ A4 @ B5 ) )
% 7.78/3.95 = ( comple6989579708249578522t_unit @ ( image_5570573867351727369t_unit @ B5 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1892_snd__image__Sigma,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( image_2486076414777270412at_nat @ product_snd_nat_nat @ ( produc457027306803732586at_nat @ A4 @ B5 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1893_range__constant,axiom,
% 7.78/3.95 ! [X2: product_unit] :
% 7.78/3.95 ( ( image_4337914935673063477t_unit
% 7.78/3.95 @ ^ [Uu: char] : X2
% 7.78/3.95 @ top_top_set_char )
% 7.78/3.95 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1894_range__constant,axiom,
% 7.78/3.95 ! [X2: $o] :
% 7.78/3.95 ( ( image_char_o
% 7.78/3.95 @ ^ [Uu: char] : X2
% 7.78/3.95 @ top_top_set_char )
% 7.78/3.95 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1895_range__constant,axiom,
% 7.78/3.95 ! [X2: nat] :
% 7.78/3.95 ( ( image_char_nat
% 7.78/3.95 @ ^ [Uu: char] : X2
% 7.78/3.95 @ top_top_set_char )
% 7.78/3.95 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1896_range__constant,axiom,
% 7.78/3.95 ! [X2: product_unit] :
% 7.78/3.95 ( ( image_2327579789247107822t_unit
% 7.78/3.95 @ ^ [Uu: rat] : X2
% 7.78/3.95 @ top_top_set_rat )
% 7.78/3.95 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1897_range__constant,axiom,
% 7.78/3.95 ! [X2: $o] :
% 7.78/3.95 ( ( image_rat_o
% 7.78/3.95 @ ^ [Uu: rat] : X2
% 7.78/3.95 @ top_top_set_rat )
% 7.78/3.95 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1898_range__constant,axiom,
% 7.78/3.95 ! [X2: nat] :
% 7.78/3.95 ( ( image_rat_nat
% 7.78/3.95 @ ^ [Uu: rat] : X2
% 7.78/3.95 @ top_top_set_rat )
% 7.78/3.95 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1899_range__constant,axiom,
% 7.78/3.95 ! [X2: rat] :
% 7.78/3.95 ( ( image_nat_rat
% 7.78/3.95 @ ^ [Uu: nat] : X2
% 7.78/3.95 @ top_top_set_nat )
% 7.78/3.95 = ( insert_rat @ X2 @ bot_bot_set_rat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1900_range__constant,axiom,
% 7.78/3.95 ! [X2: int] :
% 7.78/3.95 ( ( image_nat_int
% 7.78/3.95 @ ^ [Uu: nat] : X2
% 7.78/3.95 @ top_top_set_nat )
% 7.78/3.95 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1901_range__constant,axiom,
% 7.78/3.95 ! [X2: product_unit] :
% 7.78/3.95 ( ( image_8730104196221521654t_unit
% 7.78/3.95 @ ^ [Uu: nat] : X2
% 7.78/3.95 @ top_top_set_nat )
% 7.78/3.95 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1902_range__constant,axiom,
% 7.78/3.95 ! [X2: $o] :
% 7.78/3.95 ( ( image_nat_o
% 7.78/3.95 @ ^ [Uu: nat] : X2
% 7.78/3.95 @ top_top_set_nat )
% 7.78/3.95 = ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1903_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_char] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_5325685772115642575t_char
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_char ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_5325685772115642575t_char
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1904_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_char] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_o_set_char
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_char ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_o_set_char
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1905_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_char] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_nat_set_char
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_char ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7965528767983648192t_char
% 7.78/3.95 @ ( image_nat_set_char
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1906_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_rat] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_4665621433434589782et_rat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_rat ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_4665621433434589782et_rat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1907_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_rat] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_o_set_rat
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_rat ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_o_set_rat
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1908_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_rat] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_nat_set_rat
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_rat ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple4298007329820168263et_rat
% 7.78/3.95 @ ( image_nat_set_rat
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1909_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_int] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_3995998972318789802et_int
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_int ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_3995998972318789802et_int
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1910_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_int] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_o_set_int
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_int ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_o_set_int
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1911_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_int] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_nat_set_int
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_int ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3628384868704368283et_int
% 7.78/3.95 @ ( image_nat_set_int
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1912_INT__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = top_top_set_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1913_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > code_integer > $o,R7: code_integer > code_integer > $o,S5: num > num > $o,S6: num > num > $o] :
% 7.78/3.95 ( ( left_u6795595883297946906nteger @ R3 )
% 7.78/3.95 => ( ( right_7281159819619925802nteger @ R3 )
% 7.78/3.95 => ( ( right_5866438497372881682nteger @ R7 )
% 7.78/3.95 => ( ( left_t2884206969071330nteger @ R7 )
% 7.78/3.95 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1914_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > code_integer > $o,R7: code_integer > int > $o,S5: num > num > $o,S6: num > num > $o] :
% 7.78/3.95 ( ( left_u6795595883297946906nteger @ R3 )
% 7.78/3.95 => ( ( right_7281159819619925802nteger @ R3 )
% 7.78/3.95 => ( ( right_7836862732553076961er_int @ R7 )
% 7.78/3.95 => ( ( left_t1735413524555719857er_int @ R7 )
% 7.78/3.95 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1915_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > int > $o,R7: int > int > $o,S5: num > num > $o,S6: num > num > $o] :
% 7.78/3.95 ( ( left_unique_int_int @ R3 )
% 7.78/3.95 => ( ( right_total_int_int @ R3 )
% 7.78/3.95 => ( ( right_unique_int_int @ R7 )
% 7.78/3.95 => ( ( left_total_int_int @ R7 )
% 7.78/3.95 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1916_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: num > num > $o,S6: num > num > $o] :
% 7.78/3.95 ( ( left_unique_int_int @ R3 )
% 7.78/3.95 => ( ( right_total_int_int @ R3 )
% 7.78/3.95 => ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1917_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: int > int > $o,S6: int > code_integer > $o] :
% 7.78/3.95 ( ( left_unique_int_int @ R3 )
% 7.78/3.95 => ( ( right_total_int_int @ R3 )
% 7.78/3.95 => ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ord_le7522433683449569238eger_o @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1918_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: product_prod_nat_nat > int > $o,R7: int > int > $o,S5: nat > nat > $o,S6: nat > nat > $o] :
% 7.78/3.95 ( ( left_u4005249686606446046at_int @ R3 )
% 7.78/3.95 => ( ( right_1157779049177982926at_int @ R3 )
% 7.78/3.95 => ( ( right_unique_int_int @ R7 )
% 7.78/3.95 => ( ( left_total_int_int @ R7 )
% 7.78/3.95 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1919_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: nat > nat > $o,S6: nat > nat > $o] :
% 7.78/3.95 ( ( left_u7296345956935681743at_nat @ R3 )
% 7.78/3.95 => ( ( right_4094035864313884895at_nat @ R3 )
% 7.78/3.95 => ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1920_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: int > int > $o,S6: int > code_integer > $o] :
% 7.78/3.95 ( ( left_u7296345956935681743at_nat @ R3 )
% 7.78/3.95 => ( ( right_4094035864313884895at_nat @ R3 )
% 7.78/3.95 => ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ord_le6141271677531915726eger_o @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1921_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: int > int > $o,R7: int > code_integer > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,S6: product_prod_nat_nat > int > $o] :
% 7.78/3.95 ( ( left_unique_int_int @ R3 )
% 7.78/3.95 => ( ( right_total_int_int @ R3 )
% 7.78/3.95 => ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ord_le8615040745438789472_int_o @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1922_neg__fun__distr1,axiom,
% 7.78/3.95 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,R7: product_prod_nat_nat > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o,S6: product_prod_nat_nat > int > $o] :
% 7.78/3.95 ( ( left_u7296345956935681743at_nat @ R3 )
% 7.78/3.95 => ( ( right_4094035864313884895at_nat @ R3 )
% 7.78/3.95 => ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ord_le2484784447047653514_int_o @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1923_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: code_integer > code_integer > $o,S6: num > num > $o,R3: int > code_integer > $o,S5: num > num > $o] :
% 7.78/3.95 ( ( right_5866438497372881682nteger @ R7 )
% 7.78/3.95 => ( ( left_t2884206969071330nteger @ R7 )
% 7.78/3.95 => ( ( left_unique_num_num @ S6 )
% 7.78/3.95 => ( ( right_total_num_num @ S6 )
% 7.78/3.95 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom8320293257703906841nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1848932251921554756er_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re40212662316476751um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1924_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: code_integer > int > $o,S6: num > num > $o,R3: int > code_integer > $o,S5: num > num > $o] :
% 7.78/3.95 ( ( right_7836862732553076961er_int @ R7 )
% 7.78/3.95 => ( ( left_t1735413524555719857er_int @ R7 )
% 7.78/3.95 => ( ( left_unique_num_num @ S6 )
% 7.78/3.95 => ( ( right_total_num_num @ S6 )
% 7.78/3.95 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcom328798225758222312er_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom7779292856395800339nt_num @ ( bNF_re6718328864250387230um_num @ R3 @ S5 ) @ ( bNF_re8313794964846168862um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1925_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: int > int > $o,S6: num > num > $o,R3: int > int > $o,S5: num > num > $o] :
% 7.78/3.95 ( ( right_unique_int_int @ R7 )
% 7.78/3.95 => ( ( left_total_int_int @ R7 )
% 7.78/3.95 => ( ( left_unique_num_num @ S6 )
% 7.78/3.95 => ( ( right_total_num_num @ S6 )
% 7.78/3.95 => ( ord_le4541714130423454556_num_o @ ( bNF_re7626690874201225453um_num @ ( relcompp_int_int_int @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom9025577121137075810nt_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re7626690874201225453um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1926_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: int > code_integer > $o,S6: num > num > $o,R3: int > int > $o,S5: num > num > $o] :
% 7.78/3.95 ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ( left_unique_num_num @ S6 )
% 7.78/3.95 => ( ( right_total_num_num @ S6 )
% 7.78/3.95 => ( ord_le6931201860925936491_num_o @ ( bNF_re6718328864250387230um_num @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcompp_num_num_num @ S5 @ S6 ) ) @ ( relcom1533066287727470739er_num @ ( bNF_re7626690874201225453um_num @ R3 @ S5 ) @ ( bNF_re6718328864250387230um_num @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1927_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: int > code_integer > $o,S6: int > code_integer > $o,R3: int > int > $o,S5: int > int > $o] :
% 7.78/3.95 ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ( left_u6795595883297946906nteger @ S6 )
% 7.78/3.95 => ( ( right_7281159819619925802nteger @ S6 )
% 7.78/3.95 => ( ord_le7522433683449569238eger_o @ ( bNF_re3379532845092657523nteger @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom7212586982944386682nteger @ ( bNF_re4712519889275205905nt_int @ R3 @ S5 ) @ ( bNF_re3379532845092657523nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1928_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: int > int > $o,S6: nat > nat > $o,R3: product_prod_nat_nat > int > $o,S5: nat > nat > $o] :
% 7.78/3.95 ( ( right_unique_int_int @ R7 )
% 7.78/3.95 => ( ( left_total_int_int @ R7 )
% 7.78/3.95 => ( ( left_unique_nat_nat @ S6 )
% 7.78/3.95 => ( ( right_total_nat_nat @ S6 )
% 7.78/3.95 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom2949942408940504938nt_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom4272412204205018633nt_nat @ ( bNF_re4555766996558763186at_nat @ R3 @ S5 ) @ ( bNF_re3715656647883201625at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1929_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: product_prod_nat_nat > int > $o,S6: nat > nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: nat > nat > $o] :
% 7.78/3.95 ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ( left_unique_nat_nat @ S6 )
% 7.78/3.95 => ( ( right_total_nat_nat @ S6 )
% 7.78/3.95 => ( ord_le1714508135640884727_nat_o @ ( bNF_re4555766996558763186at_nat @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcompp_nat_nat_nat @ S5 @ S6 ) ) @ ( relcom531901107642208332nt_nat @ ( bNF_re8246922863344978751at_nat @ R3 @ S5 ) @ ( bNF_re4555766996558763186at_nat @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1930_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: product_prod_nat_nat > int > $o,S6: int > code_integer > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: int > int > $o] :
% 7.78/3.95 ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ( left_u6795595883297946906nteger @ S6 )
% 7.78/3.95 => ( ( right_7281159819619925802nteger @ S6 )
% 7.78/3.95 => ( ord_le6141271677531915726eger_o @ ( bNF_re6202762543029211035nteger @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom967497705283160040nteger @ S5 @ S6 ) ) @ ( relcom4574826104943343961nteger @ ( bNF_re20414067882207223nt_int @ R3 @ S5 ) @ ( bNF_re6202762543029211035nteger @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1931_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: int > code_integer > $o,S6: product_prod_nat_nat > int > $o,R3: int > int > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.95 ( ( right_8475562212078014689nteger @ R7 )
% 7.78/3.95 => ( ( left_t2374113004080657585nteger @ R7 )
% 7.78/3.95 => ( ( left_u4005249686606446046at_int @ S6 )
% 7.78/3.95 => ( ( right_1157779049177982926at_int @ S6 )
% 7.78/3.95 => ( ord_le8615040745438789472_int_o @ ( bNF_re2828929484557863493at_int @ ( relcom967497705283160040nteger @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom2127790875031262553er_int @ ( bNF_re8766404587435608311at_nat @ R3 @ S5 ) @ ( bNF_re2828929484557863493at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1932_neg__fun__distr2,axiom,
% 7.78/3.95 ! [R7: product_prod_nat_nat > int > $o,S6: product_prod_nat_nat > int > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.95 ( ( right_8621877368619751767at_int @ R7 )
% 7.78/3.95 => ( ( left_t1861001511420785031at_int @ R7 )
% 7.78/3.95 => ( ( left_u4005249686606446046at_int @ S6 )
% 7.78/3.95 => ( ( right_1157779049177982926at_int @ S6 )
% 7.78/3.95 => ( ord_le2484784447047653514_int_o @ ( bNF_re7400052026677387805at_int @ ( relcom8911704206367525917at_int @ R3 @ R7 ) @ ( relcom8911704206367525917at_int @ S5 @ S6 ) ) @ ( relcom4982215633375716084nt_int @ ( bNF_re2241393799969408733at_nat @ R3 @ S5 ) @ ( bNF_re7400052026677387805at_int @ R7 @ S6 ) ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1933_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr5564308138774400199at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( ord_le3091953645718357095at_nat @ R
% 7.78/3.95 @ ( produc4441300235185154312at_nat @ A4
% 7.78/3.95 @ ^ [Uu: produc3843707927480180839at_nat] : A4 ) )
% 7.78/3.95 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.95 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.95 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_o7446464703481863270at_nat @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1934_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr8693737435421807431at_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ord_le3000389064537975527at_nat @ R
% 7.78/3.95 @ ( produc2761391749766926216at_nat @ A4
% 7.78/3.95 @ ^ [Uu: product_prod_nat_nat] : A4 ) )
% 7.78/3.95 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.95 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_o7122697186039111552at_nat @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1935_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Product_prod_o_o,A4: set_o] :
% 7.78/3.95 ( ( ord_le192195778054999463od_o_o @ R
% 7.78/3.95 @ ( product_Sigma_o_o @ A4
% 7.78/3.95 @ ^ [Uu: $o] : A4 ) )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_on_o @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1936_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr7459493094073627847at_nat,A4: set_se5479201105039950375at_nat] :
% 7.78/3.95 ( ( ord_le5997549366648089703at_nat @ R
% 7.78/3.95 @ ( produc6258361011560675592at_nat @ A4
% 7.78/3.95 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A4 ) )
% 7.78/3.95 => ( ! [X: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( member6273874620674182256at_nat @ X @ A4 )
% 7.78/3.95 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_o6272981002401706822at_nat @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1937_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr4329608150637261639at_nat,A4: set_se7855581050983116737at_nat] :
% 7.78/3.95 ( ( ord_le1268244103169919719at_nat @ R
% 7.78/3.95 @ ( produc7726050920695093128at_nat @ A4
% 7.78/3.95 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A4 ) )
% 7.78/3.95 => ( ! [X: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( member2643936169264416010at_nat @ X @ A4 )
% 7.78/3.95 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_o6955724340487615712at_nat @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1938_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr958786334691620121nt_int,A4: set_int] :
% 7.78/3.95 ( ( ord_le2843351958646193337nt_int @ R
% 7.78/3.95 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.95 @ ^ [Uu: int] : A4 ) )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_on_int @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1939_refl__onI,axiom,
% 7.78/3.95 ! [R: set_Pr1261947904930325089at_nat,A4: set_nat] :
% 7.78/3.95 ( ( ord_le3146513528884898305at_nat @ R
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : A4 ) )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R ) )
% 7.78/3.95 => ( refl_on_nat @ A4 @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1940_refl__on__def,axiom,
% 7.78/3.95 ( refl_o6272981002401706822at_nat
% 7.78/3.95 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 7.78/3.95 ( ( ord_le5997549366648089703at_nat @ R5
% 7.78/3.95 @ ( produc6258361011560675592at_nat @ A6
% 7.78/3.95 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A6 ) )
% 7.78/3.95 & ! [X4: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 7.78/3.95 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1941_refl__on__def,axiom,
% 7.78/3.95 ( refl_o6955724340487615712at_nat
% 7.78/3.95 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( ord_le1268244103169919719at_nat @ R5
% 7.78/3.95 @ ( produc7726050920695093128at_nat @ A6
% 7.78/3.95 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A6 ) )
% 7.78/3.95 & ! [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 7.78/3.95 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1942_refl__on__def,axiom,
% 7.78/3.95 ( refl_on_int
% 7.78/3.95 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 7.78/3.95 ( ( ord_le2843351958646193337nt_int @ R5
% 7.78/3.95 @ ( produc1453890548195736866nt_int @ A6
% 7.78/3.95 @ ^ [Uu: int] : A6 ) )
% 7.78/3.95 & ! [X4: int] :
% 7.78/3.95 ( ( member_int @ X4 @ A6 )
% 7.78/3.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1943_refl__on__def,axiom,
% 7.78/3.95 ( refl_on_nat
% 7.78/3.95 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ord_le3146513528884898305at_nat @ R5
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A6
% 7.78/3.95 @ ^ [Uu: nat] : A6 ) )
% 7.78/3.95 & ! [X4: nat] :
% 7.78/3.95 ( ( member_nat @ X4 @ A6 )
% 7.78/3.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ X4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1944_image__insert,axiom,
% 7.78/3.95 ! [F: int > int,A: int,B5: set_int] :
% 7.78/3.95 ( ( image_int_int @ F @ ( insert_int @ A @ B5 ) )
% 7.78/3.95 = ( insert_int @ ( F @ A ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1945_image__insert,axiom,
% 7.78/3.95 ! [F: int > nat,A: int,B5: set_int] :
% 7.78/3.95 ( ( image_int_nat @ F @ ( insert_int @ A @ B5 ) )
% 7.78/3.95 = ( insert_nat @ ( F @ A ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1946_image__insert,axiom,
% 7.78/3.95 ! [F: nat > rat,A: nat,B5: set_nat] :
% 7.78/3.95 ( ( image_nat_rat @ F @ ( insert_nat @ A @ B5 ) )
% 7.78/3.95 = ( insert_rat @ ( F @ A ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1947_image__insert,axiom,
% 7.78/3.95 ! [F: nat > int,A: nat,B5: set_nat] :
% 7.78/3.95 ( ( image_nat_int @ F @ ( insert_nat @ A @ B5 ) )
% 7.78/3.95 = ( insert_int @ ( F @ A ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1948_image__insert,axiom,
% 7.78/3.95 ! [F: nat > nat,A: nat,B5: set_nat] :
% 7.78/3.95 ( ( image_nat_nat @ F @ ( insert_nat @ A @ B5 ) )
% 7.78/3.95 = ( insert_nat @ ( F @ A ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1949_image__insert,axiom,
% 7.78/3.95 ! [F: nat > product_unit,A: nat,B5: set_nat] :
% 7.78/3.95 ( ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ B5 ) )
% 7.78/3.95 = ( insert_Product_unit @ ( F @ A ) @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1950_image__insert,axiom,
% 7.78/3.95 ! [F: nat > $o,A: nat,B5: set_nat] :
% 7.78/3.95 ( ( image_nat_o @ F @ ( insert_nat @ A @ B5 ) )
% 7.78/3.95 = ( insert_o @ ( F @ A ) @ ( image_nat_o @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1951_image__insert,axiom,
% 7.78/3.95 ! [F: product_unit > nat,A: product_unit,B5: set_Product_unit] :
% 7.78/3.95 ( ( image_875570014554754200it_nat @ F @ ( insert_Product_unit @ A @ B5 ) )
% 7.78/3.95 = ( insert_nat @ ( F @ A ) @ ( image_875570014554754200it_nat @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1952_image__insert,axiom,
% 7.78/3.95 ! [F: product_unit > product_unit,A: product_unit,B5: set_Product_unit] :
% 7.78/3.95 ( ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ B5 ) )
% 7.78/3.95 = ( insert_Product_unit @ ( F @ A ) @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1953_image__insert,axiom,
% 7.78/3.95 ! [F: product_unit > $o,A: product_unit,B5: set_Product_unit] :
% 7.78/3.95 ( ( image_Product_unit_o @ F @ ( insert_Product_unit @ A @ B5 ) )
% 7.78/3.95 = ( insert_o @ ( F @ A ) @ ( image_Product_unit_o @ F @ B5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1954_insert__image,axiom,
% 7.78/3.95 ! [X2: $o,A4: set_o,F: $o > nat] :
% 7.78/3.95 ( ( member_o @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_nat @ ( F @ X2 ) @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.95 = ( image_o_nat @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1955_insert__image,axiom,
% 7.78/3.95 ! [X2: $o,A4: set_o,F: $o > product_unit] :
% 7.78/3.95 ( ( member_o @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_Product_unit @ ( F @ X2 ) @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( image_o_Product_unit @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1956_insert__image,axiom,
% 7.78/3.95 ! [X2: $o,A4: set_o,F: $o > $o] :
% 7.78/3.95 ( ( member_o @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_o @ ( F @ X2 ) @ ( image_o_o @ F @ A4 ) )
% 7.78/3.95 = ( image_o_o @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1957_insert__image,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,F: nat > rat] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_rat @ ( F @ X2 ) @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.95 = ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1958_insert__image,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,F: nat > int] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_int @ ( F @ X2 ) @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.95 = ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1959_insert__image,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_nat @ ( F @ X2 ) @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.95 = ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1960_insert__image,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,F: nat > product_unit] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_Product_unit @ ( F @ X2 ) @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1961_insert__image,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,F: nat > $o] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_o @ ( F @ X2 ) @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.95 = ( image_nat_o @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1962_insert__image,axiom,
% 7.78/3.95 ! [X2: int,A4: set_int,F: int > int] :
% 7.78/3.95 ( ( member_int @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_int @ ( F @ X2 ) @ ( image_int_int @ F @ A4 ) )
% 7.78/3.95 = ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1963_insert__image,axiom,
% 7.78/3.95 ! [X2: int,A4: set_int,F: int > nat] :
% 7.78/3.95 ( ( member_int @ X2 @ A4 )
% 7.78/3.95 => ( ( insert_nat @ ( F @ X2 ) @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.95 = ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1964_SUP__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( complete_Sup_Sup_nat
% 7.78/3.95 @ ( image_nat_nat
% 7.78/3.95 @ ^ [X4: nat] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1965_SUP__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_set_nat] :
% 7.78/3.95 ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_7916887816326733075et_nat
% 7.78/3.95 @ ^ [X4: set_nat] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1966_SUP__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_int] :
% 7.78/3.95 ( ( complete_Sup_Sup_int
% 7.78/3.95 @ ( image_int_int
% 7.78/3.95 @ ^ [X4: int] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_int @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1967_SUP__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_405062704495631173t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1968_INF__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( complete_Inf_Inf_nat
% 7.78/3.95 @ ( image_nat_nat
% 7.78/3.95 @ ^ [X4: nat] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1969_INF__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_set_nat] :
% 7.78/3.95 ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_7916887816326733075et_nat
% 7.78/3.95 @ ^ [X4: set_nat] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1970_INF__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_int] :
% 7.78/3.95 ( ( complete_Inf_Inf_int
% 7.78/3.95 @ ( image_int_int
% 7.78/3.95 @ ^ [X4: int] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_int @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1971_INF__identity__eq,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_405062704495631173t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : X4
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1972_UN__I,axiom,
% 7.78/3.95 ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
% 7.78/3.95 ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1973_UN__I,axiom,
% 7.78/3.95 ! [A: $o,A4: set_o,B: int,B5: $o > set_int] :
% 7.78/3.95 ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1974_UN__I,axiom,
% 7.78/3.95 ! [A: nat,A4: set_nat,B: $o,B5: nat > set_o] :
% 7.78/3.95 ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1975_UN__I,axiom,
% 7.78/3.95 ! [A: nat,A4: set_nat,B: int,B5: nat > set_int] :
% 7.78/3.95 ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1976_UN__I,axiom,
% 7.78/3.95 ! [A: int,A4: set_int,B: $o,B5: int > set_o] :
% 7.78/3.95 ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1977_UN__I,axiom,
% 7.78/3.95 ! [A: int,A4: set_int,B: int,B5: int > set_int] :
% 7.78/3.95 ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1978_UN__I,axiom,
% 7.78/3.95 ! [A: $o,A4: set_o,B: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1979_UN__I,axiom,
% 7.78/3.95 ! [A: nat,A4: set_nat,B: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1980_UN__I,axiom,
% 7.78/3.95 ! [A: int,A4: set_int,B: nat,B5: int > set_nat] :
% 7.78/3.95 ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1981_UN__I,axiom,
% 7.78/3.95 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.95 => ( ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_501298686397505212_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1982_INT__I,axiom,
% 7.78/3.95 ! [A4: set_o,B: $o,B5: $o > set_o] :
% 7.78/3.95 ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1983_INT__I,axiom,
% 7.78/3.95 ! [A4: set_o,B: int,B5: $o > set_int] :
% 7.78/3.95 ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1984_INT__I,axiom,
% 7.78/3.95 ! [A4: set_nat,B: $o,B5: nat > set_o] :
% 7.78/3.95 ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1985_INT__I,axiom,
% 7.78/3.95 ! [A4: set_nat,B: int,B5: nat > set_int] :
% 7.78/3.95 ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1986_INT__I,axiom,
% 7.78/3.95 ! [A4: set_int,B: $o,B5: int > set_o] :
% 7.78/3.95 ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1987_INT__I,axiom,
% 7.78/3.95 ! [A4: set_int,B: int,B5: int > set_int] :
% 7.78/3.95 ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1988_INT__I,axiom,
% 7.78/3.95 ! [A4: set_o,B: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1989_INT__I,axiom,
% 7.78/3.95 ! [A4: set_nat,B: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1990_INT__I,axiom,
% 7.78/3.95 ! [A4: set_int,B: nat,B5: int > set_nat] :
% 7.78/3.95 ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1991_INT__I,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,B: $o,B5: product_prod_nat_nat > set_o] :
% 7.78/3.95 ( ! [X: product_prod_nat_nat] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ X ) ) )
% 7.78/3.95 => ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_501298686397505212_set_o @ B5 @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1992_SUP__id__eq,axiom,
% 7.78/3.95 ! [A4: set_o] :
% 7.78/3.95 ( ( complete_Sup_Sup_o @ ( image_o_o @ id_o @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_o @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1993_SUP__id__eq,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ id_nat @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1994_SUP__id__eq,axiom,
% 7.78/3.95 ! [A4: set_set_nat] :
% 7.78/3.95 ( ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ id_set_nat @ A4 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1995_SUP__id__eq,axiom,
% 7.78/3.95 ! [A4: set_int] :
% 7.78/3.95 ( ( complete_Sup_Sup_int @ ( image_int_int @ id_int @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_int @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1996_SUP__id__eq,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ id_Product_unit @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1997_INF__id__eq,axiom,
% 7.78/3.95 ! [A4: set_o] :
% 7.78/3.95 ( ( complete_Inf_Inf_o @ ( image_o_o @ id_o @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_o @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1998_INF__id__eq,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ id_nat @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_1999_INF__id__eq,axiom,
% 7.78/3.95 ! [A4: set_set_nat] :
% 7.78/3.95 ( ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ id_set_nat @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2000_INF__id__eq,axiom,
% 7.78/3.95 ! [A4: set_int] :
% 7.78/3.95 ( ( complete_Inf_Inf_int @ ( image_int_int @ id_int @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_int @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2001_INF__id__eq,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ id_Product_unit @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2002_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [I2: product_unit] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2003_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_3160451284896210088et_nat
% 7.78/3.95 @ ^ [I2: produc3843707927480180839at_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2004_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_15824709712370754et_nat
% 7.78/3.95 @ ^ [I2: product_prod_nat_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2005_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_o,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [I2: $o] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2006_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [I2: nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2007_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_405062704495631173t_unit
% 7.78/3.95 @ ^ [I2: product_unit] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2008_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_7082456443403096939t_unit
% 7.78/3.95 @ ^ [I2: produc3843707927480180839at_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2009_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_6169909464789311569t_unit
% 7.78/3.95 @ ^ [I2: product_prod_nat_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2010_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_o,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_o_Product_unit
% 7.78/3.95 @ ^ [I2: $o] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2011_SUP__const,axiom,
% 7.78/3.95 ! [A4: set_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit
% 7.78/3.95 @ ( image_8730104196221521654t_unit
% 7.78/3.95 @ ^ [I2: nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2012_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [I2: product_unit] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2013_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_3160451284896210088et_nat
% 7.78/3.95 @ ^ [I2: produc3843707927480180839at_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2014_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_15824709712370754et_nat
% 7.78/3.95 @ ^ [I2: product_prod_nat_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2015_INF__const,axiom,
% 7.78/3.95 ! [A4: set_o,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [I2: $o] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2016_INF__const,axiom,
% 7.78/3.95 ! [A4: set_nat,F: set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [I2: nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2017_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_405062704495631173t_unit
% 7.78/3.95 @ ^ [I2: product_unit] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2018_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_7082456443403096939t_unit
% 7.78/3.95 @ ^ [I2: produc3843707927480180839at_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2019_INF__const,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_6169909464789311569t_unit
% 7.78/3.95 @ ^ [I2: product_prod_nat_nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2020_INF__const,axiom,
% 7.78/3.95 ! [A4: set_o,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_o_Product_unit
% 7.78/3.95 @ ^ [I2: $o] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2021_INF__const,axiom,
% 7.78/3.95 ! [A4: set_nat,F: product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit
% 7.78/3.95 @ ( image_8730104196221521654t_unit
% 7.78/3.95 @ ^ [I2: nat] : F
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = F ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2022_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_Product_unit] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2023_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_o] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_6930536745178679216_set_o
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_6930536745178679216_set_o
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2024_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_Product_unit] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2025_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_o] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2026_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_Product_unit] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2027_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_o] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2028_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2029_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_o,C: set_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [Y5: $o] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2030_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_nat,C: set_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [Y5: nat] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2031_UN__constant,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,C: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_3617315916088684441at_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = bot_bo2099793752762293965at_nat ) )
% 7.78/3.95 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_3617315916088684441at_nat
% 7.78/3.95 @ ^ [Y5: product_unit] : C
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = C ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2032_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: product_unit,B5: product_unit > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2033_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: $o,B5: product_unit > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_6930536745178679216_set_o
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_6930536745178679216_set_o
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2034_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2035_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: $o,B5: $o > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2036_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2037_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: $o,B5: nat > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_o ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2038_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: nat,B5: product_unit > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2039_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2040_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bot_set_nat ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2041_UN__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: product_prod_nat_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_3617315916088684441at_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = bot_bo2099793752762293965at_nat ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_3617315916088684441at_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) )
% 7.78/3.95 = ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2042_UN__singleton,axiom,
% 7.78/3.95 ! [A4: set_Product_unit] :
% 7.78/3.95 ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = A4 ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2043_UN__singleton,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( comple4364388969068068532at_nat
% 7.78/3.95 @ ( image_7364710425340685989at_nat
% 7.78/3.95 @ ^ [X4: produc3843707927480180839at_nat] : ( insert9069300056098147895at_nat @ X4 @ bot_bo228742789529271731at_nat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = A4 ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2044_UN__singleton,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_5423882813909314213at_nat
% 7.78/3.95 @ ^ [X4: product_prod_nat_nat] : ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = A4 ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2045_UN__singleton,axiom,
% 7.78/3.95 ! [A4: set_o] :
% 7.78/3.95 ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ X4 @ bot_bot_set_o )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = A4 ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2046_UN__singleton,axiom,
% 7.78/3.95 ! [A4: set_nat] :
% 7.78/3.95 ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ X4 @ bot_bot_set_nat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = A4 ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2047_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: set_Pr4329608150637261639at_nat] : ( refl_o6272981002401706822at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2048_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: int] : ( refl_on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2049_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: set_Pr1261947904930325089at_nat] : ( refl_o6955724340487615712at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2050_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: product_unit] : ( refl_on_Product_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2051_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: produc3843707927480180839at_nat] : ( refl_o7446464703481863270at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2052_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: product_prod_nat_nat] : ( refl_o7122697186039111552at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2053_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: $o] : ( refl_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2054_refl__on__singleton,axiom,
% 7.78/3.95 ! [X2: nat] : ( refl_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2055_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple7216939928495492468t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2056_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: $o,B5: $o > set_o] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple3063163877087187839_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2057_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple7216939928495492468t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_4824033694279209942t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2058_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: $o,B5: nat > set_o] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple3063163877087187839_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2059_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: product_unit,B5: int > set_Product_unit] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple7216939928495492468t_unit
% 7.78/3.95 @ ( image_8658272795163236474t_unit
% 7.78/3.95 @ ^ [X4: int] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2060_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: $o,B5: int > set_o] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple3063163877087187839_set_o
% 7.78/3.95 @ ( image_int_set_o
% 7.78/3.95 @ ^ [X4: int] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2061_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2062_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2063_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: nat,B5: int > set_nat] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_int_set_nat
% 7.78/3.95 @ ^ [X4: int] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2064_INT__insert__distrib,axiom,
% 7.78/3.95 ! [U: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,A: product_unit,B5: product_prod_nat_nat > set_Product_unit] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple7216939928495492468t_unit
% 7.78/3.95 @ ( image_121980125215734065t_unit
% 7.78/3.95 @ ^ [X4: product_prod_nat_nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple7216939928495492468t_unit @ ( image_121980125215734065t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2065_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2066_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: $o,B5: $o > set_o] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2067_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2068_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: $o,B5: nat > set_o] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2069_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: product_unit,B5: int > set_Product_unit] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_8658272795163236474t_unit
% 7.78/3.95 @ ^ [X4: int] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2070_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: $o,B5: int > set_o] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_int_set_o
% 7.78/3.95 @ ^ [X4: int] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2071_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: $o,A4: set_o,A: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ( member_o @ U @ A4 )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2072_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: nat,A4: set_nat,A: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( member_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2073_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: int,A4: set_int,A: nat,B5: int > set_nat] :
% 7.78/3.95 ( ( member_int @ U @ A4 )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_int_set_nat
% 7.78/3.95 @ ^ [X4: int] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2074_UN__insert__distrib,axiom,
% 7.78/3.95 ! [U: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,A: product_unit,B5: product_prod_nat_nat > set_Product_unit] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ U @ A4 )
% 7.78/3.95 => ( ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_121980125215734065t_unit
% 7.78/3.95 @ ^ [X4: product_prod_nat_nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_121980125215734065t_unit @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2075_Sigma__Union,axiom,
% 7.78/3.95 ! [X5: set_set_nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ X5 ) @ B5 )
% 7.78/3.95 = ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_6521575952113991828at_nat
% 7.78/3.95 @ ^ [A6: set_nat] : ( produc457027306803732586at_nat @ A6 @ B5 )
% 7.78/3.95 @ X5 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2076_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2077_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_nat @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2078_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > int,D: $o > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Inf_Inf_int @ ( image_o_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_int @ ( image_o_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2079_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_int @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2080_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Inf_Inf_int @ ( image_int_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Inf_Inf_int @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2081_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > product_unit,D: $o > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2082_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > product_unit,D: nat > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2083_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > product_unit,D: int > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2084_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > set_nat,D: $o > set_nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2085_INF__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2086_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2087_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > nat,D: int > nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_nat @ ( image_int_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2088_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > int,D: $o > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Sup_Sup_int @ ( image_o_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_int @ ( image_o_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2089_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > int,D: nat > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_int @ ( image_nat_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2090_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > int,D: int > int] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( complete_Sup_Sup_int @ ( image_int_int @ C3 @ A4 ) )
% 7.78/3.95 = ( complete_Sup_Sup_int @ ( image_int_int @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2091_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > product_unit,D: $o > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2092_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > product_unit,D: nat > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2093_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,C3: int > product_unit,D: int > product_unit] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ C3 @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2094_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,C3: $o > set_nat,D: $o > set_nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2095_SUP__cong,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,C3: nat > set_nat,D: nat > set_nat] :
% 7.78/3.95 ( ( A4 = B5 )
% 7.78/3.95 => ( ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ B5 )
% 7.78/3.95 => ( ( C3 @ X )
% 7.78/3.95 = ( D @ X ) ) )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ C3 @ A4 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ D @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2096_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: product_unit,A4: set_Product_unit,X5: set_Product_unit] :
% 7.78/3.95 ( ( member_Product_unit @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_le3507040750410214029t_unit @ X5 @ A4 )
% 7.78/3.95 => ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2097_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,X5: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( member8757157785044589968at_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_le1268244103169919719at_nat @ X5 @ A4 )
% 7.78/3.95 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2098_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,X5: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_le3146513528884898305at_nat @ X5 @ A4 )
% 7.78/3.95 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2099_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: $o,A4: set_o,X5: set_o] :
% 7.78/3.95 ( ( member_o @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_less_eq_set_o @ X5 @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_o @ ( insert_o @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2100_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: nat,A4: set_nat,X5: set_nat] :
% 7.78/3.95 ( ( member_nat @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_less_eq_set_nat @ X5 @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2101_insert__subsetI,axiom,
% 7.78/3.95 ! [X2: int,A4: set_int,X5: set_int] :
% 7.78/3.95 ( ( member_int @ X2 @ A4 )
% 7.78/3.95 => ( ( ord_less_eq_set_int @ X5 @ A4 )
% 7.78/3.95 => ( ord_less_eq_set_int @ ( insert_int @ X2 @ X5 ) @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2102_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: product_unit,B5: product_unit > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_7778121751606633509t_unit
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2103_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: $o,B5: product_unit > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_6930536745178679216_set_o
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2104_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: product_unit,B5: $o > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_663195431845683034t_unit
% 7.78/3.95 @ ^ [X4: $o] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2105_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: $o,B5: $o > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_o_set_o
% 7.78/3.95 @ ^ [X4: $o] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2106_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: product_unit,B5: nat > set_Product_unit] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_Product_unit @ A @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple3349607820504768346t_unit
% 7.78/3.95 @ ( image_4824033694279209942t_unit
% 7.78/3.95 @ ^ [X4: nat] : ( insert_Product_unit @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2107_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: $o,B5: nat > set_o] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_o @ A @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple90263536869209701_set_o
% 7.78/3.95 @ ( image_nat_set_o
% 7.78/3.95 @ ^ [X4: nat] : ( insert_o @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2108_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: nat,B5: product_unit > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_8173849991827986510et_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2109_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_o,A: nat,B5: $o > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_o )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_o_set_nat
% 7.78/3.95 @ ^ [X4: $o] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2110_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_nat,A: nat,B5: nat > set_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 7.78/3.95 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.95 => ( ( insert_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2111_UN__extend__simps_I1_J,axiom,
% 7.78/3.95 ! [C3: set_Product_unit,A: product_prod_nat_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 7.78/3.95 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ( insert8211810215607154385at_nat @ A @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 7.78/3.95 = ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_3617315916088684441at_nat
% 7.78/3.95 @ ^ [X4: product_unit] : ( insert8211810215607154385at_nat @ A @ ( B5 @ X4 ) )
% 7.78/3.95 @ C3 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2112_Sigma__def,axiom,
% 7.78/3.95 ( produc6258361011560675592at_nat
% 7.78/3.95 = ( ^ [A6: set_se5479201105039950375at_nat,B6: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat] :
% 7.78/3.95 ( comple7342073961973170484at_nat
% 7.78/3.95 @ ( image_1124969593608450885at_nat
% 7.78/3.95 @ ^ [X4: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( comple7342073961973170484at_nat
% 7.78/3.95 @ ( image_1124969593608450885at_nat
% 7.78/3.95 @ ^ [Y5: set_Pr4329608150637261639at_nat] : ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ bot_bo4948859079157340979at_nat )
% 7.78/3.95 @ ( B6 @ X4 ) ) )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2113_Sigma__def,axiom,
% 7.78/3.95 ( produc6237731129814287028at_num
% 7.78/3.95 = ( ^ [A6: set_nat,B6: nat > set_num] :
% 7.78/3.95 ( comple1400524285282149784at_num
% 7.78/3.95 @ ( image_2893549341467670548at_num
% 7.78/3.95 @ ^ [X4: nat] :
% 7.78/3.95 ( comple1400524285282149784at_num
% 7.78/3.95 @ ( image_4778453735051108682at_num
% 7.78/3.95 @ ^ [Y5: num] : ( insert8920054152555992091at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ bot_bo7038385379056416535at_num )
% 7.78/3.95 @ ( B6 @ X4 ) ) )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2114_Sigma__def,axiom,
% 7.78/3.95 ( produc1453890548195736866nt_int
% 7.78/3.95 = ( ^ [A6: set_int,B6: int > set_int] :
% 7.78/3.95 ( comple5382143125604098054nt_int
% 7.78/3.95 @ ( image_8635204845542730022nt_int
% 7.78/3.95 @ ^ [X4: int] :
% 7.78/3.95 ( comple5382143125604098054nt_int
% 7.78/3.95 @ ( image_8635204845542730022nt_int
% 7.78/3.95 @ ^ [Y5: int] : ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ bot_bo1796632182523588997nt_int )
% 7.78/3.95 @ ( B6 @ X4 ) ) )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2115_Sigma__def,axiom,
% 7.78/3.95 ( produc7726050920695093128at_nat
% 7.78/3.95 = ( ^ [A6: set_se7855581050983116737at_nat,B6: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.95 ( comple4364388969068068532at_nat
% 7.78/3.95 @ ( image_6898982319499645995at_nat
% 7.78/3.95 @ ^ [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( comple4364388969068068532at_nat
% 7.78/3.95 @ ( image_6898982319499645995at_nat
% 7.78/3.95 @ ^ [Y5: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ bot_bo228742789529271731at_nat )
% 7.78/3.95 @ ( B6 @ X4 ) ) )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2116_Sigma__def,axiom,
% 7.78/3.95 ( produc457027306803732586at_nat
% 7.78/3.95 = ( ^ [A6: set_nat,B6: nat > set_nat] :
% 7.78/3.95 ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_7178329752028323786at_nat
% 7.78/3.95 @ ^ [X4: nat] :
% 7.78/3.95 ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_7178329752028323786at_nat
% 7.78/3.95 @ ^ [Y5: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ bot_bo2099793752762293965at_nat )
% 7.78/3.95 @ ( B6 @ X4 ) ) )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2117_UN__Times__distrib,axiom,
% 7.78/3.95 ! [E2: nat > set_nat,F4: nat > set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.95 ( ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_5423882813909314213at_nat
% 7.78/3.95 @ ( produc8197505143624133779at_nat
% 7.78/3.95 @ ^ [A5: nat,B4: nat] :
% 7.78/3.95 ( produc457027306803732586at_nat @ ( E2 @ A5 )
% 7.78/3.95 @ ^ [Uu: nat] : ( F4 @ B4 ) ) )
% 7.78/3.95 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.95 @ ^ [Uu: nat] : B5 ) ) )
% 7.78/3.95 = ( produc457027306803732586at_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ E2 @ A4 ) )
% 7.78/3.95 @ ^ [Uu: nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F4 @ B5 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2118_right__total__OO,axiom,
% 7.78/3.95 ! [A4: product_prod_nat_nat > product_prod_nat_nat > $o,B5: product_prod_nat_nat > int > $o] :
% 7.78/3.95 ( ( right_4094035864313884895at_nat @ A4 )
% 7.78/3.95 => ( ( right_1157779049177982926at_int @ B5 )
% 7.78/3.95 => ( right_1157779049177982926at_int @ ( relcom8911704206367525917at_int @ A4 @ B5 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2119_right__total__OO,axiom,
% 7.78/3.95 ! [A4: int > int > $o,B5: int > code_integer > $o] :
% 7.78/3.95 ( ( right_total_int_int @ A4 )
% 7.78/3.95 => ( ( right_7281159819619925802nteger @ B5 )
% 7.78/3.95 => ( right_7281159819619925802nteger @ ( relcom967497705283160040nteger @ A4 @ B5 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2120_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat] :
% 7.78/3.95 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.95 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2121_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat] :
% 7.78/3.95 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.95 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2122_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_o,R: set_Product_prod_o_o,A: $o] :
% 7.78/3.95 ( ( refl_on_o @ A4 @ R )
% 7.78/3.95 => ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2123_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 7.78/3.95 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2124_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 7.78/3.95 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2125_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat] :
% 7.78/3.95 ( ( refl_on_nat @ A4 @ R )
% 7.78/3.95 => ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2126_refl__onD,axiom,
% 7.78/3.95 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int] :
% 7.78/3.95 ( ( refl_on_int @ A4 @ R )
% 7.78/3.95 => ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ R ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2127_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 7.78/3.95 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member8757157785044589968at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2128_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.78/3.95 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member8440522571783428010at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2129_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_o,R: set_Product_prod_o_o,X2: $o,Y3: $o] :
% 7.78/3.95 ( ( refl_on_o @ A4 @ R )
% 7.78/3.95 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_o @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2130_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member6273874620674182256at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2131_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member2643936169264416010at_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2132_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,X2: nat,Y3: nat] :
% 7.78/3.95 ( ( refl_on_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_nat @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2133_refl__onD1,axiom,
% 7.78/3.95 ! [A4: set_int,R: set_Pr958786334691620121nt_int,X2: int,Y3: int] :
% 7.78/3.95 ( ( refl_on_int @ A4 @ R )
% 7.78/3.95 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_int @ X2 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2134_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 7.78/3.95 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member8757157785044589968at_nat @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2135_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.78/3.95 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member8440522571783428010at_nat @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2136_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_o,R: set_Product_prod_o_o,X2: $o,Y3: $o] :
% 7.78/3.95 ( ( refl_on_o @ A4 @ R )
% 7.78/3.95 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_o @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2137_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.95 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member6273874620674182256at_nat @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2138_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.95 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member2643936169264416010at_nat @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2139_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,X2: nat,Y3: nat] :
% 7.78/3.95 ( ( refl_on_nat @ A4 @ R )
% 7.78/3.95 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_nat @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2140_refl__onD2,axiom,
% 7.78/3.95 ! [A4: set_int,R: set_Pr958786334691620121nt_int,X2: int,Y3: int] :
% 7.78/3.95 ( ( refl_on_int @ A4 @ R )
% 7.78/3.95 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R )
% 7.78/3.95 => ( member_int @ Y3 @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2141_INT__extend__simps_I8_J,axiom,
% 7.78/3.95 ! [B5: nat > set_nat,A4: set_set_nat] :
% 7.78/3.95 ( ( comple7806235888213564991et_nat
% 7.78/3.95 @ ( image_7916887816326733075et_nat
% 7.78/3.95 @ ^ [Y5: set_nat] : ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ Y5 ) )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2142_Id__on__def,axiom,
% 7.78/3.95 ( id_on_3275838214495744996at_nat
% 7.78/3.95 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 7.78/3.95 ( comple7342073961973170484at_nat
% 7.78/3.95 @ ( image_1124969593608450885at_nat
% 7.78/3.95 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X4 @ X4 ) @ bot_bo4948859079157340979at_nat )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2143_Id__on__def,axiom,
% 7.78/3.95 ( id_on_int
% 7.78/3.95 = ( ^ [A6: set_int] :
% 7.78/3.95 ( comple5382143125604098054nt_int
% 7.78/3.95 @ ( image_8635204845542730022nt_int
% 7.78/3.95 @ ^ [X4: int] : ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X4 @ X4 ) @ bot_bo1796632182523588997nt_int )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2144_Id__on__def,axiom,
% 7.78/3.95 ( id_on_6713504163309144702at_nat
% 7.78/3.95 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 7.78/3.95 ( comple4364388969068068532at_nat
% 7.78/3.95 @ ( image_6898982319499645995at_nat
% 7.78/3.95 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X4 @ X4 ) @ bot_bo228742789529271731at_nat )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2145_Id__on__def,axiom,
% 7.78/3.95 ( id_on_nat
% 7.78/3.95 = ( ^ [A6: set_nat] :
% 7.78/3.95 ( comple5685304695842803022at_nat
% 7.78/3.95 @ ( image_7178329752028323786at_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X4 @ X4 ) @ bot_bo2099793752762293965at_nat )
% 7.78/3.95 @ A6 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2146_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: product_unit > set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2147_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2148_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2149_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_o,F: $o > set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2150_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_nat,F: nat > set_nat] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2151_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Product_unit,F: product_unit > product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2152_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo228742789529271731at_nat )
% 7.78/3.95 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2153_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 7.78/3.95 ( ( A4 != bot_bo2099793752762293965at_nat )
% 7.78/3.95 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2154_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_o,F: $o > product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_o )
% 7.78/3.95 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2155_INF__le__SUP,axiom,
% 7.78/3.95 ! [A4: set_nat,F: nat > product_unit] :
% 7.78/3.95 ( ( A4 != bot_bot_set_nat )
% 7.78/3.95 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2156_right__unique__OO,axiom,
% 7.78/3.95 ! [A4: product_prod_nat_nat > product_prod_nat_nat > $o,B5: product_prod_nat_nat > int > $o] :
% 7.78/3.95 ( ( right_1383565826979811350at_nat @ A4 )
% 7.78/3.95 => ( ( right_8621877368619751767at_int @ B5 )
% 7.78/3.95 => ( right_8621877368619751767at_int @ ( relcom8911704206367525917at_int @ A4 @ B5 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2157_right__unique__OO,axiom,
% 7.78/3.95 ! [A4: int > int > $o,B5: int > code_integer > $o] :
% 7.78/3.95 ( ( right_unique_int_int @ A4 )
% 7.78/3.95 => ( ( right_8475562212078014689nteger @ B5 )
% 7.78/3.95 => ( right_8475562212078014689nteger @ ( relcom967497705283160040nteger @ A4 @ B5 ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2158_INT__E,axiom,
% 7.78/3.95 ! [B: $o,B5: $o > set_o,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2159_INT__E,axiom,
% 7.78/3.95 ! [B: $o,B5: nat > set_o,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2160_INT__E,axiom,
% 7.78/3.95 ! [B: $o,B5: int > set_o,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_o @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_int @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2161_INT__E,axiom,
% 7.78/3.95 ! [B: int,B5: $o > set_int,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2162_INT__E,axiom,
% 7.78/3.95 ! [B: int,B5: nat > set_int,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2163_INT__E,axiom,
% 7.78/3.95 ! [B: int,B5: int > set_int,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_int @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_int @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2164_INT__E,axiom,
% 7.78/3.95 ! [B: nat,B5: $o > set_nat,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2165_INT__E,axiom,
% 7.78/3.95 ! [B: nat,B5: nat > set_nat,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_nat @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2166_INT__E,axiom,
% 7.78/3.95 ! [B: nat,B5: int > set_nat,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_int @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2167_INT__E,axiom,
% 7.78/3.95 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ B @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ~ ( member8440522571783428010at_nat @ B @ ( B5 @ A ) )
% 7.78/3.95 => ~ ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2168_INT__D,axiom,
% 7.78/3.95 ! [B: $o,B5: $o > set_o,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2169_INT__D,axiom,
% 7.78/3.95 ! [B: $o,B5: nat > set_o,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2170_INT__D,axiom,
% 7.78/3.95 ! [B: $o,B5: int > set_o,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_o @ B @ ( comple3063163877087187839_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( member_o @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2171_INT__D,axiom,
% 7.78/3.95 ! [B: int,B5: $o > set_int,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2172_INT__D,axiom,
% 7.78/3.95 ! [B: int,B5: nat > set_int,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2173_INT__D,axiom,
% 7.78/3.95 ! [B: int,B5: int > set_int,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( member_int @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2174_INT__D,axiom,
% 7.78/3.95 ! [B: nat,B5: $o > set_nat,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2175_INT__D,axiom,
% 7.78/3.95 ! [B: nat,B5: nat > set_nat,A4: set_nat,A: nat] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_nat @ A @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2176_INT__D,axiom,
% 7.78/3.95 ! [B: nat,B5: int > set_nat,A4: set_int,A: int] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_int @ A @ A4 )
% 7.78/3.95 => ( member_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2177_INT__D,axiom,
% 7.78/3.95 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o,A: $o] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ B @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ( ( member_o @ A @ A4 )
% 7.78/3.95 => ( member8440522571783428010at_nat @ B @ ( B5 @ A ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2178_UN__E,axiom,
% 7.78/3.95 ! [B: $o,B5: $o > set_o,A4: set_o] :
% 7.78/3.95 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2179_UN__E,axiom,
% 7.78/3.95 ! [B: $o,B5: nat > set_o,A4: set_nat] :
% 7.78/3.95 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2180_UN__E,axiom,
% 7.78/3.95 ! [B: $o,B5: int > set_o,A4: set_int] :
% 7.78/3.95 ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2181_UN__E,axiom,
% 7.78/3.95 ! [B: int,B5: $o > set_int,A4: set_o] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2182_UN__E,axiom,
% 7.78/3.95 ! [B: int,B5: nat > set_int,A4: set_nat] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2183_UN__E,axiom,
% 7.78/3.95 ! [B: int,B5: int > set_int,A4: set_int] :
% 7.78/3.95 ( ( member_int @ B @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ~ ( member_int @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2184_UN__E,axiom,
% 7.78/3.95 ! [B: nat,B5: $o > set_nat,A4: set_o] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2185_UN__E,axiom,
% 7.78/3.95 ! [B: nat,B5: nat > set_nat,A4: set_nat] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: nat] :
% 7.78/3.95 ( ( member_nat @ X @ A4 )
% 7.78/3.95 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2186_UN__E,axiom,
% 7.78/3.95 ! [B: nat,B5: int > set_nat,A4: set_int] :
% 7.78/3.95 ( ( member_nat @ B @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: int] :
% 7.78/3.95 ( ( member_int @ X @ A4 )
% 7.78/3.95 => ~ ( member_nat @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2187_UN__E,axiom,
% 7.78/3.95 ! [B: product_prod_nat_nat,B5: $o > set_Pr1261947904930325089at_nat,A4: set_o] :
% 7.78/3.95 ( ( member8440522571783428010at_nat @ B @ ( comple5685304695842803022at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) )
% 7.78/3.95 => ~ ! [X: $o] :
% 7.78/3.95 ( ( member_o @ X @ A4 )
% 7.78/3.95 => ~ ( member8440522571783428010at_nat @ B @ ( B5 @ X ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2188_UNION__singleton__eq__range,axiom,
% 7.78/3.95 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.95 ( ( comple3890839924845867745et_rat
% 7.78/3.95 @ ( image_nat_set_rat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_rat @ ( F @ X4 ) @ bot_bot_set_rat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( image_nat_rat @ F @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2189_UNION__singleton__eq__range,axiom,
% 7.78/3.95 ! [F: nat > int,A4: set_nat] :
% 7.78/3.95 ( ( comple3221217463730067765et_int
% 7.78/3.95 @ ( image_nat_set_int
% 7.78/3.95 @ ^ [X4: nat] : ( insert_int @ ( F @ X4 ) @ bot_bot_set_int )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( image_nat_int @ F @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2190_UNION__singleton__eq__range,axiom,
% 7.78/3.95 ! [F: int > int,A4: set_int] :
% 7.78/3.95 ( ( comple3221217463730067765et_int
% 7.78/3.95 @ ( image_int_set_int
% 7.78/3.95 @ ^ [X4: int] : ( insert_int @ ( F @ X4 ) @ bot_bot_set_int )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( image_int_int @ F @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2191_UNION__singleton__eq__range,axiom,
% 7.78/3.95 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.95 ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_nat_set_nat
% 7.78/3.95 @ ^ [X4: nat] : ( insert_nat @ ( F @ X4 ) @ bot_bot_set_nat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( image_nat_nat @ F @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2192_UNION__singleton__eq__range,axiom,
% 7.78/3.95 ! [F: int > nat,A4: set_int] :
% 7.78/3.95 ( ( comple7399068483239264473et_nat
% 7.78/3.95 @ ( image_int_set_nat
% 7.78/3.95 @ ^ [X4: int] : ( insert_nat @ ( F @ X4 ) @ bot_bot_set_nat )
% 7.78/3.95 @ A4 ) )
% 7.78/3.95 = ( image_int_nat @ F @ A4 ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2193_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,G: $o > product_unit,F: $o > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2194_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_nat,G: nat > product_unit,F: $o > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2195_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_int,G: int > product_unit,F: $o > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2196_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_o,G: $o > product_unit,F: nat > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2197_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,G: nat > product_unit,F: nat > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2198_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_int,G: int > product_unit,F: nat > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2199_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_o,G: $o > product_unit,F: int > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2200_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_nat,G: nat > product_unit,F: int > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2201_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,G: int > product_unit,F: int > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2202_INF__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,G: $o > set_nat,F: $o > set_nat] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ ( G @ X6 ) @ ( F @ I4 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ J2 ) ) ) )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.95 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2203_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,F: $o > product_unit,G: $o > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2204_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_nat,F: $o > product_unit,G: nat > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2205_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_int,F: $o > product_unit,G: int > product_unit] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2206_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_o,F: nat > product_unit,G: $o > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2207_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2208_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_nat,B5: set_int,F: nat > product_unit,G: int > product_unit] :
% 7.78/3.95 ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2209_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_o,F: int > product_unit,G: $o > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2210_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_nat,F: int > product_unit,G: nat > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: nat] :
% 7.78/3.95 ( ( member_nat @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: nat] :
% 7.78/3.95 ( ( member_nat @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2211_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_int,B5: set_int,F: int > product_unit,G: int > product_unit] :
% 7.78/3.95 ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ A4 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ B5 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: int] :
% 7.78/3.95 ( ( member_int @ J2 @ B5 )
% 7.78/3.95 => ? [X6: int] :
% 7.78/3.95 ( ( member_int @ X6 @ A4 )
% 7.78/3.95 & ( ord_le3221252021190050221t_unit @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.95 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2212_SUP__eq,axiom,
% 7.78/3.95 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 7.78/3.95 ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ A4 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ B5 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ ( F @ I4 ) @ ( G @ X6 ) ) ) )
% 7.78/3.95 => ( ! [J2: $o] :
% 7.78/3.95 ( ( member_o @ J2 @ B5 )
% 7.78/3.95 => ? [X6: $o] :
% 7.78/3.95 ( ( member_o @ X6 @ A4 )
% 7.78/3.95 & ( ord_less_eq_set_nat @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
% 7.78/3.95 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.95 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2213_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_int,F: int > product_unit,X2: product_unit] :
% 7.78/3.95 ( ( I3 != bot_bot_set_int )
% 7.78/3.95 => ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2214_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 7.78/3.95 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ! [I4: product_unit] :
% 7.78/3.95 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2215_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 7.78/3.95 ( ( I3 != bot_bot_set_o )
% 7.78/3.95 => ( ! [I4: $o] :
% 7.78/3.95 ( ( member_o @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2216_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 7.78/3.95 ( ( I3 != bot_bot_set_nat )
% 7.78/3.95 => ( ! [I4: nat] :
% 7.78/3.95 ( ( member_nat @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2217_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_int,F: int > set_nat,X2: set_nat] :
% 7.78/3.95 ( ( I3 != bot_bot_set_int )
% 7.78/3.95 => ( ! [I4: int] :
% 7.78/3.95 ( ( member_int @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2218_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 7.78/3.95 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.95 => ( ! [I4: product_unit] :
% 7.78/3.95 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.95 => ( ( F @ I4 )
% 7.78/3.95 = X2 ) )
% 7.78/3.95 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 7.78/3.95 = X2 ) ) ) ).
% 7.78/3.95
% 7.78/3.95 thf(fact_2219_INF__eq__const,axiom,
% 7.78/3.95 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 7.78/3.95 ( ( I3 != bot_bot_set_o )
% 7.78/3.95 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2220_INF__eq__const,axiom,
% 7.78/3.96 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2221_INF__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2222_INF__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2223_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_int,F: int > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2224_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2225_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2226_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2227_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_int,F: int > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2228_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2229_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2230_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2231_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2232_SUP__eq__const,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ( F @ I4 )
% 7.78/3.96 = X2 ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2233_INF__image,axiom,
% 7.78/3.96 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_o @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_o @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2234_INF__image,axiom,
% 7.78/3.96 ! [G: rat > nat,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_nat @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2235_INF__image,axiom,
% 7.78/3.96 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2236_INF__image,axiom,
% 7.78/3.96 ! [G: nat > nat,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_nat @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2237_INF__image,axiom,
% 7.78/3.96 ! [G: int > nat,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2238_INF__image,axiom,
% 7.78/3.96 ! [G: int > nat,F: int > int,A4: set_int] :
% 7.78/3.96 ( ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ ( image_int_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_nat @ ( image_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2239_INF__image,axiom,
% 7.78/3.96 ! [G: rat > int,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_int @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2240_INF__image,axiom,
% 7.78/3.96 ! [G: nat > int,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2241_INF__image,axiom,
% 7.78/3.96 ! [G: nat > int,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( complete_Inf_Inf_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2242_INF__image,axiom,
% 7.78/3.96 ! [G: int > int,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( complete_Inf_Inf_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Inf_Inf_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2243_SUP__image,axiom,
% 7.78/3.96 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_o @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_o @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2244_SUP__image,axiom,
% 7.78/3.96 ! [G: rat > nat,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_nat @ ( image_rat_nat @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_rat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2245_SUP__image,axiom,
% 7.78/3.96 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2246_SUP__image,axiom,
% 7.78/3.96 ! [G: nat > nat,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_nat @ ( image_int_nat @ ( comp_nat_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2247_SUP__image,axiom,
% 7.78/3.96 ! [G: int > nat,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_int_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2248_SUP__image,axiom,
% 7.78/3.96 ! [G: int > nat,F: int > int,A4: set_int] :
% 7.78/3.96 ( ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ ( image_int_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_nat @ ( image_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2249_SUP__image,axiom,
% 7.78/3.96 ! [G: rat > int,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_int @ ( image_rat_int @ G @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_rat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2250_SUP__image,axiom,
% 7.78/3.96 ! [G: nat > int,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_nat_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2251_SUP__image,axiom,
% 7.78/3.96 ! [G: nat > int,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( complete_Sup_Sup_int @ ( image_nat_int @ G @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_int @ ( image_int_int @ ( comp_nat_int_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2252_SUP__image,axiom,
% 7.78/3.96 ! [G: int > int,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( complete_Sup_Sup_int @ ( image_int_int @ G @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.96 = ( complete_Sup_Sup_int @ ( image_nat_int @ ( comp_int_int_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2253_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,U: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2254_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,U: set_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2255_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_o,U: set_nat,F: $o > set_nat] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2256_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_nat,U: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2257_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,U: set_nat,F: int > set_nat] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2258_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,U: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2259_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,U: product_unit,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2260_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_o,U: product_unit,F: $o > product_unit] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2261_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_nat,U: product_unit,F: nat > product_unit] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2262_INF__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,U: product_unit,F: int > product_unit] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2263_INF__lower2,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2264_INF__lower2,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2265_INF__lower2,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > set_nat,U: set_nat] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2266_INF__lower2,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2267_INF__lower2,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > set_nat,U: set_nat] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2268_INF__lower2,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2269_INF__lower2,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2270_INF__lower2,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > product_unit,U: product_unit] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2271_INF__lower2,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2272_INF__lower2,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > product_unit,U: product_unit] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ ( F @ I ) @ U )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2273_INF__lower,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2274_INF__lower,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2275_INF__lower,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > set_nat] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2276_INF__lower,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2277_INF__lower,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > set_nat] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2278_INF__lower,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2279_INF__lower,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2280_INF__lower,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > product_unit] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2281_INF__lower,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > product_unit] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2282_INF__lower,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > product_unit] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( F @ I ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2283_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,X2: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2284_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,X2: set_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2285_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_o,X2: set_nat,F: $o > set_nat] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: $o] :
% 7.78/3.96 ( ( member_o @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2286_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_nat,X2: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: nat] :
% 7.78/3.96 ( ( member_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2287_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_int,X2: set_nat,F: int > set_nat] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: int] :
% 7.78/3.96 ( ( member_int @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2288_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,X2: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2289_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,X2: product_unit,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2290_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_o,X2: product_unit,F: $o > product_unit] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: $o] :
% 7.78/3.96 ( ( member_o @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2291_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_nat,X2: product_unit,F: nat > product_unit] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: nat] :
% 7.78/3.96 ( ( member_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2292_INF__eqI,axiom,
% 7.78/3.96 ! [A4: set_int,X2: product_unit,F: int > product_unit] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: int] :
% 7.78/3.96 ( ( member_int @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ ( F @ I5 ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ Y @ X2 ) )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2293_SUP__upper2,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,U: set_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2294_SUP__upper2,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,U: set_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2295_SUP__upper2,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,U: set_nat,F: $o > set_nat] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2296_SUP__upper2,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,U: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2297_SUP__upper2,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,U: set_nat,F: int > set_nat] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ( ord_less_eq_set_nat @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2298_SUP__upper2,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,U: product_unit,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2299_SUP__upper2,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,U: product_unit,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2300_SUP__upper2,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,U: product_unit,F: $o > product_unit] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2301_SUP__upper2,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,U: product_unit,F: nat > product_unit] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2302_SUP__upper2,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,U: product_unit,F: int > product_unit] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ I ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2303_SUP__upper,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2304_SUP__upper,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2305_SUP__upper,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > set_nat] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2306_SUP__upper,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2307_SUP__upper,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > set_nat] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2308_SUP__upper,axiom,
% 7.78/3.96 ! [I: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2309_SUP__upper,axiom,
% 7.78/3.96 ! [I: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2310_SUP__upper,axiom,
% 7.78/3.96 ! [I: $o,A4: set_o,F: $o > product_unit] :
% 7.78/3.96 ( ( member_o @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2311_SUP__upper,axiom,
% 7.78/3.96 ! [I: nat,A4: set_nat,F: nat > product_unit] :
% 7.78/3.96 ( ( member_nat @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2312_SUP__upper,axiom,
% 7.78/3.96 ! [I: int,A4: set_int,F: int > product_unit] :
% 7.78/3.96 ( ( member_int @ I @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2313_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2314_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2315_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > set_nat,U: set_nat] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2316_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > set_nat,U: set_nat] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2317_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > set_nat,U: set_nat] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2318_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2319_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2320_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2321_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > product_unit,U: product_unit] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2322_SUP__least,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > product_unit,U: product_unit] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ U ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2323_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2324_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2325_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > set_nat,X2: set_nat] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: $o] :
% 7.78/3.96 ( ( member_o @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2326_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > set_nat,X2: set_nat] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: nat] :
% 7.78/3.96 ( ( member_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2327_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > set_nat,X2: set_nat] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: set_nat] :
% 7.78/3.96 ( ! [I5: int] :
% 7.78/3.96 ( ( member_int @ I5 @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2328_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ! [I4: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2329_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2330_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > product_unit,X2: product_unit] :
% 7.78/3.96 ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: $o] :
% 7.78/3.96 ( ( member_o @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2331_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > product_unit,X2: product_unit] :
% 7.78/3.96 ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: nat] :
% 7.78/3.96 ( ( member_nat @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2332_SUP__eqI,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > product_unit,X2: product_unit] :
% 7.78/3.96 ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ X2 ) )
% 7.78/3.96 => ( ! [Y: product_unit] :
% 7.78/3.96 ( ! [I5: int] :
% 7.78/3.96 ( ( member_int @ I5 @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I5 ) @ Y ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ X2 @ Y ) )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.96 = X2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2333_INT__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: rat > set_nat,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7806235888213564991et_nat @ ( image_rat_set_nat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2334_INT__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: nat > set_nat,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2335_INT__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: int > set_nat,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2336_INT__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: nat > set_nat,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_int_set_nat
% 7.78/3.96 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2337_INT__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: int > set_nat,F: int > int,A4: set_int] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_int_set_nat
% 7.78/3.96 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2338_INT__lower,axiom,
% 7.78/3.96 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2339_INT__lower,axiom,
% 7.78/3.96 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2340_INT__lower,axiom,
% 7.78/3.96 ! [A: $o,A4: set_o,B5: $o > set_nat] :
% 7.78/3.96 ( ( member_o @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2341_INT__lower,axiom,
% 7.78/3.96 ! [A: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.96 ( ( member_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2342_INT__lower,axiom,
% 7.78/3.96 ! [A: int,A4: set_int,B5: int > set_nat] :
% 7.78/3.96 ( ( member_int @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) @ ( B5 @ A ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2343_INT__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,C3: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2344_INT__greatest,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,C3: set_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2345_INT__greatest,axiom,
% 7.78/3.96 ! [A4: set_o,C3: set_nat,B5: $o > set_nat] :
% 7.78/3.96 ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2346_INT__greatest,axiom,
% 7.78/3.96 ! [A4: set_nat,C3: set_nat,B5: nat > set_nat] :
% 7.78/3.96 ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2347_INT__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,C3: set_nat,B5: int > set_nat] :
% 7.78/3.96 ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( B5 @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C3 @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2348_INT__anti__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ G @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2349_INT__anti__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ G @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2350_INT__anti__mono,axiom,
% 7.78/3.96 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2351_INT__anti__mono,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ G @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2352_INT__anti__mono,axiom,
% 7.78/3.96 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ B5 ) ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ G @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2353_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_int,C: int] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_int )
% 7.78/3.96 => ( ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_int ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_int @ C @ bot_bot_set_int ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2354_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_int,C: nat] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_int )
% 7.78/3.96 => ( ( image_int_nat
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_nat ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( image_int_nat
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2355_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2356_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: $o] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_Product_unit_o
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_o ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_Product_unit_o
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_o @ C @ bot_bot_set_o ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2357_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: nat] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_875570014554754200it_nat
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_nat ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( image_875570014554754200it_nat
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2358_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_Product_unit
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_Product_unit
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2359_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_o,C: $o] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_o
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_o ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_o
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_o @ C @ bot_bot_set_o ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2360_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_o,C: nat] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_nat
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_nat ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( image_o_nat
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2361_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_nat,C: rat] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( image_nat_rat
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_rat ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( image_nat_rat
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_rat @ C @ bot_bot_set_rat ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2362_image__constant__conv,axiom,
% 7.78/3.96 ! [A4: set_nat,C: int] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( image_nat_int
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = bot_bot_set_int ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( image_nat_int
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_int @ C @ bot_bot_set_int ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2363_image__constant,axiom,
% 7.78/3.96 ! [X2: nat,A4: set_nat,C: rat] :
% 7.78/3.96 ( ( member_nat @ X2 @ A4 )
% 7.78/3.96 => ( ( image_nat_rat
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_rat @ C @ bot_bot_set_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2364_image__constant,axiom,
% 7.78/3.96 ! [X2: nat,A4: set_nat,C: int] :
% 7.78/3.96 ( ( member_nat @ X2 @ A4 )
% 7.78/3.96 => ( ( image_nat_int
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_int @ C @ bot_bot_set_int ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2365_image__constant,axiom,
% 7.78/3.96 ! [X2: int,A4: set_int,C: int] :
% 7.78/3.96 ( ( member_int @ X2 @ A4 )
% 7.78/3.96 => ( ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_int @ C @ bot_bot_set_int ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2366_image__constant,axiom,
% 7.78/3.96 ! [X2: $o,A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( member_o @ X2 @ A4 )
% 7.78/3.96 => ( ( image_o_Product_unit
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2367_image__constant,axiom,
% 7.78/3.96 ! [X2: nat,A4: set_nat,C: product_unit] :
% 7.78/3.96 ( ( member_nat @ X2 @ A4 )
% 7.78/3.96 => ( ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2368_image__constant,axiom,
% 7.78/3.96 ! [X2: int,A4: set_int,C: product_unit] :
% 7.78/3.96 ( ( member_int @ X2 @ A4 )
% 7.78/3.96 => ( ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2369_image__constant,axiom,
% 7.78/3.96 ! [X2: $o,A4: set_o,C: $o] :
% 7.78/3.96 ( ( member_o @ X2 @ A4 )
% 7.78/3.96 => ( ( image_o_o
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2370_image__constant,axiom,
% 7.78/3.96 ! [X2: nat,A4: set_nat,C: $o] :
% 7.78/3.96 ( ( member_nat @ X2 @ A4 )
% 7.78/3.96 => ( ( image_nat_o
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2371_image__constant,axiom,
% 7.78/3.96 ! [X2: int,A4: set_int,C: $o] :
% 7.78/3.96 ( ( member_int @ X2 @ A4 )
% 7.78/3.96 => ( ( image_int_o
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_o @ C @ bot_bot_set_o ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2372_image__constant,axiom,
% 7.78/3.96 ! [X2: $o,A4: set_o,C: nat] :
% 7.78/3.96 ( ( member_o @ X2 @ A4 )
% 7.78/3.96 => ( ( image_o_nat
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 )
% 7.78/3.96 = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2373_UN__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: rat > set_nat,F: nat > rat,A4: set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_rat_set_nat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2374_UN__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: nat > set_nat,F: nat > nat,A4: set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2375_UN__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: int > set_nat,F: nat > int,A4: set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_nat_set_nat
% 7.78/3.96 @ ^ [A5: nat] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2376_UN__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: nat > set_nat,F: int > nat,A4: set_int] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_int_set_nat
% 7.78/3.96 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2377_UN__extend__simps_I10_J,axiom,
% 7.78/3.96 ! [B5: int > set_nat,F: int > int,A4: set_int] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_int_set_nat
% 7.78/3.96 @ ^ [A5: int] : ( B5 @ ( F @ A5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2378_UN__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2379_UN__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2380_UN__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2381_UN__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2382_UN__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2383_UN__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2384_UN__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bot_set_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2385_UN__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bot_set_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2386_UN__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bot_set_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2387_UN__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.96 ( ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bo2099793752762293965at_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2388_UN__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2389_UN__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2390_UN__mono,axiom,
% 7.78/3.96 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2391_UN__mono,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2392_UN__mono,axiom,
% 7.78/3.96 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2393_UN__least,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat,C3: set_nat] :
% 7.78/3.96 ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2394_UN__least,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat,C3: set_nat] :
% 7.78/3.96 ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2395_UN__least,axiom,
% 7.78/3.96 ! [A4: set_o,B5: $o > set_nat,C3: set_nat] :
% 7.78/3.96 ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2396_UN__least,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: nat > set_nat,C3: set_nat] :
% 7.78/3.96 ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2397_UN__least,axiom,
% 7.78/3.96 ! [A4: set_int,B5: int > set_nat,C3: set_nat] :
% 7.78/3.96 ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) @ C3 ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2398_UN__upper,axiom,
% 7.78/3.96 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2399_UN__upper,axiom,
% 7.78/3.96 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2400_UN__upper,axiom,
% 7.78/3.96 ! [A: $o,A4: set_o,B5: $o > set_nat] :
% 7.78/3.96 ( ( member_o @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2401_UN__upper,axiom,
% 7.78/3.96 ! [A: nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.96 ( ( member_nat @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2402_UN__upper,axiom,
% 7.78/3.96 ! [A: int,A4: set_int,B5: int > set_nat] :
% 7.78/3.96 ( ( member_int @ A @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2403_Union__natural,axiom,
% 7.78/3.96 ! [F: int > int] :
% 7.78/3.96 ( ( comp_s8709038167382007543et_int @ comple3221217463730067765et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) ) )
% 7.78/3.96 = ( comp_s2487324123861929025et_int @ ( image_int_int @ F ) @ comple3221217463730067765et_int ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2404_Union__natural,axiom,
% 7.78/3.96 ! [F: nat > rat] :
% 7.78/3.96 ( ( comp_s703482200030188019et_nat @ comple3890839924845867745et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) ) )
% 7.78/3.96 = ( comp_s6435139744279249717et_nat @ ( image_nat_rat @ F ) @ comple7399068483239264473et_nat ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2405_Union__natural,axiom,
% 7.78/3.96 ! [F: nat > int] :
% 7.78/3.96 ( ( comp_s1975749275458958491et_nat @ comple3221217463730067765et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) ) )
% 7.78/3.96 = ( comp_s3768223441818958217et_nat @ ( image_nat_int @ F ) @ comple7399068483239264473et_nat ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2406_Union__natural,axiom,
% 7.78/3.96 ! [F: int > nat] :
% 7.78/3.96 ( ( comp_s6907669228194913343et_int @ comple7399068483239264473et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) ) )
% 7.78/3.96 = ( comp_s5712175470073906149et_int @ ( image_int_nat @ F ) @ comple3221217463730067765et_int ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2407_Union__natural,axiom,
% 7.78/3.96 ! [F: nat > nat] :
% 7.78/3.96 ( ( comp_s174380336271864291et_nat @ comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) ) )
% 7.78/3.96 = ( comp_s6993074788030935341et_nat @ ( image_nat_nat @ F ) @ comple7399068483239264473et_nat ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2408_image__Union,axiom,
% 7.78/3.96 ! [F: int > int,S5: set_set_int] :
% 7.78/3.96 ( ( image_int_int @ F @ ( comple3221217463730067765et_int @ S5 ) )
% 7.78/3.96 = ( comple3221217463730067765et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ S5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2409_image__Union,axiom,
% 7.78/3.96 ! [F: int > nat,S5: set_set_int] :
% 7.78/3.96 ( ( image_int_nat @ F @ ( comple3221217463730067765et_int @ S5 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ S5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2410_image__Union,axiom,
% 7.78/3.96 ! [F: nat > rat,S5: set_set_nat] :
% 7.78/3.96 ( ( image_nat_rat @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 7.78/3.96 = ( comple3890839924845867745et_rat @ ( image_4408659257933336347et_rat @ ( image_nat_rat @ F ) @ S5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2411_image__Union,axiom,
% 7.78/3.96 ! [F: nat > int,S5: set_set_nat] :
% 7.78/3.96 ( ( image_nat_int @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 7.78/3.96 = ( comple3221217463730067765et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ S5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2412_image__Union,axiom,
% 7.78/3.96 ! [F: nat > nat,S5: set_set_nat] :
% 7.78/3.96 ( ( image_nat_nat @ F @ ( comple7399068483239264473et_nat @ S5 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ S5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2413_UN__extend__simps_I8_J,axiom,
% 7.78/3.96 ! [B5: nat > set_nat,A4: set_set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_7916887816326733075et_nat
% 7.78/3.96 @ ^ [Y5: set_nat] : ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ Y5 ) )
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2414_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_int,F: int > product_unit,C: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: int] :
% 7.78/3.96 ( ( member_int @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2415_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,F: product_unit > product_unit,C: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2416_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_o,F: $o > product_unit,C: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: $o] :
% 7.78/3.96 ( ( member_o @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2417_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_nat,F: nat > product_unit,C: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: nat] :
% 7.78/3.96 ( ( member_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2418_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_int,F: int > set_nat,C: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: int] :
% 7.78/3.96 ( ( member_int @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2419_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,F: product_unit > set_nat,C: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2420_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_o,F: $o > set_nat,C: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: $o] :
% 7.78/3.96 ( ( member_o @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2421_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_nat,F: nat > set_nat,C: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: nat] :
% 7.78/3.96 ( ( member_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2422_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,C: product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2423_INF__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,C: set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ I4 ) @ C ) )
% 7.78/3.96 => ( ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2424_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_int,C: product_unit,F: int > product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: int] :
% 7.78/3.96 ( ( member_int @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2425_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,C: product_unit,F: product_unit > product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2426_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_o,C: product_unit,F: $o > product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: $o] :
% 7.78/3.96 ( ( member_o @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2427_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_nat,C: product_unit,F: nat > product_unit] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: nat] :
% 7.78/3.96 ( ( member_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2428_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_int,C: set_nat,F: int > set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_int )
% 7.78/3.96 => ( ! [I4: int] :
% 7.78/3.96 ( ( member_int @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: int] :
% 7.78/3.96 ( ( member_int @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2429_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Product_unit,C: set_nat,F: product_unit > set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [I4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2430_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_o,C: set_nat,F: $o > set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_o )
% 7.78/3.96 => ( ! [I4: $o] :
% 7.78/3.96 ( ( member_o @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: $o] :
% 7.78/3.96 ( ( member_o @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2431_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_nat,C: set_nat,F: nat > set_nat] :
% 7.78/3.96 ( ( I3 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [I4: nat] :
% 7.78/3.96 ( ( member_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: nat] :
% 7.78/3.96 ( ( member_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2432_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,C: product_unit,F: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2433_SUP__eq__iff,axiom,
% 7.78/3.96 ! [I3: set_Pr1261947904930325089at_nat,C: set_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.96 => ( ! [I4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ I4 @ I3 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ C @ ( F @ I4 ) ) )
% 7.78/3.96 => ( ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ I3 ) )
% 7.78/3.96 = C )
% 7.78/3.96 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.96 => ( ( F @ X4 )
% 7.78/3.96 = C ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2434_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: char > product_unit,A: product_unit,X2: char] :
% 7.78/3.96 ( ( ( image_4337914935673063477t_unit @ F @ top_top_set_char )
% 7.78/3.96 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2435_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: char > $o,A: $o,X2: char] :
% 7.78/3.96 ( ( ( image_char_o @ F @ top_top_set_char )
% 7.78/3.96 = ( insert_o @ A @ bot_bot_set_o ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2436_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: char > nat,A: nat,X2: char] :
% 7.78/3.96 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.96 = ( insert_nat @ A @ bot_bot_set_nat ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2437_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: rat > product_unit,A: product_unit,X2: rat] :
% 7.78/3.96 ( ( ( image_2327579789247107822t_unit @ F @ top_top_set_rat )
% 7.78/3.96 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2438_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: rat > $o,A: $o,X2: rat] :
% 7.78/3.96 ( ( ( image_rat_o @ F @ top_top_set_rat )
% 7.78/3.96 = ( insert_o @ A @ bot_bot_set_o ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2439_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: rat > nat,A: nat,X2: rat] :
% 7.78/3.96 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.96 = ( insert_nat @ A @ bot_bot_set_nat ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2440_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: nat > rat,A: rat,X2: nat] :
% 7.78/3.96 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.96 = ( insert_rat @ A @ bot_bot_set_rat ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2441_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: nat > int,A: int,X2: nat] :
% 7.78/3.96 ( ( ( image_nat_int @ F @ top_top_set_nat )
% 7.78/3.96 = ( insert_int @ A @ bot_bot_set_int ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2442_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: nat > product_unit,A: product_unit,X2: nat] :
% 7.78/3.96 ( ( ( image_8730104196221521654t_unit @ F @ top_top_set_nat )
% 7.78/3.96 = ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2443_range__eq__singletonD,axiom,
% 7.78/3.96 ! [F: nat > $o,A: $o,X2: nat] :
% 7.78/3.96 ( ( ( image_nat_o @ F @ top_top_set_nat )
% 7.78/3.96 = ( insert_o @ A @ bot_bot_set_o ) )
% 7.78/3.96 => ( ( F @ X2 )
% 7.78/3.96 = A ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2444_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ B5 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2445_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ B5 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2446_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_o,A4: set_o,F: $o > set_nat,G: $o > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ B5 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2447_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_nat,A4: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ B5 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2448_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_int,A4: set_int,F: int > set_nat,G: int > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ B5 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2449_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,G: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ B5 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2450_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,G: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ B5 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2451_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_o,A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ B5 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2452_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_nat,A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ B5 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2453_INF__superset__mono,axiom,
% 7.78/3.96 ! [B5: set_int,A4: set_int,F: int > product_unit,G: int > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ B5 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2454_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,G: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2455_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,G: product_prod_nat_nat > set_nat] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2456_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_o,B5: set_o,F: $o > set_nat,G: $o > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2457_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2458_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_int,B5: set_int,F: int > set_nat,G: int > set_nat] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2459_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > product_unit,G: produc3843707927480180839at_nat > product_unit] :
% 7.78/3.96 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2460_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,G: product_prod_nat_nat > product_unit] :
% 7.78/3.96 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2461_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_o,B5: set_o,F: $o > product_unit,G: $o > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2462_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2463_SUP__subset__mono,axiom,
% 7.78/3.96 ! [A4: set_int,B5: set_int,F: int > product_unit,G: int > product_unit] :
% 7.78/3.96 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2464_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2465_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2466_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2467_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_char] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2468_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: set_char] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2469_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: set_char] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2470_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_rat] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2471_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: set_rat] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2472_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: set_rat] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2473_INF__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_int] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2474_INF__empty,axiom,
% 7.78/3.96 ! [F: product_unit > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2475_INF__empty,axiom,
% 7.78/3.96 ! [F: $o > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2476_INF__empty,axiom,
% 7.78/3.96 ! [F: nat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2477_INF__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2478_INF__empty,axiom,
% 7.78/3.96 ! [F: $o > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_o_set_char @ F @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2479_INF__empty,axiom,
% 7.78/3.96 ! [F: nat > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_nat_set_char @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2480_INF__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2481_INF__empty,axiom,
% 7.78/3.96 ! [F: $o > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_o_set_rat @ F @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2482_INF__empty,axiom,
% 7.78/3.96 ! [F: nat > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2483_INF__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_int] :
% 7.78/3.96 ( ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_int ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2484_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2485_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2486_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_Product_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2487_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_Product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_7778121751606633509t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_7778121751606633509t_unit
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2488_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_o] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_6930536745178679216_set_o
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_set_o ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_6930536745178679216_set_o
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2489_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: set_Product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_663195431845683034t_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_663195431845683034t_unit
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2490_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_o,C: set_o] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_o_set_o
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_set_o ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_o_set_o
% 7.78/3.96 @ ^ [Y5: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2491_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: set_Product_unit] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_4824033694279209942t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3349607820504768346t_unit
% 7.78/3.96 @ ( image_4824033694279209942t_unit
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2492_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_nat,C: set_o] :
% 7.78/3.96 ( ( ( A4 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_nat_set_o
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_set_o ) )
% 7.78/3.96 & ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple90263536869209701_set_o
% 7.78/3.96 @ ( image_nat_set_o
% 7.78/3.96 @ ^ [Y5: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2493_SUP__constant,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_nat] :
% 7.78/3.96 ( ( ( A4 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = bot_bot_set_nat ) )
% 7.78/3.96 & ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [Y5: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2494_SUP__empty,axiom,
% 7.78/3.96 ! [F: product_unit > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bot_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2495_SUP__empty,axiom,
% 7.78/3.96 ! [F: $o > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bot_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2496_SUP__empty,axiom,
% 7.78/3.96 ! [F: nat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bot_Product_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2497_SUP__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2498_SUP__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2499_SUP__empty,axiom,
% 7.78/3.96 ! [F: $o > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ F @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2500_SUP__empty,axiom,
% 7.78/3.96 ! [F: $o > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ F @ bot_bot_set_o ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2501_SUP__empty,axiom,
% 7.78/3.96 ! [F: nat > set_Product_unit] :
% 7.78/3.96 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bo3957492148770167129t_unit ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2502_SUP__empty,axiom,
% 7.78/3.96 ! [F: nat > set_o] :
% 7.78/3.96 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ F @ bot_bot_set_nat ) )
% 7.78/3.96 = bot_bot_set_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2503_SUP__empty,axiom,
% 7.78/3.96 ! [F: product_unit > set_nat] :
% 7.78/3.96 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = bot_bot_set_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2504_INT__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2505_INT__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_o_set_char @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2506_INT__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_char] :
% 7.78/3.96 ( ( comple7965528767983648192t_char @ ( image_nat_set_char @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_set_char ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2507_INT__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2508_INT__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_o_set_rat @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2509_INT__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_rat] :
% 7.78/3.96 ( ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2510_INT__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_int] :
% 7.78/3.96 ( ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_int ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2511_INT__empty,axiom,
% 7.78/3.96 ! [B5: $o > set_int] :
% 7.78/3.96 ( ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ bot_bot_set_o ) )
% 7.78/3.96 = top_top_set_int ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2512_INT__empty,axiom,
% 7.78/3.96 ! [B5: nat > set_int] :
% 7.78/3.96 ( ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ bot_bot_set_nat ) )
% 7.78/3.96 = top_top_set_int ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2513_INT__empty,axiom,
% 7.78/3.96 ! [B5: product_unit > set_nat] :
% 7.78/3.96 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.96 = top_top_set_nat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2514_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_int,C: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( complete_Inf_Inf_nat
% 7.78/3.96 @ ( image_int_nat
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2515_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( complete_Inf_Inf_nat
% 7.78/3.96 @ ( image_nat_nat
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2516_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_int,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( complete_Inf_Inf_int
% 7.78/3.96 @ ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2517_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: int] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( complete_Inf_Inf_int
% 7.78/3.96 @ ( image_873079544045703924it_int
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2518_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_o,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( complete_Inf_Inf_int
% 7.78/3.96 @ ( image_o_int
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2519_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( complete_Inf_Inf_int
% 7.78/3.96 @ ( image_nat_int
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2520_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2521_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2522_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2523_cINF__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_nat] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2524_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_int,C: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( complete_Sup_Sup_nat
% 7.78/3.96 @ ( image_int_nat
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2525_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( complete_Sup_Sup_nat
% 7.78/3.96 @ ( image_nat_nat
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2526_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_int,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ( complete_Sup_Sup_int
% 7.78/3.96 @ ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2527_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: int] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( complete_Sup_Sup_int
% 7.78/3.96 @ ( image_873079544045703924it_int
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2528_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_o,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( complete_Sup_Sup_int
% 7.78/3.96 @ ( image_o_int
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2529_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( complete_Sup_Sup_int
% 7.78/3.96 @ ( image_nat_int
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2530_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_405062704495631173t_unit
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2531_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_o,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_o_Product_unit
% 7.78/3.96 @ ^ [X4: $o] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2532_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_nat,C: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2533_cSUP__const,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,C: set_nat] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : C
% 7.78/3.96 @ A4 ) )
% 7.78/3.96 = C ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2534_SUP__INF,axiom,
% 7.78/3.96 ! [P2: char > char > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8077363282794994245t_unit
% 7.78/3.96 @ ^ [X4: char > char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_to8079350907815874599r_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2535_SUP__INF,axiom,
% 7.78/3.96 ! [P2: char > rat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_6940606515012899070t_unit
% 7.78/3.96 @ ^ [X4: rat > char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2536_SUP__INF,axiom,
% 7.78/3.96 ! [P2: char > nat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4600008085730780422t_unit
% 7.78/3.96 @ ^ [X4: nat > char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_nat_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2537_SUP__INF,axiom,
% 7.78/3.96 ! [P2: char > int > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4409302170498516394t_unit
% 7.78/3.96 @ ^ [X4: int > char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 @ top_top_set_int_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2538_SUP__INF,axiom,
% 7.78/3.96 ! [P2: rat > char > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_7615136836863079294t_unit
% 7.78/3.96 @ ^ [X4: char > rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2539_SUP__INF,axiom,
% 7.78/3.96 ! [P2: rat > rat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_1193274288206594871t_unit
% 7.78/3.96 @ ^ [X4: rat > rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2540_SUP__INF,axiom,
% 7.78/3.96 ! [P2: rat > nat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_340470173791133503t_unit
% 7.78/3.96 @ ^ [X4: nat > rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_nat_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2541_SUP__INF,axiom,
% 7.78/3.96 ! [P2: rat > int > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4174709274675160035t_unit
% 7.78/3.96 @ ^ [X4: int > rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 @ top_top_set_int_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2542_SUP__INF,axiom,
% 7.78/3.96 ! [P2: nat > char > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_108929247839792006t_unit
% 7.78/3.96 @ ^ [X4: char > nat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char_nat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2543_SUP__INF,axiom,
% 7.78/3.96 ! [P2: nat > rat > product_unit] :
% 7.78/3.96 ( ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2910438736038083391t_unit
% 7.78/3.96 @ ^ [X4: rat > nat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] : ( P2 @ ( X4 @ Y5 ) @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_nat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2544_INF__SUP,axiom,
% 7.78/3.96 ! [P2: char > char > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8077363282794994245t_unit
% 7.78/3.96 @ ^ [F2: char > char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_to8079350907815874599r_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2545_INF__SUP,axiom,
% 7.78/3.96 ! [P2: char > rat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_6940606515012899070t_unit
% 7.78/3.96 @ ^ [F2: rat > char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2546_INF__SUP,axiom,
% 7.78/3.96 ! [P2: char > nat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4600008085730780422t_unit
% 7.78/3.96 @ ^ [F2: nat > char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_nat_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2547_INF__SUP,axiom,
% 7.78/3.96 ! [P2: char > int > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4409302170498516394t_unit
% 7.78/3.96 @ ^ [F2: int > char] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [X4: int] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 @ top_top_set_int_char ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2548_INF__SUP,axiom,
% 7.78/3.96 ! [P2: rat > char > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_7615136836863079294t_unit
% 7.78/3.96 @ ^ [F2: char > rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2549_INF__SUP,axiom,
% 7.78/3.96 ! [P2: rat > rat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_1193274288206594871t_unit
% 7.78/3.96 @ ^ [F2: rat > rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2550_INF__SUP,axiom,
% 7.78/3.96 ! [P2: rat > nat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [Y5: nat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_340470173791133503t_unit
% 7.78/3.96 @ ^ [F2: nat > rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_nat_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2551_INF__SUP,axiom,
% 7.78/3.96 ! [P2: rat > int > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [Y5: int] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_4174709274675160035t_unit
% 7.78/3.96 @ ^ [F2: int > rat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_5846526143423701914t_unit
% 7.78/3.96 @ ^ [X4: int] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_int ) )
% 7.78/3.96 @ top_top_set_int_rat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2552_INF__SUP,axiom,
% 7.78/3.96 ! [P2: nat > char > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [Y5: char] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_108929247839792006t_unit
% 7.78/3.96 @ ^ [F2: char > nat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_4337914935673063477t_unit
% 7.78/3.96 @ ^ [X4: char] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_char ) )
% 7.78/3.96 @ top_top_set_char_nat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2553_INF__SUP,axiom,
% 7.78/3.96 ! [P2: nat > rat > product_unit] :
% 7.78/3.96 ( ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [Y5: rat] :
% 7.78/3.96 ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_8730104196221521654t_unit
% 7.78/3.96 @ ^ [X4: nat] : ( P2 @ X4 @ Y5 )
% 7.78/3.96 @ top_top_set_nat ) )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 = ( comple4687483117567863418t_unit
% 7.78/3.96 @ ( image_2910438736038083391t_unit
% 7.78/3.96 @ ^ [F2: rat > nat] :
% 7.78/3.96 ( comple2584293577114468500t_unit
% 7.78/3.96 @ ( image_2327579789247107822t_unit
% 7.78/3.96 @ ^ [X4: rat] : ( P2 @ ( F2 @ X4 ) @ X4 )
% 7.78/3.96 @ top_top_set_rat ) )
% 7.78/3.96 @ top_top_set_rat_nat ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2554_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,M3: nat,F: int > nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2555_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,M3: nat,F: product_unit > nat] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2556_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_o,M3: nat,F: $o > nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2557_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_nat,M3: nat,F: nat > nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_nat @ M3 @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2558_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,M3: int,F: int > int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2559_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,M3: int,F: product_unit > int] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2560_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_o,M3: int,F: $o > int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2561_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_nat,M3: int,F: nat > int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_less_eq_int @ M3 @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2562_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_int,M3: product_unit,F: int > product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ M3 @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2563_cINF__greatest,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,M3: product_unit,F: product_unit > product_unit] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ M3 @ ( F @ X ) ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ M3 @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2564_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > nat,M: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2565_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,F: product_unit > nat,M: nat] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2566_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > nat,M: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2567_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > nat,M: nat] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2568_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > int,M: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2569_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,F: product_unit > int,M: int] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2570_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_o,F: $o > int,M: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_o )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2571_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_nat,F: nat > int,M: int] :
% 7.78/3.96 ( ( A4 != bot_bot_set_nat )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2572_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_int,F: int > product_unit,M: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bot_set_int )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2573_cSUP__least,axiom,
% 7.78/3.96 ! [A4: set_Product_unit,F: product_unit > product_unit,M: product_unit] :
% 7.78/3.96 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ! [X: product_unit] :
% 7.78/3.96 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ M ) )
% 7.78/3.96 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ M ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2574_UN__constant__eq,axiom,
% 7.78/3.96 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > set_nat,C: set_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.96 => ( ! [X: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.96 => ( ( F @ X )
% 7.78/3.96 = C ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ F @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2575_UN__constant__eq,axiom,
% 7.78/3.96 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > set_nat,C: set_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.96 => ( ! [X: product_prod_nat_nat] :
% 7.78/3.96 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.96 => ( ( F @ X )
% 7.78/3.96 = C ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2576_UN__constant__eq,axiom,
% 7.78/3.96 ! [A: $o,A4: set_o,F: $o > set_nat,C: set_nat] :
% 7.78/3.96 ( ( member_o @ A @ A4 )
% 7.78/3.96 => ( ! [X: $o] :
% 7.78/3.96 ( ( member_o @ X @ A4 )
% 7.78/3.96 => ( ( F @ X )
% 7.78/3.96 = C ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2577_UN__constant__eq,axiom,
% 7.78/3.96 ! [A: nat,A4: set_nat,F: nat > set_nat,C: set_nat] :
% 7.78/3.96 ( ( member_nat @ A @ A4 )
% 7.78/3.96 => ( ! [X: nat] :
% 7.78/3.96 ( ( member_nat @ X @ A4 )
% 7.78/3.96 => ( ( F @ X )
% 7.78/3.96 = C ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2578_UN__constant__eq,axiom,
% 7.78/3.96 ! [A: int,A4: set_int,F: int > set_nat,C: set_nat] :
% 7.78/3.96 ( ( member_int @ A @ A4 )
% 7.78/3.96 => ( ! [X: int] :
% 7.78/3.96 ( ( member_int @ X @ A4 )
% 7.78/3.96 => ( ( F @ X )
% 7.78/3.96 = C ) )
% 7.78/3.96 => ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A4 ) )
% 7.78/3.96 = C ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2579_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 7.78/3.96 ( ( refl_o7446464703481863270at_nat @ A4 @ R )
% 7.78/3.96 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 7.78/3.96 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.96 & ( member8757157785044589968at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2580_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 7.78/3.96 ( ( refl_o7122697186039111552at_nat @ A4 @ R )
% 7.78/3.96 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 7.78/3.96 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.96 & ( member8440522571783428010at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2581_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_o,R: set_Product_prod_o_o,A: $o,B: $o] :
% 7.78/3.96 ( ( refl_on_o @ A4 @ R )
% 7.78/3.96 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 7.78/3.96 => ( ( member_o @ A @ A4 )
% 7.78/3.96 & ( member_o @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2582_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.96 ( ( refl_o6272981002401706822at_nat @ A4 @ R )
% 7.78/3.96 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 7.78/3.96 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 7.78/3.96 & ( member6273874620674182256at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2583_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.96 ( ( refl_o6955724340487615712at_nat @ A4 @ R )
% 7.78/3.96 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 7.78/3.96 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 7.78/3.96 & ( member2643936169264416010at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2584_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 7.78/3.96 ( ( refl_on_nat @ A4 @ R )
% 7.78/3.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 7.78/3.96 => ( ( member_nat @ A @ A4 )
% 7.78/3.96 & ( member_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2585_refl__on__domain,axiom,
% 7.78/3.96 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 7.78/3.96 ( ( refl_on_int @ A4 @ R )
% 7.78/3.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 7.78/3.96 => ( ( member_int @ A @ A4 )
% 7.78/3.96 & ( member_int @ B @ A4 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2586_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: set_char,B5: product_unit > set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_5325685772115642575t_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2587_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: set_char,B5: $o > set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_o_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2588_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: set_char,B5: nat > set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ A4 @ ( comple4338141846124676698t_char @ ( image_nat_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2589_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: set_rat,B5: product_unit > set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_4665621433434589782et_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2590_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: set_rat,B5: $o > set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_o_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2591_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: set_rat,B5: nat > set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ A4 @ ( comple3890839924845867745et_rat @ ( image_nat_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2592_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: set_int,B5: product_unit > set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2593_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: set_int,B5: $o > set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_o_set_int
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_o_set_int
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2594_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: set_int,B5: nat > set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_nat_set_int
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_nat_set_int
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ A4 @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2595_INT__simps_I4_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_nat ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2596_relcompp__bot2,axiom,
% 7.78/3.96 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 7.78/3.96 ( ( relcom8911704206367525917at_int @ R3 @ bot_bo5438875203632553179_int_o )
% 7.78/3.96 = bot_bo5438875203632553179_int_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2597_relcompp__bot2,axiom,
% 7.78/3.96 ! [R3: int > int > $o] :
% 7.78/3.96 ( ( relcom967497705283160040nteger @ R3 @ bot_bo341146761387662761eger_o )
% 7.78/3.96 = bot_bo341146761387662761eger_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2598_relcompp__bot1,axiom,
% 7.78/3.96 ! [R3: product_prod_nat_nat > int > $o] :
% 7.78/3.96 ( ( relcom8911704206367525917at_int @ bot_bo4898103413517107610_nat_o @ R3 )
% 7.78/3.96 = bot_bo5438875203632553179_int_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2599_relcompp__bot1,axiom,
% 7.78/3.96 ! [R3: int > code_integer > $o] :
% 7.78/3.96 ( ( relcom967497705283160040nteger @ bot_bot_int_int_o @ R3 )
% 7.78/3.96 = bot_bo341146761387662761eger_o ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2600_surj__diff__right,axiom,
% 7.78/3.96 ! [A: int] :
% 7.78/3.96 ( ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.96 @ top_top_set_int )
% 7.78/3.96 = top_top_set_int ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2601_surj__diff__right,axiom,
% 7.78/3.96 ! [A: rat] :
% 7.78/3.96 ( ( image_rat_rat
% 7.78/3.96 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.96 @ top_top_set_rat )
% 7.78/3.96 = top_top_set_rat ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2602_surj__diff__right,axiom,
% 7.78/3.96 ! [A: code_integer] :
% 7.78/3.96 ( ( image_4470545334726330049nteger
% 7.78/3.96 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.96 @ top_to4645266643341252675nteger )
% 7.78/3.96 = top_to4645266643341252675nteger ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2603_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_5325685772115642575t_char
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2604_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_o_set_char
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2605_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_char ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple7965528767983648192t_char
% 7.78/3.96 @ ( image_nat_set_char
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2606_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_4665621433434589782et_rat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2607_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_o_set_rat
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2608_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_rat ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple4298007329820168263et_rat
% 7.78/3.96 @ ( image_nat_set_rat
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2609_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_3995998972318789802et_int
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2610_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_o_set_int
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_o )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_o_set_int
% 7.78/3.96 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2611_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 7.78/3.96 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_nat_set_int
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_int ) )
% 7.78/3.96 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.96 => ( ( comple3628384868704368283et_int
% 7.78/3.96 @ ( image_nat_set_int
% 7.78/3.96 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2612_INT__simps_I3_J,axiom,
% 7.78/3.96 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.96 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = top_top_set_nat ) )
% 7.78/3.96 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.96 => ( ( comple7806235888213564991et_nat
% 7.78/3.96 @ ( image_8173849991827986510et_nat
% 7.78/3.96 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.96 @ C3 ) )
% 7.78/3.96 = ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2613_Sigma__Diff__distrib1,axiom,
% 7.78/3.96 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 7.78/3.96 ( ( produc457027306803732586at_nat @ ( minus_minus_set_nat @ I3 @ J3 ) @ C3 )
% 7.78/3.96 = ( minus_1356011639430497352at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2614_translation__subtract__diff,axiom,
% 7.78/3.96 ! [A: int,S2: set_int,T2: set_int] :
% 7.78/3.96 ( ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.96 @ ( minus_minus_set_int @ S2 @ T2 ) )
% 7.78/3.96 = ( minus_minus_set_int
% 7.78/3.96 @ ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.96 @ S2 )
% 7.78/3.96 @ ( image_int_int
% 7.78/3.96 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.96 @ T2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2615_translation__subtract__diff,axiom,
% 7.78/3.96 ! [A: rat,S2: set_rat,T2: set_rat] :
% 7.78/3.96 ( ( image_rat_rat
% 7.78/3.96 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.96 @ ( minus_minus_set_rat @ S2 @ T2 ) )
% 7.78/3.96 = ( minus_minus_set_rat
% 7.78/3.96 @ ( image_rat_rat
% 7.78/3.96 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.96 @ S2 )
% 7.78/3.96 @ ( image_rat_rat
% 7.78/3.96 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.96 @ T2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2616_translation__subtract__diff,axiom,
% 7.78/3.96 ! [A: code_integer,S2: set_Code_integer,T2: set_Code_integer] :
% 7.78/3.96 ( ( image_4470545334726330049nteger
% 7.78/3.96 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.96 @ ( minus_2355218937544613996nteger @ S2 @ T2 ) )
% 7.78/3.96 = ( minus_2355218937544613996nteger
% 7.78/3.96 @ ( image_4470545334726330049nteger
% 7.78/3.96 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.96 @ S2 )
% 7.78/3.96 @ ( image_4470545334726330049nteger
% 7.78/3.96 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.96 @ T2 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2617_Times__Diff__distrib1,axiom,
% 7.78/3.96 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 7.78/3.96 ( ( produc457027306803732586at_nat @ ( minus_minus_set_nat @ A4 @ B5 )
% 7.78/3.96 @ ^ [Uu: nat] : C3 )
% 7.78/3.96 = ( minus_1356011639430497352at_nat
% 7.78/3.96 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.96 @ ^ [Uu: nat] : C3 )
% 7.78/3.96 @ ( produc457027306803732586at_nat @ B5
% 7.78/3.96 @ ^ [Uu: nat] : C3 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2618_Sigma__Diff__distrib2,axiom,
% 7.78/3.96 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 7.78/3.96 ( ( produc457027306803732586at_nat @ I3
% 7.78/3.96 @ ^ [I2: nat] : ( minus_minus_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 7.78/3.96 = ( minus_1356011639430497352at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2619_Sup__SUP__eq,axiom,
% 7.78/3.96 ( comple1177764198577243945_nat_o
% 7.78/3.96 = ( ^ [S4: set_Pr7010166363911110284_nat_o,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2620_Sup__SUP__eq,axiom,
% 7.78/3.96 ( complete_Sup_Sup_o_o
% 7.78/3.96 = ( ^ [S4: set_o_o,X4: $o] : ( member_o @ X4 @ ( comple90263536869209701_set_o @ ( image_o_o_set_o @ collect_o @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2621_Sup__SUP__eq,axiom,
% 7.78/3.96 ( comple6496622788309502864_int_o
% 7.78/3.96 = ( ^ [S4: set_int_o,X4: int] : ( member_int @ X4 @ ( comple3221217463730067765et_int @ ( image_int_o_set_int @ collect_int @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2622_Sup__SUP__eq,axiom,
% 7.78/3.96 ( comple1901448594430626575_nat_o
% 7.78/3.96 = ( ^ [S4: set_Pr5582243495563764594_nat_o,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2623_Sup__SUP__eq,axiom,
% 7.78/3.96 ( comple342879659800731223_int_o
% 7.78/3.96 = ( ^ [S4: set_Pr8049984349381595834_int_o,X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ ( comple5382143125604098054nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2624_Sup__SUP__eq,axiom,
% 7.78/3.96 ( comple8317665133742190828_nat_o
% 7.78/3.96 = ( ^ [S4: set_nat_o,X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ ( image_nat_o_set_nat @ collect_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2625_Inf__INT__eq,axiom,
% 7.78/3.96 ( comple8183010123678664591_nat_o
% 7.78/3.96 = ( ^ [S4: set_Pr7010166363911110284_nat_o,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2626_Inf__INT__eq,axiom,
% 7.78/3.96 ( complete_Inf_Inf_o_o
% 7.78/3.96 = ( ^ [S4: set_o_o,X4: $o] : ( member_o @ X4 @ ( comple3063163877087187839_set_o @ ( image_o_o_set_o @ collect_o @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2627_Inf__INT__eq,axiom,
% 7.78/3.96 ( comple4393433247856107946_int_o
% 7.78/3.96 = ( ^ [S4: set_int_o,X4: int] : ( member_int @ X4 @ ( comple3628384868704368283et_int @ ( image_int_o_set_int @ collect_int @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2628_Inf__INT__eq,axiom,
% 7.78/3.96 ( comple6265855634338933877_nat_o
% 7.78/3.96 = ( ^ [S4: set_Pr5582243495563764594_nat_o,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2629_Inf__INT__eq,axiom,
% 7.78/3.96 ( comple4707286699709038525_int_o
% 7.78/3.96 = ( ^ [S4: set_Pr8049984349381595834_int_o,X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ ( comple1626965760690514720nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2630_Inf__INT__eq,axiom,
% 7.78/3.96 ( comple6214475593288795910_nat_o
% 7.78/3.96 = ( ^ [S4: set_nat_o,X4: nat] : ( member_nat @ X4 @ ( comple7806235888213564991et_nat @ ( image_nat_o_set_nat @ collect_nat @ S4 ) ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2631_INF__Int__eq2,axiom,
% 7.78/3.96 ! [S5: set_se7592288975875140775at_nat] :
% 7.78/3.96 ( ( comple5307621999477653941_nat_o
% 7.78/3.96 @ ( image_5337237954834410540_nat_o
% 7.78/3.96 @ ^ [I2: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.96 @ S5 ) )
% 7.78/3.96 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple4403251139954110286at_nat @ S5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2632_INF__Int__eq2,axiom,
% 7.78/3.96 ! [S5: set_se5479201105039950375at_nat] :
% 7.78/3.96 ( ( comple8322679762649017525_nat_o
% 7.78/3.96 @ ( image_6595146019508340652_nat_o
% 7.78/3.96 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.96 @ S5 ) )
% 7.78/3.96 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple6751905152567503566at_nat @ S5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2633_INF__Int__eq2,axiom,
% 7.78/3.96 ! [S5: set_se4826145725398303499at_num] :
% 7.78/3.96 ( ( comple2433913294995299363_num_o
% 7.78/3.96 @ ( image_2055017250723459638_num_o
% 7.78/3.96 @ ^ [I2: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ I2 )
% 7.78/3.96 @ S5 ) )
% 7.78/3.96 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple6868718957223342258at_num @ S5 ) ) ) ) ).
% 7.78/3.96
% 7.78/3.96 thf(fact_2634_INF__Int__eq2,axiom,
% 7.78/3.96 ! [S5: set_se7855581050983116737at_nat] :
% 7.78/3.96 ( ( comple1675732732025788397_nat_o
% 7.78/3.96 @ ( image_6923511907955291850_nat_o
% 7.78/3.96 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple1930127330929219688at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2635_INF__Int__eq2,axiom,
% 7.78/3.97 ! [S5: set_se6260736226359567993nt_int] :
% 7.78/3.97 ( ( comple5770381748412298549_int_o
% 7.78/3.97 @ ( image_4446226961036766042_int_o
% 7.78/3.97 @ ^ [I2: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple1626965760690514720nt_int @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2636_SUP__Sup__eq2,axiom,
% 7.78/3.97 ! [S5: set_se7592288975875140775at_nat] :
% 7.78/3.97 ( ( comple4502628867940267931_nat_o
% 7.78/3.97 @ ( image_5337237954834410540_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr7459493094073627847at_nat,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple7342073961973170484at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2637_SUP__Sup__eq2,axiom,
% 7.78/3.97 ! [S5: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( ( comple493620192902636699_nat_o
% 7.78/3.97 @ ( image_6595146019508340652_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple4364388969068068532at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2638_SUP__Sup__eq2,axiom,
% 7.78/3.97 ! [S5: set_se4826145725398303499at_num] :
% 7.78/3.97 ( ( comple4350791933526045961_num_o
% 7.78/3.97 @ ( image_2055017250723459638_num_o
% 7.78/3.97 @ ^ [I2: set_Pr6200539531224447659at_num,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple1400524285282149784at_num @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2639_SUP__Sup__eq2,axiom,
% 7.78/3.97 ! [S5: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( comple3592611370556534995_nat_o
% 7.78/3.97 @ ( image_6923511907955291850_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple5685304695842803022at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2640_SUP__Sup__eq2,axiom,
% 7.78/3.97 ! [S5: set_se6260736226359567993nt_int] :
% 7.78/3.97 ( ( comple7687260386943045147_int_o
% 7.78/3.97 @ ( image_4446226961036766042_int_o
% 7.78/3.97 @ ^ [I2: set_Pr958786334691620121nt_int,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple5382143125604098054nt_int @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2641_SUP__Sup__eq,axiom,
% 7.78/3.97 ! [S5: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( ( comple1177764198577243945_nat_o
% 7.78/3.97 @ ( image_4859512832475012440_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple4364388969068068532at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2642_SUP__Sup__eq,axiom,
% 7.78/3.97 ! [S5: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( comple1901448594430626575_nat_o
% 7.78/3.97 @ ( image_5253903537071781336_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple5685304695842803022at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2643_SUP__Sup__eq,axiom,
% 7.78/3.97 ! [S5: set_set_o] :
% 7.78/3.97 ( ( complete_Sup_Sup_o_o
% 7.78/3.97 @ ( image_set_o_o_o
% 7.78/3.97 @ ^ [I2: set_o,X4: $o] : ( member_o @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: $o] : ( member_o @ X4 @ ( comple90263536869209701_set_o @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2644_SUP__Sup__eq,axiom,
% 7.78/3.97 ! [S5: set_set_int] :
% 7.78/3.97 ( ( comple6496622788309502864_int_o
% 7.78/3.97 @ ( image_set_int_int_o
% 7.78/3.97 @ ^ [I2: set_int,X4: int] : ( member_int @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: int] : ( member_int @ X4 @ ( comple3221217463730067765et_int @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2645_SUP__Sup__eq,axiom,
% 7.78/3.97 ! [S5: set_set_nat] :
% 7.78/3.97 ( ( comple8317665133742190828_nat_o
% 7.78/3.97 @ ( image_set_nat_nat_o
% 7.78/3.97 @ ^ [I2: set_nat,X4: nat] : ( member_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( comple7399068483239264473et_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2646_INF__Int__eq,axiom,
% 7.78/3.97 ! [S5: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( ( comple8183010123678664591_nat_o
% 7.78/3.97 @ ( image_4859512832475012440_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr4329608150637261639at_nat,X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( comple6751905152567503566at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2647_INF__Int__eq,axiom,
% 7.78/3.97 ! [S5: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( comple6265855634338933877_nat_o
% 7.78/3.97 @ ( image_5253903537071781336_nat_o
% 7.78/3.97 @ ^ [I2: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( comple1930127330929219688at_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2648_INF__Int__eq,axiom,
% 7.78/3.97 ! [S5: set_set_o] :
% 7.78/3.97 ( ( complete_Inf_Inf_o_o
% 7.78/3.97 @ ( image_set_o_o_o
% 7.78/3.97 @ ^ [I2: set_o,X4: $o] : ( member_o @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: $o] : ( member_o @ X4 @ ( comple3063163877087187839_set_o @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2649_INF__Int__eq,axiom,
% 7.78/3.97 ! [S5: set_set_int] :
% 7.78/3.97 ( ( comple4393433247856107946_int_o
% 7.78/3.97 @ ( image_set_int_int_o
% 7.78/3.97 @ ^ [I2: set_int,X4: int] : ( member_int @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: int] : ( member_int @ X4 @ ( comple3628384868704368283et_int @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2650_INF__Int__eq,axiom,
% 7.78/3.97 ! [S5: set_set_nat] :
% 7.78/3.97 ( ( comple6214475593288795910_nat_o
% 7.78/3.97 @ ( image_set_nat_nat_o
% 7.78/3.97 @ ^ [I2: set_nat,X4: nat] : ( member_nat @ X4 @ I2 )
% 7.78/3.97 @ S5 ) )
% 7.78/3.97 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( comple7806235888213564991et_nat @ S5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2651_Sup__set__def,axiom,
% 7.78/3.97 ( comple4364388969068068532at_nat
% 7.78/3.97 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( collec6321179662152712658at_nat
% 7.78/3.97 @ ^ [X4: produc3843707927480180839at_nat] : ( complete_Sup_Sup_o @ ( image_3568060456209098518_nat_o @ ( member8757157785044589968at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2652_Sup__set__def,axiom,
% 7.78/3.97 ( comple90263536869209701_set_o
% 7.78/3.97 = ( ^ [A6: set_set_o] :
% 7.78/3.97 ( collect_o
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Sup_Sup_o @ ( image_set_o_o @ ( member_o @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2653_Sup__set__def,axiom,
% 7.78/3.97 ( comple3221217463730067765et_int
% 7.78/3.97 = ( ^ [A6: set_set_int] :
% 7.78/3.97 ( collect_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Sup_Sup_o @ ( image_set_int_o @ ( member_int @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2654_Sup__set__def,axiom,
% 7.78/3.97 ( comple5685304695842803022at_nat
% 7.78/3.97 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( collec3392354462482085612at_nat
% 7.78/3.97 @ ^ [X4: product_prod_nat_nat] : ( complete_Sup_Sup_o @ ( image_7457375456213313148_nat_o @ ( member8440522571783428010at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2655_Sup__set__def,axiom,
% 7.78/3.97 ( comple5382143125604098054nt_int
% 7.78/3.97 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 7.78/3.97 ( collec213857154873943460nt_int
% 7.78/3.97 @ ^ [X4: product_prod_int_int] : ( complete_Sup_Sup_o @ ( image_701744273176368580_int_o @ ( member5262025264175285858nt_int @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2656_Sup__set__def,axiom,
% 7.78/3.97 ( comple7399068483239264473et_nat
% 7.78/3.97 = ( ^ [A6: set_set_nat] :
% 7.78/3.97 ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] : ( complete_Sup_Sup_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2657_Inf__set__def,axiom,
% 7.78/3.97 ( comple6751905152567503566at_nat
% 7.78/3.97 = ( ^ [A6: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( collec6321179662152712658at_nat
% 7.78/3.97 @ ^ [X4: produc3843707927480180839at_nat] : ( complete_Inf_Inf_o @ ( image_3568060456209098518_nat_o @ ( member8757157785044589968at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2658_Inf__set__def,axiom,
% 7.78/3.97 ( comple3063163877087187839_set_o
% 7.78/3.97 = ( ^ [A6: set_set_o] :
% 7.78/3.97 ( collect_o
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Inf_Inf_o @ ( image_set_o_o @ ( member_o @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2659_Inf__set__def,axiom,
% 7.78/3.97 ( comple3628384868704368283et_int
% 7.78/3.97 = ( ^ [A6: set_set_int] :
% 7.78/3.97 ( collect_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Inf_Inf_o @ ( image_set_int_o @ ( member_int @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2660_Inf__set__def,axiom,
% 7.78/3.97 ( comple1930127330929219688at_nat
% 7.78/3.97 = ( ^ [A6: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( collec3392354462482085612at_nat
% 7.78/3.97 @ ^ [X4: product_prod_nat_nat] : ( complete_Inf_Inf_o @ ( image_7457375456213313148_nat_o @ ( member8440522571783428010at_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2661_Inf__set__def,axiom,
% 7.78/3.97 ( comple1626965760690514720nt_int
% 7.78/3.97 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 7.78/3.97 ( collec213857154873943460nt_int
% 7.78/3.97 @ ^ [X4: product_prod_int_int] : ( complete_Inf_Inf_o @ ( image_701744273176368580_int_o @ ( member5262025264175285858nt_int @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2662_Inf__set__def,axiom,
% 7.78/3.97 ( comple7806235888213564991et_nat
% 7.78/3.97 = ( ^ [A6: set_set_nat] :
% 7.78/3.97 ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] : ( complete_Inf_Inf_o @ ( image_set_nat_o @ ( member_nat @ X4 ) @ A6 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2663_image__diff__subset,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_rat @ ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2664_image__diff__subset,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2665_image__diff__subset,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2666_image__diff__subset,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,B5: set_int] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2667_image__diff__subset,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2668_Inf__INT__eq2,axiom,
% 7.78/3.97 ( comple5307621999477653941_nat_o
% 7.78/3.97 = ( ^ [S4: set_se7255092946006855566_nat_o,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple4403251139954110286at_nat @ ( image_5694205205332509994at_nat @ collec7872792499061297490at_nat @ ( image_5235725667318448191_nat_o @ produc9020218426428501292_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2669_Inf__INT__eq2,axiom,
% 7.78/3.97 ( comple8322679762649017525_nat_o
% 7.78/3.97 = ( ^ [S4: set_se9180647916752606350_nat_o,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple6751905152567503566at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2670_Inf__INT__eq2,axiom,
% 7.78/3.97 ( comple2433913294995299363_num_o
% 7.78/3.97 = ( ^ [S4: set_nat_num_o,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple6868718957223342258at_num @ ( image_6580737572886966642at_num @ collec4100598399430923318at_num @ ( image_8484515203959327177_num_o @ produc4927758841916487424_num_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2671_Inf__INT__eq2,axiom,
% 7.78/3.97 ( comple1675732732025788397_nat_o
% 7.78/3.97 = ( ^ [S4: set_nat_nat_o,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple1930127330929219688at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2672_Inf__INT__eq2,axiom,
% 7.78/3.97 ( comple5770381748412298549_int_o
% 7.78/3.97 = ( ^ [S4: set_int_int_o,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple1626965760690514720nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ ( image_1365644804893650413_int_o @ produc4947309494688390418_int_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2673_Sup__SUP__eq2,axiom,
% 7.78/3.97 ( comple4502628867940267931_nat_o
% 7.78/3.97 = ( ^ [S4: set_se7255092946006855566_nat_o,X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( comple7342073961973170484at_nat @ ( image_5694205205332509994at_nat @ collec7872792499061297490at_nat @ ( image_5235725667318448191_nat_o @ produc9020218426428501292_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2674_Sup__SUP__eq2,axiom,
% 7.78/3.97 ( comple493620192902636699_nat_o
% 7.78/3.97 = ( ^ [S4: set_se9180647916752606350_nat_o,X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( comple4364388969068068532at_nat @ ( image_4902389024228248874at_nat @ collec6321179662152712658at_nat @ ( image_6226802281960588479_nat_o @ produc410239310623530412_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2675_Sup__SUP__eq2,axiom,
% 7.78/3.97 ( comple4350791933526045961_num_o
% 7.78/3.97 = ( ^ [S4: set_nat_num_o,X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( comple1400524285282149784at_num @ ( image_6580737572886966642at_num @ collec4100598399430923318at_num @ ( image_8484515203959327177_num_o @ produc4927758841916487424_num_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2676_Sup__SUP__eq2,axiom,
% 7.78/3.97 ( comple3592611370556534995_nat_o
% 7.78/3.97 = ( ^ [S4: set_nat_nat_o,X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( comple5685304695842803022at_nat @ ( image_7124889717316225246at_nat @ collec3392354462482085612at_nat @ ( image_7429393840292777309_nat_o @ produc6081775807080527818_nat_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2677_Sup__SUP__eq2,axiom,
% 7.78/3.97 ( comple7687260386943045147_int_o
% 7.78/3.97 = ( ^ [S4: set_int_int_o,X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( comple5382143125604098054nt_int @ ( image_4447441447610994254nt_int @ collec213857154873943460nt_int @ ( image_1365644804893650413_int_o @ produc4947309494688390418_int_o @ S4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2678_bot__empty__eq2,axiom,
% 7.78/3.97 ( bot_bo3364206721330744218_nat_o
% 7.78/3.97 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ bot_bo4948859079157340979at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2679_bot__empty__eq2,axiom,
% 7.78/3.97 ( bot_bot_nat_num_o
% 7.78/3.97 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ bot_bo7038385379056416535at_num ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2680_bot__empty__eq2,axiom,
% 7.78/3.97 ( bot_bot_int_int_o
% 7.78/3.97 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2681_bot__empty__eq2,axiom,
% 7.78/3.97 ( bot_bo394778441745866138_nat_o
% 7.78/3.97 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2682_bot__empty__eq2,axiom,
% 7.78/3.97 ( bot_bot_nat_nat_o
% 7.78/3.97 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2683_top__empty__eq2,axiom,
% 7.78/3.97 ( top_to1326704617074743934_nat_o
% 7.78/3.97 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ top_to5281548843312042519at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2684_top__empty__eq2,axiom,
% 7.78/3.97 ( top_to8903224817164384382_nat_o
% 7.78/3.97 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ top_to6833984726390702231at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2685_top__empty__eq2,axiom,
% 7.78/3.97 ( top_top_nat_num_o
% 7.78/3.97 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ top_to385025497714130939at_num ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2686_top__empty__eq2,axiom,
% 7.78/3.97 ( top_top_nat_nat_o
% 7.78/3.97 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ top_to4669805908274784177at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2687_top__empty__eq2,axiom,
% 7.78/3.97 ( top_top_int_int_o
% 7.78/3.97 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ top_to4366644338036079209nt_int ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2688_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_set_int,X2: int,A4: set_int] :
% 7.78/3.97 ( ! [C2: set_int] :
% 7.78/3.97 ( ( member_set_int @ C2 @ B5 )
% 7.78/3.97 => ~ ( member_int @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member_set_int @ A4 @ ( image_524474410958335435et_int @ ( insert_int @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member_int @ X2 @ A4 )
% 7.78/3.97 & ( member_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2689_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_set_Product_unit,X2: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ! [C2: set_Product_unit] :
% 7.78/3.97 ( ( member5877623283571906838t_unit @ C2 @ B5 )
% 7.78/3.97 => ~ ( member_Product_unit @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member5877623283571906838t_unit @ A4 @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member_Product_unit @ X2 @ A4 )
% 7.78/3.97 & ( member5877623283571906838t_unit @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2690_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_se5479201105039950375at_nat,X2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ! [C2: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( member6273874620674182256at_nat @ C2 @ B5 )
% 7.78/3.97 => ~ ( member8757157785044589968at_nat @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member6273874620674182256at_nat @ A4 @ ( image_4303274092540115909at_nat @ ( insert9069300056098147895at_nat @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member8757157785044589968at_nat @ X2 @ A4 )
% 7.78/3.97 & ( member6273874620674182256at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2691_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_se7855581050983116737at_nat,X2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ! [C2: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( member2643936169264416010at_nat @ C2 @ B5 )
% 7.78/3.97 => ~ ( member8440522571783428010at_nat @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member2643936169264416010at_nat @ A4 @ ( image_3684629450409544005at_nat @ ( insert8211810215607154385at_nat @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 7.78/3.97 & ( member2643936169264416010at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2692_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_set_o,X2: $o,A4: set_o] :
% 7.78/3.97 ( ! [C2: set_o] :
% 7.78/3.97 ( ( member_set_o @ C2 @ B5 )
% 7.78/3.97 => ~ ( member_o @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member_set_o @ A4 @ ( image_set_o_set_o @ ( insert_o @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member_o @ X2 @ A4 )
% 7.78/3.97 & ( member_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2693_in__image__insert__iff,axiom,
% 7.78/3.97 ! [B5: set_set_nat,X2: nat,A4: set_nat] :
% 7.78/3.97 ( ! [C2: set_nat] :
% 7.78/3.97 ( ( member_set_nat @ C2 @ B5 )
% 7.78/3.97 => ~ ( member_nat @ X2 @ C2 ) )
% 7.78/3.97 => ( ( member_set_nat @ A4 @ ( image_7916887816326733075et_nat @ ( insert_nat @ X2 ) @ B5 ) )
% 7.78/3.97 = ( ( member_nat @ X2 @ A4 )
% 7.78/3.97 & ( member_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2694_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_5325685772115642575t_char
% 7.78/3.97 @ ^ [X4: product_unit] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2695_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_o_set_char
% 7.78/3.97 @ ^ [X4: $o] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2696_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_char @ top_top_set_char @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_nat_set_char
% 7.78/3.97 @ ^ [X4: nat] : ( minus_minus_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2697_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_4665621433434589782et_rat
% 7.78/3.97 @ ^ [X4: product_unit] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2698_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_o_set_rat
% 7.78/3.97 @ ^ [X4: $o] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2699_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_rat @ top_top_set_rat @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_nat_set_rat
% 7.78/3.97 @ ^ [X4: nat] : ( minus_minus_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2700_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2701_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2702_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_int @ top_top_set_int @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( minus_minus_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2703_INT__extend__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( minus_minus_set_nat @ top_top_set_nat @ B5 ) ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2704_INT__extend__simps_I4_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = A4 ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2705_INT__extend__simps_I4_J,axiom,
% 7.78/3.97 ! [C3: set_Pr4329608150637261639at_nat,A4: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = A4 ) )
% 7.78/3.97 & ( ( C3 != bot_bo228742789529271731at_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_3160451284896210088et_nat
% 7.78/3.97 @ ^ [X4: produc3843707927480180839at_nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2706_INT__extend__simps_I4_J,axiom,
% 7.78/3.97 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = A4 ) )
% 7.78/3.97 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_15824709712370754et_nat
% 7.78/3.97 @ ^ [X4: product_prod_nat_nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2707_INT__extend__simps_I4_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = A4 ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [X4: $o] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2708_INT__extend__simps_I4_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = A4 ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( minus_minus_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_nat_set_nat
% 7.78/3.97 @ ^ [X4: nat] : ( minus_minus_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2709_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: set_Pr4329608150637261639at_nat] : ( order_1878278401035043452at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2710_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: int] : ( order_4471489696718655927on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2711_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: set_Pr1261947904930325089at_nat] : ( order_5942792088423767318at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2712_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: product_unit] : ( order_888282469287196226t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2713_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: produc3843707927480180839at_nat] : ( order_2711500226769404828at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2714_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: product_prod_nat_nat] : ( order_7480980593162297270at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2715_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: $o] : ( order_6238756238976269133r_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2716_linear__order__on__singleton,axiom,
% 7.78/3.97 ! [X2: nat] : ( order_4473980167227706203on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2717_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: set_Pr4329608150637261639at_nat] : ( total_5117575981256876747at_nat @ ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ X2 @ X2 ) @ bot_bo4948859079157340979at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2718_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: int] : ( total_on_int @ ( insert_int @ X2 @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2719_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: set_Pr1261947904930325089at_nat] : ( total_7212417256332265445at_nat @ ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X2 @ X2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2720_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: product_unit] : ( total_5665700600833547665t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X2 @ X2 ) @ bot_bo1654022762305692595t_unit ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2721_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: produc3843707927480180839at_nat] : ( total_1513685709984341995at_nat @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X2 @ X2 ) @ bot_bo7193250159860175667at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2722_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: product_prod_nat_nat] : ( total_3592101749530773125at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X2 @ X2 ) @ bot_bo5327735625951526323at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2723_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: $o] : ( total_on_o @ ( insert_o @ X2 @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X2 @ X2 ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2724_total__on__singleton,axiom,
% 7.78/3.97 ! [X2: nat] : ( total_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2725_relation__of__def,axiom,
% 7.78/3.97 ( order_8308734813930759573at_nat
% 7.78/3.97 = ( ^ [P4: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o,A6: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( collec7872792499061297490at_nat
% 7.78/3.97 @ ( produc9020218426428501292_nat_o
% 7.78/3.97 @ ^ [A5: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A5 @ B4 )
% 7.78/3.97 @ ( produc6258361011560675592at_nat @ A6
% 7.78/3.97 @ ^ [Uu: set_Pr4329608150637261639at_nat] : A6 ) )
% 7.78/3.97 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2726_relation__of__def,axiom,
% 7.78/3.97 ( order_8809246210994205103at_nat
% 7.78/3.97 = ( ^ [P4: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o,A6: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( collec6321179662152712658at_nat
% 7.78/3.97 @ ( produc410239310623530412_nat_o
% 7.78/3.97 @ ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ B4 )
% 7.78/3.97 @ ( produc7726050920695093128at_nat @ A6
% 7.78/3.97 @ ^ [Uu: set_Pr1261947904930325089at_nat] : A6 ) )
% 7.78/3.97 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2727_relation__of__def,axiom,
% 7.78/3.97 ( order_1962693441708344834of_nat
% 7.78/3.97 = ( ^ [P4: nat > nat > $o,A6: set_nat] :
% 7.78/3.97 ( collec3392354462482085612at_nat
% 7.78/3.97 @ ( produc6081775807080527818_nat_o
% 7.78/3.97 @ ^ [A5: nat,B4: nat] :
% 7.78/3.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 )
% 7.78/3.97 @ ( produc457027306803732586at_nat @ A6
% 7.78/3.97 @ ^ [Uu: nat] : A6 ) )
% 7.78/3.97 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2728_relation__of__def,axiom,
% 7.78/3.97 ( order_1960202971199294558of_int
% 7.78/3.97 = ( ^ [P4: int > int > $o,A6: set_int] :
% 7.78/3.97 ( collec213857154873943460nt_int
% 7.78/3.97 @ ( produc4947309494688390418_int_o
% 7.78/3.97 @ ^ [A5: int,B4: int] :
% 7.78/3.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 )
% 7.78/3.97 @ ( produc1453890548195736866nt_int @ A6
% 7.78/3.97 @ ^ [Uu: int] : A6 ) )
% 7.78/3.97 & ( P4 @ A5 @ B4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2729_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: nat,A4: set_nat,B: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( produc5506539147108004339t_unit @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 = ( insert6804906068341198690t_unit @ ( produc3434450474625521892t_unit @ A @ B )
% 7.78/3.97 @ ( sup_su4209953369189666580t_unit
% 7.78/3.97 @ ( produc5506539147108004339t_unit @ A4
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 @ ( produc5506539147108004339t_unit @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2730_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: nat,A4: set_nat,B: $o,B5: set_o] :
% 7.78/3.97 ( ( product_Sigma_nat_o @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 = ( insert2233377226759017069_nat_o @ ( product_Pair_nat_o @ A @ B )
% 7.78/3.97 @ ( sup_su503371503184139039_nat_o
% 7.78/3.97 @ ( product_Sigma_nat_o @ A4
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 @ ( product_Sigma_nat_o @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2731_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: product_unit,A4: set_Product_unit,B: nat,B5: set_nat] :
% 7.78/3.97 ( ( produc6875377002296012693it_nat @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_nat @ B @ B5 ) )
% 7.78/3.97 = ( insert6879346373837673660it_nat @ ( produc4803288329813530246it_nat @ A @ B )
% 7.78/3.97 @ ( sup_su1639320892072265582it_nat
% 7.78/3.97 @ ( produc6875377002296012693it_nat @ A4
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_nat @ B @ B5 ) )
% 7.78/3.97 @ ( produc6875377002296012693it_nat @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2732_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: product_unit,A4: set_Product_unit,B: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( produc6121607364029222536t_unit @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 = ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ A @ B )
% 7.78/3.97 @ ( sup_su6481247232241170203t_unit
% 7.78/3.97 @ ( produc6121607364029222536t_unit @ A4
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 @ ( produc6121607364029222536t_unit @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2733_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: product_unit,A4: set_Product_unit,B: $o,B5: set_o] :
% 7.78/3.97 ( ( produc4996980317674386579unit_o @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 = ( insert3586912282507785154unit_o @ ( produc8487917018914037602unit_o @ A @ B )
% 7.78/3.97 @ ( sup_su2851927382625014182unit_o
% 7.78/3.97 @ ( produc4996980317674386579unit_o @ A4
% 7.78/3.97 @ ^ [Uu: product_unit] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 @ ( produc4996980317674386579unit_o @ ( insert_Product_unit @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: product_unit] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2734_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: $o,A4: set_o,B: nat,B5: set_nat] :
% 7.78/3.97 ( ( product_Sigma_o_nat @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 7.78/3.97 = ( insert7948214739558299847_o_nat @ ( product_Pair_o_nat @ A @ B )
% 7.78/3.97 @ ( sup_su8679140417860611193_o_nat
% 7.78/3.97 @ ( product_Sigma_o_nat @ A4
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_nat @ B @ B5 ) )
% 7.78/3.97 @ ( product_Sigma_o_nat @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2735_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: $o,A4: set_o,B: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( produc411009820408249917t_unit @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 = ( insert9112848208840649964t_unit @ ( produc3901946521647900940t_unit @ A @ B )
% 7.78/3.97 @ ( sup_su4058753791541417424t_unit
% 7.78/3.97 @ ( produc411009820408249917t_unit @ A4
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_Product_unit @ B @ B5 ) )
% 7.78/3.97 @ ( produc411009820408249917t_unit @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2736_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: $o,A4: set_o,B: $o,B5: set_o] :
% 7.78/3.97 ( ( product_Sigma_o_o @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 = ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B )
% 7.78/3.97 @ ( sup_su5769328420594410459od_o_o
% 7.78/3.97 @ ( product_Sigma_o_o @ A4
% 7.78/3.97 @ ^ [Uu: $o] : ( insert_o @ B @ B5 ) )
% 7.78/3.97 @ ( product_Sigma_o_o @ ( insert_o @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: $o] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2737_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: nat,A4: set_nat,B: num,B5: set_num] :
% 7.78/3.97 ( ( produc6237731129814287028at_num @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_num @ B @ B5 ) )
% 7.78/3.97 = ( insert8920054152555992091at_num @ ( product_Pair_nat_num @ A @ B )
% 7.78/3.97 @ ( sup_su2042722026077122175at_num
% 7.78/3.97 @ ( produc6237731129814287028at_num @ A4
% 7.78/3.97 @ ^ [Uu: nat] : ( insert_num @ B @ B5 ) )
% 7.78/3.97 @ ( produc6237731129814287028at_num @ ( insert_nat @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: nat] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2738_insert__Times__insert,axiom,
% 7.78/3.97 ! [A: int,A4: set_int,B: int,B5: set_int] :
% 7.78/3.97 ( ( produc1453890548195736866nt_int @ ( insert_int @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 7.78/3.97 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B )
% 7.78/3.97 @ ( sup_su6024340866399070445nt_int
% 7.78/3.97 @ ( produc1453890548195736866nt_int @ A4
% 7.78/3.97 @ ^ [Uu: int] : ( insert_int @ B @ B5 ) )
% 7.78/3.97 @ ( produc1453890548195736866nt_int @ ( insert_int @ A @ A4 )
% 7.78/3.97 @ ^ [Uu: int] : B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2739_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_char,B5: product_unit > set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_5325685772115642575t_char
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_5325685772115642575t_char
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2740_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_char,B5: $o > set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_o_set_char
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_o_set_char
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_o_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2741_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_char,B5: nat > set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_nat_set_char
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_nat_set_char
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_char @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ A4 @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2742_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_rat,B5: product_unit > set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_4665621433434589782et_rat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_4665621433434589782et_rat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2743_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_rat,B5: $o > set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_o_set_rat
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_o_set_rat
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2744_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_rat,B5: nat > set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_nat_set_rat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_nat_set_rat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_rat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ A4 @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2745_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_int,B5: product_unit > set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2746_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_int,B5: $o > set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2747_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_int,B5: nat > set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_int @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ A4 @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2748_INT__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2749_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_5325685772115642575t_char
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_5325685772115642575t_char
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_5325685772115642575t_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2750_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_o_set_char
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_o_set_char
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_o_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2751_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_char,B5: set_char] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_nat_set_char
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_char ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7965528767983648192t_char
% 7.78/3.97 @ ( image_nat_set_char
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_char @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_char @ ( comple7965528767983648192t_char @ ( image_nat_set_char @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2752_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_4665621433434589782et_rat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_4665621433434589782et_rat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_4665621433434589782et_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2753_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_o_set_rat
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_o_set_rat
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_o_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2754_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_rat,B5: set_rat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_nat_set_rat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_rat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple4298007329820168263et_rat
% 7.78/3.97 @ ( image_nat_set_rat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_rat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ ( comple4298007329820168263et_rat @ ( image_nat_set_rat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2755_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_3995998972318789802et_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2756_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_o_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2757_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_int,B5: set_int] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_int ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3628384868704368283et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_set_int @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2758_INT__simps_I1_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = top_top_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2759_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2760_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2761_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2762_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2763_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2764_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2765_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2766_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2767_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2768_cSUP__UNION,axiom,
% 7.78/3.97 ! [A4: set_nat,B5: nat > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ! [X: nat] :
% 7.78/3.97 ( ( member_nat @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2769_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_int_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2770_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2771_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_int,B5: int > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ! [X: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_int_set_int
% 7.78/3.97 @ ^ [X4: int] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_int_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2772_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2773_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2774_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,B5: product_unit > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ! [X: product_unit] :
% 7.78/3.97 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_3995998972318789802et_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [X4: product_unit] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2775_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_o_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2776_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_Product_unit,F: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2777_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_o,B5: $o > set_o,F: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ! [X: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_o ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_o_set_int
% 7.78/3.97 @ ^ [X4: $o] : ( image_o_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [X4: $o] : ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2778_cINF__UNION,axiom,
% 7.78/3.97 ! [A4: set_nat,B5: nat > set_int,F: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ! [X: nat] :
% 7.78/3.97 ( ( member_nat @ X @ A4 )
% 7.78/3.97 => ( ( B5 @ X )
% 7.78/3.97 != bot_bot_set_int ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( comple3221217463730067765et_int
% 7.78/3.97 @ ( image_nat_set_int
% 7.78/3.97 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.97 @ A4 ) ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( comple3221217463730067765et_int @ ( image_nat_set_int @ B5 @ A4 ) ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( B5 @ X4 ) ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2779_Ex__inj__on__UNION__Sigma,axiom,
% 7.78/3.97 ! [A4: nat > set_nat,I3: set_nat] :
% 7.78/3.97 ? [F5: nat > product_prod_nat_nat] :
% 7.78/3.97 ( ( inj_on5538052773655684606at_nat @ F5 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.97 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) @ ( produc457027306803732586at_nat @ I3 @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2780_prod__set__simps_I1_J,axiom,
% 7.78/3.97 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( basic_1274512288150691911at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.97 = ( insert2290795007606087959at_nat @ X2 @ bot_bo1534825418459847827at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2781_prod__set__simps_I1_J,axiom,
% 7.78/3.97 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( basic_3661821009137050567at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.97 = ( insert9200635055090092081at_nat @ X2 @ bot_bo3083307316010499117at_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2782_prod__set__simps_I1_J,axiom,
% 7.78/3.97 ! [X2: int,Y3: int] :
% 7.78/3.97 ( ( basic_fsts_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.97 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2783_prod__set__simps_I1_J,axiom,
% 7.78/3.97 ! [X2: nat,Y3: num] :
% 7.78/3.97 ( ( basic_fsts_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.97 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2784_prod__set__simps_I1_J,axiom,
% 7.78/3.97 ! [X2: nat,Y3: nat] :
% 7.78/3.97 ( ( basic_fsts_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.97 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2785_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: int > $o,F: int > nat,G: int > nat,S5: set_int] :
% 7.78/3.97 ( ( image_int_nat
% 7.78/3.97 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_sup_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ S5 @ ( collect_int @ P2 ) ) )
% 7.78/3.97 @ ( image_int_nat @ G
% 7.78/3.97 @ ( inf_inf_set_int @ S5
% 7.78/3.97 @ ( collect_int
% 7.78/3.97 @ ^ [X4: int] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2786_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: int > $o,F: int > int,G: int > int,S5: set_int] :
% 7.78/3.97 ( ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( if_int @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_sup_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ S5 @ ( collect_int @ P2 ) ) )
% 7.78/3.97 @ ( image_int_int @ G
% 7.78/3.97 @ ( inf_inf_set_int @ S5
% 7.78/3.97 @ ( collect_int
% 7.78/3.97 @ ^ [X4: int] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2787_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: nat > $o,F: nat > rat,G: nat > rat,S5: set_nat] :
% 7.78/3.97 ( ( image_nat_rat
% 7.78/3.97 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_sup_set_rat @ ( image_nat_rat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_nat_rat @ G
% 7.78/3.97 @ ( inf_inf_set_nat @ S5
% 7.78/3.97 @ ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2788_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: nat > $o,F: nat > nat,G: nat > nat,S5: set_nat] :
% 7.78/3.97 ( ( image_nat_nat
% 7.78/3.97 @ ^ [X4: nat] : ( if_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_nat_nat @ G
% 7.78/3.97 @ ( inf_inf_set_nat @ S5
% 7.78/3.97 @ ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2789_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: nat > $o,F: nat > int,G: nat > int,S5: set_nat] :
% 7.78/3.97 ( ( image_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( if_int @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_sup_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_nat_int @ G
% 7.78/3.97 @ ( inf_inf_set_nat @ S5
% 7.78/3.97 @ ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2790_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: nat > $o,F: nat > produc859450856879609959at_nat,G: nat > produc859450856879609959at_nat,S5: set_nat] :
% 7.78/3.97 ( ( image_3276603626957510736at_nat
% 7.78/3.97 @ ^ [X4: nat] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( image_3276603626957510736at_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_3276603626957510736at_nat @ G
% 7.78/3.97 @ ( inf_inf_set_nat @ S5
% 7.78/3.97 @ ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2791_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: product_prod_int_int > $o,F: product_prod_int_int > produc859450856879609959at_nat,G: product_prod_int_int > produc859450856879609959at_nat,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.97 ( ( image_8858061497167895027at_nat
% 7.78/3.97 @ ^ [X4: product_prod_int_int] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( image_8858061497167895027at_nat @ F @ ( inf_in2269163501485487111nt_int @ S5 @ ( collec213857154873943460nt_int @ P2 ) ) )
% 7.78/3.97 @ ( image_8858061497167895027at_nat @ G
% 7.78/3.97 @ ( inf_in2269163501485487111nt_int @ S5
% 7.78/3.97 @ ( collec213857154873943460nt_int
% 7.78/3.97 @ ^ [X4: product_prod_int_int] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2792_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: product_prod_nat_nat > $o,F: product_prod_nat_nat > produc859450856879609959at_nat,G: product_prod_nat_nat > produc859450856879609959at_nat,S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( image_1119892238107900587at_nat
% 7.78/3.97 @ ^ [X4: product_prod_nat_nat] : ( if_Pro4507677147265585453at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( image_1119892238107900587at_nat @ F @ ( inf_in2572325071724192079at_nat @ S5 @ ( collec3392354462482085612at_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_1119892238107900587at_nat @ G
% 7.78/3.97 @ ( inf_in2572325071724192079at_nat @ S5
% 7.78/3.97 @ ( collec3392354462482085612at_nat
% 7.78/3.97 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2793_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: nat > $o,F: nat > produc3843707927480180839at_nat,G: nat > produc3843707927480180839at_nat,S5: set_nat] :
% 7.78/3.97 ( ( image_2499013659892586576at_nat
% 7.78/3.97 @ ^ [X4: nat] : ( if_Pro3594990065127090477at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( image_2499013659892586576at_nat @ F @ ( inf_inf_set_nat @ S5 @ ( collect_nat @ P2 ) ) )
% 7.78/3.97 @ ( image_2499013659892586576at_nat @ G
% 7.78/3.97 @ ( inf_inf_set_nat @ S5
% 7.78/3.97 @ ( collect_nat
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2794_if__image__distrib,axiom,
% 7.78/3.97 ! [P2: product_prod_int_int > $o,F: product_prod_int_int > produc3843707927480180839at_nat,G: product_prod_int_int > produc3843707927480180839at_nat,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.97 ( ( image_6029125644611338739at_nat
% 7.78/3.97 @ ^ [X4: product_prod_int_int] : ( if_Pro3594990065127090477at_nat @ ( P2 @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ S5 )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( image_6029125644611338739at_nat @ F @ ( inf_in2269163501485487111nt_int @ S5 @ ( collec213857154873943460nt_int @ P2 ) ) )
% 7.78/3.97 @ ( image_6029125644611338739at_nat @ G
% 7.78/3.97 @ ( inf_in2269163501485487111nt_int @ S5
% 7.78/3.97 @ ( collec213857154873943460nt_int
% 7.78/3.97 @ ^ [X4: product_prod_int_int] :
% 7.78/3.97 ~ ( P2 @ X4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2795_UN__Un,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2796_UN__Un,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2797_UN__Un,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2798_UN__Un,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2799_UN__Un,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2800_UN__Un,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2801_bdd__below__image__inf,axiom,
% 7.78/3.97 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 7.78/3.97 ( ( condit1103211067700513672ow_rat
% 7.78/3.97 @ ( image_nat_rat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.97 & ( condit1103211067700513672ow_rat @ ( image_nat_rat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2802_bdd__below__image__inf,axiom,
% 7.78/3.97 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 7.78/3.97 ( ( condit1738341127787009408ow_nat
% 7.78/3.97 @ ( image_nat_nat
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 & ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2803_bdd__below__image__inf,axiom,
% 7.78/3.97 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 7.78/3.97 ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( inf_inf_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 & ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2804_bdd__below__image__inf,axiom,
% 7.78/3.97 ! [F: int > nat,G: int > nat,A4: set_int] :
% 7.78/3.97 ( ( condit1738341127787009408ow_nat
% 7.78/3.97 @ ( image_int_nat
% 7.78/3.97 @ ^ [X4: int] : ( inf_inf_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 & ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2805_bdd__below__image__inf,axiom,
% 7.78/3.97 ! [F: int > int,G: int > int,A4: set_int] :
% 7.78/3.97 ( ( condit1735850657277959132ow_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( inf_inf_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 & ( condit1735850657277959132ow_int @ ( image_int_int @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2806_bdd__above__image__sup,axiom,
% 7.78/3.97 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 7.78/3.97 ( ( condit1579696412822616692ve_rat
% 7.78/3.97 @ ( image_nat_rat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.97 & ( condit1579696412822616692ve_rat @ ( image_nat_rat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2807_bdd__above__image__sup,axiom,
% 7.78/3.97 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 7.78/3.97 ( ( condit2214826472909112428ve_nat
% 7.78/3.97 @ ( image_nat_nat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 & ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2808_bdd__above__image__sup,axiom,
% 7.78/3.97 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 7.78/3.97 ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 & ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2809_bdd__above__image__sup,axiom,
% 7.78/3.97 ! [F: int > nat,G: int > nat,A4: set_int] :
% 7.78/3.97 ( ( condit2214826472909112428ve_nat
% 7.78/3.97 @ ( image_int_nat
% 7.78/3.97 @ ^ [X4: int] : ( sup_sup_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 & ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2810_bdd__above__image__sup,axiom,
% 7.78/3.97 ! [F: int > int,G: int > int,A4: set_int] :
% 7.78/3.97 ( ( condit2212336002400062152ve_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [X4: int] : ( sup_sup_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ A4 ) )
% 7.78/3.97 = ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 & ( condit2212336002400062152ve_int @ ( image_int_int @ G @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2811_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_Product_unit,B5: product_unit > set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_7778121751606633509t_unit
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_7778121751606633509t_unit
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2812_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_o,B5: product_unit > set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_6930536745178679216_set_o
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_6930536745178679216_set_o
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2813_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_Product_unit,B5: $o > set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_663195431845683034t_unit
% 7.78/3.97 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_663195431845683034t_unit
% 7.78/3.97 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2814_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_o,B5: $o > set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_o_set_o
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_o_set_o
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2815_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_Product_unit,B5: nat > set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_4824033694279209942t_unit
% 7.78/3.97 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_4824033694279209942t_unit
% 7.78/3.97 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ A4 @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2816_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_o,B5: nat > set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_nat_set_o
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_nat_set_o
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_o @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ A4 @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2817_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2818_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2819_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_nat_set_nat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_nat_set_nat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2820_UN__simps_I3_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: set_Pr1261947904930325089at_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple5685304695842803022at_nat
% 7.78/3.97 @ ( image_3617315916088684441at_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo2099793752762293965at_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple5685304695842803022at_nat
% 7.78/3.97 @ ( image_3617315916088684441at_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su6327502436637775413at_nat @ A4 @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2821_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_Product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_7778121751606633509t_unit
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_7778121751606633509t_unit
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2822_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_o,B5: set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_6930536745178679216_set_o
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_6930536745178679216_set_o
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2823_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_Product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_663195431845683034t_unit
% 7.78/3.97 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_663195431845683034t_unit
% 7.78/3.97 @ ^ [X4: $o] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2824_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_o,B5: set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_o_set_o
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_o_set_o
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_o_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2825_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_Product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_4824033694279209942t_unit
% 7.78/3.97 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple3349607820504768346t_unit
% 7.78/3.97 @ ( image_4824033694279209942t_unit
% 7.78/3.97 @ ^ [X4: nat] : ( sup_su793286257634532545t_unit @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2826_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_o,B5: set_o] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_nat_set_o
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_o ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple90263536869209701_set_o
% 7.78/3.97 @ ( image_nat_set_o
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_o @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2827_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2828_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_o )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2829_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_nat_set_nat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bot_set_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_nat_set_nat
% 7.78/3.97 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2830_UN__simps_I2_J,axiom,
% 7.78/3.97 ! [C3: set_Product_unit,A4: product_unit > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple5685304695842803022at_nat
% 7.78/3.97 @ ( image_3617315916088684441at_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = bot_bo2099793752762293965at_nat ) )
% 7.78/3.97 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( comple5685304695842803022at_nat
% 7.78/3.97 @ ( image_3617315916088684441at_nat
% 7.78/3.97 @ ^ [X4: product_unit] : ( sup_su6327502436637775413at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.97 @ C3 ) )
% 7.78/3.97 = ( sup_su6327502436637775413at_nat @ ( comple5685304695842803022at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2831_UN__insert,axiom,
% 7.78/3.97 ! [B5: nat > set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2832_UN__insert,axiom,
% 7.78/3.97 ! [B5: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2833_UN__insert,axiom,
% 7.78/3.97 ! [B5: $o > set_nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2834_UN__insert,axiom,
% 7.78/3.97 ! [B5: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( B5 @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2835_UN__insert,axiom,
% 7.78/3.97 ! [B5: nat > set_Pr8693737435421807431at_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2836_UN__insert,axiom,
% 7.78/3.97 ! [B5: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2837_UN__insert,axiom,
% 7.78/3.97 ! [B5: $o > set_Pr8693737435421807431at_nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2838_UN__insert,axiom,
% 7.78/3.97 ! [B5: product_prod_nat_nat > set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( B5 @ A ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2839_UN__insert,axiom,
% 7.78/3.97 ! [B5: nat > set_Pr4329608150637261639at_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( B5 @ A ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2840_UN__insert,axiom,
% 7.78/3.97 ! [B5: product_unit > set_Pr4329608150637261639at_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( B5 @ A ) @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2841_inj__apsnd,axiom,
% 7.78/3.97 ! [F: code_integer > code_integer] :
% 7.78/3.97 ( ( inj_on20428373856169009nteger @ ( produc6499014454317279255nteger @ F ) @ top_to2363841527343591755nteger )
% 7.78/3.97 = ( inj_on1158064722259180589nteger @ F @ top_to4645266643341252675nteger ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2842_INT__insert,axiom,
% 7.78/3.97 ! [B5: nat > set_Pr1261947904930325089at_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2843_INT__insert,axiom,
% 7.78/3.97 ! [B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2844_INT__insert,axiom,
% 7.78/3.97 ! [B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2845_INT__insert,axiom,
% 7.78/3.97 ! [B5: product_unit > set_Pr1261947904930325089at_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2846_INT__insert,axiom,
% 7.78/3.97 ! [B5: $o > set_Pr1261947904930325089at_nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( B5 @ A ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2847_INT__insert,axiom,
% 7.78/3.97 ! [B5: nat > set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2848_INT__insert,axiom,
% 7.78/3.97 ! [B5: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2849_INT__insert,axiom,
% 7.78/3.97 ! [B5: produc3843707927480180839at_nat > set_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2850_INT__insert,axiom,
% 7.78/3.97 ! [B5: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2851_INT__insert,axiom,
% 7.78/3.97 ! [B5: $o > set_nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( B5 @ A ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2852_inj__on__apsnd,axiom,
% 7.78/3.97 ! [F: code_integer > code_integer,A4: set_Code_integer] :
% 7.78/3.97 ( ( inj_on20428373856169009nteger @ ( produc6499014454317279255nteger @ F )
% 7.78/3.97 @ ( produc5882431272649516420nteger @ top_to4645266643341252675nteger
% 7.78/3.97 @ ^ [Uu: code_integer] : A4 ) )
% 7.78/3.97 = ( inj_on1158064722259180589nteger @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2853_inj__on__insert,axiom,
% 7.78/3.97 ! [F: int > nat,A: int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ ( insert_int @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.97 & ~ ( member_nat @ ( F @ A ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2854_inj__on__insert,axiom,
% 7.78/3.97 ! [F: int > int,A: int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ ( insert_int @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.97 & ~ ( member_int @ ( F @ A ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2855_inj__on__insert,axiom,
% 7.78/3.97 ! [F: product_unit > $o,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( inj_on8854722734121536060unit_o @ F @ ( insert_Product_unit @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on8854722734121536060unit_o @ F @ A4 )
% 7.78/3.97 & ~ ( member_o @ ( F @ A ) @ ( image_Product_unit_o @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2856_inj__on__insert,axiom,
% 7.78/3.97 ! [F: product_unit > nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( inj_on8430439091780834860it_nat @ F @ ( insert_Product_unit @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on8430439091780834860it_nat @ F @ A4 )
% 7.78/3.97 & ~ ( member_nat @ ( F @ A ) @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2857_inj__on__insert,axiom,
% 7.78/3.97 ! [F: product_unit > int,A: product_unit,A4: set_Product_unit] :
% 7.78/3.97 ( ( inj_on8427948621271784584it_int @ F @ ( insert_Product_unit @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on8427948621271784584it_int @ F @ A4 )
% 7.78/3.97 & ~ ( member_int @ ( F @ A ) @ ( image_873079544045703924it_int @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2858_inj__on__insert,axiom,
% 7.78/3.97 ! [F: $o > $o,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ ( insert_o @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_o_o @ F @ A4 )
% 7.78/3.97 & ~ ( member_o @ ( F @ A ) @ ( image_o_o @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2859_inj__on__insert,axiom,
% 7.78/3.97 ! [F: $o > nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_nat @ F @ ( insert_o @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_o_nat @ F @ A4 )
% 7.78/3.97 & ~ ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2860_inj__on__insert,axiom,
% 7.78/3.97 ! [F: $o > int,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_int @ F @ ( insert_o @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_o_int @ F @ A4 )
% 7.78/3.97 & ~ ( member_int @ ( F @ A ) @ ( image_o_int @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2861_inj__on__insert,axiom,
% 7.78/3.97 ! [F: nat > rat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ ( insert_nat @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 & ~ ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2862_inj__on__insert,axiom,
% 7.78/3.97 ! [F: nat > $o,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_o @ F @ ( insert_nat @ A @ A4 ) )
% 7.78/3.97 = ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.97 & ~ ( member_o @ ( F @ A ) @ ( image_nat_o @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2863_inj__on__Un__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 => ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.97 = ( image_nat_rat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2864_inj__on__Un__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 => ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.97 = ( image_nat_nat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2865_inj__on__Un__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 => ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.97 = ( image_nat_int @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2866_inj__on__Un__image__eq__iff,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 => ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.97 = ( image_int_nat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2867_inj__on__Un__image__eq__iff,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 => ( ( ( image_int_int @ F @ A4 )
% 7.78/3.97 = ( image_int_int @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2868_Sigma__Un__distrib1,axiom,
% 7.78/3.97 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ ( sup_sup_set_nat @ I3 @ J3 ) @ C3 )
% 7.78/3.97 = ( sup_su6327502436637775413at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2869_Sigma__Un__distrib1,axiom,
% 7.78/3.97 ! [I3: set_Pr1261947904930325089at_nat,J3: set_Pr1261947904930325089at_nat,C3: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( produc2761391749766926216at_nat @ ( sup_su6327502436637775413at_nat @ I3 @ J3 ) @ C3 )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( produc2761391749766926216at_nat @ I3 @ C3 ) @ ( produc2761391749766926216at_nat @ J3 @ C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2870_Sigma__Un__distrib1,axiom,
% 7.78/3.97 ! [I3: set_se7855581050983116737at_nat,J3: set_se7855581050983116737at_nat,C3: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ I3 @ J3 ) @ C3 )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I3 @ C3 ) @ ( produc7726050920695093128at_nat @ J3 @ C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2871_Sigma__Int__distrib1,axiom,
% 7.78/3.97 ! [I3: set_nat,J3: set_nat,C3: nat > set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ I3 @ J3 ) @ C3 )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( produc457027306803732586at_nat @ I3 @ C3 ) @ ( produc457027306803732586at_nat @ J3 @ C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2872_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,G: nat > rat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_nat_rat @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_rat )
% 7.78/3.97 => ( inj_on_nat_rat
% 7.78/3.97 @ ^ [X4: nat] : ( if_rat @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2873_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,G: nat > int,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_nat_int @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_int )
% 7.78/3.97 => ( inj_on_nat_int
% 7.78/3.97 @ ^ [X4: nat] : ( if_int @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2874_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,G: int > int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_int_int @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_int )
% 7.78/3.97 => ( inj_on_int_int
% 7.78/3.97 @ ^ [X4: int] : ( if_int @ ( member_int @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2875_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: $o > product_unit,A4: set_o,G: $o > product_unit,B5: set_o] :
% 7.78/3.97 ( ( inj_on4268752236855399398t_unit @ F @ A4 )
% 7.78/3.97 => ( ( inj_on4268752236855399398t_unit @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_in4660618365625256667t_unit @ ( image_o_Product_unit @ F @ A4 ) @ ( image_o_Product_unit @ G @ B5 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( inj_on4268752236855399398t_unit
% 7.78/3.97 @ ^ [X4: $o] : ( if_Product_unit @ ( member_o @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2876_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: nat > product_unit,A4: set_nat,G: nat > product_unit,B5: set_nat] :
% 7.78/3.97 ( ( inj_on7061601236592826506t_unit @ F @ A4 )
% 7.78/3.97 => ( ( inj_on7061601236592826506t_unit @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_in4660618365625256667t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) @ ( image_8730104196221521654t_unit @ G @ B5 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( inj_on7061601236592826506t_unit
% 7.78/3.97 @ ^ [X4: nat] : ( if_Product_unit @ ( member_nat @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2877_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: int > product_unit,A4: set_int,G: int > product_unit,B5: set_int] :
% 7.78/3.97 ( ( inj_on4178023183795006766t_unit @ F @ A4 )
% 7.78/3.97 => ( ( inj_on4178023183795006766t_unit @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_in4660618365625256667t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( inj_on4178023183795006766t_unit
% 7.78/3.97 @ ^ [X4: int] : ( if_Product_unit @ ( member_int @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2878_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: $o > $o,A4: set_o,G: $o > $o,B5: set_o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_o_o @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_o @ ( image_o_o @ F @ A4 ) @ ( image_o_o @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_o )
% 7.78/3.97 => ( inj_on_o_o
% 7.78/3.97 @ ^ [X4: $o] :
% 7.78/3.97 ( ( ( member_o @ X4 @ A4 )
% 7.78/3.97 => ( F @ X4 ) )
% 7.78/3.97 & ( ~ ( member_o @ X4 @ A4 )
% 7.78/3.97 => ( G @ X4 ) ) )
% 7.78/3.97 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2879_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_nat_o @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_o @ ( image_nat_o @ F @ A4 ) @ ( image_nat_o @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_o )
% 7.78/3.97 => ( inj_on_nat_o
% 7.78/3.97 @ ^ [X4: nat] :
% 7.78/3.97 ( ( ( member_nat @ X4 @ A4 )
% 7.78/3.97 => ( F @ X4 ) )
% 7.78/3.97 & ( ~ ( member_nat @ X4 @ A4 )
% 7.78/3.97 => ( G @ X4 ) ) )
% 7.78/3.97 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2880_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: int > $o,A4: set_int,G: int > $o,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_o @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_int_o @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_o @ ( image_int_o @ F @ A4 ) @ ( image_int_o @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_o )
% 7.78/3.97 => ( inj_on_int_o
% 7.78/3.97 @ ^ [X4: int] :
% 7.78/3.97 ( ( ( member_int @ X4 @ A4 )
% 7.78/3.97 => ( F @ X4 ) )
% 7.78/3.97 & ( ~ ( member_int @ X4 @ A4 )
% 7.78/3.97 => ( G @ X4 ) ) )
% 7.78/3.97 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2881_inj__on__disjoint__Un,axiom,
% 7.78/3.97 ! [F: $o > nat,A4: set_o,G: $o > nat,B5: set_o] :
% 7.78/3.97 ( ( inj_on_o_nat @ F @ A4 )
% 7.78/3.97 => ( ( inj_on_o_nat @ G @ B5 )
% 7.78/3.97 => ( ( ( inf_inf_set_nat @ ( image_o_nat @ F @ A4 ) @ ( image_o_nat @ G @ B5 ) )
% 7.78/3.97 = bot_bot_set_nat )
% 7.78/3.97 => ( inj_on_o_nat
% 7.78/3.97 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ A4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.97 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2882_Sigma__Un__distrib2,axiom,
% 7.78/3.97 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ I3
% 7.78/3.97 @ ^ [I2: nat] : ( sup_sup_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 7.78/3.97 = ( sup_su6327502436637775413at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2883_Sigma__Un__distrib2,axiom,
% 7.78/3.97 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( produc2761391749766926216at_nat @ I3
% 7.78/3.97 @ ^ [I2: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( produc2761391749766926216at_nat @ I3 @ A4 ) @ ( produc2761391749766926216at_nat @ I3 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2884_Sigma__Un__distrib2,axiom,
% 7.78/3.97 ! [I3: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat,B5: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( produc7726050920695093128at_nat @ I3
% 7.78/3.97 @ ^ [I2: set_Pr1261947904930325089at_nat] : ( sup_su3642409539654194069at_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( produc7726050920695093128at_nat @ I3 @ A4 ) @ ( produc7726050920695093128at_nat @ I3 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2885_Times__Un__distrib1,axiom,
% 7.78/3.97 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ ( sup_sup_set_nat @ A4 @ B5 )
% 7.78/3.97 @ ^ [Uu: nat] : C3 )
% 7.78/3.97 = ( sup_su6327502436637775413at_nat
% 7.78/3.97 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.97 @ ^ [Uu: nat] : C3 )
% 7.78/3.97 @ ( produc457027306803732586at_nat @ B5
% 7.78/3.97 @ ^ [Uu: nat] : C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2886_Times__Un__distrib1,axiom,
% 7.78/3.97 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( produc2761391749766926216at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 )
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : C3 )
% 7.78/3.97 = ( sup_su718114333110466843at_nat
% 7.78/3.97 @ ( produc2761391749766926216at_nat @ A4
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : C3 )
% 7.78/3.97 @ ( produc2761391749766926216at_nat @ B5
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2887_Times__Un__distrib1,axiom,
% 7.78/3.97 ! [A4: set_se7855581050983116737at_nat,B5: set_se7855581050983116737at_nat,C3: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( ( produc7726050920695093128at_nat @ ( sup_su3642409539654194069at_nat @ A4 @ B5 )
% 7.78/3.97 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat
% 7.78/3.97 @ ( produc7726050920695093128at_nat @ A4
% 7.78/3.97 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 )
% 7.78/3.97 @ ( produc7726050920695093128at_nat @ B5
% 7.78/3.97 @ ^ [Uu: set_Pr1261947904930325089at_nat] : C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2888_Times__Int__Times,axiom,
% 7.78/3.97 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( inf_in4302113700860409141at_nat
% 7.78/3.97 @ ( produc2761391749766926216at_nat @ A4
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : B5 )
% 7.78/3.97 @ ( produc2761391749766926216at_nat @ C3
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : D ) )
% 7.78/3.97 = ( produc2761391749766926216at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ C3 )
% 7.78/3.97 @ ^ [Uu: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ B5 @ D ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2889_Times__Int__Times,axiom,
% 7.78/3.97 ! [A4: set_nat,B5: set_nat,C3: set_nat,D: set_nat] :
% 7.78/3.97 ( ( inf_in2572325071724192079at_nat
% 7.78/3.97 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.97 @ ^ [Uu: nat] : B5 )
% 7.78/3.97 @ ( produc457027306803732586at_nat @ C3
% 7.78/3.97 @ ^ [Uu: nat] : D ) )
% 7.78/3.97 = ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ A4 @ C3 )
% 7.78/3.97 @ ^ [Uu: nat] : ( inf_inf_set_nat @ B5 @ D ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2890_Sigma__Int__distrib2,axiom,
% 7.78/3.97 ! [I3: set_nat,A4: nat > set_nat,B5: nat > set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ I3
% 7.78/3.97 @ ^ [I2: nat] : ( inf_inf_set_nat @ ( A4 @ I2 ) @ ( B5 @ I2 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( produc457027306803732586at_nat @ I3 @ A4 ) @ ( produc457027306803732586at_nat @ I3 @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2891_Times__Int__distrib1,axiom,
% 7.78/3.97 ! [A4: set_nat,B5: set_nat,C3: set_nat] :
% 7.78/3.97 ( ( produc457027306803732586at_nat @ ( inf_inf_set_nat @ A4 @ B5 )
% 7.78/3.97 @ ^ [Uu: nat] : C3 )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat
% 7.78/3.97 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.97 @ ^ [Uu: nat] : C3 )
% 7.78/3.97 @ ( produc457027306803732586at_nat @ B5
% 7.78/3.97 @ ^ [Uu: nat] : C3 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2892_inj__on__Un,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 & ( inj_on_nat_rat @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_rat @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_rat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_rat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2893_inj__on__Un,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.97 & ( inj_on_nat_int @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_int @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_int ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2894_inj__on__Un,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.97 & ( inj_on_int_int @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_int @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_int ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2895_inj__on__Un,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.97 & ( inj_on_nat_nat @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_nat @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2896_inj__on__Un,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.97 & ( inj_on_int_nat @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_nat @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2897_inj__on__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( inj_on1041401102088758999t_unit @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on1041401102088758999t_unit @ F @ A4 )
% 7.78/3.97 & ( inj_on1041401102088758999t_unit @ F @ B5 )
% 7.78/3.97 & ( ( inf_in4660618365625256667t_unit @ ( image_8487516615895632747t_unit @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_8487516615895632747t_unit @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2898_inj__on__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > $o,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( inj_on991952103320416098_nat_o @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on991952103320416098_nat_o @ F @ A4 )
% 7.78/3.97 & ( inj_on991952103320416098_nat_o @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_o @ ( image_3275415580317762038_nat_o @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_3275415580317762038_nat_o @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_o ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2899_inj__on__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( inj_on490725545064285830at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on490725545064285830at_nat @ F @ A4 )
% 7.78/3.97 & ( inj_on490725545064285830at_nat @ F @ B5 )
% 7.78/3.97 & ( ( inf_inf_set_nat @ ( image_6160980552072806642at_nat @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_6160980552072806642at_nat @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bot_set_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2900_inj__on__Un,axiom,
% 7.78/3.97 ! [F: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( inj_on3108384905993948887t_unit @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on3108384905993948887t_unit @ F @ A4 )
% 7.78/3.97 & ( inj_on3108384905993948887t_unit @ F @ B5 )
% 7.78/3.97 & ( ( inf_in4660618365625256667t_unit @ ( image_7082456443403096939t_unit @ F @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) @ ( image_7082456443403096939t_unit @ F @ ( minus_3314409938677909166at_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2901_inj__on__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > product_prod_nat_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( inj_on229527429751349963at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( ( inj_on229527429751349963at_nat @ F @ A4 )
% 7.78/3.97 & ( inj_on229527429751349963at_nat @ F @ B5 )
% 7.78/3.97 & ( ( inf_in2572325071724192079at_nat @ ( image_6706873702294942047at_nat @ F @ ( minus_8321449233255521966at_nat @ A4 @ B5 ) ) @ ( image_6706873702294942047at_nat @ F @ ( minus_8321449233255521966at_nat @ B5 @ A4 ) ) )
% 7.78/3.97 = bot_bo2099793752762293965at_nat ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2902_inj__on__image,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ ( comple3221217463730067765et_int @ A4 ) )
% 7.78/3.97 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2903_inj__on__image,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ ( comple3221217463730067765et_int @ A4 ) )
% 7.78/3.97 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2904_inj__on__image,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 7.78/3.97 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2905_inj__on__image,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 7.78/3.97 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2906_inj__on__image,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 7.78/3.97 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2907_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,B5: set_int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2908_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2909_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,B5: set_int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2910_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2911_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,B5: set_o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2912_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2913_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2914_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,B5: set_o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2915_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2916_cSUP__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2917_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,B5: set_int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2918_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2919_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,B5: set_int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2920_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2921_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,B5: set_o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2922_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ B5 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2923_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2924_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,B5: set_o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( sup_sup_set_o @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2925_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,B5: set_nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2926_cINF__union,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,B5: set_Product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2927_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2928_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2929_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2930_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.97 => ( ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2931_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.97 => ( ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2932_inj__on__image__Int,axiom,
% 7.78/3.97 ! [F: product_prod_nat_nat > product_prod_nat_nat,C3: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( inj_on8969904277767023793at_nat @ F @ C3 )
% 7.78/3.97 => ( ( ord_le3146513528884898305at_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_le3146513528884898305at_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( image_5168914502847457605at_nat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ ( image_5168914502847457605at_nat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2933_image__Int,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.97 => ( ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2934_image__Int,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.97 => ( ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2935_image__Int,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.97 => ( ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2936_image__Int,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.97 => ( ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2937_image__Int,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.97 => ( ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2938_image__Int,axiom,
% 7.78/3.97 ! [F: char > product_prod_nat_nat,A4: set_char,B5: set_char] :
% 7.78/3.97 ( ( inj_on1021528964648911549at_nat @ F @ top_top_set_char )
% 7.78/3.97 => ( ( image_8382823969816519465at_nat @ F @ ( inf_inf_set_char @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_8382823969816519465at_nat @ F @ A4 ) @ ( image_8382823969816519465at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2939_image__Int,axiom,
% 7.78/3.97 ! [F: rat > product_prod_nat_nat,A4: set_rat,B5: set_rat] :
% 7.78/3.97 ( ( inj_on8867882244352206326at_nat @ F @ top_top_set_rat )
% 7.78/3.97 => ( ( image_9175953278516507234at_nat @ F @ ( inf_inf_set_rat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_9175953278516507234at_nat @ F @ A4 ) @ ( image_9175953278516507234at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2940_image__Int,axiom,
% 7.78/3.97 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on5538052773655684606at_nat @ F @ top_top_set_nat )
% 7.78/3.97 => ( ( image_5846123807819985514at_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ ( image_5846123807819985514at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2941_image__Int,axiom,
% 7.78/3.97 ! [F: int > product_prod_nat_nat,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on8575894858119818402at_nat @ F @ top_top_set_int )
% 7.78/3.97 => ( ( image_8883965892284119310at_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_8883965892284119310at_nat @ F @ A4 ) @ ( image_8883965892284119310at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2942_image__Int,axiom,
% 7.78/3.97 ! [F: list_nat > product_prod_nat_nat,A4: set_list_nat,B5: set_list_nat] :
% 7.78/3.97 ( ( inj_on7574789179980466158at_nat @ F @ top_top_set_list_nat )
% 7.78/3.97 => ( ( image_2795870212791037530at_nat @ F @ ( inf_inf_set_list_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( image_2795870212791037530at_nat @ F @ A4 ) @ ( image_2795870212791037530at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2943_inj__on__image__Pow,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2944_inj__on__image__Pow,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.97 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2945_inj__on__image__Pow,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.97 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ ( pow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2946_inj__on__image__Pow,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.97 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ ( pow_int @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2947_inj__on__image__Pow,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.97 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ ( pow_int @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2948_inj__on__image__Fpow,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 => ( inj_on1096178645466186887et_rat @ ( image_nat_rat @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2949_inj__on__image__Fpow,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.97 => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2950_inj__on__image__Fpow,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.97 => ( inj_on426556184350386907et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2951_inj__on__image__Fpow,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.97 => ( inj_on1389844818000382683et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2952_inj__on__image__Fpow,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.97 => ( inj_on6435365835345961783et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2953_inj__on__imageI2,axiom,
% 7.78/3.97 ! [F3: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_o @ ( comp_o_o_nat @ F3 @ F ) @ A4 )
% 7.78/3.97 => ( inj_on_nat_o @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2954_inj__on__imageI2,axiom,
% 7.78/3.97 ! [F3: nat > num,F: int > nat,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_num @ ( comp_nat_num_int @ F3 @ F ) @ A4 )
% 7.78/3.97 => ( inj_on_int_nat @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2955_inj__on__imageI2,axiom,
% 7.78/3.97 ! [F3: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 )
% 7.78/3.97 => ( inj_on_nat_nat @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2956_inj__on__imageI2,axiom,
% 7.78/3.97 ! [F3: int > nat,F: int > int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ ( comp_int_nat_int @ F3 @ F ) @ A4 )
% 7.78/3.97 => ( inj_on_int_int @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2957_inj__on__imageI2,axiom,
% 7.78/3.97 ! [F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,A4: set_Code_integer] :
% 7.78/3.97 ( ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F3 @ F ) @ A4 )
% 7.78/3.97 => ( inj_on108595395805848489nteger @ F @ A4 ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2958_SUP__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_6654316230217496229at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2959_SUP__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_3876558564303283877at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2960_SUP__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ A4 ) ) @ ( comple2748534634209756852at_nat @ ( image_7260680879217540773at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2961_SUP__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ A4 ) ) @ ( comple4364388969068068532at_nat @ ( image_7364710425340685989at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2962_SUP__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2963_SUP__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2964_SUP__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8487516615895632747t_unit @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2965_SUP__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_7082456443403096939t_unit @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2966_INF__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2967_INF__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2968_INF__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2969_INF__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2970_INF__union,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > product_unit,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8487516615895632747t_unit @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2971_INF__union,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > product_unit,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_7082456443403096939t_unit @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2972_image__Un,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( image_nat_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_sup_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2973_image__Un,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( image_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2974_image__Un,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( image_nat_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_sup_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2975_image__Un,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( image_int_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2976_image__Un,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( image_int_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_sup_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2977_image__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > produc859450856879609959at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( image_6321802852832981957at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( image_6321802852832981957at_nat @ F @ A4 ) @ ( image_6321802852832981957at_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2978_image__Un,axiom,
% 7.78/3.97 ! [F: produc859450856879609959at_nat > produc3843707927480180839at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( image_7637461350386011077at_nat @ F @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( image_7637461350386011077at_nat @ F @ A4 ) @ ( image_7637461350386011077at_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2979_image__Un,axiom,
% 7.78/3.97 ! [F: produc3843707927480180839at_nat > produc859450856879609959at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( image_5653576389946358725at_nat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( image_5653576389946358725at_nat @ F @ A4 ) @ ( image_5653576389946358725at_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2980_image__Un,axiom,
% 7.78/3.97 ! [F: produc3843707927480180839at_nat > produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( image_960689587819713477at_nat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( image_960689587819713477at_nat @ F @ A4 ) @ ( image_960689587819713477at_nat @ F @ B5 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2981_INT__Un,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_1384942819424619199at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2982_INT__Un,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ A4 ) ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2983_INT__Un,axiom,
% 7.78/3.97 ! [M: produc859450856879609959at_nat > set_nat,A4: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ ( sup_su718114333110466843at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_2819269535336293544et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2984_INT__Un,axiom,
% 7.78/3.97 ! [M: produc3843707927480180839at_nat > set_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ M @ B5 ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2985_inj__on__convol__ident,axiom,
% 7.78/3.97 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X5: set_se5479201105039950375at_nat] :
% 7.78/3.97 ( inj_on1468925692805905105at_nat
% 7.78/3.97 @ ^ [X4: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ X4 @ ( F @ X4 ) )
% 7.78/3.97 @ X5 ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2986_inj__on__convol__ident,axiom,
% 7.78/3.97 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X5: set_se7855581050983116737at_nat] :
% 7.78/3.97 ( inj_on699426629415580343at_nat
% 7.78/3.97 @ ^ [X4: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ X4 @ ( F @ X4 ) )
% 7.78/3.97 @ X5 ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2987_inj__on__convol__ident,axiom,
% 7.78/3.97 ! [F: nat > num,X5: set_nat] :
% 7.78/3.97 ( inj_on6246296710604522312at_num
% 7.78/3.97 @ ^ [X4: nat] : ( product_Pair_nat_num @ X4 @ ( F @ X4 ) )
% 7.78/3.97 @ X5 ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2988_inj__on__convol__ident,axiom,
% 7.78/3.97 ! [F: nat > nat,X5: set_nat] :
% 7.78/3.97 ( inj_on5538052773655684606at_nat
% 7.78/3.97 @ ^ [X4: nat] : ( product_Pair_nat_nat @ X4 @ ( F @ X4 ) )
% 7.78/3.97 @ X5 ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2989_inj__on__convol__ident,axiom,
% 7.78/3.97 ! [F: int > int,X5: set_int] :
% 7.78/3.97 ( inj_on5397397550511676250nt_int
% 7.78/3.97 @ ^ [X4: int] : ( product_Pair_int_int @ X4 @ ( F @ X4 ) )
% 7.78/3.97 @ X5 ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2990_total__onI,axiom,
% 7.78/3.97 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
% 7.78/3.97 ( ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 7.78/3.97 ( ( member8757157785044589968at_nat @ X @ A4 )
% 7.78/3.97 => ( ( member8757157785044589968at_nat @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
% 7.78/3.97 | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_1513685709984341995at_nat @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2991_total__onI,axiom,
% 7.78/3.97 ! [A4: set_o,R: set_Product_prod_o_o] :
% 7.78/3.97 ( ! [X: $o,Y: $o] :
% 7.78/3.97 ( ( member_o @ X @ A4 )
% 7.78/3.97 => ( ( member_o @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 7.78/3.97 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_on_o @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2992_total__onI,axiom,
% 7.78/3.97 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat] :
% 7.78/3.97 ( ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( member6273874620674182256at_nat @ X @ A4 )
% 7.78/3.97 => ( ( member6273874620674182256at_nat @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ R )
% 7.78/3.97 | ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_5117575981256876747at_nat @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2993_total__onI,axiom,
% 7.78/3.97 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( member2643936169264416010at_nat @ X @ A4 )
% 7.78/3.97 => ( ( member2643936169264416010at_nat @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
% 7.78/3.97 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_7212417256332265445at_nat @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2994_total__onI,axiom,
% 7.78/3.97 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ! [X: nat,Y: nat] :
% 7.78/3.97 ( ( member_nat @ X @ A4 )
% 7.78/3.97 => ( ( member_nat @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 7.78/3.97 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_on_nat @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2995_total__onI,axiom,
% 7.78/3.97 ! [A4: set_int,R: set_Pr958786334691620121nt_int] :
% 7.78/3.97 ( ! [X: int,Y: int] :
% 7.78/3.97 ( ( member_int @ X @ A4 )
% 7.78/3.97 => ( ( member_int @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 7.78/3.97 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_on_int @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2996_total__onI,axiom,
% 7.78/3.97 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 7.78/3.97 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.97 => ( ( member8440522571783428010at_nat @ Y @ A4 )
% 7.78/3.97 => ( ( X != Y )
% 7.78/3.97 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R )
% 7.78/3.97 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y @ X ) @ R ) ) ) ) )
% 7.78/3.97 => ( total_3592101749530773125at_nat @ A4 @ R ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2997_total__on__def,axiom,
% 7.78/3.97 ( total_5117575981256876747at_nat
% 7.78/3.97 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 7.78/3.97 ! [X4: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 7.78/3.97 => ! [Y5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 7.78/3.97 => ( ( X4 != Y5 )
% 7.78/3.97 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R5 )
% 7.78/3.97 | ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2998_total__on__def,axiom,
% 7.78/3.97 ( total_7212417256332265445at_nat
% 7.78/3.97 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ! [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 7.78/3.97 => ! [Y5: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 7.78/3.97 => ( ( X4 != Y5 )
% 7.78/3.97 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R5 )
% 7.78/3.97 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_2999_total__on__def,axiom,
% 7.78/3.97 ( total_on_nat
% 7.78/3.97 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ! [X4: nat] :
% 7.78/3.97 ( ( member_nat @ X4 @ A6 )
% 7.78/3.97 => ! [Y5: nat] :
% 7.78/3.97 ( ( member_nat @ Y5 @ A6 )
% 7.78/3.97 => ( ( X4 != Y5 )
% 7.78/3.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R5 )
% 7.78/3.97 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3000_total__on__def,axiom,
% 7.78/3.97 ( total_on_int
% 7.78/3.97 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 7.78/3.97 ! [X4: int] :
% 7.78/3.97 ( ( member_int @ X4 @ A6 )
% 7.78/3.97 => ! [Y5: int] :
% 7.78/3.97 ( ( member_int @ Y5 @ A6 )
% 7.78/3.97 => ( ( X4 != Y5 )
% 7.78/3.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R5 )
% 7.78/3.97 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3001_total__on__def,axiom,
% 7.78/3.97 ( total_3592101749530773125at_nat
% 7.78/3.97 = ( ^ [A6: set_Pr1261947904930325089at_nat,R5: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ! [X4: product_prod_nat_nat] :
% 7.78/3.97 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 7.78/3.97 => ! [Y5: product_prod_nat_nat] :
% 7.78/3.97 ( ( member8440522571783428010at_nat @ Y5 @ A6 )
% 7.78/3.97 => ( ( X4 != Y5 )
% 7.78/3.97 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R5 )
% 7.78/3.97 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y5 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3002_SUP__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3003_SUP__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3004_SUP__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > set_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3005_SUP__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > product_unit] :
% 7.78/3.97 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3006_INF__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3007_INF__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > set_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3008_INF__UNIV__bool__expand,axiom,
% 7.78/3.97 ! [A4: $o > product_unit] :
% 7.78/3.97 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3009_fun_Oinj__map,axiom,
% 7.78/3.97 ! [F: $o > $o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ top_top_set_o )
% 7.78/3.97 => ( inj_on_nat_o_nat_o @ ( comp_o_o_nat @ F ) @ top_top_set_nat_o ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3010_fun_Oinj__map,axiom,
% 7.78/3.97 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.97 ( ( inj_on3998011822705705585nteger @ F @ top_to3804862627464599871nteger )
% 7.78/3.97 => ( inj_on5500977043710295017nteger @ ( comp_C8797469213163452608nteger @ F ) @ top_to3639204395728341691nteger ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3011_fun_Oinj__map,axiom,
% 7.78/3.97 ! [F: nat > num] :
% 7.78/3.97 ( ( inj_on_nat_num @ F @ top_top_set_nat )
% 7.78/3.97 => ( inj_on5377432224680912883nt_num @ ( comp_nat_num_int @ F ) @ top_top_set_int_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3012_fun_Oinj__map,axiom,
% 7.78/3.97 ! [F: nat > nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.97 => ( inj_on2461717442902640625at_nat @ ( comp_nat_nat_nat @ F ) @ top_top_set_nat_nat ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3013_fun_Oinj__map,axiom,
% 7.78/3.97 ! [F: int > nat] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.97 => ( inj_on856898432580761861nt_nat @ ( comp_int_nat_int @ F ) @ top_top_set_int_int ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3014_Un__eq__UN,axiom,
% 7.78/3.97 ( sup_su718114333110466843at_nat
% 7.78/3.97 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( comple2748534634209756852at_nat
% 7.78/3.97 @ ( image_8493167801588156084at_nat
% 7.78/3.97 @ ^ [B4: $o] : ( if_set1508868558775481357at_nat @ B4 @ A6 @ B6 )
% 7.78/3.97 @ top_top_set_o ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3015_Un__eq__UN,axiom,
% 7.78/3.97 ( sup_su5525570899277871387at_nat
% 7.78/3.97 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( comple4364388969068068532at_nat
% 7.78/3.97 @ ( image_2496312346330513076at_nat
% 7.78/3.97 @ ^ [B4: $o] : ( if_set3208018901896979469at_nat @ B4 @ A6 @ B6 )
% 7.78/3.97 @ top_top_set_o ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3016_Un__eq__UN,axiom,
% 7.78/3.97 ( sup_sup_set_nat
% 7.78/3.97 = ( ^ [A6: set_nat,B6: set_nat] :
% 7.78/3.97 ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_o_set_nat
% 7.78/3.97 @ ^ [B4: $o] : ( if_set_nat @ B4 @ A6 @ B6 )
% 7.78/3.97 @ top_top_set_o ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3017_UN__bool__eq,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.97 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_su718114333110466843at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3018_UN__bool__eq,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr4329608150637261639at_nat] :
% 7.78/3.97 ( ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_su5525570899277871387at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3019_UN__bool__eq,axiom,
% 7.78/3.97 ! [A4: $o > set_nat] :
% 7.78/3.97 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3020_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,G: int > nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_nat
% 7.78/3.97 @ ( image_int_nat
% 7.78/3.97 @ ^ [A5: int] : ( sup_sup_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3021_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_nat
% 7.78/3.97 @ ( image_nat_nat
% 7.78/3.97 @ ^ [A5: nat] : ( sup_sup_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3022_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,G: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [A5: int] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3023_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,G: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [A5: product_unit] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3024_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,G: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [A5: $o] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3025_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Sup_Sup_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [A5: nat] : ( sup_sup_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3026_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,G: product_unit > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple4687483117567863418t_unit
% 7.78/3.97 @ ( image_405062704495631173t_unit
% 7.78/3.97 @ ^ [A5: product_unit] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3027_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple4687483117567863418t_unit
% 7.78/3.97 @ ( image_o_Product_unit
% 7.78/3.97 @ ^ [A5: $o] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3028_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple4687483117567863418t_unit
% 7.78/3.97 @ ( image_8730104196221521654t_unit
% 7.78/3.97 @ ^ [A5: nat] : ( sup_sup_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3029_conditionally__complete__lattice__class_OSUP__sup__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,G: product_unit > set_nat] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( comple7399068483239264473et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [A5: product_unit] : ( sup_sup_set_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3030_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,G: int > nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_nat
% 7.78/3.97 @ ( image_int_nat
% 7.78/3.97 @ ^ [A5: int] : ( inf_inf_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3031_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_nat
% 7.78/3.97 @ ( image_nat_nat
% 7.78/3.97 @ ^ [A5: nat] : ( inf_inf_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3032_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,G: int > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_int_int
% 7.78/3.97 @ ^ [A5: int] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3033_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,G: product_unit > int] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_873079544045703924it_int
% 7.78/3.97 @ ^ [A5: product_unit] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3034_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,G: $o > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_o_int
% 7.78/3.97 @ ^ [A5: $o] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3035_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ G @ A4 ) ) )
% 7.78/3.97 = ( complete_Inf_Inf_int
% 7.78/3.97 @ ( image_nat_int
% 7.78/3.97 @ ^ [A5: nat] : ( inf_inf_int @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3036_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,G: product_unit > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit
% 7.78/3.97 @ ( image_405062704495631173t_unit
% 7.78/3.97 @ ^ [A5: product_unit] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3037_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,G: $o > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit
% 7.78/3.97 @ ( image_o_Product_unit
% 7.78/3.97 @ ^ [A5: $o] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3038_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,G: nat > product_unit] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ G @ A4 ) ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit
% 7.78/3.97 @ ( image_8730104196221521654t_unit
% 7.78/3.97 @ ^ [A5: nat] : ( inf_inf_Product_unit @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3039_cINF__inf__distrib,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,G: product_unit > set_nat] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) )
% 7.78/3.97 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ G @ A4 ) ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat
% 7.78/3.97 @ ( image_8173849991827986510et_nat
% 7.78/3.97 @ ^ [A5: product_unit] : ( inf_inf_set_nat @ ( F @ A5 ) @ ( G @ A5 ) )
% 7.78/3.97 @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3040_fsts_Ointros,axiom,
% 7.78/3.97 ! [P: produc7812382424243267045t_unit] : ( member_ref_a @ ( produc473321116828791851t_unit @ P ) @ ( basic_685971451221398055t_unit @ P ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3041_fsts_Osimps,axiom,
% 7.78/3.97 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 7.78/3.97 ( ( member_ref_a @ A @ ( basic_685971451221398055t_unit @ P ) )
% 7.78/3.97 = ( A
% 7.78/3.97 = ( produc473321116828791851t_unit @ P ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3042_fsts_Ocases,axiom,
% 7.78/3.97 ! [A: ref_a,P: produc7812382424243267045t_unit] :
% 7.78/3.97 ( ( member_ref_a @ A @ ( basic_685971451221398055t_unit @ P ) )
% 7.78/3.97 => ( A
% 7.78/3.97 = ( produc473321116828791851t_unit @ P ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3043_INT__bool__eq,axiom,
% 7.78/3.97 ! [A4: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.97 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( inf_in2572325071724192079at_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3044_INT__bool__eq,axiom,
% 7.78/3.97 ! [A4: $o > set_nat] :
% 7.78/3.97 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ top_top_set_o ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3045_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: nat > nat,A4: set_nat,A: nat] :
% 7.78/3.97 ( ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( member_nat @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3046_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: int > nat,A4: set_int,A: int] :
% 7.78/3.97 ( ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 = ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( member_int @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3047_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: $o > int,A4: set_o,A: $o] :
% 7.78/3.97 ( ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( member_o @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3048_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: nat > int,A4: set_nat,A: nat] :
% 7.78/3.97 ( ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( member_nat @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3049_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: int > int,A4: set_int,A: int] :
% 7.78/3.97 ( ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( member_int @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3050_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: $o > product_unit,A4: set_o,A: $o] :
% 7.78/3.97 ( ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( member_o @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3051_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: nat > product_unit,A4: set_nat,A: nat] :
% 7.78/3.97 ( ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( member_nat @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3052_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: int > product_unit,A4: set_int,A: int] :
% 7.78/3.97 ( ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( member_int @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3053_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: $o > set_nat,A4: set_o,A: $o] :
% 7.78/3.97 ( ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( member_o @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3054_cSUP__eq__cINF__D,axiom,
% 7.78/3.97 ! [F: nat > set_nat,A4: set_nat,A: nat] :
% 7.78/3.97 ( ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.97 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( member_nat @ A @ A4 )
% 7.78/3.97 => ( ( F @ A )
% 7.78/3.97 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3055_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,A: int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ ( insert_int @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_nat @ ( F @ A ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3056_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_nat @ ( F @ A ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3057_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,A: int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_int_int @ F @ ( insert_int @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3058_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3059_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,A: $o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_o_int @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3060_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Sup_Sup_int @ ( image_nat_int @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_int @ ( F @ A ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3061_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3062_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,A: $o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3063_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3064_cSUP__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3065_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > nat,A: int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ ( insert_int @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_nat @ ( F @ A ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3066_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > nat,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_nat @ ( F @ A ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3067_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_int,F: int > int,A: int] :
% 7.78/3.97 ( ( A4 != bot_bot_set_int )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_int_int @ F @ ( insert_int @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3068_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > int,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3069_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > int,A: $o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_o_int @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3070_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > int,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 => ( ( complete_Inf_Inf_int @ ( image_nat_int @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_int @ ( F @ A ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3071_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > product_unit,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3072_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_o,F: $o > product_unit,A: $o] :
% 7.78/3.97 ( ( A4 != bot_bot_set_o )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3073_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_nat,F: nat > product_unit,A: nat] :
% 7.78/3.97 ( ( A4 != bot_bot_set_nat )
% 7.78/3.97 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3074_cINF__insert,axiom,
% 7.78/3.97 ! [A4: set_Product_unit,F: product_unit > set_nat,A: product_unit] :
% 7.78/3.97 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.97 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) )
% 7.78/3.97 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.97 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3075_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > $o,B5: set_o,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ B5 )
% 7.78/3.97 => ( ( member_o @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.97 => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3076_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > nat,B5: set_o,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_nat @ F @ B5 )
% 7.78/3.97 => ( ( member_o @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.97 => ( ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3077_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > int,B5: set_o,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_int @ F @ B5 )
% 7.78/3.97 => ( ( member_o @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.97 => ( ( member_int @ ( F @ A ) @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3078_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: nat > rat,B5: set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ B5 )
% 7.78/3.97 => ( ( member_nat @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.97 => ( ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.97 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3079_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: nat > $o,B5: set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_o @ F @ B5 )
% 7.78/3.97 => ( ( member_nat @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.97 => ( ( member_o @ ( F @ A ) @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.97 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3080_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: nat > nat,B5: set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ B5 )
% 7.78/3.97 => ( ( member_nat @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.97 => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.97 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3081_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: nat > int,B5: set_nat,A: nat,A4: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ B5 )
% 7.78/3.97 => ( ( member_nat @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.97 => ( ( member_int @ ( F @ A ) @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.97 = ( member_nat @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3082_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: int > $o,B5: set_int,A: int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_o @ F @ B5 )
% 7.78/3.97 => ( ( member_int @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.97 => ( ( member_o @ ( F @ A ) @ ( image_int_o @ F @ A4 ) )
% 7.78/3.97 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3083_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: int > nat,B5: set_int,A: int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ B5 )
% 7.78/3.97 => ( ( member_int @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.97 => ( ( member_nat @ ( F @ A ) @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.97 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3084_inj__on__image__mem__iff,axiom,
% 7.78/3.97 ! [F: int > int,B5: set_int,A: int,A4: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ B5 )
% 7.78/3.97 => ( ( member_int @ A @ B5 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.97 => ( ( member_int @ ( F @ A ) @ ( image_int_int @ F @ A4 ) )
% 7.78/3.97 = ( member_int @ A @ A4 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3085_inj__on__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.97 = ( image_nat_rat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3086_inj__on__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_nat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.97 = ( image_nat_nat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3087_inj__on__image__eq__iff,axiom,
% 7.78/3.97 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on_nat_int @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.97 => ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.97 = ( image_nat_int @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3088_inj__on__image__eq__iff,axiom,
% 7.78/3.97 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.97 => ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.97 = ( image_int_nat @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3089_inj__on__image__eq__iff,axiom,
% 7.78/3.97 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.97 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ A4 @ C3 )
% 7.78/3.97 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.97 => ( ( ( image_int_int @ F @ A4 )
% 7.78/3.97 = ( image_int_int @ F @ B5 ) )
% 7.78/3.97 = ( A4 = B5 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3090_subset__image__inj,axiom,
% 7.78/3.97 ! [S5: set_rat,F: nat > rat,T3: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_rat @ S5 @ ( image_nat_rat @ F @ T3 ) )
% 7.78/3.97 = ( ? [U2: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 7.78/3.97 & ( inj_on_nat_rat @ F @ U2 )
% 7.78/3.97 & ( S5
% 7.78/3.97 = ( image_nat_rat @ F @ U2 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3091_subset__image__inj,axiom,
% 7.78/3.97 ! [S5: set_nat,F: nat > nat,T3: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_nat @ S5 @ ( image_nat_nat @ F @ T3 ) )
% 7.78/3.97 = ( ? [U2: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 7.78/3.97 & ( inj_on_nat_nat @ F @ U2 )
% 7.78/3.97 & ( S5
% 7.78/3.97 = ( image_nat_nat @ F @ U2 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3092_subset__image__inj,axiom,
% 7.78/3.97 ! [S5: set_int,F: nat > int,T3: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_int @ S5 @ ( image_nat_int @ F @ T3 ) )
% 7.78/3.97 = ( ? [U2: set_nat] :
% 7.78/3.97 ( ( ord_less_eq_set_nat @ U2 @ T3 )
% 7.78/3.97 & ( inj_on_nat_int @ F @ U2 )
% 7.78/3.97 & ( S5
% 7.78/3.97 = ( image_nat_int @ F @ U2 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3093_subset__image__inj,axiom,
% 7.78/3.97 ! [S5: set_nat,F: int > nat,T3: set_int] :
% 7.78/3.97 ( ( ord_less_eq_set_nat @ S5 @ ( image_int_nat @ F @ T3 ) )
% 7.78/3.97 = ( ? [U2: set_int] :
% 7.78/3.97 ( ( ord_less_eq_set_int @ U2 @ T3 )
% 7.78/3.97 & ( inj_on_int_nat @ F @ U2 )
% 7.78/3.97 & ( S5
% 7.78/3.97 = ( image_int_nat @ F @ U2 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3094_subset__image__inj,axiom,
% 7.78/3.97 ! [S5: set_int,F: int > int,T3: set_int] :
% 7.78/3.97 ( ( ord_less_eq_set_int @ S5 @ ( image_int_int @ F @ T3 ) )
% 7.78/3.97 = ( ? [U2: set_int] :
% 7.78/3.97 ( ( ord_less_eq_set_int @ U2 @ T3 )
% 7.78/3.97 & ( inj_on_int_int @ F @ U2 )
% 7.78/3.97 & ( S5
% 7.78/3.97 = ( image_int_int @ F @ U2 ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3095_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: product_unit > product_unit,A4: set_Product_unit,X2: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( inj_on8151373323710067377t_unit @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 7.78/3.97 = ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 7.78/3.97 ( ~ ( member_Product_unit @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_Product_unit @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_405062704495631173t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3096_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: $o > product_unit,A4: set_o,X2: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( inj_on4268752236855399398t_unit @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 7.78/3.97 = ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: $o,A8: set_o] :
% 7.78/3.97 ( ~ ( member_o @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_o @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_o_Product_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3097_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: nat > rat,A4: set_nat,X2: rat,B5: set_rat] :
% 7.78/3.97 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_rat @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_rat @ X2 @ B5 )
% 7.78/3.97 = ( image_nat_rat @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: nat,A8: set_nat] :
% 7.78/3.97 ( ~ ( member_nat @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_nat @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_nat_rat @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3098_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: nat > product_unit,A4: set_nat,X2: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( inj_on7061601236592826506t_unit @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 7.78/3.97 = ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: nat,A8: set_nat] :
% 7.78/3.97 ( ~ ( member_nat @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_nat @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_8730104196221521654t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3099_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: int > product_unit,A4: set_int,X2: product_unit,B5: set_Product_unit] :
% 7.78/3.97 ( ( inj_on4178023183795006766t_unit @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_Product_unit @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_Product_unit @ X2 @ B5 )
% 7.78/3.97 = ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: int,A8: set_int] :
% 7.78/3.97 ( ~ ( member_int @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_int @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_5846526143423701914t_unit @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3100_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: product_unit > $o,A4: set_Product_unit,X2: $o,B5: set_o] :
% 7.78/3.97 ( ( inj_on8854722734121536060unit_o @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_o @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_o @ X2 @ B5 )
% 7.78/3.97 = ( image_Product_unit_o @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 7.78/3.97 ( ~ ( member_Product_unit @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_Product_unit @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_Product_unit_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3101_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: $o > $o,A4: set_o,X2: $o,B5: set_o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_o @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_o @ X2 @ B5 )
% 7.78/3.97 = ( image_o_o @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: $o,A8: set_o] :
% 7.78/3.97 ( ~ ( member_o @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_o @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_o_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3102_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: nat > $o,A4: set_nat,X2: $o,B5: set_o] :
% 7.78/3.97 ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_o @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_o @ X2 @ B5 )
% 7.78/3.97 = ( image_nat_o @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: nat,A8: set_nat] :
% 7.78/3.97 ( ~ ( member_nat @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_nat @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_nat_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3103_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: int > $o,A4: set_int,X2: $o,B5: set_o] :
% 7.78/3.97 ( ( inj_on_int_o @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_o @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_o @ X2 @ B5 )
% 7.78/3.97 = ( image_int_o @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: int,A8: set_int] :
% 7.78/3.97 ( ~ ( member_int @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_int @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_int_o @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3104_inj__img__insertE,axiom,
% 7.78/3.97 ! [F: product_unit > nat,A4: set_Product_unit,X2: nat,B5: set_nat] :
% 7.78/3.97 ( ( inj_on8430439091780834860it_nat @ F @ A4 )
% 7.78/3.97 => ( ~ ( member_nat @ X2 @ B5 )
% 7.78/3.97 => ( ( ( insert_nat @ X2 @ B5 )
% 7.78/3.97 = ( image_875570014554754200it_nat @ F @ A4 ) )
% 7.78/3.97 => ~ ! [X8: product_unit,A8: set_Product_unit] :
% 7.78/3.97 ( ~ ( member_Product_unit @ X8 @ A8 )
% 7.78/3.97 => ( ( A4
% 7.78/3.97 = ( insert_Product_unit @ X8 @ A8 ) )
% 7.78/3.97 => ( ( X2
% 7.78/3.97 = ( F @ X8 ) )
% 7.78/3.97 => ( B5
% 7.78/3.97 != ( image_875570014554754200it_nat @ F @ A8 ) ) ) ) ) ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3105_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > $o,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_o @ F @ top_top_set_o )
% 7.78/3.97 => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3106_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > nat,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_nat @ F @ top_top_set_o )
% 7.78/3.97 => ( ( member_nat @ ( F @ A ) @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3107_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: $o > int,A: $o,A4: set_o] :
% 7.78/3.97 ( ( inj_on_o_int @ F @ top_top_set_o )
% 7.78/3.97 => ( ( member_int @ ( F @ A ) @ ( image_o_int @ F @ A4 ) )
% 7.78/3.97 = ( member_o @ A @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3108_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: char > $o,A: char,A4: set_char] :
% 7.78/3.97 ( ( inj_on_char_o @ F @ top_top_set_char )
% 7.78/3.97 => ( ( member_o @ ( F @ A ) @ ( image_char_o @ F @ A4 ) )
% 7.78/3.97 = ( member_char @ A @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3109_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: char > nat,A: char,A4: set_char] :
% 7.78/3.97 ( ( inj_on_char_nat @ F @ top_top_set_char )
% 7.78/3.97 => ( ( member_nat @ ( F @ A ) @ ( image_char_nat @ F @ A4 ) )
% 7.78/3.97 = ( member_char @ A @ A4 ) ) ) ).
% 7.78/3.97
% 7.78/3.97 thf(fact_3110_inj__image__mem__iff,axiom,
% 7.78/3.97 ! [F: char > int,A: char,A4: set_char] :
% 7.78/3.97 ( ( inj_on_char_int @ F @ top_top_set_char )
% 7.78/3.97 => ( ( member_int @ ( F @ A ) @ ( image_char_int @ F @ A4 ) )
% 7.78/3.97 = ( member_char @ A @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3111_inj__image__mem__iff,axiom,
% 7.78/3.98 ! [F: rat > $o,A: rat,A4: set_rat] :
% 7.78/3.98 ( ( inj_on_rat_o @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_o @ ( F @ A ) @ ( image_rat_o @ F @ A4 ) )
% 7.78/3.98 = ( member_rat @ A @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3112_inj__image__mem__iff,axiom,
% 7.78/3.98 ! [F: rat > nat,A: rat,A4: set_rat] :
% 7.78/3.98 ( ( inj_on_rat_nat @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_nat @ ( F @ A ) @ ( image_rat_nat @ F @ A4 ) )
% 7.78/3.98 = ( member_rat @ A @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3113_inj__image__mem__iff,axiom,
% 7.78/3.98 ! [F: rat > int,A: rat,A4: set_rat] :
% 7.78/3.98 ( ( inj_on_rat_int @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_int @ ( F @ A ) @ ( image_rat_int @ F @ A4 ) )
% 7.78/3.98 = ( member_rat @ A @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3114_inj__image__mem__iff,axiom,
% 7.78/3.98 ! [F: nat > rat,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( member_rat @ ( F @ A ) @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 = ( member_nat @ A @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3115_inj__image__eq__iff,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ( image_nat_rat @ F @ A4 )
% 7.78/3.98 = ( image_nat_rat @ F @ B5 ) )
% 7.78/3.98 = ( A4 = B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3116_inj__image__eq__iff,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ( image_nat_nat @ F @ A4 )
% 7.78/3.98 = ( image_nat_nat @ F @ B5 ) )
% 7.78/3.98 = ( A4 = B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3117_inj__image__eq__iff,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ( image_nat_int @ F @ A4 )
% 7.78/3.98 = ( image_nat_int @ F @ B5 ) )
% 7.78/3.98 = ( A4 = B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3118_inj__image__eq__iff,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ( image_int_nat @ F @ A4 )
% 7.78/3.98 = ( image_int_nat @ F @ B5 ) )
% 7.78/3.98 = ( A4 = B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3119_inj__image__eq__iff,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ( image_int_int @ F @ A4 )
% 7.78/3.98 = ( image_int_int @ F @ B5 ) )
% 7.78/3.98 = ( A4 = B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3120_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: char > $o,B: $o] :
% 7.78/3.98 ( ( inj_on_char_o @ F @ top_top_set_char )
% 7.78/3.98 => ( ( member_o @ B @ ( image_char_o @ F @ top_top_set_char ) )
% 7.78/3.98 = ( ? [X4: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3121_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: char > nat,B: nat] :
% 7.78/3.98 ( ( inj_on_char_nat @ F @ top_top_set_char )
% 7.78/3.98 => ( ( member_nat @ B @ ( image_char_nat @ F @ top_top_set_char ) )
% 7.78/3.98 = ( ? [X4: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3122_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: char > int,B: int] :
% 7.78/3.98 ( ( inj_on_char_int @ F @ top_top_set_char )
% 7.78/3.98 => ( ( member_int @ B @ ( image_char_int @ F @ top_top_set_char ) )
% 7.78/3.98 = ( ? [X4: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: char] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3123_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: rat > $o,B: $o] :
% 7.78/3.98 ( ( inj_on_rat_o @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_o @ B @ ( image_rat_o @ F @ top_top_set_rat ) )
% 7.78/3.98 = ( ? [X4: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3124_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: rat > nat,B: nat] :
% 7.78/3.98 ( ( inj_on_rat_nat @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_nat @ B @ ( image_rat_nat @ F @ top_top_set_rat ) )
% 7.78/3.98 = ( ? [X4: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3125_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: rat > int,B: int] :
% 7.78/3.98 ( ( inj_on_rat_int @ F @ top_top_set_rat )
% 7.78/3.98 => ( ( member_int @ B @ ( image_rat_int @ F @ top_top_set_rat ) )
% 7.78/3.98 = ( ? [X4: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: rat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3126_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: nat > rat,B: rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( member_rat @ B @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 7.78/3.98 = ( ? [X4: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3127_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: nat > $o,B: $o] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
% 7.78/3.98 = ( ? [X4: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3128_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: nat > nat,B: nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 7.78/3.98 = ( ? [X4: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3129_range__ex1__eq,axiom,
% 7.78/3.98 ! [F: nat > int,B: int] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( member_int @ B @ ( image_nat_int @ F @ top_top_set_nat ) )
% 7.78/3.98 = ( ? [X4: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ X4 ) )
% 7.78/3.98 & ! [Y5: nat] :
% 7.78/3.98 ( ( B
% 7.78/3.98 = ( F @ Y5 ) )
% 7.78/3.98 => ( Y5 = X4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3130_comp__inj__on,axiom,
% 7.78/3.98 ! [F: nat > $o,A4: set_nat,G: $o > $o] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_o_o @ G @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3131_comp__inj__on,axiom,
% 7.78/3.98 ! [F: code_integer > code_integer > code_integer,A4: set_Code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.98 ( ( inj_on108595395805848489nteger @ F @ A4 )
% 7.78/3.98 => ( ( inj_on3998011822705705585nteger @ G @ ( image_2177946750938214461nteger @ F @ A4 ) )
% 7.78/3.98 => ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3132_comp__inj__on,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,G: nat > nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3133_comp__inj__on,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,G: nat > num] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_nat_num @ G @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3134_comp__inj__on,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,G: int > nat] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_int_nat @ G @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3135_inj__on__imageI,axiom,
% 7.78/3.98 ! [G: $o > $o,F: nat > $o,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 )
% 7.78/3.98 => ( inj_on_o_o @ G @ ( image_nat_o @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3136_inj__on__imageI,axiom,
% 7.78/3.98 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,A4: set_Code_integer] :
% 7.78/3.98 ( ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ A4 )
% 7.78/3.98 => ( inj_on3998011822705705585nteger @ G @ ( image_2177946750938214461nteger @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3137_inj__on__imageI,axiom,
% 7.78/3.98 ! [G: nat > nat,F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 )
% 7.78/3.98 => ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3138_inj__on__imageI,axiom,
% 7.78/3.98 ! [G: nat > num,F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_num @ ( comp_nat_num_int @ G @ F ) @ A4 )
% 7.78/3.98 => ( inj_on_nat_num @ G @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3139_inj__on__imageI,axiom,
% 7.78/3.98 ! [G: int > nat,F: int > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ ( comp_int_nat_int @ G @ F ) @ A4 )
% 7.78/3.98 => ( inj_on_int_nat @ G @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3140_comp__inj__on__iff,axiom,
% 7.78/3.98 ! [F: nat > $o,A4: set_nat,F3: $o > $o] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_o_o @ F3 @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 = ( inj_on_nat_o @ ( comp_o_o_nat @ F3 @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3141_comp__inj__on__iff,axiom,
% 7.78/3.98 ! [F: code_integer > code_integer > code_integer,A4: set_Code_integer,F3: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.98 ( ( inj_on108595395805848489nteger @ F @ A4 )
% 7.78/3.98 => ( ( inj_on3998011822705705585nteger @ F3 @ ( image_2177946750938214461nteger @ F @ A4 ) )
% 7.78/3.98 = ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F3 @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3142_comp__inj__on__iff,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,F3: nat > nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_nat_nat @ F3 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 = ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3143_comp__inj__on__iff,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,F3: nat > num] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_nat_num @ F3 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 = ( inj_on_int_num @ ( comp_nat_num_int @ F3 @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3144_comp__inj__on__iff,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,F3: int > nat] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F3 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 = ( inj_on_int_nat @ ( comp_int_nat_int @ F3 @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3145_inj__compose,axiom,
% 7.78/3.98 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer] :
% 7.78/3.98 ( ( inj_on3998011822705705585nteger @ F @ top_to3804862627464599871nteger )
% 7.78/3.98 => ( ( inj_on108595395805848489nteger @ G @ top_to4645266643341252675nteger )
% 7.78/3.98 => ( inj_on7031512951821619701nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ top_to4645266643341252675nteger ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3146_inj__compose,axiom,
% 7.78/3.98 ! [F: $o > $o,G: nat > $o] :
% 7.78/3.98 ( ( inj_on_o_o @ F @ top_top_set_o )
% 7.78/3.98 => ( ( inj_on_nat_o @ G @ top_top_set_nat )
% 7.78/3.98 => ( inj_on_nat_o @ ( comp_o_o_nat @ F @ G ) @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3147_inj__compose,axiom,
% 7.78/3.98 ! [F: nat > nat,G: nat > nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 7.78/3.98 => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3148_inj__compose,axiom,
% 7.78/3.98 ! [F: nat > num,G: int > nat] :
% 7.78/3.98 ( ( inj_on_nat_num @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( inj_on_int_nat @ G @ top_top_set_int )
% 7.78/3.98 => ( inj_on_int_num @ ( comp_nat_num_int @ F @ G ) @ top_top_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3149_inj__compose,axiom,
% 7.78/3.98 ! [F: int > nat,G: int > int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( inj_on_int_int @ G @ top_top_set_int )
% 7.78/3.98 => ( inj_on_int_nat @ ( comp_int_nat_int @ F @ G ) @ top_top_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3150_inf__Sup,axiom,
% 7.78/3.98 ! [A: set_Pr1261947904930325089at_nat,B5: set_se7855581050983116737at_nat] :
% 7.78/3.98 ( ( inf_in2572325071724192079at_nat @ A @ ( comple5685304695842803022at_nat @ B5 ) )
% 7.78/3.98 = ( comple5685304695842803022at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3151_inf__Sup,axiom,
% 7.78/3.98 ! [A: set_nat,B5: set_set_nat] :
% 7.78/3.98 ( ( inf_inf_set_nat @ A @ ( comple7399068483239264473et_nat @ B5 ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3152_inf__Sup,axiom,
% 7.78/3.98 ! [A: product_unit,B5: set_Product_unit] :
% 7.78/3.98 ( ( inf_inf_Product_unit @ A @ ( comple4687483117567863418t_unit @ B5 ) )
% 7.78/3.98 = ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ ( inf_inf_Product_unit @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3153_sup__Inf,axiom,
% 7.78/3.98 ! [A: set_Pr8693737435421807431at_nat,B5: set_se6425085446898223655at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A @ ( comple6332534001959699150at_nat @ B5 ) )
% 7.78/3.98 = ( comple6332534001959699150at_nat @ ( image_1013614488123988933at_nat @ ( sup_su718114333110466843at_nat @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3154_sup__Inf,axiom,
% 7.78/3.98 ! [A: set_Pr4329608150637261639at_nat,B5: set_se5479201105039950375at_nat] :
% 7.78/3.98 ( ( sup_su5525570899277871387at_nat @ A @ ( comple6751905152567503566at_nat @ B5 ) )
% 7.78/3.98 = ( comple6751905152567503566at_nat @ ( image_4303274092540115909at_nat @ ( sup_su5525570899277871387at_nat @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3155_sup__Inf,axiom,
% 7.78/3.98 ! [A: set_nat,B5: set_set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A @ ( comple7806235888213564991et_nat @ B5 ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( sup_sup_set_nat @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3156_sup__Inf,axiom,
% 7.78/3.98 ! [A: product_unit,B5: set_Product_unit] :
% 7.78/3.98 ( ( sup_sup_Product_unit @ A @ ( comple2584293577114468500t_unit @ B5 ) )
% 7.78/3.98 = ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ ( sup_sup_Product_unit @ A ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3157_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,M: nat,F: $o > nat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3158_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M: nat,F: nat > nat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3159_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,M: nat,F: int > nat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3160_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,M: int,F: $o > int] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3161_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M: int,F: nat > int] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3162_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,M: int,F: int > int] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3163_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,M: rat,F: $o > rat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3164_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M: rat,F: nat > rat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3165_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,M: rat,F: int > rat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3166_bdd__below_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,M: code_integer,F: $o > code_integer] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_le3102999989581377725nteger @ M @ ( F @ X ) ) )
% 7.78/3.98 => ( condit4933233095834890765nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3167_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_o,M3: nat,F: $o > nat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3168_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M3: nat,F: nat > nat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3169_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_int,M3: nat,F: int > nat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3170_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_o,M3: int,F: $o > int] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3171_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M3: int,F: nat > int] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3172_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_int,M3: int,F: int > int] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3173_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_o,M3: rat,F: $o > rat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3174_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_nat,M3: rat,F: nat > rat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3175_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_int,M3: rat,F: int > rat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3176_bdd__belowI2,axiom,
% 7.78/3.98 ! [A4: set_o,M3: code_integer,F: $o > code_integer] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_le3102999989581377725nteger @ M3 @ ( F @ X ) ) )
% 7.78/3.98 => ( condit4933233095834890765nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3177_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > nat,M: nat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3178_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > nat,M: nat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3179_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > nat,M: nat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3180_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > int,M: int] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3181_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > int,M: int] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3182_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > int,M: int] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3183_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > rat,M: rat] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit1579696412822616692ve_rat @ ( image_o_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3184_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > rat,M: rat] :
% 7.78/3.98 ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3185_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > rat,M: rat] :
% 7.78/3.98 ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_rat @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit1579696412822616692ve_rat @ ( image_int_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3186_bdd__above_OI2,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > code_integer,M: code_integer] :
% 7.78/3.98 ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_le3102999989581377725nteger @ ( F @ X ) @ M ) )
% 7.78/3.98 => ( condit1118808407379112185nteger @ ( image_o_Code_integer @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3187_image__Int__subset,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3188_image__Int__subset,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3189_image__Int__subset,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,B5: set_nat] : ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( inf_inf_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3190_image__Int__subset,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,B5: set_int] : ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( inf_inf_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3191_image__Int__subset,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( inf_inf_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3192_image__Int__subset,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) @ ( inf_in2572325071724192079at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ ( image_5168914502847457605at_nat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3193_swap__inj__on,axiom,
% 7.78/3.98 ! [A4: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( inj_on3942866938762682161at_nat
% 7.78/3.98 @ ( produc5456455677105495163at_nat
% 7.78/3.98 @ ^ [I2: set_Pr4329608150637261639at_nat,J: set_Pr4329608150637261639at_nat] : ( produc9060074326276436823at_nat @ J @ I2 ) )
% 7.78/3.98 @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3194_swap__inj__on,axiom,
% 7.78/3.98 ! [A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( inj_on8430303779476321073at_nat
% 7.78/3.98 @ ( produc7548845685434208379at_nat
% 7.78/3.98 @ ^ [I2: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat] : ( produc2922128104949294807at_nat @ J @ I2 ) )
% 7.78/3.98 @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3195_swap__inj__on,axiom,
% 7.78/3.98 ! [A4: set_Pr3280342998896498603um_nat] :
% 7.78/3.98 ( inj_on2339680571444523825at_num
% 7.78/3.98 @ ( produc5219324331026901427at_num
% 7.78/3.98 @ ^ [I2: num,J: nat] : ( product_Pair_nat_num @ J @ I2 ) )
% 7.78/3.98 @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3196_swap__inj__on,axiom,
% 7.78/3.98 ! [A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( inj_on8969904277767023793at_nat
% 7.78/3.98 @ ( produc2626176000494625587at_nat
% 7.78/3.98 @ ^ [I2: nat,J: nat] : ( product_Pair_nat_nat @ J @ I2 ) )
% 7.78/3.98 @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3197_swap__inj__on,axiom,
% 7.78/3.98 ! [A4: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( inj_on6454360653267994289nt_int
% 7.78/3.98 @ ( produc4245557441103728435nt_int
% 7.78/3.98 @ ^ [I2: int,J: int] : ( product_Pair_int_int @ J @ I2 ) )
% 7.78/3.98 @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3198_SUP__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > product_unit] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3199_SUP__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > product_unit] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3200_SUP__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > product_unit] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3201_SUP__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3202_SUP__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3203_SUP__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3204_SUP__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > product_unit] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_Product_unit @ ( A4 @ K ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3205_SUP__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3206_SUP__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3207_SUP__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3208_Sup__inf,axiom,
% 7.78/3.98 ! [B5: set_se7855581050983116737at_nat,A: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( inf_in2572325071724192079at_nat @ ( comple5685304695842803022at_nat @ B5 ) @ A )
% 7.78/3.98 = ( comple5685304695842803022at_nat
% 7.78/3.98 @ ( image_3684629450409544005at_nat
% 7.78/3.98 @ ^ [B4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3209_Sup__inf,axiom,
% 7.78/3.98 ! [B5: set_set_nat,A: set_nat] :
% 7.78/3.98 ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ B5 ) @ A )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_7916887816326733075et_nat
% 7.78/3.98 @ ^ [B4: set_nat] : ( inf_inf_set_nat @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3210_Sup__inf,axiom,
% 7.78/3.98 ! [B5: set_Product_unit,A: product_unit] :
% 7.78/3.98 ( ( inf_inf_Product_unit @ ( comple4687483117567863418t_unit @ B5 ) @ A )
% 7.78/3.98 = ( comple4687483117567863418t_unit
% 7.78/3.98 @ ( image_405062704495631173t_unit
% 7.78/3.98 @ ^ [B4: product_unit] : ( inf_inf_Product_unit @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3211_Inf__sup,axiom,
% 7.78/3.98 ! [B5: set_se6425085446898223655at_nat,A: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ ( comple6332534001959699150at_nat @ B5 ) @ A )
% 7.78/3.98 = ( comple6332534001959699150at_nat
% 7.78/3.98 @ ( image_1013614488123988933at_nat
% 7.78/3.98 @ ^ [B4: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3212_Inf__sup,axiom,
% 7.78/3.98 ! [B5: set_se5479201105039950375at_nat,A: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( sup_su5525570899277871387at_nat @ ( comple6751905152567503566at_nat @ B5 ) @ A )
% 7.78/3.98 = ( comple6751905152567503566at_nat
% 7.78/3.98 @ ( image_4303274092540115909at_nat
% 7.78/3.98 @ ^ [B4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3213_Inf__sup,axiom,
% 7.78/3.98 ! [B5: set_set_nat,A: set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ ( comple7806235888213564991et_nat @ B5 ) @ A )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_7916887816326733075et_nat
% 7.78/3.98 @ ^ [B4: set_nat] : ( sup_sup_set_nat @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3214_Inf__sup,axiom,
% 7.78/3.98 ! [B5: set_Product_unit,A: product_unit] :
% 7.78/3.98 ( ( sup_sup_Product_unit @ ( comple2584293577114468500t_unit @ B5 ) @ A )
% 7.78/3.98 = ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_405062704495631173t_unit
% 7.78/3.98 @ ^ [B4: product_unit] : ( sup_sup_Product_unit @ B4 @ A )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3215_INF__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > product_unit] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3216_INF__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > product_unit] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3217_INF__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > product_unit] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3218_INF__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3219_INF__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3220_INF__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3221_INF__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > product_unit] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_Product_unit @ ( A4 @ K ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3222_INF__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3223_INF__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3224_INF__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3225_translation__subtract__Int,axiom,
% 7.78/3.98 ! [A: int,S2: set_int,T2: set_int] :
% 7.78/3.98 ( ( image_int_int
% 7.78/3.98 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.98 @ ( inf_inf_set_int @ S2 @ T2 ) )
% 7.78/3.98 = ( inf_inf_set_int
% 7.78/3.98 @ ( image_int_int
% 7.78/3.98 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.98 @ S2 )
% 7.78/3.98 @ ( image_int_int
% 7.78/3.98 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 7.78/3.98 @ T2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3226_translation__subtract__Int,axiom,
% 7.78/3.98 ! [A: rat,S2: set_rat,T2: set_rat] :
% 7.78/3.98 ( ( image_rat_rat
% 7.78/3.98 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.98 @ ( inf_inf_set_rat @ S2 @ T2 ) )
% 7.78/3.98 = ( inf_inf_set_rat
% 7.78/3.98 @ ( image_rat_rat
% 7.78/3.98 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.98 @ S2 )
% 7.78/3.98 @ ( image_rat_rat
% 7.78/3.98 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 7.78/3.98 @ T2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3227_translation__subtract__Int,axiom,
% 7.78/3.98 ! [A: code_integer,S2: set_Code_integer,T2: set_Code_integer] :
% 7.78/3.98 ( ( image_4470545334726330049nteger
% 7.78/3.98 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.98 @ ( inf_in1364745209274528805nteger @ S2 @ T2 ) )
% 7.78/3.98 = ( inf_in1364745209274528805nteger
% 7.78/3.98 @ ( image_4470545334726330049nteger
% 7.78/3.98 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.98 @ S2 )
% 7.78/3.98 @ ( image_4470545334726330049nteger
% 7.78/3.98 @ ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ X4 @ A )
% 7.78/3.98 @ T2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3228_UN__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3229_UN__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3230_UN__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3231_UN__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( A4 @ K ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3232_UN__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3233_UN__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3234_UN__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_525487068563185620at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_525487068563185620at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3235_UN__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( A4 @ K ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3236_UN__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( A4 @ K ) @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3237_UN__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( A4 @ K ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3238_INT__absorb,axiom,
% 7.78/3.98 ! [K: produc3843707927480180839at_nat,I3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member8757157785044589968at_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3239_INT__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3240_INT__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3241_INT__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3242_INT__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( A4 @ K ) @ ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_8938366415781434990at_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3243_INT__absorb,axiom,
% 7.78/3.98 ! [K: produc3843707927480180839at_nat,I3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.98 ( ( member8757157785044589968at_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3244_INT__absorb,axiom,
% 7.78/3.98 ! [K: product_prod_nat_nat,I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3245_INT__absorb,axiom,
% 7.78/3.98 ! [K: $o,I3: set_o,A4: $o > set_nat] :
% 7.78/3.98 ( ( member_o @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3246_INT__absorb,axiom,
% 7.78/3.98 ! [K: nat,I3: set_nat,A4: nat > set_nat] :
% 7.78/3.98 ( ( member_nat @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3247_INT__absorb,axiom,
% 7.78/3.98 ! [K: int,I3: set_int,A4: int > set_nat] :
% 7.78/3.98 ( ( member_int @ K @ I3 )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( A4 @ K ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_int_set_nat @ A4 @ I3 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3248_Int__Union2,axiom,
% 7.78/3.98 ! [B5: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( inf_in2572325071724192079at_nat @ ( comple5685304695842803022at_nat @ B5 ) @ A4 )
% 7.78/3.98 = ( comple5685304695842803022at_nat
% 7.78/3.98 @ ( image_3684629450409544005at_nat
% 7.78/3.98 @ ^ [C5: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ C5 @ A4 )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3249_Int__Union2,axiom,
% 7.78/3.98 ! [B5: set_set_nat,A4: set_nat] :
% 7.78/3.98 ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ B5 ) @ A4 )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_7916887816326733075et_nat
% 7.78/3.98 @ ^ [C5: set_nat] : ( inf_inf_set_nat @ C5 @ A4 )
% 7.78/3.98 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3250_Int__Union,axiom,
% 7.78/3.98 ! [A4: set_Pr1261947904930325089at_nat,B5: set_se7855581050983116737at_nat] :
% 7.78/3.98 ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple5685304695842803022at_nat @ B5 ) )
% 7.78/3.98 = ( comple5685304695842803022at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A4 ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3251_Int__Union,axiom,
% 7.78/3.98 ! [A4: set_nat,B5: set_set_nat] :
% 7.78/3.98 ( ( inf_inf_set_nat @ A4 @ ( comple7399068483239264473et_nat @ B5 ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A4 ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3252_Un__Inter,axiom,
% 7.78/3.98 ! [A4: set_Pr8693737435421807431at_nat,B5: set_se6425085446898223655at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple6332534001959699150at_nat @ B5 ) )
% 7.78/3.98 = ( comple6332534001959699150at_nat @ ( image_1013614488123988933at_nat @ ( sup_su718114333110466843at_nat @ A4 ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3253_Un__Inter,axiom,
% 7.78/3.98 ! [A4: set_Pr4329608150637261639at_nat,B5: set_se5479201105039950375at_nat] :
% 7.78/3.98 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple6751905152567503566at_nat @ B5 ) )
% 7.78/3.98 = ( comple6751905152567503566at_nat @ ( image_4303274092540115909at_nat @ ( sup_su5525570899277871387at_nat @ A4 ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3254_Un__Inter,axiom,
% 7.78/3.98 ! [A4: set_nat,B5: set_set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B5 ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( sup_sup_set_nat @ A4 ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3255_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_rat,A7: set_nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_rat )
% 7.78/3.98 => ( ( ? [F2: rat > nat] :
% 7.78/3.98 ( ( inj_on_rat_nat @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_nat @ ( image_rat_nat @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: nat > rat] :
% 7.78/3.98 ( ( image_nat_rat @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3256_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_int,A7: set_nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( ? [F2: int > nat] :
% 7.78/3.98 ( ( inj_on_int_nat @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_nat @ ( image_int_nat @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: nat > int] :
% 7.78/3.98 ( ( image_nat_int @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3257_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_int,A7: set_int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( ? [F2: int > int] :
% 7.78/3.98 ( ( inj_on_int_int @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_int @ ( image_int_int @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: int > int] :
% 7.78/3.98 ( ( image_int_int @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3258_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_nat,A7: set_rat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( ? [F2: nat > rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: rat > nat] :
% 7.78/3.98 ( ( image_rat_nat @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3259_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_nat,A7: set_nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( ? [F2: nat > nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: nat > nat] :
% 7.78/3.98 ( ( image_nat_nat @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3260_inj__on__iff__surj,axiom,
% 7.78/3.98 ! [A4: set_nat,A7: set_int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( ? [F2: nat > int] :
% 7.78/3.98 ( ( inj_on_nat_int @ F2 @ A4 )
% 7.78/3.98 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ A4 ) @ A7 ) ) )
% 7.78/3.98 = ( ? [G3: int > nat] :
% 7.78/3.98 ( ( image_int_nat @ G3 @ A7 )
% 7.78/3.98 = A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3261_Int__Inter__eq_I1_J,axiom,
% 7.78/3.98 ! [B8: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( B8 = bot_bo3083307316010499117at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ B8 ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( B8 != bot_bo3083307316010499117at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ B8 ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat @ ( image_3684629450409544005at_nat @ ( inf_in2572325071724192079at_nat @ A4 ) @ B8 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3262_Int__Inter__eq_I1_J,axiom,
% 7.78/3.98 ! [B8: set_set_nat,A4: set_nat] :
% 7.78/3.98 ( ( ( B8 = bot_bot_set_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B8 ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( B8 != bot_bot_set_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ B8 ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ ( inf_inf_set_nat @ A4 ) @ B8 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3263_Int__Inter__eq_I2_J,axiom,
% 7.78/3.98 ! [B8: set_se7855581050983116737at_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( B8 = bot_bo3083307316010499117at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ B8 ) @ A4 )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( B8 != bot_bo3083307316010499117at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ B8 ) @ A4 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_3684629450409544005at_nat
% 7.78/3.98 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B6 @ A4 )
% 7.78/3.98 @ B8 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3264_Int__Inter__eq_I2_J,axiom,
% 7.78/3.98 ! [B8: set_set_nat,A4: set_nat] :
% 7.78/3.98 ( ( ( B8 = bot_bot_set_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ B8 ) @ A4 )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( B8 != bot_bot_set_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ B8 ) @ A4 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_7916887816326733075et_nat
% 7.78/3.98 @ ^ [B6: set_nat] : ( inf_inf_set_nat @ B6 @ A4 )
% 7.78/3.98 @ B8 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3265_inj__image__subset__iff,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3266_inj__image__subset__iff,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3267_inj__image__subset__iff,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3268_inj__image__subset__iff,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) )
% 7.78/3.98 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3269_inj__image__subset__iff,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) )
% 7.78/3.98 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3270_inj__on__image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.98 => ( ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3271_inj__on__image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.98 => ( ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3272_inj__on__image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ B5 @ C3 )
% 7.78/3.98 => ( ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3273_inj__on__image__set__diff,axiom,
% 7.78/3.98 ! [F: int > nat,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.98 => ( ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3274_inj__on__image__set__diff,axiom,
% 7.78/3.98 ! [F: int > int,C3: set_int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ B5 @ C3 )
% 7.78/3.98 => ( ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3275_image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( image_nat_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_rat @ ( image_nat_rat @ F @ A4 ) @ ( image_nat_rat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3276_image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3277_image__set__diff,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3278_image__set__diff,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3279_image__set__diff,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 7.78/3.98 = ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3280_cINF__lower2,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o,X2: $o,U: nat] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3281_cINF__lower2,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,X2: nat,U: nat] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3282_cINF__lower2,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,X2: int,U: nat] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3283_cINF__lower2,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o,X2: $o,U: int] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3284_cINF__lower2,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,X2: nat,U: int] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3285_cINF__lower2,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,X2: int,U: int] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3286_cINF__lower2,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_o,X2: $o,U: product_unit] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3287_cINF__lower2,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat,X2: nat,U: product_unit] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3288_cINF__lower2,axiom,
% 7.78/3.98 ! [F: int > product_unit,A4: set_int,X2: int,U: product_unit] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3289_cINF__lower2,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A4: set_o,X2: $o,U: set_nat] :
% 7.78/3.98 ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( F @ X2 ) @ U )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ U ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3290_cINF__lower,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o,X2: $o] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3291_cINF__lower,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,X2: nat] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3292_cINF__lower,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,X2: int] :
% 7.78/3.98 ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3293_cINF__lower,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o,X2: $o] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3294_cINF__lower,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,X2: nat] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3295_cINF__lower,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,X2: int] :
% 7.78/3.98 ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3296_cINF__lower,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_o,X2: $o] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3297_cINF__lower,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat,X2: nat] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3298_cINF__lower,axiom,
% 7.78/3.98 ! [F: int > product_unit,A4: set_int,X2: int] :
% 7.78/3.98 ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3299_cINF__lower,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A4: set_o,X2: $o] :
% 7.78/3.98 ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) @ ( F @ X2 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3300_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o,X2: $o,U: nat] :
% 7.78/3.98 ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3301_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,X2: nat,U: nat] :
% 7.78/3.98 ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3302_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,X2: int,U: nat] :
% 7.78/3.98 ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3303_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o,X2: $o,U: int] :
% 7.78/3.98 ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3304_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,X2: nat,U: int] :
% 7.78/3.98 ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3305_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,X2: int,U: int] :
% 7.78/3.98 ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3306_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_o,X2: $o,U: product_unit] :
% 7.78/3.98 ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3307_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat,X2: nat,U: product_unit] :
% 7.78/3.98 ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3308_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: int > product_unit,A4: set_int,X2: int,U: product_unit] :
% 7.78/3.98 ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3309_cSUP__upper2,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A4: set_o,X2: $o,U: set_nat] :
% 7.78/3.98 ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ U @ ( F @ X2 ) )
% 7.78/3.98 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3310_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > nat] :
% 7.78/3.98 ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3311_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > nat] :
% 7.78/3.98 ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3312_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > nat] :
% 7.78/3.98 ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3313_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > int] :
% 7.78/3.98 ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3314_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > int] :
% 7.78/3.98 ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3315_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > int] :
% 7.78/3.98 ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X2 ) @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3316_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > product_unit] :
% 7.78/3.98 ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3317_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > product_unit] :
% 7.78/3.98 ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3318_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > product_unit] :
% 7.78/3.98 ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3319_cSUP__upper,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > set_nat] :
% 7.78/3.98 ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3320_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_nat,F: product_unit > set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3321_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_nat,F: $o > set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ bot_bot_set_o ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3322_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ bot_bot_set_nat ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3323_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_nat,F: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ bot_bo2099793752762293965at_nat ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3324_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr8693737435421807431at_nat,F: product_unit > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3325_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr8693737435421807431at_nat,F: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ bot_bot_set_o ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3326_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr8693737435421807431at_nat,F: nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ bot_bot_set_nat ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3327_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr4329608150637261639at_nat,F: product_unit > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3328_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr8693737435421807431at_nat,F: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ bot_bo2099793752762293965at_nat ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3329_Union__image__empty,axiom,
% 7.78/3.98 ! [A4: set_Pr4329608150637261639at_nat,F: $o > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ F @ bot_bot_set_o ) ) )
% 7.78/3.98 = A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3330_Union__image__insert,axiom,
% 7.78/3.98 ! [F: nat > set_nat,A: nat,B5: set_nat] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3331_Union__image__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_nat,A: product_unit,B5: set_Product_unit] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3332_Union__image__insert,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A: $o,B5: set_o] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3333_Union__image__insert,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3334_Union__image__insert,axiom,
% 7.78/3.98 ! [F: nat > set_Pr8693737435421807431at_nat,A: nat,B5: set_nat] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3335_Union__image__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,B5: set_Product_unit] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3336_Union__image__insert,axiom,
% 7.78/3.98 ! [F: $o > set_Pr8693737435421807431at_nat,A: $o,B5: set_o] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ ( insert_o @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3337_Union__image__insert,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ ( insert8211810215607154385at_nat @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3338_Union__image__insert,axiom,
% 7.78/3.98 ! [F: nat > set_Pr4329608150637261639at_nat,A: nat,B5: set_nat] :
% 7.78/3.98 ( ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ F @ ( insert_nat @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su5525570899277871387at_nat @ ( F @ A ) @ ( comple4364388969068068532at_nat @ ( image_1087905878993176368at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3339_Union__image__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_Pr4329608150637261639at_nat,A: product_unit,B5: set_Product_unit] :
% 7.78/3.98 ( ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ ( insert_Product_unit @ A @ B5 ) ) )
% 7.78/3.98 = ( sup_su5525570899277871387at_nat @ ( F @ A ) @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ F @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3340_SUP__insert,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3341_SUP__insert,axiom,
% 7.78/3.98 ! [F: product_unit > product_unit,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3342_SUP__insert,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A: $o,A4: set_o] :
% 7.78/3.98 ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3343_SUP__insert,axiom,
% 7.78/3.98 ! [F: nat > set_nat,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3344_SUP__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3345_SUP__insert,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A: $o,A4: set_o] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3346_SUP__insert,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_unit,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_Product_unit @ ( F @ A ) @ ( comple4687483117567863418t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3347_SUP__insert,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > set_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( F @ A ) @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3348_SUP__insert,axiom,
% 7.78/3.98 ! [F: nat > set_Pr8693737435421807431at_nat,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3349_SUP__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_Pr8693737435421807431at_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( F @ A ) @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3350_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,F: product_unit > product_unit,X2: product_unit] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_405062704495631173t_unit
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3351_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_o,F: $o > product_unit,X2: product_unit] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_o_Product_unit
% 7.78/3.98 @ ^ [I2: $o] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3352_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_nat,F: nat > product_unit,X2: product_unit] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_8730104196221521654t_unit
% 7.78/3.98 @ ^ [I2: nat] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3353_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,F: product_unit > set_nat,X2: set_nat] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3354_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_o,F: $o > set_nat,X2: set_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [I2: $o] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3355_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_nat,F: nat > set_nat,X2: set_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [I2: nat] : ( inf_inf_set_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3356_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_unit,X2: product_unit] :
% 7.78/3.98 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_6169909464789311569t_unit
% 7.78/3.98 @ ^ [I2: product_prod_nat_nat] : ( inf_inf_Product_unit @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3357_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,F: product_unit > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_3617315916088684441at_nat
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3358_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_o,F: $o > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7077428525161401678at_nat
% 7.78/3.98 @ ^ [I2: $o] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3359_INF__inf__const2,axiom,
% 7.78/3.98 ! [I3: set_nat,F: nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7178329752028323786at_nat
% 7.78/3.98 @ ^ [I2: nat] : ( inf_in2572325071724192079at_nat @ ( F @ I2 ) @ X2 )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ I3 ) ) @ X2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3360_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,X2: product_unit,F: product_unit > product_unit] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_405062704495631173t_unit
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3361_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_o,X2: product_unit,F: $o > product_unit] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_o_Product_unit
% 7.78/3.98 @ ^ [I2: $o] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3362_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_nat,X2: product_unit,F: nat > product_unit] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_8730104196221521654t_unit
% 7.78/3.98 @ ^ [I2: nat] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3363_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,X2: set_nat,F: product_unit > set_nat] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3364_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_o,X2: set_nat,F: $o > set_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [I2: $o] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3365_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_nat,X2: set_nat,F: nat > set_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [I2: nat] : ( inf_inf_set_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3366_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_Pr1261947904930325089at_nat,X2: product_unit,F: product_prod_nat_nat > product_unit] :
% 7.78/3.98 ( ( I3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_6169909464789311569t_unit
% 7.78/3.98 @ ^ [I2: product_prod_nat_nat] : ( inf_inf_Product_unit @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ X2 @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3367_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_Product_unit,X2: set_Pr1261947904930325089at_nat,F: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_3617315916088684441at_nat
% 7.78/3.98 @ ^ [I2: product_unit] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3368_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_o,X2: set_Pr1261947904930325089at_nat,F: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7077428525161401678at_nat
% 7.78/3.98 @ ^ [I2: $o] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3369_INF__inf__const1,axiom,
% 7.78/3.98 ! [I3: set_nat,X2: set_Pr1261947904930325089at_nat,F: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7178329752028323786at_nat
% 7.78/3.98 @ ^ [I2: nat] : ( inf_in2572325071724192079at_nat @ X2 @ ( F @ I2 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ X2 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ I3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3370_INF__insert,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3371_INF__insert,axiom,
% 7.78/3.98 ! [F: product_unit > product_unit,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3372_INF__insert,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A: $o,A4: set_o] :
% 7.78/3.98 ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3373_INF__insert,axiom,
% 7.78/3.98 ! [F: nat > set_nat,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3374_INF__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3375_INF__insert,axiom,
% 7.78/3.98 ! [F: $o > set_nat,A: $o,A4: set_o] :
% 7.78/3.98 ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_set_nat @ ( F @ A ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3376_INF__insert,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_unit,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ ( insert8211810215607154385at_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_inf_Product_unit @ ( F @ A ) @ ( comple2584293577114468500t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3377_INF__insert,axiom,
% 7.78/3.98 ! [F: nat > set_Pr1261947904930325089at_nat,A: nat,A4: set_nat] :
% 7.78/3.98 ( ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ ( insert_nat @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3378_INF__insert,axiom,
% 7.78/3.98 ! [F: product_unit > set_Pr1261947904930325089at_nat,A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ ( insert_Product_unit @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3379_INF__insert,axiom,
% 7.78/3.98 ! [F: $o > set_Pr1261947904930325089at_nat,A: $o,A4: set_o] :
% 7.78/3.98 ( ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ ( insert_o @ A @ A4 ) ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( F @ A ) @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3380_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3381_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3382_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [X4: nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3383_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_15824709712370754et_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( sup_sup_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3384_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: product_unit > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_7288820656315755647at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3385_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: $o > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_8493167801588156084at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3386_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: nat > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_4592875511192039216at_nat
% 7.78/3.98 @ ^ [X4: nat] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3387_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: product_unit > set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple4364388969068068532at_nat
% 7.78/3.98 @ ( image_5172358348707908735at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_su5525570899277871387at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3388_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_5803077947706746251at_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( sup_su718114333110466843at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3389_UN__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: $o > set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple4364388969068068532at_nat
% 7.78/3.98 @ ( image_2496312346330513076at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_su5525570899277871387at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3390_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3391_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3392_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [X4: nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3393_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_sup_set_nat @ A4 @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_15824709712370754et_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( sup_sup_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3394_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: set_Pr8693737435421807431at_nat,B5: product_unit > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_7288820656315755647at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_7288820656315755647at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3395_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: set_Pr8693737435421807431at_nat,B5: $o > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_8493167801588156084at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_8493167801588156084at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3396_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: set_Pr8693737435421807431at_nat,B5: nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_4592875511192039216at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_4592875511192039216at_nat
% 7.78/3.98 @ ^ [X4: nat] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3397_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: set_Pr4329608150637261639at_nat,B5: product_unit > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_5172358348707908735at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple4364388969068068532at_nat
% 7.78/3.98 @ ( image_5172358348707908735at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( sup_su5525570899277871387at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3398_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: set_Pr8693737435421807431at_nat,B5: product_prod_nat_nat > set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( sup_su718114333110466843at_nat @ A4 @ ( comple2748534634209756852at_nat @ ( image_5803077947706746251at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple2748534634209756852at_nat
% 7.78/3.98 @ ( image_5803077947706746251at_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( sup_su718114333110466843at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3399_UN__extend__simps_I3_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: set_Pr4329608150637261639at_nat,B5: $o > set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( comple4364388969068068532at_nat @ ( image_2496312346330513076at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple4364388969068068532at_nat
% 7.78/3.98 @ ( image_2496312346330513076at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( sup_su5525570899277871387at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3400_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: product_unit > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_3617315916088684441at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3401_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7979982168039674559at_nat
% 7.78/3.98 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3402_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_5423882813909314213at_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3403_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: $o > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7077428525161401678at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3404_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: nat > set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7178329752028323786at_nat
% 7.78/3.98 @ ^ [X4: nat] : ( inf_in2572325071724192079at_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3405_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: product_unit > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3406_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Pr4329608150637261639at_nat,A4: produc3843707927480180839at_nat > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_3160451284896210088et_nat
% 7.78/3.98 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3407_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_15824709712370754et_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3408_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: $o > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [X4: $o] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3409_INT__extend__simps_I1_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: nat > set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = B5 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A4 @ C3 ) ) @ B5 )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [X4: nat] : ( inf_inf_set_nat @ ( A4 @ X4 ) @ B5 )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3410_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: set_Pr1261947904930325089at_nat,B5: product_unit > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_3617315916088684441at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_3617315916088684441at_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3411_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr4329608150637261639at_nat,A4: set_Pr1261947904930325089at_nat,B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7979982168039674559at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7979982168039674559at_nat
% 7.78/3.98 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3412_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_5423882813909314213at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_5423882813909314213at_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3413_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: set_Pr1261947904930325089at_nat,B5: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7077428525161401678at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7077428525161401678at_nat
% 7.78/3.98 @ ^ [X4: $o] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3414_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: set_Pr1261947904930325089at_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple1930127330929219688at_nat
% 7.78/3.98 @ ( image_7178329752028323786at_nat
% 7.78/3.98 @ ^ [X4: nat] : ( inf_in2572325071724192079at_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3415_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Product_unit,A4: set_nat,B5: product_unit > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3416_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr4329608150637261639at_nat,A4: set_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo228742789529271731at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_3160451284896210088et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_3160451284896210088et_nat
% 7.78/3.98 @ ^ [X4: produc3843707927480180839at_nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3417_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_Pr1261947904930325089at_nat,A4: set_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bo2099793752762293965at_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_15824709712370754et_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_15824709712370754et_nat
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3418_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_o,A4: set_nat,B5: $o > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_o )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_o )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [X4: $o] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3419_INT__extend__simps_I2_J,axiom,
% 7.78/3.98 ! [C3: set_nat,A4: set_nat,B5: nat > set_nat] :
% 7.78/3.98 ( ( ( C3 = bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = A4 ) )
% 7.78/3.98 & ( ( C3 != bot_bot_set_nat )
% 7.78/3.98 => ( ( inf_inf_set_nat @ A4 @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ C3 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [X4: nat] : ( inf_inf_set_nat @ A4 @ ( B5 @ X4 ) )
% 7.78/3.98 @ C3 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3420_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3421_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3422_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3423_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: nat] :
% 7.78/3.98 ( ( member_nat @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3424_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3425_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3426_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3427_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: nat] :
% 7.78/3.98 ( ( member_nat @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3428_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3429_le__cINF__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3430_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_int,F: nat > nat,A4: set_nat,G: int > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: int] :
% 7.78/3.98 ( ( member_int @ M4 @ B5 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3431_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_int,F: int > nat,A4: set_int,G: int > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: int] :
% 7.78/3.98 ( ( member_int @ M4 @ B5 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3432_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_Product_unit,F: nat > nat,A4: set_nat,G: product_unit > nat] :
% 7.78/3.98 ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ M4 @ B5 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3433_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_Product_unit,F: int > nat,A4: set_int,G: product_unit > nat] :
% 7.78/3.98 ( ( B5 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ M4 @ B5 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3434_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_o,F: nat > nat,A4: set_nat,G: $o > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: $o] :
% 7.78/3.98 ( ( member_o @ M4 @ B5 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3435_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_o,F: int > nat,A4: set_int,G: $o > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: $o] :
% 7.78/3.98 ( ( member_o @ M4 @ B5 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3436_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_nat,F: nat > nat,A4: set_nat,G: nat > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: nat] :
% 7.78/3.98 ( ( member_nat @ M4 @ B5 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3437_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_nat,F: int > nat,A4: set_int,G: nat > nat] :
% 7.78/3.98 ( ( B5 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: nat] :
% 7.78/3.98 ( ( member_nat @ M4 @ B5 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3438_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_int,F: nat > int,A4: set_nat,G: int > int] :
% 7.78/3.98 ( ( B5 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: int] :
% 7.78/3.98 ( ( member_int @ M4 @ B5 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3439_cINF__mono,axiom,
% 7.78/3.98 ! [B5: set_int,F: int > int,A4: set_int,G: int > int] :
% 7.78/3.98 ( ( B5 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ! [M4: int] :
% 7.78/3.98 ( ( member_int @ M4 @ B5 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ A4 )
% 7.78/3.98 & ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ M4 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3440_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3441_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3442_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3443_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > nat,U: nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: nat] :
% 7.78/3.98 ( ( member_nat @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3444_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_int,F: int > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3445_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3446_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3447_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_nat,F: nat > int,U: int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: nat] :
% 7.78/3.98 ( ( member_nat @ X4 @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3448_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3449_cSUP__le__iff,axiom,
% 7.78/3.98 ! [A4: set_o,F: $o > product_unit,U: product_unit] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ U )
% 7.78/3.98 = ( ! [X4: $o] :
% 7.78/3.98 ( ( member_o @ X4 @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X4 ) @ U ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3450_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: nat > nat,B5: set_nat,F: int > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: int] :
% 7.78/3.98 ( ( member_int @ N2 @ A4 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3451_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: int] :
% 7.78/3.98 ( ( member_int @ N2 @ A4 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3452_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: nat > nat,B5: set_nat,F: product_unit > nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ N2 @ A4 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3453_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: int > nat,B5: set_int,F: product_unit > nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ N2 @ A4 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3454_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: nat > nat,B5: set_nat,F: $o > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: $o] :
% 7.78/3.98 ( ( member_o @ N2 @ A4 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3455_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: int > nat,B5: set_int,F: $o > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: $o] :
% 7.78/3.98 ( ( member_o @ N2 @ A4 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3456_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: nat] :
% 7.78/3.98 ( ( member_nat @ N2 @ A4 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3457_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: int > nat,B5: set_int,F: nat > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: nat] :
% 7.78/3.98 ( ( member_nat @ N2 @ A4 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_nat @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3458_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: nat > int,B5: set_nat,F: int > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: int] :
% 7.78/3.98 ( ( member_int @ N2 @ A4 )
% 7.78/3.98 => ? [X6: nat] :
% 7.78/3.98 ( ( member_nat @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3459_cSUP__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ B5 ) )
% 7.78/3.98 => ( ! [N2: int] :
% 7.78/3.98 ( ( member_int @ N2 @ A4 )
% 7.78/3.98 => ? [X6: int] :
% 7.78/3.98 ( ( member_int @ X6 @ B5 )
% 7.78/3.98 & ( ord_less_eq_int @ ( F @ N2 ) @ ( G @ X6 ) ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3460_prod__set__defs_I1_J,axiom,
% 7.78/3.98 ( basic_685971451221398055t_unit
% 7.78/3.98 = ( ^ [P3: produc7812382424243267045t_unit] : ( insert_ref_a @ ( produc473321116828791851t_unit @ P3 ) @ bot_bot_set_ref_a ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3461_image__INT,axiom,
% 7.78/3.98 ! [F: int > int,C3: set_int,A4: set_o,B5: $o > set_int,J4: $o] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_o @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple3628384868704368283et_int
% 7.78/3.98 @ ( image_o_set_int
% 7.78/3.98 @ ^ [X4: $o] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3462_image__INT,axiom,
% 7.78/3.98 ! [F: int > int,C3: set_int,A4: set_nat,B5: nat > set_int,J4: nat] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_nat @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple3628384868704368283et_int
% 7.78/3.98 @ ( image_nat_set_int
% 7.78/3.98 @ ^ [X4: nat] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3463_image__INT,axiom,
% 7.78/3.98 ! [F: int > int,C3: set_int,A4: set_int,B5: int > set_int,J4: int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ C3 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_int @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_int @ F @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple3628384868704368283et_int
% 7.78/3.98 @ ( image_int_set_int
% 7.78/3.98 @ ^ [X4: int] : ( image_int_int @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3464_image__INT,axiom,
% 7.78/3.98 ! [F: int > nat,C3: set_int,A4: set_o,B5: $o > set_int,J4: $o] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_o @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_o_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [X4: $o] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3465_image__INT,axiom,
% 7.78/3.98 ! [F: int > nat,C3: set_int,A4: set_nat,B5: nat > set_int,J4: nat] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_nat @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_nat_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [X4: nat] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3466_image__INT,axiom,
% 7.78/3.98 ! [F: int > nat,C3: set_int,A4: set_int,B5: int > set_int,J4: int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ C3 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_int @ J4 @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ F @ ( comple3628384868704368283et_int @ ( image_int_set_int @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple7806235888213564991et_nat
% 7.78/3.98 @ ( image_int_set_nat
% 7.78/3.98 @ ^ [X4: int] : ( image_int_nat @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3467_image__INT,axiom,
% 7.78/3.98 ! [F: nat > rat,C3: set_nat,A4: set_o,B5: $o > set_nat,J4: $o] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ C3 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_o @ J4 @ A4 )
% 7.78/3.98 => ( ( image_nat_rat @ F @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple4298007329820168263et_rat
% 7.78/3.98 @ ( image_o_set_rat
% 7.78/3.98 @ ^ [X4: $o] : ( image_nat_rat @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3468_image__INT,axiom,
% 7.78/3.98 ! [F: nat > int,C3: set_nat,A4: set_o,B5: $o > set_nat,J4: $o] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ C3 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_o @ J4 @ A4 )
% 7.78/3.98 => ( ( image_nat_int @ F @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple3628384868704368283et_int
% 7.78/3.98 @ ( image_o_set_int
% 7.78/3.98 @ ^ [X4: $o] : ( image_nat_int @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3469_image__INT,axiom,
% 7.78/3.98 ! [F: nat > rat,C3: set_nat,A4: set_nat,B5: nat > set_nat,J4: nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ C3 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_nat @ J4 @ A4 )
% 7.78/3.98 => ( ( image_nat_rat @ F @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple4298007329820168263et_rat
% 7.78/3.98 @ ( image_nat_set_rat
% 7.78/3.98 @ ^ [X4: nat] : ( image_nat_rat @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3470_image__INT,axiom,
% 7.78/3.98 ! [F: nat > int,C3: set_nat,A4: set_nat,B5: nat > set_nat,J4: nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ C3 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( B5 @ X ) @ C3 ) )
% 7.78/3.98 => ( ( member_nat @ J4 @ A4 )
% 7.78/3.98 => ( ( image_nat_int @ F @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.98 = ( comple3628384868704368283et_int
% 7.78/3.98 @ ( image_nat_set_int
% 7.78/3.98 @ ^ [X4: nat] : ( image_nat_int @ F @ ( B5 @ X4 ) )
% 7.78/3.98 @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3471_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3472_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > nat,B5: set_Product_unit,F: product_unit > nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3473_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: $o > nat,B5: set_o,F: $o > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3474_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ G @ B5 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3475_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3476_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > int,B5: set_Product_unit,F: product_unit > int] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3477_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: $o > int,B5: set_o,F: $o > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3478_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: nat > int,B5: set_nat,F: nat > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ B5 )
% 7.78/3.98 => ( ord_less_eq_int @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int @ G @ B5 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3479_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > product_unit,B5: set_int,F: int > product_unit] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ B5 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3480_cINF__superset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > product_unit,B5: set_Product_unit,F: product_unit > product_unit] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ B5 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( G @ X ) @ ( F @ X ) ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3481_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > nat,B5: set_int,F: int > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3482_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > nat,B5: set_Product_unit,F: product_unit > nat] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3483_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: $o > nat,B5: set_o,F: $o > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3484_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: nat > nat,B5: set_nat,F: nat > nat] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3485_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > int,B5: set_int,F: int > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_int_int @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3486_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > int,B5: set_Product_unit,F: product_unit > int] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3487_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_o,G: $o > int,B5: set_o,F: $o > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_o_int @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3488_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_nat,G: nat > int,B5: set_nat,F: nat > int] :
% 7.78/3.98 ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ A4 )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3489_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_int,G: int > product_unit,B5: set_int,F: int > product_unit] :
% 7.78/3.98 ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: int] :
% 7.78/3.98 ( ( member_int @ X @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3490_cSUP__subset__mono,axiom,
% 7.78/3.98 ! [A4: set_Product_unit,G: product_unit > product_unit,B5: set_Product_unit,F: product_unit > product_unit] :
% 7.78/3.98 ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ A4 @ B5 )
% 7.78/3.98 => ( ! [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ A4 )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ X ) @ ( G @ X ) ) )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ G @ B5 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3491_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: int > set_Product_unit,I: int,B5: set_Product_unit,J3: set_int] :
% 7.78/3.98 ( ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ ( fun_up5054257004045450754t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_Product_unit @ ( member_int @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3492_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: int > set_o,I: int,B5: set_o,J3: set_int] :
% 7.78/3.98 ( ( comple90263536869209701_set_o @ ( image_int_set_o @ ( fun_upd_int_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_int_set_o @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_o @ ( member_int @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3493_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: product_unit > set_Product_unit,I: product_unit,B5: set_Product_unit,J3: set_Product_unit] :
% 7.78/3.98 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ ( fun_up488859312337516701t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_Product_unit @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3494_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: product_unit > set_o,I: product_unit,B5: set_o,J3: set_Product_unit] :
% 7.78/3.98 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ ( fun_up1762901246852280360_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_o @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3495_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: $o > set_Product_unit,I: $o,B5: set_Product_unit,J3: set_o] :
% 7.78/3.98 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ ( fun_up4718931970374059986t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ A4 @ ( minus_minus_set_o @ J3 @ ( insert_o @ I @ bot_bot_set_o ) ) ) ) @ ( if_set_Product_unit @ ( member_o @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3496_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: $o > set_o,I: $o,B5: set_o,J3: set_o] :
% 7.78/3.98 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ ( fun_upd_o_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_o_set_o @ A4 @ ( minus_minus_set_o @ J3 @ ( insert_o @ I @ bot_bot_set_o ) ) ) ) @ ( if_set_o @ ( member_o @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3497_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: nat > set_Product_unit,I: nat,B5: set_Product_unit,J3: set_nat] :
% 7.78/3.98 ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ ( fun_up1220017903161424222t_unit @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ A4 @ ( minus_minus_set_nat @ J3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) ) ) @ ( if_set_Product_unit @ ( member_nat @ I @ J3 ) @ B5 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3498_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: nat > set_o,I: nat,B5: set_o,J3: set_nat] :
% 7.78/3.98 ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ ( fun_upd_nat_set_o @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_nat_set_o @ A4 @ ( minus_minus_set_nat @ J3 @ ( insert_nat @ I @ bot_bot_set_nat ) ) ) ) @ ( if_set_o @ ( member_nat @ I @ J3 ) @ B5 @ bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3499_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: int > set_nat,I: int,B5: set_nat,J3: set_int] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ ( fun_upd_int_set_nat @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ A4 @ ( minus_minus_set_int @ J3 @ ( insert_int @ I @ bot_bot_set_int ) ) ) ) @ ( if_set_nat @ ( member_int @ I @ J3 ) @ B5 @ bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3500_UNION__fun__upd,axiom,
% 7.78/3.98 ! [A4: product_unit > set_nat,I: product_unit,B5: set_nat,J3: set_Product_unit] :
% 7.78/3.98 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ ( fun_up4569834200710200790et_nat @ A4 @ I @ B5 ) @ J3 ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A4 @ ( minus_6452836326544984404t_unit @ J3 @ ( insert_Product_unit @ I @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_nat @ ( member_Product_unit @ I @ J3 ) @ B5 @ bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3501_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > rat,G: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( image_2021340605491722874at_rat
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_rat_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc8728714639637146746at_rat @ ( image_nat_rat @ F @ A4 )
% 7.78/3.98 @ ^ [X4: rat] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3502_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > rat,G: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( image_5529569163885119602at_nat
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_rat_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc140472662868866674at_nat @ ( image_nat_rat @ F @ A4 )
% 7.78/3.98 @ ^ [X4: rat] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3503_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > rat,G: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( image_1351718144375922894at_int
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_rat_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc137982192359816398at_int @ ( image_nat_rat @ F @ A4 )
% 7.78/3.98 @ ^ [X4: rat] : ( image_nat_int @ G @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X4 @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3504_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > int,G: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( image_3337248961327643342nt_rat
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_int_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc821250958618291406nt_rat @ ( image_nat_int @ F @ A4 )
% 7.78/3.98 @ ^ [X4: int] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3505_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( image_6845477519721040070nt_nat
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc1456381018704787142nt_nat @ ( image_nat_int @ F @ A4 )
% 7.78/3.98 @ ^ [X4: int] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3506_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: int > int,G: int > nat,A4: set_int] :
% 7.78/3.98 ( ( image_659947567330398058nt_nat
% 7.78/3.98 @ ^ [X4: int] : ( product_Pair_int_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc1456381018704787142nt_nat @ ( image_int_int @ F @ A4 )
% 7.78/3.98 @ ^ [X4: int] : ( image_int_nat @ G @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3507_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > int,G: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( image_2667626500211843362nt_int
% 7.78/3.98 @ ^ [X4: nat] : ( product_Pair_int_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc1453890548195736866nt_int @ ( image_nat_int @ F @ A4 )
% 7.78/3.98 @ ^ [X4: int] : ( image_nat_int @ G @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3508_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: int > int,G: int > int,A4: set_int] :
% 7.78/3.98 ( ( image_5705468584675977158nt_int
% 7.78/3.98 @ ^ [X4: int] : ( product_Pair_int_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc1453890548195736866nt_int @ ( image_int_int @ F @ A4 )
% 7.78/3.98 @ ^ [X4: int] : ( image_int_int @ G @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X4 @ bot_bot_set_int ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3509_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > product_unit,G: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( image_469905907365485675it_rat
% 7.78/3.98 @ ^ [X4: nat] : ( produc4168158269727034510it_rat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc6240246942209516957it_rat @ ( image_8730104196221521654t_unit @ F @ A4 )
% 7.78/3.98 @ ^ [X4: product_unit] : ( image_nat_rat @ G @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3510_image__split__eq__Sigma,axiom,
% 7.78/3.98 ! [F: nat > product_unit,G: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( image_3978134465758882403it_nat
% 7.78/3.98 @ ^ [X4: nat] : ( produc4803288329813530246it_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 7.78/3.98 @ A4 )
% 7.78/3.98 = ( produc6875377002296012693it_nat @ ( image_8730104196221521654t_unit @ F @ A4 )
% 7.78/3.98 @ ^ [X4: product_unit] : ( image_nat_nat @ G @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X4 @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3511_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: num,C3: set_num,G: num > $o,X2: num] :
% 7.78/3.98 ( ( member_num @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_num_o @ G @ C3 )
% 7.78/3.98 => ( ( comp_o_num_num
% 7.78/3.98 @ ^ [I2: $o] : ( if_num @ ( member_o @ I2 @ ( image_num_o @ G @ C3 ) ) @ ( the_inv_into_num_o @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_num @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3512_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: num,C3: set_num,G: num > nat,X2: num] :
% 7.78/3.98 ( ( member_num @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_num_nat @ G @ C3 )
% 7.78/3.98 => ( ( comp_nat_num_num
% 7.78/3.98 @ ^ [I2: nat] : ( if_num @ ( member_nat @ I2 @ ( image_num_nat @ G @ C3 ) ) @ ( the_inv_into_num_nat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_num @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3513_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: num,C3: set_num,G: num > int,X2: num] :
% 7.78/3.98 ( ( member_num @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_num_int @ G @ C3 )
% 7.78/3.98 => ( ( comp_int_num_num
% 7.78/3.98 @ ^ [I2: int] : ( if_num @ ( member_int @ I2 @ ( image_num_int @ G @ C3 ) ) @ ( the_inv_into_num_int @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_num @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3514_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: $o,C3: set_o,G: $o > $o,X2: $o] :
% 7.78/3.98 ( ( member_o @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_o_o @ G @ C3 )
% 7.78/3.98 => ( ( comp_o_o_o
% 7.78/3.98 @ ^ [I2: $o] :
% 7.78/3.98 ( ( ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_o @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_o @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3515_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: $o,C3: set_o,G: $o > nat,X2: $o] :
% 7.78/3.98 ( ( member_o @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_o_nat @ G @ C3 )
% 7.78/3.98 => ( ( comp_nat_o_o
% 7.78/3.98 @ ^ [I2: nat] :
% 7.78/3.98 ( ( ( member_nat @ I2 @ ( image_o_nat @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_nat @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_nat @ I2 @ ( image_o_nat @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_o @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3516_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: $o,C3: set_o,G: $o > int,X2: $o] :
% 7.78/3.98 ( ( member_o @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_o_int @ G @ C3 )
% 7.78/3.98 => ( ( comp_int_o_o
% 7.78/3.98 @ ^ [I2: int] :
% 7.78/3.98 ( ( ( member_int @ I2 @ ( image_o_int @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_int @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_int @ I2 @ ( image_o_int @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_o @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3517_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: nat,C3: set_nat,G: nat > rat,X2: nat] :
% 7.78/3.98 ( ( member_nat @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_nat_rat @ G @ C3 )
% 7.78/3.98 => ( ( comp_rat_nat_nat
% 7.78/3.98 @ ^ [I2: rat] : ( if_nat @ ( member_rat @ I2 @ ( image_nat_rat @ G @ C3 ) ) @ ( the_inv_into_nat_rat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_nat @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3518_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: nat,C3: set_nat,G: nat > $o,X2: nat] :
% 7.78/3.98 ( ( member_nat @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_nat_o @ G @ C3 )
% 7.78/3.98 => ( ( comp_o_nat_nat
% 7.78/3.98 @ ^ [I2: $o] : ( if_nat @ ( member_o @ I2 @ ( image_nat_o @ G @ C3 ) ) @ ( the_inv_into_nat_o @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_nat @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3519_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: nat,C3: set_nat,G: nat > nat,X2: nat] :
% 7.78/3.98 ( ( member_nat @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_nat_nat @ G @ C3 )
% 7.78/3.98 => ( ( comp_nat_nat_nat
% 7.78/3.98 @ ^ [I2: nat] : ( if_nat @ ( member_nat @ I2 @ ( image_nat_nat @ G @ C3 ) ) @ ( the_inv_into_nat_nat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_nat @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3520_If__the__inv__into__f__f,axiom,
% 7.78/3.98 ! [I: nat,C3: set_nat,G: nat > int,X2: nat] :
% 7.78/3.98 ( ( member_nat @ I @ C3 )
% 7.78/3.98 => ( ( inj_on_nat_int @ G @ C3 )
% 7.78/3.98 => ( ( comp_int_nat_nat
% 7.78/3.98 @ ^ [I2: int] : ( if_nat @ ( member_int @ I2 @ ( image_nat_int @ G @ C3 ) ) @ ( the_inv_into_nat_int @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ G
% 7.78/3.98 @ I )
% 7.78/3.98 = ( id_nat @ I ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3521_Field__insert,axiom,
% 7.78/3.98 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,R: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( field_1428494348145443988at_nat @ ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su474284620922681339at_nat @ ( insert2290795007606087959at_nat @ A @ ( insert2290795007606087959at_nat @ B @ bot_bo1534825418459847827at_nat ) ) @ ( field_1428494348145443988at_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3522_Field__insert,axiom,
% 7.78/3.98 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3523_Field__insert,axiom,
% 7.78/3.98 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_sup_set_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3524_Field__insert,axiom,
% 7.78/3.98 ! [A: produc859450856879609959at_nat,B: produc859450856879609959at_nat,R: set_Pr553994874890374343at_nat] :
% 7.78/3.98 ( ( field_3044959742847878580at_nat @ ( insert5475735164933346999at_nat @ ( produc4662710985925991255at_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su718114333110466843at_nat @ ( insert5050368324300391991at_nat @ A @ ( insert5050368324300391991at_nat @ B @ bot_bo5327735625951526323at_nat ) ) @ ( field_3044959742847878580at_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3525_Field__insert,axiom,
% 7.78/3.98 ! [A: product_unit,B: product_unit,R: set_Pr5094982260447487303t_unit] :
% 7.78/3.98 ( ( field_Product_unit @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( field_Product_unit @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3526_Field__insert,axiom,
% 7.78/3.98 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,R: set_Pr5564308138774400199at_nat] :
% 7.78/3.98 ( ( field_2862844103579723188at_nat @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) @ ( field_2862844103579723188at_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3527_Field__insert,axiom,
% 7.78/3.98 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,R: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( field_4706345496283612622at_nat @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) @ ( field_4706345496283612622at_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3528_Field__insert,axiom,
% 7.78/3.98 ! [A: $o,B: $o,R: set_Product_prod_o_o] :
% 7.78/3.98 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_sup_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3529_Field__insert,axiom,
% 7.78/3.98 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
% 7.78/3.98 = ( sup_sup_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3530_bdd__below__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( order_2045666486212196060at_rat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3531_bdd__below__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_2680796546298691796at_nat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3532_bdd__below__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_2678306075789641520at_int @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3533_bdd__below__image__antimono,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_3680150258199746352nt_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3534_bdd__below__image__antimono,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_3677659787690696076nt_int @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3535_bdd__above__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( order_2045666486212196060at_rat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3536_bdd__above__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_2680796546298691796at_nat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3537_bdd__above__image__antimono,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_2678306075789641520at_int @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3538_bdd__above__image__antimono,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_3680150258199746352nt_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3539_bdd__above__image__antimono,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_3677659787690696076nt_int @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3540_the__inv__f__o__f__id,axiom,
% 7.78/3.98 ! [F: nat > nat,Z2: nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( comp_nat_nat_nat @ ( the_inv_into_nat_nat @ top_top_set_nat @ F ) @ F @ Z2 )
% 7.78/3.98 = ( id_nat @ Z2 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3541_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: product_unit > $o,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 7.78/3.98 ( ( inj_on8854722734121536060unit_o @ G @ C3 )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 => ( member2370919827131729009t_unit
% 7.78/3.98 @ ^ [I2: $o] : ( if_Product_unit @ ( member_o @ I2 @ ( image_Product_unit_o @ G @ C3 ) ) @ ( the_in43325605794470270unit_o @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We8730861560085513481t_unit @ top_top_set_o @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3542_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: $o > $o,C3: set_o,B5: set_o,X2: $o] :
% 7.78/3.98 ( ( inj_on_o_o @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 7.78/3.98 => ( member_o_o
% 7.78/3.98 @ ^ [I2: $o] :
% 7.78/3.98 ( ( ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_o @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_o @ I2 @ ( image_o_o @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ ( bNF_We7690717809131995284nc_o_o @ top_top_set_o @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3543_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: nat > $o,C3: set_nat,B5: set_nat,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_o @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 7.78/3.98 => ( member_o_nat
% 7.78/3.98 @ ^ [I2: $o] : ( if_nat @ ( member_o @ I2 @ ( image_nat_o @ G @ C3 ) ) @ ( the_inv_into_nat_o @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We6830391624356636116_o_nat @ top_top_set_o @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3544_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: product_unit > char,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 7.78/3.98 ( ( inj_on1959294024837303853t_char @ G @ C3 )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 => ( member379592906918970460t_unit
% 7.78/3.98 @ ^ [I2: char] : ( if_Product_unit @ ( member_char @ I2 @ ( image_7248553556944771225t_char @ G @ C3 ) ) @ ( the_in3194898024646563179t_char @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We7396736742984212070t_unit @ top_top_set_char @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3545_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: $o > char,C3: set_o,B5: set_o,X2: $o] :
% 7.78/3.98 ( ( inj_on_o_char @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 7.78/3.98 => ( member_char_o
% 7.78/3.98 @ ^ [I2: char] :
% 7.78/3.98 ( ( ( member_char @ I2 @ ( image_o_char @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_char @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_char @ I2 @ ( image_o_char @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ ( bNF_We6174688282833725809char_o @ top_top_set_char @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3546_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: nat > char,C3: set_nat,B5: set_nat,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_char @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 7.78/3.98 => ( member_char_nat
% 7.78/3.98 @ ^ [I2: char] : ( if_nat @ ( member_char @ I2 @ ( image_nat_char @ G @ C3 ) ) @ ( the_in9023905271258939222t_char @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We935846424581991991ar_nat @ top_top_set_char @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3547_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: product_unit > rat,C3: set_Product_unit,B5: set_Product_unit,X2: product_unit] :
% 7.78/3.98 ( ( inj_on7795309031694339124it_rat @ G @ C3 )
% 7.78/3.98 => ( ( ord_le3507040750410214029t_unit @ C3 @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 7.78/3.98 => ( member7011034171605722901t_unit
% 7.78/3.98 @ ^ [I2: rat] : ( if_Product_unit @ ( member_rat @ I2 @ ( image_240439954468258464it_rat @ G @ C3 ) ) @ ( the_in3915408195775746418it_rat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We8564238559827753503t_unit @ top_top_set_rat @ ( sup_su793286257634532545t_unit @ B5 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3548_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: $o > rat,C3: set_o,B5: set_o,X2: $o] :
% 7.78/3.98 ( ( inj_on_o_rat @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ C3 @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 7.78/3.98 => ( member_rat_o
% 7.78/3.98 @ ^ [I2: rat] :
% 7.78/3.98 ( ( ( member_rat @ I2 @ ( image_o_rat @ G @ C3 ) )
% 7.78/3.98 => ( the_inv_into_o_rat @ C3 @ G @ I2 ) )
% 7.78/3.98 & ( ~ ( member_rat @ I2 @ ( image_o_rat @ G @ C3 ) )
% 7.78/3.98 => X2 ) )
% 7.78/3.98 @ ( bNF_We6195730058148253354_rat_o @ top_top_set_rat @ ( sup_sup_set_o @ B5 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3549_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: nat > rat,C3: set_nat,B5: set_nat,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 7.78/3.98 => ( member_rat_nat
% 7.78/3.98 @ ^ [I2: rat] : ( if_nat @ ( member_rat @ I2 @ ( image_nat_rat @ G @ C3 ) ) @ ( the_inv_into_nat_rat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We7223962090624190782at_nat @ top_top_set_rat @ ( sup_sup_set_nat @ B5 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3550_If__the__inv__into__in__Func,axiom,
% 7.78/3.98 ! [G: int > nat,C3: set_int,B5: set_int,X2: int] :
% 7.78/3.98 ( ( inj_on_int_nat @ G @ C3 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ C3 @ ( sup_sup_set_int @ B5 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 7.78/3.98 => ( member_nat_int
% 7.78/3.98 @ ^ [I2: nat] : ( if_int @ ( member_nat @ I2 @ ( image_int_nat @ G @ C3 ) ) @ ( the_inv_into_int_nat @ C3 @ G @ I2 ) @ X2 )
% 7.78/3.98 @ ( bNF_We7538026264050006418at_int @ top_top_set_nat @ ( sup_sup_set_int @ B5 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3551_mono__cInf,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o] :
% 7.78/3.98 ( ( order_mono_o_nat @ F )
% 7.78/3.98 => ( ( condit5413489452508810728elow_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3552_mono__cInf,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3553_mono__cInf,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o] :
% 7.78/3.98 ( ( order_mono_o_int @ F )
% 7.78/3.98 => ( ( condit5413489452508810728elow_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3554_mono__cInf,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3555_mono__cInf,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_o] :
% 7.78/3.98 ( ( order_7782127260464396005t_unit @ F )
% 7.78/3.98 => ( ( condit5413489452508810728elow_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_o @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3556_mono__cInf,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.98 ( ( order_5727276828720722763t_unit @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3557_mono__cInf,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3558_mono__cInf,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_int @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3559_mono__cInf,axiom,
% 7.78/3.98 ! [F: int > product_unit,A4: set_int] :
% 7.78/3.98 ( ( order_2843698775922903023t_unit @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_int @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3560_mono__cInf,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit9161856309968323677t_unit @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3561_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: int > nat,I3: set_int] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_int_nat
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3562_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: nat > nat,I3: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_nat_nat
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3563_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > int,A4: int > nat,I3: set_int] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_int
% 7.78/3.98 @ ( image_int_int
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3564_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > int,A4: nat > nat,I3: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_int @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_int
% 7.78/3.98 @ ( image_nat_int
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3565_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: int > nat,I3: set_int] :
% 7.78/3.98 ( ( order_5727276828720722763t_unit @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ ( image_int_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_5846526143423701914t_unit
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3566_mono__cINF,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: nat > nat,I3: set_nat] :
% 7.78/3.98 ( ( order_5727276828720722763t_unit @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( complete_Inf_Inf_nat @ ( image_nat_nat @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( comple2584293577114468500t_unit
% 7.78/3.98 @ ( image_8730104196221521654t_unit
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3567_mono__cINF,axiom,
% 7.78/3.98 ! [F: int > nat,A4: int > int,I3: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_int_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_int_int @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_int_nat
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3568_mono__cINF,axiom,
% 7.78/3.98 ! [F: int > nat,A4: product_unit > int,I3: set_Product_unit] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_875570014554754200it_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3569_mono__cINF,axiom,
% 7.78/3.98 ! [F: int > nat,A4: $o > int,I3: set_o] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_o_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_o_int @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_o_nat
% 7.78/3.98 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3570_mono__cINF,axiom,
% 7.78/3.98 ! [F: int > nat,A4: nat > int,I3: set_nat] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ ( image_nat_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat @ ( F @ ( complete_Inf_Inf_int @ ( image_nat_int @ A4 @ I3 ) ) )
% 7.78/3.98 @ ( complete_Inf_Inf_nat
% 7.78/3.98 @ ( image_nat_nat
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3571_relcompp__distrib2,axiom,
% 7.78/3.98 ! [S5: product_prod_nat_nat > product_prod_nat_nat > $o,T3: product_prod_nat_nat > product_prod_nat_nat > $o,R3: product_prod_nat_nat > int > $o] :
% 7.78/3.98 ( ( relcom8911704206367525917at_int @ ( sup_su362511073950362882_nat_o @ S5 @ T3 ) @ R3 )
% 7.78/3.98 = ( sup_su5231854730092680051_int_o @ ( relcom8911704206367525917at_int @ S5 @ R3 ) @ ( relcom8911704206367525917at_int @ T3 @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3572_relcompp__distrib2,axiom,
% 7.78/3.98 ! [S5: int > int > $o,T3: int > int > $o,R3: int > code_integer > $o] :
% 7.78/3.98 ( ( relcom967497705283160040nteger @ ( sup_sup_int_int_o @ S5 @ T3 ) @ R3 )
% 7.78/3.98 = ( sup_su1544571744061072657eger_o @ ( relcom967497705283160040nteger @ S5 @ R3 ) @ ( relcom967497705283160040nteger @ T3 @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3573_relcompp__distrib,axiom,
% 7.78/3.98 ! [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S5: product_prod_nat_nat > int > $o,T3: product_prod_nat_nat > int > $o] :
% 7.78/3.98 ( ( relcom8911704206367525917at_int @ R3 @ ( sup_su5231854730092680051_int_o @ S5 @ T3 ) )
% 7.78/3.98 = ( sup_su5231854730092680051_int_o @ ( relcom8911704206367525917at_int @ R3 @ S5 ) @ ( relcom8911704206367525917at_int @ R3 @ T3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3574_relcompp__distrib,axiom,
% 7.78/3.98 ! [R3: int > int > $o,S5: int > code_integer > $o,T3: int > code_integer > $o] :
% 7.78/3.98 ( ( relcom967497705283160040nteger @ R3 @ ( sup_su1544571744061072657eger_o @ S5 @ T3 ) )
% 7.78/3.98 = ( sup_su1544571744061072657eger_o @ ( relcom967497705283160040nteger @ R3 @ S5 ) @ ( relcom967497705283160040nteger @ R3 @ T3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3575_Field__Union,axiom,
% 7.78/3.98 ! [R3: set_se7855581050983116737at_nat] :
% 7.78/3.98 ( ( field_nat @ ( comple5685304695842803022at_nat @ R3 ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_5853224409075402146et_nat @ field_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3576_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.98 => ( ( image_rat_nat @ ( the_inv_into_nat_rat @ A4 @ F ) @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3577_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: rat > nat,A4: set_rat] :
% 7.78/3.98 ( ( inj_on_rat_nat @ F @ A4 )
% 7.78/3.98 => ( ( image_nat_rat @ ( the_inv_into_rat_nat @ A4 @ F ) @ ( image_rat_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3578_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A4 @ F ) @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3579_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ( image_nat_int @ ( the_inv_into_int_nat @ A4 @ F ) @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3580_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ ( the_inv_into_nat_int @ A4 @ F ) @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3581_the__inv__into__onto,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ( image_int_int @ ( the_inv_into_int_int @ A4 @ F ) @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3582_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: char > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( image_8382823969816519465at_nat @ F @ ( vimage8942442433166402803at_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_8382823969816519465at_nat @ F @ top_top_set_char ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3583_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: list_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( image_2795870212791037530at_nat @ F @ ( vimage8527374361057053988at_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_2795870212791037530at_nat @ F @ top_top_set_list_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3584_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: rat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( image_9175953278516507234at_nat @ F @ ( vimage2119786153496215084at_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_9175953278516507234at_nat @ F @ top_top_set_rat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3585_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_rat] :
% 7.78/3.98 ( ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) )
% 7.78/3.98 = ( inf_inf_set_rat @ A4 @ ( image_nat_rat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3586_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( image_nat_nat @ F @ ( vimage_nat_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ A4 @ ( image_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3587_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_int] :
% 7.78/3.98 ( ( image_nat_int @ F @ ( vimage_nat_int @ F @ A4 ) )
% 7.78/3.98 = ( inf_inf_set_int @ A4 @ ( image_nat_int @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3588_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( image_5846123807819985514at_nat @ F @ ( vimage8013328719654469172at_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_5846123807819985514at_nat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3589_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_nat] :
% 7.78/3.98 ( ( image_int_nat @ F @ ( vimage_int_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_inf_set_nat @ A4 @ ( image_int_nat @ F @ top_top_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3590_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( image_int_int @ F @ ( vimage_int_int @ F @ A4 ) )
% 7.78/3.98 = ( inf_inf_set_int @ A4 @ ( image_int_int @ F @ top_top_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3591_image__vimage__eq,axiom,
% 7.78/3.98 ! [F: int > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( image_8883965892284119310at_nat @ F @ ( vimage1827798767263827160at_nat @ F @ A4 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ A4 @ ( image_8883965892284119310at_nat @ F @ top_top_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3592_vimage__comp,axiom,
% 7.78/3.98 ! [F: nat > $o,G: $o > $o,X2: set_o] :
% 7.78/3.98 ( ( vimage_nat_o @ F @ ( vimage_o_o @ G @ X2 ) )
% 7.78/3.98 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) @ X2 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3593_vimage__comp,axiom,
% 7.78/3.98 ! [F: int > nat,G: nat > num,X2: set_num] :
% 7.78/3.98 ( ( vimage_int_nat @ F @ ( vimage_nat_num @ G @ X2 ) )
% 7.78/3.98 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) @ X2 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3594_vimage__comp,axiom,
% 7.78/3.98 ! [F: nat > nat,G: nat > nat,X2: set_nat] :
% 7.78/3.98 ( ( vimage_nat_nat @ F @ ( vimage_nat_nat @ G @ X2 ) )
% 7.78/3.98 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ X2 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3595_vimage__comp,axiom,
% 7.78/3.98 ! [F: int > int,G: int > nat,X2: set_nat] :
% 7.78/3.98 ( ( vimage_int_int @ F @ ( vimage_int_nat @ G @ X2 ) )
% 7.78/3.98 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) @ X2 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3596_vimage__comp,axiom,
% 7.78/3.98 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,X2: set_Pr4111642102156807771nteger] :
% 7.78/3.98 ( ( vimage6029918387083761651nteger @ F @ ( vimage4289680085338140859nteger @ G @ X2 ) )
% 7.78/3.98 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ X2 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3597_set_Ocompositionality,axiom,
% 7.78/3.98 ! [F: nat > $o,G: $o > $o,Set: set_o] :
% 7.78/3.98 ( ( vimage_nat_o @ F @ ( vimage_o_o @ G @ Set ) )
% 7.78/3.98 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) @ Set ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3598_set_Ocompositionality,axiom,
% 7.78/3.98 ! [F: int > nat,G: nat > num,Set: set_num] :
% 7.78/3.98 ( ( vimage_int_nat @ F @ ( vimage_nat_num @ G @ Set ) )
% 7.78/3.98 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) @ Set ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3599_set_Ocompositionality,axiom,
% 7.78/3.98 ! [F: nat > nat,G: nat > nat,Set: set_nat] :
% 7.78/3.98 ( ( vimage_nat_nat @ F @ ( vimage_nat_nat @ G @ Set ) )
% 7.78/3.98 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ Set ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3600_set_Ocompositionality,axiom,
% 7.78/3.98 ! [F: int > int,G: int > nat,Set: set_nat] :
% 7.78/3.98 ( ( vimage_int_int @ F @ ( vimage_int_nat @ G @ Set ) )
% 7.78/3.98 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) @ Set ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3601_set_Ocompositionality,axiom,
% 7.78/3.98 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Set: set_Pr4111642102156807771nteger] :
% 7.78/3.98 ( ( vimage6029918387083761651nteger @ F @ ( vimage4289680085338140859nteger @ G @ Set ) )
% 7.78/3.98 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ Set ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3602_FieldI2,axiom,
% 7.78/3.98 ! [I: produc3843707927480180839at_nat,J4: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
% 7.78/3.98 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member8757157785044589968at_nat @ J4 @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3603_FieldI2,axiom,
% 7.78/3.98 ! [I: product_prod_nat_nat,J4: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member8440522571783428010at_nat @ J4 @ ( field_4706345496283612622at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3604_FieldI2,axiom,
% 7.78/3.98 ! [I: $o,J4: $o,R3: set_Product_prod_o_o] :
% 7.78/3.98 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_o @ J4 @ ( field_o @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3605_FieldI2,axiom,
% 7.78/3.98 ! [I: set_Pr4329608150637261639at_nat,J4: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member6273874620674182256at_nat @ J4 @ ( field_1428494348145443988at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3606_FieldI2,axiom,
% 7.78/3.98 ! [I: set_Pr1261947904930325089at_nat,J4: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member2643936169264416010at_nat @ J4 @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3607_FieldI2,axiom,
% 7.78/3.98 ! [I: nat,J4: nat,R3: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_nat @ J4 @ ( field_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3608_FieldI2,axiom,
% 7.78/3.98 ! [I: int,J4: int,R3: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_int @ J4 @ ( field_int @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3609_FieldI1,axiom,
% 7.78/3.98 ! [I: produc3843707927480180839at_nat,J4: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
% 7.78/3.98 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3610_FieldI1,axiom,
% 7.78/3.98 ! [I: product_prod_nat_nat,J4: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member8440522571783428010at_nat @ I @ ( field_4706345496283612622at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3611_FieldI1,axiom,
% 7.78/3.98 ! [I: $o,J4: $o,R3: set_Product_prod_o_o] :
% 7.78/3.98 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_o @ I @ ( field_o @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3612_FieldI1,axiom,
% 7.78/3.98 ! [I: set_Pr4329608150637261639at_nat,J4: set_Pr4329608150637261639at_nat,R3: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member6273874620674182256at_nat @ I @ ( field_1428494348145443988at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3613_FieldI1,axiom,
% 7.78/3.98 ! [I: set_Pr1261947904930325089at_nat,J4: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3614_FieldI1,axiom,
% 7.78/3.98 ! [I: nat,J4: nat,R3: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_nat @ I @ ( field_nat @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3615_FieldI1,axiom,
% 7.78/3.98 ! [I: int,J4: int,R3: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J4 ) @ R3 )
% 7.78/3.98 => ( member_int @ I @ ( field_int @ R3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3616_inf__Int__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( inf_in6969519006101653788_nat_o
% 7.78/3.98 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( inf_in2456762090751560885at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3617_inf__Int__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( inf_in6124848772414083356_nat_o
% 7.78/3.98 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( inf_in7913087082777306421at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3618_inf__Int__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 7.78/3.98 ( ( inf_inf_nat_num_o
% 7.78/3.98 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( inf_in7510916698018314649at_num @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3619_inf__Int__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( inf_inf_int_int_o
% 7.78/3.98 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( inf_in2269163501485487111nt_int @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3620_inf__Int__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( inf_inf_nat_nat_o
% 7.78/3.98 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( inf_in2572325071724192079at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3621_fun__upd__comp,axiom,
% 7.78/3.98 ! [F: $o > $o,G: nat > $o,X2: nat,Y3: $o] :
% 7.78/3.98 ( ( comp_o_o_nat @ F @ ( fun_upd_nat_o @ G @ X2 @ Y3 ) )
% 7.78/3.98 = ( fun_upd_nat_o @ ( comp_o_o_nat @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3622_fun__upd__comp,axiom,
% 7.78/3.98 ! [F: nat > num,G: int > nat,X2: int,Y3: nat] :
% 7.78/3.98 ( ( comp_nat_num_int @ F @ ( fun_upd_int_nat @ G @ X2 @ Y3 ) )
% 7.78/3.98 = ( fun_upd_int_num @ ( comp_nat_num_int @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3623_fun__upd__comp,axiom,
% 7.78/3.98 ! [F: nat > nat,G: nat > nat,X2: nat,Y3: nat] :
% 7.78/3.98 ( ( comp_nat_nat_nat @ F @ ( fun_upd_nat_nat @ G @ X2 @ Y3 ) )
% 7.78/3.98 = ( fun_upd_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3624_fun__upd__comp,axiom,
% 7.78/3.98 ! [F: int > nat,G: int > int,X2: int,Y3: int] :
% 7.78/3.98 ( ( comp_int_nat_int @ F @ ( fun_upd_int_int @ G @ X2 @ Y3 ) )
% 7.78/3.98 = ( fun_upd_int_nat @ ( comp_int_nat_int @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3625_fun__upd__comp,axiom,
% 7.78/3.98 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X2: code_integer,Y3: code_integer > code_integer] :
% 7.78/3.98 ( ( comp_C8797469213163452608nteger @ F @ ( fun_up8056716234270145717nteger @ G @ X2 @ Y3 ) )
% 7.78/3.98 = ( fun_up8139772397987072257nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ X2 @ ( F @ Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3626_image__vimage__subset,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_rat] : ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) ) @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3627_image__vimage__subset,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( vimage_nat_nat @ F @ A4 ) ) @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3628_image__vimage__subset,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_int] : ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( vimage_nat_int @ F @ A4 ) ) @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3629_image__vimage__subset,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_nat] : ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( vimage_int_nat @ F @ A4 ) ) @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3630_image__vimage__subset,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ F @ ( vimage_int_int @ F @ A4 ) ) @ A4 ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3631_image__subset__iff__subset__vimage,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.98 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_rat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3632_image__subset__iff__subset__vimage,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_nat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3633_image__subset__iff__subset__vimage,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.98 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.98 = ( ord_less_eq_set_nat @ A4 @ ( vimage_nat_int @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3634_image__subset__iff__subset__vimage,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.98 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.98 = ( ord_less_eq_set_int @ A4 @ ( vimage_int_nat @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3635_image__subset__iff__subset__vimage,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.98 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.98 = ( ord_less_eq_set_int @ A4 @ ( vimage_int_int @ F @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3636_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: char > char,A4: set_char] :
% 7.78/3.98 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( image_char_char @ F @ ( vimage_char_char @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3637_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: char > rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( image_char_rat @ F @ ( vimage_char_rat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3638_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: char > nat,A4: set_nat] :
% 7.78/3.98 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( image_char_nat @ F @ ( vimage_char_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3639_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: char > int,A4: set_int] :
% 7.78/3.98 ( ( ( image_char_int @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_int )
% 7.78/3.98 => ( ( image_char_int @ F @ ( vimage_char_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3640_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: rat > char,A4: set_char] :
% 7.78/3.98 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( image_rat_char @ F @ ( vimage_rat_char @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3641_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: rat > rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( image_rat_rat @ F @ ( vimage_rat_rat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3642_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: rat > nat,A4: set_nat] :
% 7.78/3.98 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( image_rat_nat @ F @ ( vimage_rat_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3643_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: rat > int,A4: set_int] :
% 7.78/3.98 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_int )
% 7.78/3.98 => ( ( image_rat_int @ F @ ( vimage_rat_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3644_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > char,A4: set_char] :
% 7.78/3.98 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( image_nat_char @ F @ ( vimage_nat_char @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3645_surj__image__vimage__eq,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( image_nat_rat @ F @ ( vimage_nat_rat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3646_bdd__below__image__mono,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_rat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit1103211067700513672ow_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3647_bdd__below__image__mono,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3648_bdd__below__image__mono,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit1738341127787009408ow_nat @ A4 )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3649_bdd__below__image__mono,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( condit1738341127787009408ow_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3650_bdd__below__image__mono,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_int @ F )
% 7.78/3.98 => ( ( condit1735850657277959132ow_int @ A4 )
% 7.78/3.98 => ( condit1735850657277959132ow_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3651_bdd__above__image__mono,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_rat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit1579696412822616692ve_rat @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3652_bdd__above__image__mono,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3653_bdd__above__image__mono,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3654_bdd__above__image__mono,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( condit2214826472909112428ve_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3655_bdd__above__image__mono,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_int @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( condit2212336002400062152ve_int @ ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3656_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr7459493094073627847at_nat,S5: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( sup_su6164525874564267778_nat_o
% 7.78/3.98 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ ( sup_su5395584912770621083at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3657_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr6200539531224447659at_num,S5: set_Pr6200539531224447659at_num] :
% 7.78/3.98 ( ( sup_sup_nat_num_o
% 7.78/3.98 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: nat,Y5: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y5 ) @ ( sup_su2042722026077122175at_num @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3658_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( sup_sup_nat_nat_o
% 7.78/3.98 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ ( sup_su6327502436637775413at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3659_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( sup_sup_int_int_o
% 7.78/3.98 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ ( sup_su6024340866399070445nt_int @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3660_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr8693737435421807431at_nat,S5: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( sup_su362511073950362882_nat_o
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ ( sup_su718114333110466843at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3661_sup__Un__eq2,axiom,
% 7.78/3.98 ! [R3: set_Pr4329608150637261639at_nat,S5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( sup_su7519161239522478338_nat_o
% 7.78/3.98 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R3 )
% 7.78/3.98 @ ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ S5 ) )
% 7.78/3.98 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ ( sup_su5525570899277871387at_nat @ R3 @ S5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3662_vimage__Union,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_set_nat] :
% 7.78/3.98 ( ( vimage_nat_nat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
% 7.78/3.98 = ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ ( vimage_nat_nat @ F ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3663_vimage__Times,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_nat,B5: set_nat] :
% 7.78/3.98 ( ( vimage2449269961533847803at_nat @ F
% 7.78/3.98 @ ( produc457027306803732586at_nat @ A4
% 7.78/3.98 @ ^ [Uu: nat] : B5 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( vimage4653281326611754070at_nat @ ( comp_P1567445206330693457at_nat @ product_fst_nat_nat @ F ) @ A4 ) @ ( vimage4653281326611754070at_nat @ ( comp_P1567445206330693457at_nat @ product_snd_nat_nat @ F ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3664_vimage__Times,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > produc7812382424243267045t_unit,A4: set_ref_a,B5: set_he8644174446132254637t_unit] :
% 7.78/3.98 ( ( vimage4308919176130087787t_unit @ F
% 7.78/3.98 @ ( produc3946373962484743846t_unit @ A4
% 7.78/3.98 @ ^ [Uu: ref_a] : B5 ) )
% 7.78/3.98 = ( inf_in2572325071724192079at_nat @ ( vimage7322659125625010723_ref_a @ ( comp_P7986581389989349338at_nat @ produc473321116828791851t_unit @ F ) @ A4 ) @ ( vimage1024995831485383111t_unit @ ( comp_P6390991081591698364at_nat @ produc1126150082675451753t_unit @ F ) @ B5 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3665_inj__on__fun__updI,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,Y3: rat,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.98 => ( ~ ( member_rat @ Y3 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_nat_rat @ ( fun_upd_nat_rat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3666_inj__on__fun__updI,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,Y3: nat,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ~ ( member_nat @ Y3 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_nat_nat @ ( fun_upd_nat_nat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3667_inj__on__fun__updI,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,Y3: nat,X2: int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ~ ( member_nat @ Y3 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3668_inj__on__fun__updI,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,Y3: int,X2: nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.98 => ( ~ ( member_int @ Y3 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_nat_int @ ( fun_upd_nat_int @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3669_inj__on__fun__updI,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,Y3: int,X2: int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ~ ( member_int @ Y3 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( inj_on_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3670_set_Ocomp,axiom,
% 7.78/3.98 ! [F: nat > $o,G: $o > $o] :
% 7.78/3.98 ( ( comp_s9189197539837705563_set_o @ ( vimage_nat_o @ F ) @ ( vimage_o_o @ G ) )
% 7.78/3.98 = ( vimage_nat_o @ ( comp_o_o_nat @ G @ F ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3671_set_Ocomp,axiom,
% 7.78/3.98 ! [F: int > nat,G: nat > num] :
% 7.78/3.98 ( ( comp_s6458263553158497821et_num @ ( vimage_int_nat @ F ) @ ( vimage_nat_num @ G ) )
% 7.78/3.98 = ( vimage_int_num @ ( comp_nat_num_int @ G @ F ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3672_set_Ocomp,axiom,
% 7.78/3.98 ! [F: nat > nat,G: nat > nat] :
% 7.78/3.98 ( ( comp_s8964582002068861047et_nat @ ( vimage_nat_nat @ F ) @ ( vimage_nat_nat @ G ) )
% 7.78/3.98 = ( vimage_nat_nat @ ( comp_nat_nat_nat @ G @ F ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3673_set_Ocomp,axiom,
% 7.78/3.98 ! [F: int > int,G: int > nat] :
% 7.78/3.98 ( ( comp_s7717450105097109807et_nat @ ( vimage_int_int @ F ) @ ( vimage_int_nat @ G ) )
% 7.78/3.98 = ( vimage_int_nat @ ( comp_int_nat_int @ G @ F ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3674_set_Ocomp,axiom,
% 7.78/3.98 ! [F: code_integer > code_integer > code_integer,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 7.78/3.98 ( ( comp_s4786119426940707554nteger @ ( vimage6029918387083761651nteger @ F ) @ ( vimage4289680085338140859nteger @ G ) )
% 7.78/3.98 = ( vimage6839621282666897215nteger @ ( comp_C8797469213163452608nteger @ G @ F ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3675_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 7.78/3.98 = top_to1996260823553986621t_unit )
% 7.78/3.98 => ( ( ( vimage7995052115951654139t_unit @ F @ A4 )
% 7.78/3.98 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 = ( A4 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3676_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: product_unit > $o,A4: set_o] :
% 7.78/3.98 ( ( ( image_Product_unit_o @ F @ top_to1996260823553986621t_unit )
% 7.78/3.98 = top_top_set_o )
% 7.78/3.98 => ( ( ( vimage8808348054653608838unit_o @ F @ A4 )
% 7.78/3.98 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 = ( A4 = bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3677_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( ( image_o_Product_unit @ F @ top_top_set_o )
% 7.78/3.98 = top_to1996260823553986621t_unit )
% 7.78/3.98 => ( ( ( vimage4222377557387472176t_unit @ F @ A4 )
% 7.78/3.98 = bot_bot_set_o )
% 7.78/3.98 = ( A4 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3678_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: $o > $o,A4: set_o] :
% 7.78/3.98 ( ( ( image_o_o @ F @ top_top_set_o )
% 7.78/3.98 = top_top_set_o )
% 7.78/3.98 => ( ( ( vimage_o_o @ F @ A4 )
% 7.78/3.98 = bot_bot_set_o )
% 7.78/3.98 = ( A4 = bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3679_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: product_unit > char,A4: set_char] :
% 7.78/3.98 ( ( ( image_7248553556944771225t_char @ F @ top_to1996260823553986621t_unit )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( ( vimage2648087219933717859t_char @ F @ A4 )
% 7.78/3.98 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 = ( A4 = bot_bot_set_char ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3680_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: $o > char,A4: set_char] :
% 7.78/3.98 ( ( ( image_o_char @ F @ top_top_set_o )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( ( vimage_o_char @ F @ A4 )
% 7.78/3.98 = bot_bot_set_o )
% 7.78/3.98 = ( A4 = bot_bot_set_char ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3681_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: product_unit > rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_240439954468258464it_rat @ F @ top_to1996260823553986621t_unit )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( ( vimage5618198413390092650it_rat @ F @ A4 )
% 7.78/3.98 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 = ( A4 = bot_bot_set_rat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3682_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: $o > rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_o_rat @ F @ top_top_set_o )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( ( vimage_o_rat @ F @ A4 )
% 7.78/3.98 = bot_bot_set_o )
% 7.78/3.98 = ( A4 = bot_bot_set_rat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3683_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: set_nat] :
% 7.78/3.98 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( ( vimage6253328473476588386it_nat @ F @ A4 )
% 7.78/3.98 = bot_bo3957492148770167129t_unit )
% 7.78/3.98 = ( A4 = bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3684_surj__vimage__empty,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_nat] :
% 7.78/3.98 ( ( ( image_o_nat @ F @ top_top_set_o )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( ( vimage_o_nat @ F @ A4 )
% 7.78/3.98 = bot_bot_set_o )
% 7.78/3.98 = ( A4 = bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3685_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: char > char,B5: set_char,A4: set_char] :
% 7.78/3.98 ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( ord_less_eq_set_char @ ( vimage_char_char @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_char @ B5 @ ( image_char_char @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3686_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: char > rat,B5: set_rat,A4: set_char] :
% 7.78/3.98 ( ( ( image_char_rat @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( ord_less_eq_set_char @ ( vimage_char_rat @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_rat @ B5 @ ( image_char_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3687_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: char > nat,B5: set_nat,A4: set_char] :
% 7.78/3.98 ( ( ( image_char_nat @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_char @ ( vimage_char_nat @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ B5 @ ( image_char_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3688_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: char > int,B5: set_int,A4: set_char] :
% 7.78/3.98 ( ( ( image_char_int @ F @ top_top_set_char )
% 7.78/3.98 = top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_char @ ( vimage_char_int @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ B5 @ ( image_char_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3689_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: rat > char,B5: set_char,A4: set_rat] :
% 7.78/3.98 ( ( ( image_rat_char @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ ( vimage_rat_char @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_char @ B5 @ ( image_rat_char @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3690_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: rat > rat,B5: set_rat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ ( vimage_rat_rat @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_rat @ B5 @ ( image_rat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3691_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: rat > nat,B5: set_nat,A4: set_rat] :
% 7.78/3.98 ( ( ( image_rat_nat @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ ( vimage_rat_nat @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_nat @ B5 @ ( image_rat_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3692_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: rat > int,B5: set_int,A4: set_rat] :
% 7.78/3.98 ( ( ( image_rat_int @ F @ top_top_set_rat )
% 7.78/3.98 = top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ ( vimage_rat_int @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_int @ B5 @ ( image_rat_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3693_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: nat > char,B5: set_char,A4: set_nat] :
% 7.78/3.98 ( ( ( image_nat_char @ F @ top_top_set_nat )
% 7.78/3.98 = top_top_set_char )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( vimage_nat_char @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_char @ B5 @ ( image_nat_char @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3694_vimage__subsetD,axiom,
% 7.78/3.98 ! [F: nat > rat,B5: set_rat,A4: set_nat] :
% 7.78/3.98 ( ( ( image_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 = top_top_set_rat )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( vimage_nat_rat @ F @ B5 ) @ A4 )
% 7.78/3.98 => ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3695_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > set_num] :
% 7.78/3.98 ( ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage5436458796434496692at_num @ ( product_Pair_nat_num @ X2 ) @ ( produc6237731129814287028at_num @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage5436458796434496692at_num @ ( product_Pair_nat_num @ X2 ) @ ( produc6237731129814287028at_num @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_num ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3696_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > set_int] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage7872673496510460816nt_int @ ( product_Pair_int_int @ X2 ) @ ( produc1453890548195736866nt_int @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage7872673496510460816nt_int @ ( product_Pair_int_int @ X2 ) @ ( produc1453890548195736866nt_int @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_int ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3697_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > set_Product_unit] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X2 ) @ ( produc411009820408249917t_unit @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X2 ) @ ( produc411009820408249917t_unit @ A4 @ F ) )
% 7.78/3.98 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3698_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > set_Product_unit] :
% 7.78/3.98 ( ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X2 ) @ ( produc5506539147108004339t_unit @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X2 ) @ ( produc5506539147108004339t_unit @ A4 @ F ) )
% 7.78/3.98 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3699_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > set_Product_unit] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X2 ) @ ( produc2622961094310184599t_unit @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X2 ) @ ( produc2622961094310184599t_unit @ A4 @ F ) )
% 7.78/3.98 = bot_bo3957492148770167129t_unit ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3700_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > set_o] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X2 ) @ ( product_Sigma_o_o @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X2 ) @ ( product_Sigma_o_o @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3701_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: nat,A4: set_nat,F: nat > set_o] :
% 7.78/3.98 ( ( ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X2 ) @ ( product_Sigma_nat_o @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_nat @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X2 ) @ ( product_Sigma_nat_o @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3702_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > set_o] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X2 ) @ ( product_Sigma_int_o @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X2 ) @ ( product_Sigma_int_o @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_o ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3703_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > set_nat] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X2 ) @ ( product_Sigma_o_nat @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X2 ) @ ( product_Sigma_o_nat @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3704_Pair__vimage__Sigma,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > set_nat] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X2 ) @ ( produc1456381018704787142nt_nat @ A4 @ F ) )
% 7.78/3.98 = ( F @ X2 ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X2 ) @ ( produc1456381018704787142nt_nat @ A4 @ F ) )
% 7.78/3.98 = bot_bot_set_nat ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3705_inj__vimage__image__eq,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( vimage_nat_rat @ F @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3706_inj__vimage__image__eq,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( vimage_nat_nat @ F @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3707_inj__vimage__image__eq,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( vimage_nat_int @ F @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3708_inj__vimage__image__eq,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( vimage_int_nat @ F @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3709_inj__vimage__image__eq,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( vimage_int_int @ F @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 = A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3710_inj__graph,axiom,
% 7.78/3.98 ( inj_on3412903767820855855at_nat
% 7.78/3.98 @ ^ [F2: nat > nat] :
% 7.78/3.98 ( collec3392354462482085612at_nat
% 7.78/3.98 @ ( produc6081775807080527818_nat_o
% 7.78/3.98 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.98 ( Y5
% 7.78/3.98 = ( F2 @ X4 ) ) ) )
% 7.78/3.98 @ top_top_set_nat_nat ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3711_inj__graph,axiom,
% 7.78/3.98 ( inj_on7039184780174133295nt_int
% 7.78/3.98 @ ^ [F2: int > int] :
% 7.78/3.98 ( collec213857154873943460nt_int
% 7.78/3.98 @ ( produc4947309494688390418_int_o
% 7.78/3.98 @ ^ [X4: int,Y5: int] :
% 7.78/3.98 ( Y5
% 7.78/3.98 = ( F2 @ X4 ) ) ) )
% 7.78/3.98 @ top_top_set_int_int ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3712_f__the__inv__into__f,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,Y3: rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.98 => ( ( member_rat @ Y3 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( ( F @ ( the_inv_into_nat_rat @ A4 @ F @ Y3 ) )
% 7.78/3.98 = Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3713_f__the__inv__into__f,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,Y3: nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ( member_nat @ Y3 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( F @ ( the_inv_into_nat_nat @ A4 @ F @ Y3 ) )
% 7.78/3.98 = Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3714_f__the__inv__into__f,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,Y3: nat] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ( member_nat @ Y3 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( F @ ( the_inv_into_int_nat @ A4 @ F @ Y3 ) )
% 7.78/3.98 = Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3715_f__the__inv__into__f,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,Y3: int] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.98 => ( ( member_int @ Y3 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( F @ ( the_inv_into_nat_int @ A4 @ F @ Y3 ) )
% 7.78/3.98 = Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3716_f__the__inv__into__f,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,Y3: int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ( member_int @ Y3 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( F @ ( the_inv_into_int_int @ A4 @ F @ Y3 ) )
% 7.78/3.98 = Y3 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3717_inj__on__the__inv__into,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.98 => ( inj_on_rat_nat @ ( the_inv_into_nat_rat @ A4 @ F ) @ ( image_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3718_inj__on__the__inv__into,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A4 @ F ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3719_inj__on__the__inv__into,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.98 => ( inj_on_int_nat @ ( the_inv_into_nat_int @ A4 @ F ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3720_inj__on__the__inv__into,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( inj_on_nat_int @ ( the_inv_into_int_nat @ A4 @ F ) @ ( image_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3721_inj__on__the__inv__into,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( inj_on_int_int @ ( the_inv_into_int_int @ A4 @ F ) @ ( image_int_int @ F @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3722_vimage__fst,axiom,
% 7.78/3.98 ! [A4: set_ref_a] :
% 7.78/3.98 ( ( vimage2910454108108208703_ref_a @ produc473321116828791851t_unit @ A4 )
% 7.78/3.98 = ( produc3946373962484743846t_unit @ A4
% 7.78/3.98 @ ^ [Uu: ref_a] : top_to3956321331435058429t_unit ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3723_vimage__fst,axiom,
% 7.78/3.98 ! [A4: set_nat] :
% 7.78/3.98 ( ( vimage4653281326611754070at_nat @ product_fst_nat_nat @ A4 )
% 7.78/3.98 = ( produc457027306803732586at_nat @ A4
% 7.78/3.98 @ ^ [Uu: nat] : top_top_set_nat ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3724_vimage__snd,axiom,
% 7.78/3.98 ! [A4: set_he8644174446132254637t_unit] :
% 7.78/3.98 ( ( vimage6116673589273818795t_unit @ produc1126150082675451753t_unit @ A4 )
% 7.78/3.98 = ( produc3946373962484743846t_unit @ top_top_set_ref_a
% 7.78/3.98 @ ^ [Uu: ref_a] : A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3725_vimage__snd,axiom,
% 7.78/3.98 ! [A4: set_nat] :
% 7.78/3.98 ( ( vimage4653281326611754070at_nat @ product_snd_nat_nat @ A4 )
% 7.78/3.98 = ( produc457027306803732586at_nat @ top_top_set_nat
% 7.78/3.98 @ ^ [Uu: nat] : A4 ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3726_mono__Sup,axiom,
% 7.78/3.98 ! [F: set_nat > set_nat,A4: set_set_nat] :
% 7.78/3.98 ( ( order_1005506198798982270et_nat @ F )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_7916887816326733075et_nat @ F @ A4 ) ) @ ( F @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3727_mono__Sup,axiom,
% 7.78/3.98 ! [F: product_unit > set_nat,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_509894322932672675et_nat @ F )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3728_mono__Sup,axiom,
% 7.78/3.98 ! [F: set_nat > product_unit,A4: set_set_nat] :
% 7.78/3.98 ( ( order_7928700340835332885t_unit @ F )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_6369283972875870912t_unit @ F @ A4 ) ) @ ( F @ ( comple7399068483239264473et_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3729_mono__Sup,axiom,
% 7.78/3.98 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_4454465170704313136t_unit @ F )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3730_mono__Inf,axiom,
% 7.78/3.98 ! [F: set_nat > set_nat,A4: set_set_nat] :
% 7.78/3.98 ( ( order_1005506198798982270et_nat @ F )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( F @ ( comple7806235888213564991et_nat @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_7916887816326733075et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3731_mono__Inf,axiom,
% 7.78/3.98 ! [F: set_nat > product_unit,A4: set_set_nat] :
% 7.78/3.98 ( ( order_7928700340835332885t_unit @ F )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( comple7806235888213564991et_nat @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_6369283972875870912t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3732_mono__Inf,axiom,
% 7.78/3.98 ! [F: product_unit > set_nat,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_509894322932672675et_nat @ F )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3733_mono__Inf,axiom,
% 7.78/3.98 ! [F: product_unit > product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_4454465170704313136t_unit @ F )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( F @ ( comple2584293577114468500t_unit @ A4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3734_Pow__insert,axiom,
% 7.78/3.98 ! [A: nat,A4: set_nat] :
% 7.78/3.98 ( ( pow_nat @ ( insert_nat @ A @ A4 ) )
% 7.78/3.98 = ( sup_sup_set_set_nat @ ( pow_nat @ A4 ) @ ( image_7916887816326733075et_nat @ ( insert_nat @ A ) @ ( pow_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3735_Pow__insert,axiom,
% 7.78/3.98 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( pow_Pr3466873192417945886at_nat @ ( insert8211810215607154385at_nat @ A @ A4 ) )
% 7.78/3.98 = ( sup_su3642409539654194069at_nat @ ( pow_Pr3466873192417945886at_nat @ A4 ) @ ( image_3684629450409544005at_nat @ ( insert8211810215607154385at_nat @ A ) @ ( pow_Pr3466873192417945886at_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3736_Pow__insert,axiom,
% 7.78/3.98 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( pow_Pr1023649790151954692at_nat @ ( insert9069300056098147895at_nat @ A @ A4 ) )
% 7.78/3.98 = ( sup_su474284620922681339at_nat @ ( pow_Pr1023649790151954692at_nat @ A4 ) @ ( image_4303274092540115909at_nat @ ( insert9069300056098147895at_nat @ A ) @ ( pow_Pr1023649790151954692at_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3737_Pow__insert,axiom,
% 7.78/3.98 ! [A: product_unit,A4: set_Product_unit] :
% 7.78/3.98 ( ( pow_Product_unit @ ( insert_Product_unit @ A @ A4 ) )
% 7.78/3.98 = ( sup_su5975557051335651745t_unit @ ( pow_Product_unit @ A4 ) @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ A ) @ ( pow_Product_unit @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3738_Pow__insert,axiom,
% 7.78/3.98 ! [A: $o,A4: set_o] :
% 7.78/3.98 ( ( pow_o @ ( insert_o @ A @ A4 ) )
% 7.78/3.98 = ( sup_sup_set_set_o @ ( pow_o @ A4 ) @ ( image_set_o_set_o @ ( insert_o @ A ) @ ( pow_o @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3739_vimage__subsetI,axiom,
% 7.78/3.98 ! [F: nat > rat,B5: set_rat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( vimage_nat_rat @ F @ B5 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3740_vimage__subsetI,axiom,
% 7.78/3.98 ! [F: nat > nat,B5: set_nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( vimage_nat_nat @ F @ B5 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3741_vimage__subsetI,axiom,
% 7.78/3.98 ! [F: nat > int,B5: set_int,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_nat @ ( vimage_nat_int @ F @ B5 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3742_vimage__subsetI,axiom,
% 7.78/3.98 ! [F: int > nat,B5: set_nat,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( vimage_int_nat @ F @ B5 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3743_vimage__subsetI,axiom,
% 7.78/3.98 ! [F: int > int,B5: set_int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ord_less_eq_set_int @ ( vimage_int_int @ F @ B5 ) @ A4 ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3744_vimage__eq__UN,axiom,
% 7.78/3.98 ( vimage4884490618288580032t_unit
% 7.78/3.98 = ( ^ [F2: nat > product_unit,B6: set_Product_unit] :
% 7.78/3.98 ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_8173849991827986510et_nat
% 7.78/3.98 @ ^ [Y5: product_unit] : ( vimage4884490618288580032t_unit @ F2 @ ( insert_Product_unit @ Y5 @ bot_bo3957492148770167129t_unit ) )
% 7.78/3.98 @ B6 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3745_vimage__eq__UN,axiom,
% 7.78/3.98 ( vimage6435164912253009178at_nat
% 7.78/3.98 = ( ^ [F2: nat > produc3843707927480180839at_nat,B6: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_3160451284896210088et_nat
% 7.78/3.98 @ ^ [Y5: produc3843707927480180839at_nat] : ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ Y5 @ bot_bo228742789529271731at_nat ) )
% 7.78/3.98 @ B6 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3746_vimage__eq__UN,axiom,
% 7.78/3.98 ( vimage8013328719654469172at_nat
% 7.78/3.98 = ( ^ [F2: nat > product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_15824709712370754et_nat
% 7.78/3.98 @ ^ [Y5: product_prod_nat_nat] : ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ Y5 @ bot_bo2099793752762293965at_nat ) )
% 7.78/3.98 @ B6 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3747_vimage__eq__UN,axiom,
% 7.78/3.98 ( vimage_nat_o
% 7.78/3.98 = ( ^ [F2: nat > $o,B6: set_o] :
% 7.78/3.98 ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_o_set_nat
% 7.78/3.98 @ ^ [Y5: $o] : ( vimage_nat_o @ F2 @ ( insert_o @ Y5 @ bot_bot_set_o ) )
% 7.78/3.98 @ B6 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3748_vimage__eq__UN,axiom,
% 7.78/3.98 ( vimage_nat_nat
% 7.78/3.98 = ( ^ [F2: nat > nat,B6: set_nat] :
% 7.78/3.98 ( comple7399068483239264473et_nat
% 7.78/3.98 @ ( image_nat_set_nat
% 7.78/3.98 @ ^ [Y5: nat] : ( vimage_nat_nat @ F2 @ ( insert_nat @ Y5 @ bot_bot_set_nat ) )
% 7.78/3.98 @ B6 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3749_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat,X2: rat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.98 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( member_nat @ ( the_inv_into_nat_rat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3750_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: $o > $o,A4: set_o,X2: $o,B5: set_o] :
% 7.78/3.98 ( ( inj_on_o_o @ F @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_o_o @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( member_o @ ( the_inv_into_o_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3751_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: nat > $o,A4: set_nat,X2: $o,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( member_nat @ ( the_inv_into_nat_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3752_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: int > $o,A4: set_int,X2: $o,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_o @ F @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_int_o @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( member_int @ ( the_inv_into_int_o @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3753_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o,X2: nat,B5: set_o] :
% 7.78/3.98 ( ( inj_on_o_nat @ F @ A4 )
% 7.78/3.98 => ( ( member_nat @ X2 @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( member_o @ ( the_inv_into_o_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3754_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat,X2: nat,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.98 => ( ( member_nat @ X2 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( member_nat @ ( the_inv_into_nat_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3755_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int,X2: nat,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.98 => ( ( member_nat @ X2 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( member_int @ ( the_inv_into_int_nat @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3756_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o,X2: int,B5: set_o] :
% 7.78/3.98 ( ( inj_on_o_int @ F @ A4 )
% 7.78/3.98 => ( ( member_int @ X2 @ ( image_o_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 7.78/3.98 => ( member_o @ ( the_inv_into_o_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3757_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat,X2: int,B5: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.98 => ( ( member_int @ X2 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 7.78/3.98 => ( member_nat @ ( the_inv_into_nat_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3758_the__inv__into__into,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int,X2: int,B5: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.98 => ( ( member_int @ X2 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 7.78/3.98 => ( member_int @ ( the_inv_into_int_int @ A4 @ F @ X2 ) @ B5 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3759_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: nat > rat,G: nat > nat,A4: set_nat,X2: rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_nat_nat @ G @ A4 )
% 7.78/3.98 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ ( image_nat_nat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_nat_rat @ A4 @ ( comp_nat_rat_nat @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_nat_nat_rat @ ( the_inv_into_nat_nat @ A4 @ G ) @ ( the_inv_into_nat_rat @ ( image_nat_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3760_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: nat > num,G: int > nat,A4: set_int,X2: num] :
% 7.78/3.98 ( ( inj_on_nat_num @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_int_nat @ G @ A4 )
% 7.78/3.98 => ( ( member_num @ X2 @ ( image_nat_num @ F @ ( image_int_nat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_int_num @ A4 @ ( comp_nat_num_int @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_nat_int_num @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_num @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3761_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: nat > rat,G: int > nat,A4: set_int,X2: rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_int_nat @ G @ A4 )
% 7.78/3.98 => ( ( member_rat @ X2 @ ( image_nat_rat @ F @ ( image_int_nat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_int_rat @ A4 @ ( comp_nat_rat_int @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_nat_int_rat @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_rat @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3762_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: $o > $o,G: nat > $o,A4: set_nat,X2: $o] :
% 7.78/3.98 ( ( inj_on_o_o @ F @ ( image_nat_o @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_nat_o @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_o_o @ F @ ( image_nat_o @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_nat_o @ A4 @ ( comp_o_o_nat @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_o_nat_o @ ( the_inv_into_nat_o @ A4 @ G ) @ ( the_inv_into_o_o @ ( image_nat_o @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3763_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: rat > $o,G: nat > rat,A4: set_nat,X2: $o] :
% 7.78/3.98 ( ( inj_on_rat_o @ F @ ( image_nat_rat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_nat_rat @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_rat_o @ F @ ( image_nat_rat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_nat_o @ A4 @ ( comp_rat_o_nat @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_rat_nat_o @ ( the_inv_into_nat_rat @ A4 @ G ) @ ( the_inv_into_rat_o @ ( image_nat_rat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3764_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: nat > $o,G: nat > nat,A4: set_nat,X2: $o] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ ( image_nat_nat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_nat_nat @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_nat_o @ F @ ( image_nat_nat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_nat_o @ A4 @ ( comp_nat_o_nat @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_nat_nat_o @ ( the_inv_into_nat_nat @ A4 @ G ) @ ( the_inv_into_nat_o @ ( image_nat_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3765_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: int > $o,G: nat > int,A4: set_nat,X2: $o] :
% 7.78/3.98 ( ( inj_on_int_o @ F @ ( image_nat_int @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_nat_int @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_int_o @ F @ ( image_nat_int @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_nat_o @ A4 @ ( comp_int_o_nat @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_int_nat_o @ ( the_inv_into_nat_int @ A4 @ G ) @ ( the_inv_into_int_o @ ( image_nat_int @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3766_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: nat > $o,G: int > nat,A4: set_int,X2: $o] :
% 7.78/3.98 ( ( inj_on_nat_o @ F @ ( image_int_nat @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_int_nat @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_nat_o @ F @ ( image_int_nat @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_int_o @ A4 @ ( comp_nat_o_int @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_nat_int_o @ ( the_inv_into_int_nat @ A4 @ G ) @ ( the_inv_into_nat_o @ ( image_int_nat @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3767_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: int > $o,G: int > int,A4: set_int,X2: $o] :
% 7.78/3.98 ( ( inj_on_int_o @ F @ ( image_int_int @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_int_int @ G @ A4 )
% 7.78/3.98 => ( ( member_o @ X2 @ ( image_int_o @ F @ ( image_int_int @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_int_o @ A4 @ ( comp_int_o_int @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_int_int_o @ ( the_inv_into_int_int @ A4 @ G ) @ ( the_inv_into_int_o @ ( image_int_int @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3768_the__inv__into__comp,axiom,
% 7.78/3.98 ! [F: $o > nat,G: $o > $o,A4: set_o,X2: nat] :
% 7.78/3.98 ( ( inj_on_o_nat @ F @ ( image_o_o @ G @ A4 ) )
% 7.78/3.98 => ( ( inj_on_o_o @ G @ A4 )
% 7.78/3.98 => ( ( member_nat @ X2 @ ( image_o_nat @ F @ ( image_o_o @ G @ A4 ) ) )
% 7.78/3.98 => ( ( the_inv_into_o_nat @ A4 @ ( comp_o_nat_o @ F @ G ) @ X2 )
% 7.78/3.98 = ( comp_o_o_nat @ ( the_inv_into_o_o @ A4 @ G ) @ ( the_inv_into_o_nat @ ( image_o_o @ G @ A4 ) @ F ) @ X2 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3769_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > int,Y3: int] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_int @ Y3 @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_int @ ( fun_upd_int_int @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_int_int @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3770_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > nat,Y3: nat] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_nat @ Y3 @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_nat @ ( fun_upd_int_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_int_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3771_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > product_unit,Y3: product_unit] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_5846526143423701914t_unit @ ( fun_up2220634978854545698t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_Product_unit @ Y3 @ ( image_5846526143423701914t_unit @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_5846526143423701914t_unit @ ( fun_up2220634978854545698t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_5846526143423701914t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3772_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: int,A4: set_int,F: int > $o,Y3: $o] :
% 7.78/3.98 ( ( ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_o @ Y3 @ ( image_int_o @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_int @ X2 @ A4 )
% 7.78/3.98 => ( ( image_int_o @ ( fun_upd_int_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_int_o @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3773_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > nat,Y3: nat] :
% 7.78/3.98 ( ( ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_nat @ Y3 @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_875570014554754200it_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3774_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > product_unit,Y3: product_unit] :
% 7.78/3.98 ( ( ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_Product_unit @ Y3 @ ( image_405062704495631173t_unit @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_405062704495631173t_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3775_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: product_unit,A4: set_Product_unit,F: product_unit > $o,Y3: $o] :
% 7.78/3.98 ( ( ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_Product_unit_o @ ( fun_up5432024876597553480unit_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_o @ Y3 @ ( image_Product_unit_o @ F @ ( minus_6452836326544984404t_unit @ A4 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_Product_unit @ X2 @ A4 )
% 7.78/3.98 => ( ( image_Product_unit_o @ ( fun_up5432024876597553480unit_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_Product_unit_o @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3776_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > nat,Y3: nat] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_nat @ Y3 @ ( image_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_nat @ ( fun_upd_o_nat @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_o_nat @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3777_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > product_unit,Y3: product_unit] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_Product_unit @ ( fun_up846054379331416818t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_Product_unit @ Y3 @ ( image_o_Product_unit @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_Product_unit @ ( fun_up846054379331416818t_unit @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_o_Product_unit @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3778_fun__upd__image,axiom,
% 7.78/3.98 ! [X2: $o,A4: set_o,F: $o > $o,Y3: $o] :
% 7.78/3.98 ( ( ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( insert_o @ Y3 @ ( image_o_o @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 7.78/3.98 & ( ~ ( member_o @ X2 @ A4 )
% 7.78/3.98 => ( ( image_o_o @ ( fun_upd_o_o @ F @ X2 @ Y3 ) @ A4 )
% 7.78/3.98 = ( image_o_o @ F @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3779_mono__cSUP,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: int > nat,I3: set_int] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_int_nat
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_nat @ ( image_int_nat @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3780_mono__cSUP,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: nat > nat,I3: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_nat_nat
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3781_mono__cSUP,axiom,
% 7.78/3.98 ! [F: int > nat,A4: int > int,I3: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_int_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_int_nat
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_int @ ( image_int_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3782_mono__cSUP,axiom,
% 7.78/3.98 ! [F: int > nat,A4: product_unit > int,I3: set_Product_unit] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_875570014554754200it_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3783_mono__cSUP,axiom,
% 7.78/3.98 ! [F: int > nat,A4: $o > int,I3: set_o] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_o_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_o_nat
% 7.78/3.98 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_int @ ( image_o_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3784_mono__cSUP,axiom,
% 7.78/3.98 ! [F: int > nat,A4: nat > int,I3: set_nat] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ ( image_nat_int @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_nat_nat
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( complete_Sup_Sup_int @ ( image_nat_int @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3785_mono__cSUP,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: int > product_unit,I3: set_int] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_int_nat
% 7.78/3.98 @ ^ [X4: int] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3786_mono__cSUP,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: product_unit > product_unit,I3: set_Product_unit] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_875570014554754200it_nat
% 7.78/3.98 @ ^ [X4: product_unit] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3787_mono__cSUP,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: $o > product_unit,I3: set_o] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_o_nat
% 7.78/3.98 @ ^ [X4: $o] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3788_mono__cSUP,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: nat > product_unit,I3: set_nat] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) )
% 7.78/3.98 => ( ( I3 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat
% 7.78/3.98 @ ( complete_Sup_Sup_nat
% 7.78/3.98 @ ( image_nat_nat
% 7.78/3.98 @ ^ [X4: nat] : ( F @ ( A4 @ X4 ) )
% 7.78/3.98 @ I3 ) )
% 7.78/3.98 @ ( F @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ A4 @ I3 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3789_mono__cSup,axiom,
% 7.78/3.98 ! [F: $o > nat,A4: set_o] :
% 7.78/3.98 ( ( order_mono_o_nat @ F )
% 7.78/3.98 => ( ( condit5488710616941104124bove_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3790_mono__cSup,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_nat @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3791_mono__cSup,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_nat @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_int @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3792_mono__cSup,axiom,
% 7.78/3.98 ! [F: product_unit > nat,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_7096114683908731117it_nat @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3793_mono__cSup,axiom,
% 7.78/3.98 ! [F: $o > int,A4: set_o] :
% 7.78/3.98 ( ( order_mono_o_int @ F )
% 7.78/3.98 => ( ( condit5488710616941104124bove_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3794_mono__cSup,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( order_mono_nat_int @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3795_mono__cSup,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( order_mono_int_int @ F )
% 7.78/3.98 => ( ( condit2212336002400062152ve_int @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_int )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_int @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3796_mono__cSup,axiom,
% 7.78/3.98 ! [F: product_unit > int,A4: set_Product_unit] :
% 7.78/3.98 ( ( order_7093624213399680841it_int @ F )
% 7.78/3.98 => ( ( condit2080475194861589617t_unit @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A4 ) ) @ ( F @ ( comple4687483117567863418t_unit @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3797_mono__cSup,axiom,
% 7.78/3.98 ! [F: $o > product_unit,A4: set_o] :
% 7.78/3.98 ( ( order_7782127260464396005t_unit @ F )
% 7.78/3.98 => ( ( condit5488710616941104124bove_o @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_o )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3798_mono__cSup,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.98 ( ( order_5727276828720722763t_unit @ F )
% 7.78/3.98 => ( ( condit2214826472909112428ve_nat @ A4 )
% 7.78/3.98 => ( ( A4 != bot_bot_set_nat )
% 7.78/3.98 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3799_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > rat,A13: set_nat,B1: set_rat,F22: int > int,B22: set_int,A24: set_int] :
% 7.78/3.98 ( ( ( image_nat_rat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_int @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_int ) )
% 7.78/3.98 => ( ( bNF_We7904740386373615514nt_rat @ B22 @ B1 )
% 7.78/3.98 = ( image_1904597124500147013nt_rat @ ( bNF_We576767280138975660at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3800_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > nat,A13: set_nat,B1: set_nat,F22: int > int,B22: set_int,A24: set_int] :
% 7.78/3.98 ( ( ( image_nat_nat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_int @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_int ) )
% 7.78/3.98 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 7.78/3.98 = ( image_5412825682893543741nt_nat @ ( bNF_We893321924073841572at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3801_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > int,A13: set_nat,B1: set_int,F22: int > int,B22: set_int,A24: set_int] :
% 7.78/3.98 ( ( ( image_nat_int @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_int @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_int ) )
% 7.78/3.98 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 7.78/3.98 = ( image_1234974663384347033nt_int @ ( bNF_We1892675635974896128nt_int @ B22 @ F1 @ F22 ) @ ( bNF_We8539870446460111250nt_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3802_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: int > nat,A13: set_int,B1: set_nat,F22: int > int,B22: set_int,A24: set_int] :
% 7.78/3.98 ( ( ( image_int_nat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_int @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_int ) )
% 7.78/3.98 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 7.78/3.98 = ( image_1600535827742230425nt_nat @ ( bNF_We1264975484310686208at_int @ B22 @ F1 @ F22 ) @ ( bNF_We8537379975951060974nt_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3803_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: int > int,A13: set_int,B1: set_int,F22: int > int,B22: set_int,A24: set_int] :
% 7.78/3.98 ( ( ( image_int_int @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_int @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ ( image_int_int @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_int ) )
% 7.78/3.98 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 7.78/3.98 = ( image_6646056845087809525nt_int @ ( bNF_We2264329196211740764nt_int @ B22 @ F1 @ F22 ) @ ( bNF_We8537379975951060974nt_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3804_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > rat,A13: set_nat,B1: set_rat,F22: int > nat,B22: set_int,A24: set_nat] :
% 7.78/3.98 ( ( ( image_nat_rat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_nat ) )
% 7.78/3.98 => ( ( bNF_We7904740386373615514nt_rat @ B22 @ B1 )
% 7.78/3.98 = ( image_696479991571767017nt_rat @ ( bNF_We579257750648025936at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3805_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > nat,A13: set_nat,B1: set_nat,F22: int > nat,B22: set_int,A24: set_nat] :
% 7.78/3.98 ( ( ( image_nat_nat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_nat ) )
% 7.78/3.98 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 7.78/3.98 = ( image_4204708549965163745nt_nat @ ( bNF_We895812394582891848at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3806_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: nat > int,A13: set_nat,B1: set_int,F22: int > nat,B22: set_int,A24: set_nat] :
% 7.78/3.98 ( ( ( image_nat_int @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_nat ) )
% 7.78/3.98 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 7.78/3.98 = ( image_26857530455967037nt_int @ ( bNF_We1895166106483946404nt_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7540516734559056694at_nat @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3807_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: int > nat,A13: set_int,B1: set_nat,F22: int > nat,B22: set_int,A24: set_nat] :
% 7.78/3.98 ( ( ( image_int_nat @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_nat ) )
% 7.78/3.98 => ( ( bNF_We8539870446460111250nt_nat @ B22 @ B1 )
% 7.78/3.98 = ( image_392418694813850429nt_nat @ ( bNF_We1267465954819736484at_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7538026264050006418at_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3808_Func__map__surj,axiom,
% 7.78/3.98 ! [F1: int > int,A13: set_int,B1: set_int,F22: int > nat,B22: set_int,A24: set_nat] :
% 7.78/3.98 ( ( ( image_int_int @ F1 @ A13 )
% 7.78/3.98 = B1 )
% 7.78/3.98 => ( ( inj_on_int_nat @ F22 @ B22 )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F22 @ B22 ) @ A24 )
% 7.78/3.98 => ( ( ( B22 = bot_bot_set_int )
% 7.78/3.98 => ( A24 = bot_bot_set_nat ) )
% 7.78/3.98 => ( ( bNF_We8537379975951060974nt_int @ B22 @ B1 )
% 7.78/3.98 = ( image_5437939712159429529nt_int @ ( bNF_We2266819666720791040nt_nat @ B22 @ F1 @ F22 ) @ ( bNF_We7538026264050006418at_int @ A24 @ A13 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3809_cofinal__def,axiom,
% 7.78/3.98 ( bNF_Ca6037544080215331608at_nat
% 7.78/3.98 = ( ^ [A6: set_se5479201105039950375at_nat,R5: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ! [X4: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member6273874620674182256at_nat @ X4 @ ( field_1428494348145443988at_nat @ R5 ) )
% 7.78/3.98 => ? [Y5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 7.78/3.98 & ( X4 != Y5 )
% 7.78/3.98 & ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3810_cofinal__def,axiom,
% 7.78/3.98 ( bNF_Ca8448034394003515314at_nat
% 7.78/3.98 = ( ^ [A6: set_se7855581050983116737at_nat,R5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ! [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member2643936169264416010at_nat @ X4 @ ( field_3145993188331922222at_nat @ R5 ) )
% 7.78/3.98 => ? [Y5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 7.78/3.98 & ( X4 != Y5 )
% 7.78/3.98 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3811_cofinal__def,axiom,
% 7.78/3.98 ( bNF_Ca5159621140400407487al_nat
% 7.78/3.98 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ! [X4: nat] :
% 7.78/3.98 ( ( member_nat @ X4 @ ( field_nat @ R5 ) )
% 7.78/3.98 => ? [Y5: nat] :
% 7.78/3.98 ( ( member_nat @ Y5 @ A6 )
% 7.78/3.98 & ( X4 != Y5 )
% 7.78/3.98 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3812_cofinal__def,axiom,
% 7.78/3.98 ( bNF_Ca5157130669891357211al_int
% 7.78/3.98 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ! [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ ( field_int @ R5 ) )
% 7.78/3.98 => ? [Y5: int] :
% 7.78/3.98 ( ( member_int @ Y5 @ A6 )
% 7.78/3.98 & ( X4 != Y5 )
% 7.78/3.98 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3813_Total__subset__Id,axiom,
% 7.78/3.98 ! [R: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( total_5117575981256876747at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 7.78/3.98 => ( ( ord_le5997549366648089703at_nat @ R @ id_set4888139568991089827at_nat )
% 7.78/3.98 => ( ( R = bot_bo4948859079157340979at_nat )
% 7.78/3.98 | ? [A3: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( R
% 7.78/3.98 = ( insert291458823148189367at_nat @ ( produc9060074326276436823at_nat @ A3 @ A3 ) @ bot_bo4948859079157340979at_nat ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3814_Total__subset__Id,axiom,
% 7.78/3.98 ! [R: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( total_on_int @ ( field_int @ R ) @ R )
% 7.78/3.98 => ( ( ord_le2843351958646193337nt_int @ R @ id_int2 )
% 7.78/3.98 => ( ( R = bot_bo1796632182523588997nt_int )
% 7.78/3.98 | ? [A3: int] :
% 7.78/3.98 ( R
% 7.78/3.98 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A3 @ A3 ) @ bot_bo1796632182523588997nt_int ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3815_Total__subset__Id,axiom,
% 7.78/3.98 ! [R: set_Pr8693737435421807431at_nat] :
% 7.78/3.98 ( ( total_3592101749530773125at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 7.78/3.98 => ( ( ord_le3000389064537975527at_nat @ R @ id_Pro2258643101195443293at_nat )
% 7.78/3.98 => ( ( R = bot_bo5327735625951526323at_nat )
% 7.78/3.98 | ? [A3: product_prod_nat_nat] :
% 7.78/3.98 ( R
% 7.78/3.98 = ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A3 @ A3 ) @ bot_bo5327735625951526323at_nat ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3816_Total__subset__Id,axiom,
% 7.78/3.98 ! [R: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( total_7212417256332265445at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 7.78/3.98 => ( ( ord_le1268244103169919719at_nat @ R @ id_set1796276052702428605at_nat )
% 7.78/3.98 => ( ( R = bot_bo228742789529271731at_nat )
% 7.78/3.98 | ? [A3: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( R
% 7.78/3.98 = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A3 @ A3 ) @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3817_Total__subset__Id,axiom,
% 7.78/3.98 ! [R: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( total_on_nat @ ( field_nat @ R ) @ R )
% 7.78/3.98 => ( ( ord_le3146513528884898305at_nat @ R @ id_nat2 )
% 7.78/3.98 => ( ( R = bot_bo2099793752762293965at_nat )
% 7.78/3.98 | ? [A3: nat] :
% 7.78/3.98 ( R
% 7.78/3.98 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A3 @ A3 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3818_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_int @ A4 )
% 7.78/3.98 => ? [X: int] :
% 7.78/3.98 ( ( member_int @ X @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ X @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3819_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: rat] :
% 7.78/3.98 ( ( member_rat @ X @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ X @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3820_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: int] :
% 7.78/3.98 ( ( member_int @ X @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3821_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.98 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3822_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > $o,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3823_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_int @ A4 )
% 7.78/3.98 => ? [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3824_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: nat] :
% 7.78/3.98 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3825_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.98 => ? [X: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3826_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.98 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ? [X: product_prod_nat_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ X @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3827_inf__img__fin__dom_H,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > $o,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( finite_finite_o @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.98 => ? [X: $o] :
% 7.78/3.98 ( ( member_o @ X @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 7.78/3.98 & ~ ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage2444243245536687506_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3828_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_int @ A4 )
% 7.78/3.98 => ~ ! [Y: int] :
% 7.78/3.98 ( ( member_int @ Y @ ( image_int_int @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3829_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: rat] :
% 7.78/3.98 ( ( member_rat @ Y @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_rat @ F @ ( insert_rat @ Y @ bot_bot_set_rat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3830_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: int] :
% 7.78/3.98 ( ( member_int @ Y @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3831_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.98 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ Y @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3832_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > $o,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: $o] :
% 7.78/3.98 ( ( member_o @ Y @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ Y @ bot_bot_set_o ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3833_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_int] :
% 7.78/3.98 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_int @ A4 )
% 7.78/3.98 => ~ ! [Y: nat] :
% 7.78/3.98 ( ( member_nat @ Y @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ F @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3834_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: nat] :
% 7.78/3.98 ( ( member_nat @ Y @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3835_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > int,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( finite_finite_int @ ( image_2483585944268220136at_int @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: int] :
% 7.78/3.98 ( ( member_int @ Y @ ( image_2483585944268220136at_int @ F @ A4 ) )
% 7.78/3.98 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage4650790856102703794at_int @ F @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3836_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ Y @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.98 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3837_inf__img__fin__domE_H,axiom,
% 7.78/3.98 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.98 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.98 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.98 => ~ ! [Y: product_prod_nat_nat] :
% 7.78/3.98 ( ( member8440522571783428010at_nat @ Y @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.98 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) @ A4 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3838_prod__set__simps_I2_J,axiom,
% 7.78/3.98 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( basic_5713354656523905413at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) )
% 7.78/3.98 = ( insert2290795007606087959at_nat @ Y3 @ bot_bo1534825418459847827at_nat ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3839_prod__set__simps_I2_J,axiom,
% 7.78/3.98 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( basic_484852565060450053at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) )
% 7.78/3.98 = ( insert9200635055090092081at_nat @ Y3 @ bot_bo3083307316010499117at_nat ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3840_prod__set__simps_I2_J,axiom,
% 7.78/3.98 ! [X2: nat,Y3: num] :
% 7.78/3.98 ( ( basic_snds_nat_num @ ( product_Pair_nat_num @ X2 @ Y3 ) )
% 7.78/3.98 = ( insert_num @ Y3 @ bot_bot_set_num ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3841_prod__set__simps_I2_J,axiom,
% 7.78/3.98 ! [X2: int,Y3: int] :
% 7.78/3.98 ( ( basic_snds_int_int @ ( product_Pair_int_int @ X2 @ Y3 ) )
% 7.78/3.98 = ( insert_int @ Y3 @ bot_bot_set_int ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3842_prod__set__simps_I2_J,axiom,
% 7.78/3.98 ! [X2: nat,Y3: nat] :
% 7.78/3.98 ( ( basic_snds_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
% 7.78/3.98 = ( insert_nat @ Y3 @ bot_bot_set_nat ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3843_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 7.78/3.98 ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 7.78/3.98 => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
% 7.78/3.98 => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
% 7.78/3.98 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ A ) @ ( minus_8235382265540049710at_nat @ R @ id_Pro5428700290092274115at_nat ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3844_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Product_prod_o_o,A: $o,B: $o] :
% 7.78/3.98 ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
% 7.78/3.98 => ( ( member_o @ A @ ( field_o @ R ) )
% 7.78/3.98 => ( ( member_o @ B @ ( field_o @ R ) )
% 7.78/3.98 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ ( minus_7052513330764642158od_o_o @ R @ id_o2 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3845_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 7.78/3.98 ( ( order_7480980593162297270at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 7.78/3.98 => ( ( member8440522571783428010at_nat @ A @ ( field_4706345496283612622at_nat @ R ) )
% 7.78/3.98 => ( ( member8440522571783428010at_nat @ B @ ( field_4706345496283612622at_nat @ R ) )
% 7.78/3.98 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ B @ A ) @ ( minus_8321449233255521966at_nat @ R @ id_Pro2258643101195443293at_nat ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3846_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( order_1878278401035043452at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 7.78/3.98 => ( ( member6273874620674182256at_nat @ A @ ( field_1428494348145443988at_nat @ R ) )
% 7.78/3.98 => ( ( member6273874620674182256at_nat @ B @ ( field_1428494348145443988at_nat @ R ) )
% 7.78/3.98 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ B @ A ) @ ( minus_8674369445256047406at_nat @ R @ id_set4888139568991089827at_nat ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3847_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 7.78/3.98 => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
% 7.78/3.98 => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
% 7.78/3.98 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3848_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 7.78/3.98 ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
% 7.78/3.98 => ( ( member_nat @ A @ ( field_nat @ R ) )
% 7.78/3.98 => ( ( member_nat @ B @ ( field_nat @ R ) )
% 7.78/3.98 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( minus_1356011639430497352at_nat @ R @ id_nat2 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3849_Linear__order__in__diff__Id,axiom,
% 7.78/3.98 ! [R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 7.78/3.98 ( ( order_4471489696718655927on_int @ ( field_int @ R ) @ R )
% 7.78/3.98 => ( ( member_int @ A @ ( field_int @ R ) )
% 7.78/3.98 => ( ( member_int @ B @ ( field_int @ R ) )
% 7.78/3.98 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 7.78/3.98 = ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A ) @ ( minus_1052850069191792384nt_int @ R @ id_int2 ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3850_aboveS__def,axiom,
% 7.78/3.98 ( order_4940263126897443436at_nat
% 7.78/3.98 = ( ^ [R5: set_Pr8693737435421807431at_nat,A5: product_prod_nat_nat] :
% 7.78/3.98 ( collec3392354462482085612at_nat
% 7.78/3.98 @ ^ [B4: product_prod_nat_nat] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3851_aboveS__def,axiom,
% 7.78/3.98 ( order_1761765819289301284nt_int
% 7.78/3.98 = ( ^ [R5: set_Pr2560585780119916871nt_int,A5: product_prod_int_int] :
% 7.78/3.98 ( collec213857154873943460nt_int
% 7.78/3.98 @ ^ [B4: product_prod_int_int] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3852_aboveS__def,axiom,
% 7.78/3.98 ( order_2442354982230848562at_nat
% 7.78/3.98 = ( ^ [R5: set_Pr7459493094073627847at_nat,A5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( collec4573900263915890866at_nat
% 7.78/3.98 @ ^ [B4: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3853_aboveS__def,axiom,
% 7.78/3.98 ( order_4440095836999870412at_nat
% 7.78/3.98 = ( ^ [R5: set_Pr4329608150637261639at_nat,A5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( collec5514110066124741708at_nat
% 7.78/3.98 @ ^ [B4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3854_aboveS__def,axiom,
% 7.78/3.98 ( order_aboveS_nat
% 7.78/3.98 = ( ^ [R5: set_Pr1261947904930325089at_nat,A5: nat] :
% 7.78/3.98 ( collect_nat
% 7.78/3.98 @ ^ [B4: nat] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3855_aboveS__def,axiom,
% 7.78/3.98 ( order_aboveS_int
% 7.78/3.98 = ( ^ [R5: set_Pr958786334691620121nt_int,A5: int] :
% 7.78/3.98 ( collect_int
% 7.78/3.98 @ ^ [B4: int] :
% 7.78/3.98 ( ( B4 != A5 )
% 7.78/3.98 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 ) @ R5 ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3856_card__vimage__inj,axiom,
% 7.78/3.98 ! [F: nat > rat,A4: set_rat] :
% 7.78/3.98 ( ( inj_on_nat_rat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_rat @ A4 @ ( image_nat_rat @ F @ top_top_set_nat ) )
% 7.78/3.98 => ( ( finite_card_nat @ ( vimage_nat_rat @ F @ A4 ) )
% 7.78/3.98 = ( finite_card_rat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3857_card__vimage__inj,axiom,
% 7.78/3.98 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 7.78/3.98 => ( ( finite_card_nat @ ( vimage_nat_nat @ F @ A4 ) )
% 7.78/3.98 = ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3858_card__vimage__inj,axiom,
% 7.78/3.98 ! [F: nat > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_nat_int @ F @ top_top_set_nat )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ ( image_nat_int @ F @ top_top_set_nat ) )
% 7.78/3.98 => ( ( finite_card_nat @ ( vimage_nat_int @ F @ A4 ) )
% 7.78/3.98 = ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3859_card__vimage__inj,axiom,
% 7.78/3.98 ! [F: int > nat,A4: set_nat] :
% 7.78/3.98 ( ( inj_on_int_nat @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_nat @ A4 @ ( image_int_nat @ F @ top_top_set_int ) )
% 7.78/3.98 => ( ( finite_card_int @ ( vimage_int_nat @ F @ A4 ) )
% 7.78/3.98 = ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3860_card__vimage__inj,axiom,
% 7.78/3.98 ! [F: int > int,A4: set_int] :
% 7.78/3.98 ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.98 => ( ( ord_less_eq_set_int @ A4 @ ( image_int_int @ F @ top_top_set_int ) )
% 7.78/3.98 => ( ( finite_card_int @ ( vimage_int_int @ F @ A4 ) )
% 7.78/3.98 = ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3861_Linear__order__Well__order__iff,axiom,
% 7.78/3.98 ! [R: set_Pr7459493094073627847at_nat] :
% 7.78/3.98 ( ( order_1878278401035043452at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 7.78/3.98 => ( ( order_423636163458052581at_nat @ ( field_1428494348145443988at_nat @ R ) @ R )
% 7.78/3.98 = ( ! [A6: set_se5479201105039950375at_nat] :
% 7.78/3.98 ( ( ord_le7966958417815640519at_nat @ A6 @ ( field_1428494348145443988at_nat @ R ) )
% 7.78/3.98 => ( ( A6 != bot_bo1534825418459847827at_nat )
% 7.78/3.98 => ? [X4: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member6273874620674182256at_nat @ X4 @ A6 )
% 7.78/3.98 & ! [Y5: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( member6273874620674182256at_nat @ Y5 @ A6 )
% 7.78/3.98 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3862_Linear__order__Well__order__iff,axiom,
% 7.78/3.98 ! [R: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 7.78/3.98 => ( ( order_1968183844437341695at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
% 7.78/3.98 = ( ! [A6: set_se7855581050983116737at_nat] :
% 7.78/3.98 ( ( ord_le2077887516847798113at_nat @ A6 @ ( field_3145993188331922222at_nat @ R ) )
% 7.78/3.98 => ( ( A6 != bot_bo3083307316010499117at_nat )
% 7.78/3.98 => ? [X4: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member2643936169264416010at_nat @ X4 @ A6 )
% 7.78/3.98 & ! [Y5: set_Pr1261947904930325089at_nat] :
% 7.78/3.98 ( ( member2643936169264416010at_nat @ Y5 @ A6 )
% 7.78/3.98 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3863_Linear__order__Well__order__iff,axiom,
% 7.78/3.98 ! [R: set_Pr958786334691620121nt_int] :
% 7.78/3.98 ( ( order_4471489696718655927on_int @ ( field_int @ R ) @ R )
% 7.78/3.98 => ( ( order_2886507596567047182on_int @ ( field_int @ R ) @ R )
% 7.78/3.98 = ( ! [A6: set_int] :
% 7.78/3.98 ( ( ord_less_eq_set_int @ A6 @ ( field_int @ R ) )
% 7.78/3.98 => ( ( A6 != bot_bot_set_int )
% 7.78/3.98 => ? [X4: int] :
% 7.78/3.98 ( ( member_int @ X4 @ A6 )
% 7.78/3.98 & ! [Y5: int] :
% 7.78/3.98 ( ( member_int @ Y5 @ A6 )
% 7.78/3.98 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3864_Linear__order__Well__order__iff,axiom,
% 7.78/3.98 ! [R: set_Pr5094982260447487303t_unit] :
% 7.78/3.98 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R ) @ R )
% 7.78/3.98 => ( ( order_3164716736300062379t_unit @ ( field_Product_unit @ R ) @ R )
% 7.78/3.98 = ( ! [A6: set_Product_unit] :
% 7.78/3.98 ( ( ord_le3507040750410214029t_unit @ A6 @ ( field_Product_unit @ R ) )
% 7.78/3.98 => ( ( A6 != bot_bo3957492148770167129t_unit )
% 7.78/3.98 => ? [X4: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ X4 @ A6 )
% 7.78/3.98 & ! [Y5: product_unit] :
% 7.78/3.98 ( ( member_Product_unit @ Y5 @ A6 )
% 7.78/3.98 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.98
% 7.78/3.98 thf(fact_3865_Linear__order__Well__order__iff,axiom,
% 7.78/3.98 ! [R: set_Pr5564308138774400199at_nat] :
% 7.78/3.98 ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 7.78/3.98 => ( ( order_2339240034117818117at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
% 7.78/3.98 = ( ! [A6: set_Pr4329608150637261639at_nat] :
% 7.78/3.98 ( ( ord_le1268244103169919719at_nat @ A6 @ ( field_2862844103579723188at_nat @ R ) )
% 7.78/3.98 => ( ( A6 != bot_bo228742789529271731at_nat )
% 7.78/3.98 => ? [X4: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ X4 @ A6 )
% 7.78/3.99 & ! [Y5: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ Y5 @ A6 )
% 7.78/3.99 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3866_Linear__order__Well__order__iff,axiom,
% 7.78/3.99 ! [R: set_Pr8693737435421807431at_nat] :
% 7.78/3.99 ( ( order_7480980593162297270at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 7.78/3.99 => ( ( order_8331247224601271455at_nat @ ( field_4706345496283612622at_nat @ R ) @ R )
% 7.78/3.99 = ( ! [A6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ord_le3146513528884898305at_nat @ A6 @ ( field_4706345496283612622at_nat @ R ) )
% 7.78/3.99 => ( ( A6 != bot_bo2099793752762293965at_nat )
% 7.78/3.99 => ? [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 7.78/3.99 & ! [Y5: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ Y5 @ A6 )
% 7.78/3.99 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3867_Linear__order__Well__order__iff,axiom,
% 7.78/3.99 ! [R: set_Product_prod_o_o] :
% 7.78/3.99 ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
% 7.78/3.99 => ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
% 7.78/3.99 = ( ! [A6: set_o] :
% 7.78/3.99 ( ( ord_less_eq_set_o @ A6 @ ( field_o @ R ) )
% 7.78/3.99 => ( ( A6 != bot_bot_set_o )
% 7.78/3.99 => ? [X4: $o] :
% 7.78/3.99 ( ( member_o @ X4 @ A6 )
% 7.78/3.99 & ! [Y5: $o] :
% 7.78/3.99 ( ( member_o @ Y5 @ A6 )
% 7.78/3.99 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3868_Linear__order__Well__order__iff,axiom,
% 7.78/3.99 ! [R: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
% 7.78/3.99 => ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
% 7.78/3.99 = ( ! [A6: set_nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ A6 @ ( field_nat @ R ) )
% 7.78/3.99 => ( ( A6 != bot_bot_set_nat )
% 7.78/3.99 => ? [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ A6 )
% 7.78/3.99 & ! [Y5: nat] :
% 7.78/3.99 ( ( member_nat @ Y5 @ A6 )
% 7.78/3.99 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ R ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3869_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_int,H: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ F4 )
% 7.78/3.99 => ( finite_finite_int @ ( image_int_int @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3870_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_int,H: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ F4 )
% 7.78/3.99 => ( finite_finite_nat @ ( image_int_nat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3871_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_Pr1261947904930325089at_nat,H: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ F4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3872_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_Pr1261947904930325089at_nat,H: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ F4 )
% 7.78/3.99 => ( finite_finite_nat @ ( image_2486076414777270412at_nat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3873_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_nat,H: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ F4 )
% 7.78/3.99 => ( finite_finite_rat @ ( image_nat_rat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3874_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_nat,H: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ F4 )
% 7.78/3.99 => ( finite_finite_int @ ( image_nat_int @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3875_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_nat,H: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ F4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3876_finite__imageI,axiom,
% 7.78/3.99 ! [F4: set_nat,H: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ F4 )
% 7.78/3.99 => ( finite_finite_nat @ ( image_nat_nat @ H @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3877_IdI,axiom,
% 7.78/3.99 ! [A: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ id_Pro2258643101195443293at_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3878_IdI,axiom,
% 7.78/3.99 ! [A: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ A ) @ id_set4888139568991089827at_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3879_IdI,axiom,
% 7.78/3.99 ! [A: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ id_set1796276052702428605at_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3880_IdI,axiom,
% 7.78/3.99 ! [A: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ id_nat2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3881_IdI,axiom,
% 7.78/3.99 ! [A: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ id_int2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3882_pair__in__Id__conv,axiom,
% 7.78/3.99 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 7.78/3.99 = ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3883_pair__in__Id__conv,axiom,
% 7.78/3.99 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ id_set4888139568991089827at_nat )
% 7.78/3.99 = ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3884_pair__in__Id__conv,axiom,
% 7.78/3.99 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
% 7.78/3.99 = ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3885_pair__in__Id__conv,axiom,
% 7.78/3.99 ! [A: nat,B: nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 7.78/3.99 = ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3886_pair__in__Id__conv,axiom,
% 7.78/3.99 ! [A: int,B: int] :
% 7.78/3.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 7.78/3.99 = ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3887_finite__UN,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) )
% 7.78/3.99 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3888_finite__UN,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) )
% 7.78/3.99 = ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3889_finite__UN,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) )
% 7.78/3.99 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3890_finite__UN,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: nat > set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) )
% 7.78/3.99 = ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3891_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite4343798906461161616at_nat @ A4 )
% 7.78/3.99 => ( ! [A3: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7979982168039674559at_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3892_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_o,B5: $o > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_o @ A4 )
% 7.78/3.99 => ( ! [A3: $o] :
% 7.78/3.99 ( ( member_o @ A3 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7077428525161401678at_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3893_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_int,B5: int > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ! [A3: int] :
% 7.78/3.99 ( ( member_int @ A3 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_8938366415781434990at_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3894_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ! [A3: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_5423882813909314213at_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3895_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: nat > set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ! [A3: nat] :
% 7.78/3.99 ( ( member_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ ( comple5685304695842803022at_nat @ ( image_7178329752028323786at_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3896_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_Pr4329608150637261639at_nat,B5: produc3843707927480180839at_nat > set_nat] :
% 7.78/3.99 ( ( finite4343798906461161616at_nat @ A4 )
% 7.78/3.99 => ( ! [A3: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_3160451284896210088et_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3897_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_o,B5: $o > set_nat] :
% 7.78/3.99 ( ( finite_finite_o @ A4 )
% 7.78/3.99 => ( ! [A3: $o] :
% 7.78/3.99 ( ( member_o @ A3 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3898_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_int,B5: int > set_nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ! [A3: int] :
% 7.78/3.99 ( ( member_int @ A3 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3899_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: product_prod_nat_nat > set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ! [A3: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3900_finite__UN__I,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: nat > set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ! [A3: nat] :
% 7.78/3.99 ( ( member_nat @ A3 @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ ( B5 @ A3 ) ) )
% 7.78/3.99 => ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3901_bdd__below__UN,axiom,
% 7.78/3.99 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ I3 )
% 7.78/3.99 => ( ( condit1738341127787009408ow_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 7.78/3.99 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.99 => ( condit1738341127787009408ow_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3902_bdd__below__UN,axiom,
% 7.78/3.99 ! [I3: set_nat,A4: nat > set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ I3 )
% 7.78/3.99 => ( ( condit1738341127787009408ow_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.99 = ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ I3 )
% 7.78/3.99 => ( condit1738341127787009408ow_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3903_bdd__above__UN,axiom,
% 7.78/3.99 ! [I3: set_Pr1261947904930325089at_nat,A4: product_prod_nat_nat > set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ I3 )
% 7.78/3.99 => ( ( condit2214826472909112428ve_nat @ ( comple7399068483239264473et_nat @ ( image_15824709712370754et_nat @ A4 @ I3 ) ) )
% 7.78/3.99 = ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ I3 )
% 7.78/3.99 => ( condit2214826472909112428ve_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3904_bdd__above__UN,axiom,
% 7.78/3.99 ! [I3: set_nat,A4: nat > set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ I3 )
% 7.78/3.99 => ( ( condit2214826472909112428ve_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A4 @ I3 ) ) )
% 7.78/3.99 = ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ I3 )
% 7.78/3.99 => ( condit2214826472909112428ve_nat @ ( A4 @ X4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3905_card__image__le,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_int_nat @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3906_card__image__le,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_int @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3907_card__image__le,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3908_card__image__le,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3909_card__image__le,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3910_surj__card__le,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_nat,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3911_surj__card__le,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3912_surj__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_rat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_rat @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3913_surj__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3914_surj__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_int,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3915_eq__card__imp__inj__on,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) )
% 7.78/3.99 => ( inj_on_int_nat @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3916_eq__card__imp__inj__on,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) )
% 7.78/3.99 => ( inj_on_int_int @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3917_eq__card__imp__inj__on,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) )
% 7.78/3.99 => ( inj_on_nat_rat @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3918_eq__card__imp__inj__on,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) )
% 7.78/3.99 => ( inj_on_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3919_eq__card__imp__inj__on,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) )
% 7.78/3.99 => ( inj_on_nat_int @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3920_inj__on__iff__eq__card,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 = ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3921_inj__on__iff__eq__card,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 = ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3922_inj__on__iff__eq__card,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 = ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3923_inj__on__iff__eq__card,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 = ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3924_inj__on__iff__eq__card,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 = ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3925_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( order_2339240034117818117at_nat @ A4 @ R )
% 7.78/3.99 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ A @ A4 )
% 7.78/3.99 & ( member8757157785044589968at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3926_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,R: set_Pr8693737435421807431at_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 7.78/3.99 ( ( order_8331247224601271455at_nat @ A4 @ R )
% 7.78/3.99 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ R )
% 7.78/3.99 => ( ( member8440522571783428010at_nat @ A @ A4 )
% 7.78/3.99 & ( member8440522571783428010at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3927_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_o,R: set_Product_prod_o_o,A: $o,B: $o] :
% 7.78/3.99 ( ( order_2615775362358406454r_on_o @ A4 @ R )
% 7.78/3.99 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
% 7.78/3.99 => ( ( member_o @ A @ A4 )
% 7.78/3.99 & ( member_o @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3928_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_se5479201105039950375at_nat,R: set_Pr7459493094073627847at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( ( order_423636163458052581at_nat @ A4 @ R )
% 7.78/3.99 => ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ R )
% 7.78/3.99 => ( ( member6273874620674182256at_nat @ A @ A4 )
% 7.78/3.99 & ( member6273874620674182256at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3929_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( order_1968183844437341695at_nat @ A4 @ R )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
% 7.78/3.99 => ( ( member2643936169264416010at_nat @ A @ A4 )
% 7.78/3.99 & ( member2643936169264416010at_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3930_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_int,R: set_Pr958786334691620121nt_int,A: int,B: int] :
% 7.78/3.99 ( ( order_2886507596567047182on_int @ A4 @ R )
% 7.78/3.99 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 7.78/3.99 => ( ( member_int @ A @ A4 )
% 7.78/3.99 & ( member_int @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3931_well__order__on__domain,axiom,
% 7.78/3.99 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
% 7.78/3.99 ( ( order_2888998067076097458on_nat @ A4 @ R )
% 7.78/3.99 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 7.78/3.99 => ( ( member_nat @ A @ A4 )
% 7.78/3.99 & ( member_nat @ B @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3932_infinite__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_rat] :
% 7.78/3.99 ( ~ ( finite_finite_rat @ S5 )
% 7.78/3.99 => ? [F5: nat > rat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F5 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3933_infinite__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_int] :
% 7.78/3.99 ( ~ ( finite_finite_int @ S5 )
% 7.78/3.99 => ? [F5: nat > int] :
% 7.78/3.99 ( ( inj_on_nat_int @ F5 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_int @ ( image_nat_int @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3934_infinite__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ~ ( finite6177210948735845034at_nat @ S5 )
% 7.78/3.99 => ? [F5: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F5 @ top_top_set_nat )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3935_infinite__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_nat] :
% 7.78/3.99 ( ~ ( finite_finite_nat @ S5 )
% 7.78/3.99 => ? [F5: nat > nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F5 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F5 @ top_top_set_nat ) @ S5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3936_infinite__iff__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_rat] :
% 7.78/3.99 ( ( ~ ( finite_finite_rat @ S5 ) )
% 7.78/3.99 = ( ? [F2: nat > rat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F2 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3937_infinite__iff__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_int] :
% 7.78/3.99 ( ( ~ ( finite_finite_int @ S5 ) )
% 7.78/3.99 = ( ? [F2: nat > int] :
% 7.78/3.99 ( ( inj_on_nat_int @ F2 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3938_infinite__iff__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ~ ( finite6177210948735845034at_nat @ S5 ) )
% 7.78/3.99 = ( ? [F2: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F2 @ top_top_set_nat )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3939_infinite__iff__countable__subset,axiom,
% 7.78/3.99 ! [S5: set_nat] :
% 7.78/3.99 ( ( ~ ( finite_finite_nat @ S5 ) )
% 7.78/3.99 = ( ? [F2: nat > nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 7.78/3.99 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ top_top_set_nat ) @ S5 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3940_IdE,axiom,
% 7.78/3.99 ! [P: produc859450856879609959at_nat] :
% 7.78/3.99 ( ( member8206827879206165904at_nat @ P @ id_Pro2258643101195443293at_nat )
% 7.78/3.99 => ~ ! [X: product_prod_nat_nat] :
% 7.78/3.99 ( P
% 7.78/3.99 != ( produc6161850002892822231at_nat @ X @ X ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3941_IdE,axiom,
% 7.78/3.99 ! [P: produc1319942482725812455at_nat] :
% 7.78/3.99 ( ( member1466754251312161552at_nat @ P @ id_set4888139568991089827at_nat )
% 7.78/3.99 => ~ ! [X: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( P
% 7.78/3.99 != ( produc9060074326276436823at_nat @ X @ X ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3942_IdE,axiom,
% 7.78/3.99 ! [P: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ P @ id_set1796276052702428605at_nat )
% 7.78/3.99 => ~ ! [X: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( P
% 7.78/3.99 != ( produc2922128104949294807at_nat @ X @ X ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3943_IdE,axiom,
% 7.78/3.99 ! [P: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ P @ id_nat2 )
% 7.78/3.99 => ~ ! [X: nat] :
% 7.78/3.99 ( P
% 7.78/3.99 != ( product_Pair_nat_nat @ X @ X ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3944_IdE,axiom,
% 7.78/3.99 ! [P: product_prod_int_int] :
% 7.78/3.99 ( ( member5262025264175285858nt_int @ P @ id_int2 )
% 7.78/3.99 => ~ ! [X: int] :
% 7.78/3.99 ( P
% 7.78/3.99 != ( product_Pair_int_int @ X @ X ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3945_IdD,axiom,
% 7.78/3.99 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 7.78/3.99 => ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3946_IdD,axiom,
% 7.78/3.99 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A @ B ) @ id_set4888139568991089827at_nat )
% 7.78/3.99 => ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3947_IdD,axiom,
% 7.78/3.99 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
% 7.78/3.99 => ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3948_IdD,axiom,
% 7.78/3.99 ! [A: nat,B: nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 7.78/3.99 => ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3949_IdD,axiom,
% 7.78/3.99 ! [A: int,B: int] :
% 7.78/3.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 7.78/3.99 => ( A = B ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3950_card__bij__eq,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int,B5: set_int,G: int > int] :
% 7.78/3.99 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_int_int @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( finite_card_int @ A4 )
% 7.78/3.99 = ( finite_card_int @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3951_card__bij__eq,axiom,
% 7.78/3.99 ! [F: rat > nat,A4: set_rat,B5: set_nat,G: nat > rat] :
% 7.78/3.99 ( ( inj_on_rat_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_rat_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_nat_rat @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( finite_card_rat @ A4 )
% 7.78/3.99 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3952_card__bij__eq,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int,B5: set_nat,G: nat > int] :
% 7.78/3.99 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_nat_int @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( finite_card_int @ A4 )
% 7.78/3.99 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3953_card__bij__eq,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on8969904277767023793at_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( finite711546835091564841at_nat @ A4 )
% 7.78/3.99 = ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3954_card__bij__eq,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,B5: set_nat,G: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on5538052773655684606at_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( finite711546835091564841at_nat @ A4 )
% 7.78/3.99 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3955_card__bij__eq,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat,B5: set_rat,G: rat > nat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_rat_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_rat_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( ( finite_card_nat @ A4 )
% 7.78/3.99 = ( finite_card_rat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3956_card__bij__eq,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat,B5: set_int,G: int > nat] :
% 7.78/3.99 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_int_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( finite_card_nat @ A4 )
% 7.78/3.99 = ( finite_card_int @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3957_card__bij__eq,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on2178005380612969504at_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( finite_card_nat @ A4 )
% 7.78/3.99 = ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3958_card__bij__eq,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat,B5: set_nat,G: nat > nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( inj_on_nat_nat @ G @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ B5 ) @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( finite_card_nat @ A4 )
% 7.78/3.99 = ( finite_card_nat @ B5 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3959_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 7.78/3.99 => ? [F5: int > int] :
% 7.78/3.99 ( ( ord_less_eq_set_int @ ( image_int_int @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on_int_int @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3960_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) )
% 7.78/3.99 => ? [F5: int > nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on_int_nat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3961_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 7.78/3.99 => ? [F5: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on8969904277767023793at_nat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3962_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 7.78/3.99 => ? [F5: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on2178005380612969504at_nat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3963_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) )
% 7.78/3.99 => ? [F5: nat > rat] :
% 7.78/3.99 ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on_nat_rat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3964_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) )
% 7.78/3.99 => ? [F5: nat > int] :
% 7.78/3.99 ( ( ord_less_eq_set_int @ ( image_nat_int @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on_nat_int @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3965_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 7.78/3.99 => ? [F5: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on5538052773655684606at_nat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3966_card__le__inj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 7.78/3.99 => ? [F5: nat > nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F5 @ A4 ) @ B5 )
% 7.78/3.99 & ( inj_on_nat_nat @ F5 @ A4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3967_card__inj__on__le,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3968_card__inj__on__le,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.99 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3969_card__inj__on__le,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.99 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3970_card__inj__on__le,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3971_card__inj__on__le,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.99 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3972_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ? [F2: int > int] :
% 7.78/3.99 ( ( inj_on_int_int @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_int @ ( image_int_int @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3973_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ? [F2: int > nat] :
% 7.78/3.99 ( ( inj_on_int_nat @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ ( image_int_nat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3974_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ? [F2: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on8969904277767023793at_nat @ F2 @ A4 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3975_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ? [F2: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( inj_on2178005380612969504at_nat @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3976_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( ( ? [F2: nat > rat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_rat @ ( image_nat_rat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_rat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3977_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ? [F2: nat > int] :
% 7.78/3.99 ( ( inj_on_nat_int @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_int @ ( image_nat_int @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3978_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ? [F2: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F2 @ A4 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3979_inj__on__iff__card__le,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ? [F2: nat > nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F2 @ A4 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ ( image_nat_nat @ F2 @ A4 ) @ B5 ) ) )
% 7.78/3.99 = ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3980_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_int,T3: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ S5 )
% 7.78/3.99 => ( ( finite_finite_int @ T3 )
% 7.78/3.99 => ( ( ( finite_card_int @ S5 )
% 7.78/3.99 = ( finite_card_int @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: int] :
% 7.78/3.99 ( ( member_int @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: int] :
% 7.78/3.99 ( ( member_int @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on_int_int @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3981_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_int,T3: set_nat,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ S5 )
% 7.78/3.99 => ( ( finite_finite_nat @ T3 )
% 7.78/3.99 => ( ( ( finite_card_int @ S5 )
% 7.78/3.99 = ( finite_card_nat @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: int] :
% 7.78/3.99 ( ( member_int @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on_int_nat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3982_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ S5 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ T3 )
% 7.78/3.99 => ( ( ( finite711546835091564841at_nat @ S5 )
% 7.78/3.99 = ( finite711546835091564841at_nat @ T3 ) )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on8969904277767023793at_nat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3983_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_Pr1261947904930325089at_nat,T3: set_nat,F: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ S5 )
% 7.78/3.99 => ( ( finite_finite_nat @ T3 )
% 7.78/3.99 => ( ( ( finite711546835091564841at_nat @ S5 )
% 7.78/3.99 = ( finite_card_nat @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on2178005380612969504at_nat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3984_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_nat,T3: set_rat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ S5 )
% 7.78/3.99 => ( ( finite_finite_rat @ T3 )
% 7.78/3.99 => ( ( ( finite_card_nat @ S5 )
% 7.78/3.99 = ( finite_card_rat @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: rat] :
% 7.78/3.99 ( ( member_rat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: nat] :
% 7.78/3.99 ( ( member_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on_nat_rat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3985_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_nat,T3: set_int,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ S5 )
% 7.78/3.99 => ( ( finite_finite_int @ T3 )
% 7.78/3.99 => ( ( ( finite_card_nat @ S5 )
% 7.78/3.99 = ( finite_card_int @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: int] :
% 7.78/3.99 ( ( member_int @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: nat] :
% 7.78/3.99 ( ( member_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on_nat_int @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3986_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_nat,T3: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ S5 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ T3 )
% 7.78/3.99 => ( ( ( finite_card_nat @ S5 )
% 7.78/3.99 = ( finite711546835091564841at_nat @ T3 ) )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: nat] :
% 7.78/3.99 ( ( member_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on5538052773655684606at_nat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3987_surjective__iff__injective__gen,axiom,
% 7.78/3.99 ! [S5: set_nat,T3: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ S5 )
% 7.78/3.99 => ( ( finite_finite_nat @ T3 )
% 7.78/3.99 => ( ( ( finite_card_nat @ S5 )
% 7.78/3.99 = ( finite_card_nat @ T3 ) )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ S5 ) @ T3 )
% 7.78/3.99 => ( ( ! [X4: nat] :
% 7.78/3.99 ( ( member_nat @ X4 @ T3 )
% 7.78/3.99 => ? [Y5: nat] :
% 7.78/3.99 ( ( member_nat @ Y5 @ S5 )
% 7.78/3.99 & ( ( F @ Y5 )
% 7.78/3.99 = X4 ) ) ) )
% 7.78/3.99 = ( inj_on_nat_nat @ F @ S5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3988_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ~ ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ? [X: int] :
% 7.78/3.99 ( ( member_int @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_int
% 7.78/3.99 @ ( collect_int
% 7.78/3.99 @ ^ [A5: int] :
% 7.78/3.99 ( ( member_int @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3989_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_o,F: $o > nat] :
% 7.78/3.99 ( ~ ( finite_finite_o @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_o_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: $o] :
% 7.78/3.99 ( ( member_o @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_o
% 7.78/3.99 @ ( collect_o
% 7.78/3.99 @ ^ [A5: $o] :
% 7.78/3.99 ( ( member_o @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3990_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > nat] :
% 7.78/3.99 ( ~ ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: int] :
% 7.78/3.99 ( ( member_int @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_int
% 7.78/3.99 @ ( collect_int
% 7.78/3.99 @ ^ [A5: int] :
% 7.78/3.99 ( ( member_int @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3991_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > rat] :
% 7.78/3.99 ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_nat
% 7.78/3.99 @ ( collect_nat
% 7.78/3.99 @ ^ [A5: nat] :
% 7.78/3.99 ( ( member_nat @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3992_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > int] :
% 7.78/3.99 ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_nat
% 7.78/3.99 @ ( collect_nat
% 7.78/3.99 @ ^ [A5: nat] :
% 7.78/3.99 ( ( member_nat @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3993_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_nat
% 7.78/3.99 @ ( collect_nat
% 7.78/3.99 @ ^ [A5: nat] :
% 7.78/3.99 ( ( member_nat @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3994_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_o,F: $o > product_prod_nat_nat] :
% 7.78/3.99 ( ~ ( finite_finite_o @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( image_3855930084881510382at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: $o] :
% 7.78/3.99 ( ( member_o @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_o
% 7.78/3.99 @ ( collect_o
% 7.78/3.99 @ ^ [A5: $o] :
% 7.78/3.99 ( ( member_o @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3995_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > product_prod_nat_nat] :
% 7.78/3.99 ( ~ ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( image_8883965892284119310at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: int] :
% 7.78/3.99 ( ( member_int @ X @ A4 )
% 7.78/3.99 & ~ ( finite_finite_int
% 7.78/3.99 @ ( collect_int
% 7.78/3.99 @ ^ [A5: int] :
% 7.78/3.99 ( ( member_int @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3996_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_Pr958786334691620121nt_int,F: product_prod_int_int > nat] :
% 7.78/3.99 ( ~ ( finite2998713641127702882nt_int @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_5044651549707136836nt_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: product_prod_int_int] :
% 7.78/3.99 ( ( member5262025264175285858nt_int @ X @ A4 )
% 7.78/3.99 & ~ ( finite2998713641127702882nt_int
% 7.78/3.99 @ ( collec213857154873943460nt_int
% 7.78/3.99 @ ^ [A5: product_prod_int_int] :
% 7.78/3.99 ( ( member5262025264175285858nt_int @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3997_pigeonhole__infinite,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [X: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X @ A4 )
% 7.78/3.99 & ~ ( finite6177210948735845034at_nat
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ^ [A5: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ A5 @ A4 )
% 7.78/3.99 & ( ( F @ A5 )
% 7.78/3.99 = ( F @ X ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3998_snds_Ointros,axiom,
% 7.78/3.99 ! [P: produc7812382424243267045t_unit] : ( member242389114213480694t_unit @ ( produc1126150082675451753t_unit @ P ) @ ( basic_1496934909540232809t_unit @ P ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_3999_snds_Osimps,axiom,
% 7.78/3.99 ! [A: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 7.78/3.99 ( ( member242389114213480694t_unit @ A @ ( basic_1496934909540232809t_unit @ P ) )
% 7.78/3.99 = ( A
% 7.78/3.99 = ( produc1126150082675451753t_unit @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4000_snds_Ocases,axiom,
% 7.78/3.99 ! [A: heap_e7401611519738050253t_unit,P: produc7812382424243267045t_unit] :
% 7.78/3.99 ( ( member242389114213480694t_unit @ A @ ( basic_1496934909540232809t_unit @ P ) )
% 7.78/3.99 => ( A
% 7.78/3.99 = ( produc1126150082675451753t_unit @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4001_card__image,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( ( finite_card_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4002_card__image,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4003_card__image,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( ( finite_card_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4004_card__image,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int] :
% 7.78/3.99 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite_card_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4005_card__image,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int] :
% 7.78/3.99 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( finite_card_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_card_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4006_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 7.78/3.99 ( ( ! [B6: set_int] :
% 7.78/3.99 ( ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_int] :
% 7.78/3.99 ( ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4007_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 7.78/3.99 ( ( ! [B6: set_rat] :
% 7.78/3.99 ( ( ( finite_finite_rat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4008_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 7.78/3.99 ( ( ! [B6: set_int] :
% 7.78/3.99 ( ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4009_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.99 ( ( ! [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5168914502847457605at_nat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_5168914502847457605at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4010_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.99 ( ( ! [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5846123807819985514at_nat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_5846123807819985514at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4011_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 7.78/3.99 ( ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_int] :
% 7.78/3.99 ( ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4012_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,P2: set_nat > $o] :
% 7.78/3.99 ( ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_2486076414777270412at_nat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_2486076414777270412at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4013_all__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 7.78/3.99 ( ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) ) )
% 7.78/3.99 => ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ! [B6: set_nat] :
% 7.78/3.99 ( ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 7.78/3.99 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4014_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 7.78/3.99 ( ( ? [B6: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4015_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat,P2: set_rat > $o] :
% 7.78/3.99 ( ( ? [B6: set_rat] :
% 7.78/3.99 ( ( finite_finite_rat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_rat @ B6 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_nat_rat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4016_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 7.78/3.99 ( ( ? [B6: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4017_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.99 ( ( ? [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_5168914502847457605at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4018_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 7.78/3.99 ( ( ? [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_5846123807819985514at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4019_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 7.78/3.99 ( ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_int @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4020_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,P2: set_nat > $o] :
% 7.78/3.99 ( ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B6 )
% 7.78/3.99 & ( ord_le3146513528884898305at_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_2486076414777270412at_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4021_ex__finite__subset__image,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 7.78/3.99 ( ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 & ( P2 @ B6 ) ) )
% 7.78/3.99 = ( ? [B6: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B6 )
% 7.78/3.99 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 7.78/3.99 & ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4022_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_int,F: int > int,A4: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_int] :
% 7.78/3.99 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_int @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_int_int @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4023_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_rat,F: nat > rat,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_nat_rat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4024_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_int,F: nat > int,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_nat_int @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4025_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ord_le3146513528884898305at_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite6177210948735845034at_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_5168914502847457605at_nat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4026_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_5846123807819985514at_nat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4027_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_nat,F: int > nat,A4: set_int] :
% 7.78/3.99 ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_int] :
% 7.78/3.99 ( ( ord_less_eq_set_int @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_int @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_int_nat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4028_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_nat,F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( ord_le3146513528884898305at_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite6177210948735845034at_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_2486076414777270412at_nat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4029_finite__subset__image,axiom,
% 7.78/3.99 ! [B5: set_nat,F: nat > nat,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ? [C2: set_nat] :
% 7.78/3.99 ( ( ord_less_eq_set_nat @ C2 @ A4 )
% 7.78/3.99 & ( finite_finite_nat @ C2 )
% 7.78/3.99 & ( B5
% 7.78/3.99 = ( image_nat_nat @ F @ C2 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4030_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_int @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4031_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_int,B5: set_nat,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_nat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4032_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4033_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,B5: set_nat,F: product_prod_nat_nat > nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_nat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4034_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_rat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ B5 @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_rat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4035_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_int,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ B5 @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_int @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4036_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ B5 @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4037_finite__surj,axiom,
% 7.78/3.99 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ( finite_finite_nat @ B5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4038_finite__image__iff,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int] :
% 7.78/3.99 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4039_finite__image__iff,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4040_finite__image__iff,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4041_finite__image__iff,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4042_finite__image__iff,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4043_finite__image__iff,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int] :
% 7.78/3.99 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4044_finite__image__iff,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4045_finite__image__iff,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 = ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4046_finite__imageD,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int] :
% 7.78/3.99 ( ( finite_finite_int @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( finite_finite_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4047_finite__imageD,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_rat @ ( image_nat_rat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4048_finite__imageD,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4049_finite__imageD,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4050_finite__imageD,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4051_finite__imageD,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( finite_finite_int @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4052_finite__imageD,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4053_finite__imageD,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4054_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: char > nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_char_nat @ G @ top_top_set_char ) )
% 7.78/3.99 => ( finite_finite_nat
% 7.78/3.99 @ ( image_char_nat
% 7.78/3.99 @ ^ [X4: char] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_char ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4055_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: rat > nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_rat_nat @ G @ top_top_set_rat ) )
% 7.78/3.99 => ( finite_finite_nat
% 7.78/3.99 @ ( image_rat_nat
% 7.78/3.99 @ ^ [X4: rat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_rat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4056_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > rat,F: rat > rat] :
% 7.78/3.99 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_rat
% 7.78/3.99 @ ( image_nat_rat
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4057_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > rat,F: rat > int] :
% 7.78/3.99 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_int
% 7.78/3.99 @ ( image_nat_int
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4058_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > int,F: int > rat] :
% 7.78/3.99 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_rat
% 7.78/3.99 @ ( image_nat_rat
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4059_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_int
% 7.78/3.99 @ ( image_nat_int
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4060_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > rat,F: rat > nat] :
% 7.78/3.99 ( ( finite_finite_rat @ ( image_nat_rat @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_nat
% 7.78/3.99 @ ( image_nat_nat
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4061_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > int,F: int > nat] :
% 7.78/3.99 ( ( finite_finite_int @ ( image_nat_int @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_nat
% 7.78/3.99 @ ( image_nat_nat
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4062_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > nat,F: nat > rat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_rat
% 7.78/3.99 @ ( image_nat_rat
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4063_finite__range__imageI,axiom,
% 7.78/3.99 ! [G: nat > nat,F: nat > int] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 7.78/3.99 => ( finite_finite_int
% 7.78/3.99 @ ( image_nat_int
% 7.78/3.99 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 7.78/3.99 @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4064_Id__fstsnd__eq,axiom,
% 7.78/3.99 ( id_Pro2258643101195443293at_nat
% 7.78/3.99 = ( collec7088162979684241874at_nat
% 7.78/3.99 @ ^ [X4: produc859450856879609959at_nat] :
% 7.78/3.99 ( ( produc3213797794245857475at_nat @ X4 )
% 7.78/3.99 = ( produc6408287024330202629at_nat @ X4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4065_Id__fstsnd__eq,axiom,
% 7.78/3.99 ( id_nat2
% 7.78/3.99 = ( collec3392354462482085612at_nat
% 7.78/3.99 @ ^ [X4: product_prod_nat_nat] :
% 7.78/3.99 ( ( product_fst_nat_nat @ X4 )
% 7.78/3.99 = ( product_snd_nat_nat @ X4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4066_Id__fstsnd__eq,axiom,
% 7.78/3.99 ( id_int2
% 7.78/3.99 = ( collec213857154873943460nt_int
% 7.78/3.99 @ ^ [X4: product_prod_int_int] :
% 7.78/3.99 ( ( product_fst_int_int @ X4 )
% 7.78/3.99 = ( product_snd_int_int @ X4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4067_finite__surj__inj,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ A4 @ ( image_int_int @ F @ A4 ) )
% 7.78/3.99 => ( inj_on_int_int @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4068_finite__surj__inj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 => ( inj_on8969904277767023793at_nat @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4069_finite__surj__inj,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ A4 @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ( inj_on_nat_nat @ F @ A4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4070_inj__on__finite,axiom,
% 7.78/3.99 ! [F: int > int,A4: set_int,B5: set_int] :
% 7.78/3.99 ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( finite_finite_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4071_inj__on__finite,axiom,
% 7.78/3.99 ! [F: nat > rat,A4: set_nat,B5: set_rat] :
% 7.78/3.99 ( ( inj_on_nat_rat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_rat @ ( image_nat_rat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_rat @ B5 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4072_inj__on__finite,axiom,
% 7.78/3.99 ! [F: nat > int,A4: set_nat,B5: set_int] :
% 7.78/3.99 ( ( inj_on_nat_int @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_int @ B5 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4073_inj__on__finite,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4074_inj__on__finite,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat,B5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( inj_on5538052773655684606at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite6177210948735845034at_nat @ B5 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4075_inj__on__finite,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int,B5: set_nat] :
% 7.78/3.99 ( ( inj_on_int_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( finite_finite_int @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4076_inj__on__finite,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat,B5: set_nat] :
% 7.78/3.99 ( ( inj_on2178005380612969504at_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( finite6177210948735845034at_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4077_inj__on__finite,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat,B5: set_nat] :
% 7.78/3.99 ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
% 7.78/3.99 => ( ( finite_finite_nat @ B5 )
% 7.78/3.99 => ( finite_finite_nat @ A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4078_endo__inj__surj,axiom,
% 7.78/3.99 ! [A4: set_int,F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ A4 )
% 7.78/3.99 => ( ( inj_on_int_int @ F @ A4 )
% 7.78/3.99 => ( ( image_int_int @ F @ A4 )
% 7.78/3.99 = A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4079_endo__inj__surj,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ( ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) @ A4 )
% 7.78/3.99 => ( ( inj_on8969904277767023793at_nat @ F @ A4 )
% 7.78/3.99 => ( ( image_5168914502847457605at_nat @ F @ A4 )
% 7.78/3.99 = A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4080_endo__inj__surj,axiom,
% 7.78/3.99 ! [A4: set_nat,F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ A4 )
% 7.78/3.99 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ A4 )
% 7.78/3.99 => ( ( inj_on_nat_nat @ F @ A4 )
% 7.78/3.99 => ( ( image_nat_nat @ F @ A4 )
% 7.78/3.99 = A4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4081_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 7.78/3.99 => ( ( ( image_5168914502847457605at_nat @ F @ top_to4669805908274784177at_nat )
% 7.78/3.99 = top_to4669805908274784177at_nat )
% 7.78/3.99 => ( inj_on8969904277767023793at_nat @ F @ top_to4669805908274784177at_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4082_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: char > char] :
% 7.78/3.99 ( ( finite_finite_char @ top_top_set_char )
% 7.78/3.99 => ( ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.99 = top_top_set_char )
% 7.78/3.99 => ( inj_on_char_char @ F @ top_top_set_char ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4083_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: list_nat > list_nat] :
% 7.78/3.99 ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 7.78/3.99 => ( ( ( image_7976474329151083847st_nat @ F @ top_top_set_list_nat )
% 7.78/3.99 = top_top_set_list_nat )
% 7.78/3.99 => ( inj_on3049792774292151987st_nat @ F @ top_top_set_list_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4084_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: rat > rat] :
% 7.78/3.99 ( ( finite_finite_rat @ top_top_set_rat )
% 7.78/3.99 => ( ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.99 = top_top_set_rat )
% 7.78/3.99 => ( inj_on_rat_rat @ F @ top_top_set_rat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4085_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ top_top_set_nat )
% 7.78/3.99 => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 7.78/3.99 = top_top_set_nat )
% 7.78/3.99 => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4086_finite__UNIV__surj__inj,axiom,
% 7.78/3.99 ! [F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ top_top_set_int )
% 7.78/3.99 => ( ( ( image_int_int @ F @ top_top_set_int )
% 7.78/3.99 = top_top_set_int )
% 7.78/3.99 => ( inj_on_int_int @ F @ top_top_set_int ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4087_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 7.78/3.99 => ( ( inj_on8969904277767023793at_nat @ F @ top_to4669805908274784177at_nat )
% 7.78/3.99 => ( ( image_5168914502847457605at_nat @ F @ top_to4669805908274784177at_nat )
% 7.78/3.99 = top_to4669805908274784177at_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4088_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: char > char] :
% 7.78/3.99 ( ( finite_finite_char @ top_top_set_char )
% 7.78/3.99 => ( ( inj_on_char_char @ F @ top_top_set_char )
% 7.78/3.99 => ( ( image_char_char @ F @ top_top_set_char )
% 7.78/3.99 = top_top_set_char ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4089_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: list_nat > list_nat] :
% 7.78/3.99 ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 7.78/3.99 => ( ( inj_on3049792774292151987st_nat @ F @ top_top_set_list_nat )
% 7.78/3.99 => ( ( image_7976474329151083847st_nat @ F @ top_top_set_list_nat )
% 7.78/3.99 = top_top_set_list_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4090_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: rat > rat] :
% 7.78/3.99 ( ( finite_finite_rat @ top_top_set_rat )
% 7.78/3.99 => ( ( inj_on_rat_rat @ F @ top_top_set_rat )
% 7.78/3.99 => ( ( image_rat_rat @ F @ top_top_set_rat )
% 7.78/3.99 = top_top_set_rat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4091_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: nat > nat] :
% 7.78/3.99 ( ( finite_finite_nat @ top_top_set_nat )
% 7.78/3.99 => ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 7.78/3.99 => ( ( image_nat_nat @ F @ top_top_set_nat )
% 7.78/3.99 = top_top_set_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4092_finite__UNIV__inj__surj,axiom,
% 7.78/3.99 ! [F: int > int] :
% 7.78/3.99 ( ( finite_finite_int @ top_top_set_int )
% 7.78/3.99 => ( ( inj_on_int_int @ F @ top_top_set_int )
% 7.78/3.99 => ( ( image_int_int @ F @ top_top_set_int )
% 7.78/3.99 = top_top_set_int ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4093_finite__vimageD,axiom,
% 7.78/3.99 ! [H: char > char,F4: set_char] :
% 7.78/3.99 ( ( finite_finite_char @ ( vimage_char_char @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_char_char @ H @ top_top_set_char )
% 7.78/3.99 = top_top_set_char )
% 7.78/3.99 => ( finite_finite_char @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4094_finite__vimageD,axiom,
% 7.78/3.99 ! [H: char > rat,F4: set_rat] :
% 7.78/3.99 ( ( finite_finite_char @ ( vimage_char_rat @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_char_rat @ H @ top_top_set_char )
% 7.78/3.99 = top_top_set_rat )
% 7.78/3.99 => ( finite_finite_rat @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4095_finite__vimageD,axiom,
% 7.78/3.99 ! [H: char > nat,F4: set_nat] :
% 7.78/3.99 ( ( finite_finite_char @ ( vimage_char_nat @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_char_nat @ H @ top_top_set_char )
% 7.78/3.99 = top_top_set_nat )
% 7.78/3.99 => ( finite_finite_nat @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4096_finite__vimageD,axiom,
% 7.78/3.99 ! [H: char > int,F4: set_int] :
% 7.78/3.99 ( ( finite_finite_char @ ( vimage_char_int @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_char_int @ H @ top_top_set_char )
% 7.78/3.99 = top_top_set_int )
% 7.78/3.99 => ( finite_finite_int @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4097_finite__vimageD,axiom,
% 7.78/3.99 ! [H: rat > char,F4: set_char] :
% 7.78/3.99 ( ( finite_finite_rat @ ( vimage_rat_char @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_rat_char @ H @ top_top_set_rat )
% 7.78/3.99 = top_top_set_char )
% 7.78/3.99 => ( finite_finite_char @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4098_finite__vimageD,axiom,
% 7.78/3.99 ! [H: rat > rat,F4: set_rat] :
% 7.78/3.99 ( ( finite_finite_rat @ ( vimage_rat_rat @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_rat_rat @ H @ top_top_set_rat )
% 7.78/3.99 = top_top_set_rat )
% 7.78/3.99 => ( finite_finite_rat @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4099_finite__vimageD,axiom,
% 7.78/3.99 ! [H: rat > nat,F4: set_nat] :
% 7.78/3.99 ( ( finite_finite_rat @ ( vimage_rat_nat @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_rat_nat @ H @ top_top_set_rat )
% 7.78/3.99 = top_top_set_nat )
% 7.78/3.99 => ( finite_finite_nat @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4100_finite__vimageD,axiom,
% 7.78/3.99 ! [H: rat > int,F4: set_int] :
% 7.78/3.99 ( ( finite_finite_rat @ ( vimage_rat_int @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_rat_int @ H @ top_top_set_rat )
% 7.78/3.99 = top_top_set_int )
% 7.78/3.99 => ( finite_finite_int @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4101_finite__vimageD,axiom,
% 7.78/3.99 ! [H: nat > char,F4: set_char] :
% 7.78/3.99 ( ( finite_finite_nat @ ( vimage_nat_char @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_nat_char @ H @ top_top_set_nat )
% 7.78/3.99 = top_top_set_char )
% 7.78/3.99 => ( finite_finite_char @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4102_finite__vimageD,axiom,
% 7.78/3.99 ! [H: nat > rat,F4: set_rat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( vimage_nat_rat @ H @ F4 ) )
% 7.78/3.99 => ( ( ( image_nat_rat @ H @ top_top_set_nat )
% 7.78/3.99 = top_top_set_rat )
% 7.78/3.99 => ( finite_finite_rat @ F4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4103_prod__set__defs_I2_J,axiom,
% 7.78/3.99 ( basic_1496934909540232809t_unit
% 7.78/3.99 = ( ^ [P3: produc7812382424243267045t_unit] : ( insert8563697753282147485t_unit @ ( produc1126150082675451753t_unit @ P3 ) @ bot_bo3686245532977126937t_unit ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4104_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: nat > product_unit,A4: set_nat] :
% 7.78/3.99 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ? [X: product_unit] :
% 7.78/3.99 ( ( member_Product_unit @ X @ ( image_8730104196221521654t_unit @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4105_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: nat > $o,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_o @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ? [X: $o] :
% 7.78/3.99 ( ( member_o @ X @ ( image_nat_o @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_nat @ ( vimage_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4106_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: int > nat,A4: set_int] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_int @ A4 )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ ( image_int_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_int @ ( vimage_int_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4107_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: nat > nat,A4: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ ( image_nat_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4108_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_unit,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite4290736615968046902t_unit @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ? [X: product_unit] :
% 7.78/3.99 ( ( member_Product_unit @ X @ ( image_6169909464789311569t_unit @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite6177210948735845034at_nat @ ( vimage3104651464403166471t_unit @ F @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4109_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: nat > product_prod_nat_nat,A4: set_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ? [X: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X @ ( image_5846123807819985514at_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_nat @ ( vimage8013328719654469172at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4110_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > $o,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_o @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ? [X: $o] :
% 7.78/3.99 ( ( member_o @ X @ ( image_3693632289388996572_nat_o @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite6177210948735845034at_nat @ ( vimage2444243245536687506_nat_o @ F @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4111_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ? [X: nat] :
% 7.78/3.99 ( ( member_nat @ X @ ( image_2486076414777270412at_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite6177210948735845034at_nat @ ( vimage4653281326611754070at_nat @ F @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4112_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: product_prod_nat_nat > product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite6177210948735845034at_nat @ A4 )
% 7.78/3.99 => ? [X: product_prod_nat_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X @ ( image_5168914502847457605at_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite6177210948735845034at_nat @ ( vimage2449269961533847803at_nat @ F @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4113_inf__img__fin__dom,axiom,
% 7.78/3.99 ! [F: nat > produc3843707927480180839at_nat,A4: set_nat] :
% 7.78/3.99 ( ( finite4343798906461161616at_nat @ ( image_2499013659892586576at_nat @ F @ A4 ) )
% 7.78/3.99 => ( ~ ( finite_finite_nat @ A4 )
% 7.78/3.99 => ? [X: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( member8757157785044589968at_nat @ X @ ( image_2499013659892586576at_nat @ F @ A4 ) )
% 7.78/3.99 & ~ ( finite_finite_nat @ ( vimage6435164912253009178at_nat @ F @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4114_nat__descend__induct,axiom,
% 7.78/3.99 ! [N3: nat,P2: nat > $o,M3: nat] :
% 7.78/3.99 ( ! [K2: nat] :
% 7.78/3.99 ( ( ord_less_nat @ N3 @ K2 )
% 7.78/3.99 => ( P2 @ K2 ) )
% 7.78/3.99 => ( ! [K2: nat] :
% 7.78/3.99 ( ( ord_less_eq_nat @ K2 @ N3 )
% 7.78/3.99 => ( ! [I5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ K2 @ I5 )
% 7.78/3.99 => ( P2 @ I5 ) )
% 7.78/3.99 => ( P2 @ K2 ) ) )
% 7.78/3.99 => ( P2 @ M3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4115_Field__natLeq__on,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( field_nat
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 7.78/3.99 = ( collect_nat
% 7.78/3.99 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4116_natLeq__on__well__order__on,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( order_2888998067076097458on_nat
% 7.78/3.99 @ ( collect_nat
% 7.78/3.99 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) )
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4117_natLeq__on__Well__order,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( order_2888998067076097458on_nat
% 7.78/3.99 @ ( field_nat
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4118_natLeq__on__wo__rel,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( bNF_We3818239936649020644el_nat
% 7.78/3.99 @ ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4119_wf__less,axiom,
% 7.78/3.99 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4120_natLess__def,axiom,
% 7.78/3.99 ( bNF_Ca8459412986667044542atLess
% 7.78/3.99 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4121_card_Ocomp__fun__commute__on,axiom,
% 7.78/3.99 ( ( comp_nat_nat_nat @ suc @ suc )
% 7.78/3.99 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4122_pred__nat__def,axiom,
% 7.78/3.99 ( pred_nat
% 7.78/3.99 = ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [M5: nat,N4: nat] :
% 7.78/3.99 ( N4
% 7.78/3.99 = ( suc @ M5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4123_zero__notin__Suc__image,axiom,
% 7.78/3.99 ! [A4: set_nat] :
% 7.78/3.99 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4124_Restr__natLeq2,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 7.78/3.99 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N3 )
% 7.78/3.99 @ ^ [Uu: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N3 ) ) )
% 7.78/3.99 = ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4125_Restr__natLeq,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 7.78/3.99 @ ( produc457027306803732586at_nat
% 7.78/3.99 @ ( collect_nat
% 7.78/3.99 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) )
% 7.78/3.99 @ ^ [Uu: nat] :
% 7.78/3.99 ( collect_nat
% 7.78/3.99 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N3 ) ) ) )
% 7.78/3.99 = ( collec3392354462482085612at_nat
% 7.78/3.99 @ ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( ( ord_less_nat @ X4 @ N3 )
% 7.78/3.99 & ( ord_less_nat @ Y5 @ N3 )
% 7.78/3.99 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4126_natLeq__def,axiom,
% 7.78/3.99 ( bNF_Ca8665028551170535155natLeq
% 7.78/3.99 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4127_rat__denum,axiom,
% 7.78/3.99 ? [F5: nat > rat] :
% 7.78/3.99 ( ( image_nat_rat @ F5 @ top_top_set_nat )
% 7.78/3.99 = top_top_set_rat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4128_greaterThan__0,axiom,
% 7.78/3.99 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 7.78/3.99 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4129_image__Suc__atLeastLessThan,axiom,
% 7.78/3.99 ! [I: nat,J4: nat] :
% 7.78/3.99 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J4 ) )
% 7.78/3.99 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4130_INT__greaterThan__UNIV,axiom,
% 7.78/3.99 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 7.78/3.99 = bot_bot_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4131_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N3 ) )
% 7.78/3.99 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4132_image__minus__const__atLeastLessThan__nat,axiom,
% 7.78/3.99 ! [C: nat,Y3: nat,X2: nat] :
% 7.78/3.99 ( ( ( ord_less_nat @ C @ Y3 )
% 7.78/3.99 => ( ( image_nat_nat
% 7.78/3.99 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 7.78/3.99 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 7.78/3.99 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 7.78/3.99 & ( ~ ( ord_less_nat @ C @ Y3 )
% 7.78/3.99 => ( ( ( ord_less_nat @ X2 @ Y3 )
% 7.78/3.99 => ( ( image_nat_nat
% 7.78/3.99 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 7.78/3.99 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 7.78/3.99 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 7.78/3.99 & ( ~ ( ord_less_nat @ X2 @ Y3 )
% 7.78/3.99 => ( ( image_nat_nat
% 7.78/3.99 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 7.78/3.99 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 7.78/3.99 = bot_bot_set_nat ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4133_surj__nat__to__rat__surj,axiom,
% 7.78/3.99 ( ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat )
% 7.78/3.99 = top_top_set_rat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4134_range__mod,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 7.78/3.99 => ( ( image_nat_nat
% 7.78/3.99 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N3 )
% 7.78/3.99 @ top_top_set_nat )
% 7.78/3.99 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4135_divmod__nat__if,axiom,
% 7.78/3.99 ( divmod_nat
% 7.78/3.99 = ( ^ [M5: nat,N4: nat] :
% 7.78/3.99 ( if_Pro6206227464963214023at_nat
% 7.78/3.99 @ ( ( N4 = zero_zero_nat )
% 7.78/3.99 | ( ord_less_nat @ M5 @ N4 ) )
% 7.78/3.99 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [Q3: nat] : ( product_Pair_nat_nat @ ( suc @ Q3 ) )
% 7.78/3.99 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4136_Rats__eq__range__nat__to__rat__surj,axiom,
% 7.78/3.99 ( field_6020823756834552118ts_rat
% 7.78/3.99 = ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4137_image__Suc__atLeastAtMost,axiom,
% 7.78/3.99 ! [I: nat,J4: nat] :
% 7.78/3.99 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J4 ) )
% 7.78/3.99 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4138_UN__atMost__UNIV,axiom,
% 7.78/3.99 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4139_atMost__Suc__eq__insert__0,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( set_ord_atMost_nat @ ( suc @ N3 ) )
% 7.78/3.99 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4140_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N3 ) )
% 7.78/3.99 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4141_image__Suc__lessThan,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N3 ) )
% 7.78/3.99 = ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4142_UN__lessThan__UNIV,axiom,
% 7.78/3.99 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4143_lessThan__Suc__eq__insert__0,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( set_ord_lessThan_nat @ ( suc @ N3 ) )
% 7.78/3.99 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4144_image__Suc__atMost,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N3 ) )
% 7.78/3.99 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4145_image__int__atLeastAtMost,axiom,
% 7.78/3.99 ! [A: nat,B: nat] :
% 7.78/3.99 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.78/3.99 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4146_image__int__atLeastLessThan,axiom,
% 7.78/3.99 ! [A: nat,B: nat] :
% 7.78/3.99 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 7.78/3.99 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4147_image__add__int__atLeastLessThan,axiom,
% 7.78/3.99 ! [L: int,U: int] :
% 7.78/3.99 ( ( image_int_int
% 7.78/3.99 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 7.78/3.99 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 7.78/3.99 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4148_pair__lessI2,axiom,
% 7.78/3.99 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 7.78/3.99 ( ( ord_less_eq_nat @ A @ B )
% 7.78/3.99 => ( ( ord_less_nat @ S2 @ T2 )
% 7.78/3.99 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_less ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4149_pair__less__iff1,axiom,
% 7.78/3.99 ! [X2: nat,Y3: nat,Z2: nat] :
% 7.78/3.99 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( product_Pair_nat_nat @ X2 @ Z2 ) ) @ fun_pair_less )
% 7.78/3.99 = ( ord_less_nat @ Y3 @ Z2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4150_total__pair__less,axiom,
% 7.78/3.99 ! [A4: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A4 @ fun_pair_less ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4151_Inf__int__def,axiom,
% 7.78/3.99 ( complete_Inf_Inf_int
% 7.78/3.99 = ( ^ [X9: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X9 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4152_wf__pair__less,axiom,
% 7.78/3.99 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4153_pair__lessI1,axiom,
% 7.78/3.99 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 7.78/3.99 ( ( ord_less_nat @ A @ B )
% 7.78/3.99 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_less ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4154_bij__betw__Suc,axiom,
% 7.78/3.99 ! [M: set_nat,N: set_nat] :
% 7.78/3.99 ( ( bij_betw_nat_nat @ suc @ M @ N )
% 7.78/3.99 = ( ( image_nat_nat @ suc @ M )
% 7.78/3.99 = N ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4155_pair__leqI2,axiom,
% 7.78/3.99 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 7.78/3.99 ( ( ord_less_eq_nat @ A @ B )
% 7.78/3.99 => ( ( ord_less_eq_nat @ S2 @ T2 )
% 7.78/3.99 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_leq ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4156_pair__leqI1,axiom,
% 7.78/3.99 ! [A: nat,B: nat,S2: nat,T2: nat] :
% 7.78/3.99 ( ( ord_less_nat @ A @ B )
% 7.78/3.99 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T2 ) ) @ fun_pair_leq ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4157_pair__leq__def,axiom,
% 7.78/3.99 ( fun_pair_leq
% 7.78/3.99 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4158_wmax__insertI,axiom,
% 7.78/3.99 ! [Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ Y3 @ YS )
% 7.78/3.99 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4159_wmin__insertI,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 7.78/3.99 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4160_smax__insertI,axiom,
% 7.78/3.99 ! [Y3: product_prod_nat_nat,Y4: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,X5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ Y3 @ Y4 )
% 7.78/3.99 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ Y4 ) @ fun_max_strict )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ X5 ) @ Y4 ) @ fun_max_strict ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4161_smin__insertI,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 7.78/3.99 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 7.78/3.99 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4162_max__rpair__set,axiom,
% 7.78/3.99 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4163_min__rpair__set,axiom,
% 7.78/3.99 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4164_wmax__emptyI,axiom,
% 7.78/3.99 ! [X5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ X5 )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X5 ) @ fun_max_weak ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4165_smax__emptyI,axiom,
% 7.78/3.99 ! [Y4: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( finite6177210948735845034at_nat @ Y4 )
% 7.78/3.99 => ( ( Y4 != bot_bo2099793752762293965at_nat )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y4 ) @ fun_max_strict ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4166_smin__emptyI,axiom,
% 7.78/3.99 ! [X5: set_Pr1261947904930325089at_nat] :
% 7.78/3.99 ( ( X5 != bot_bo2099793752762293965at_nat )
% 7.78/3.99 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4167_wmin__emptyI,axiom,
% 7.78/3.99 ! [X5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4168_max__strict__def,axiom,
% 7.78/3.99 ( fun_max_strict
% 7.78/3.99 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4169_min__strict__def,axiom,
% 7.78/3.99 ( fun_min_strict
% 7.78/3.99 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4170_min__weak__def,axiom,
% 7.78/3.99 ( fun_min_weak
% 7.78/3.99 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4171_max__weak__def,axiom,
% 7.78/3.99 ( fun_max_weak
% 7.78/3.99 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4172_image__atLeastZeroLessThan__int,axiom,
% 7.78/3.99 ! [U: int] :
% 7.78/3.99 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 7.78/3.99 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 7.78/3.99 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4173_UN__atLeast__UNIV,axiom,
% 7.78/3.99 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4174_trans__pair__less,axiom,
% 7.78/3.99 trans_4347625901269045472at_nat @ fun_pair_less ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4175_less__eq__int_Orep__eq,axiom,
% 7.78/3.99 ( ord_less_eq_int
% 7.78/3.99 = ( ^ [X4: int,Xa3: int] :
% 7.78/3.99 ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [Y5: nat,Z4: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V3 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 7.78/3.99 @ ( rep_Integ @ X4 )
% 7.78/3.99 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4176_nat_Orep__eq,axiom,
% 7.78/3.99 ( nat2
% 7.78/3.99 = ( ^ [X4: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4177_less__int_Orep__eq,axiom,
% 7.78/3.99 ( ord_less_int
% 7.78/3.99 = ( ^ [X4: int,Xa3: int] :
% 7.78/3.99 ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [Y5: nat,Z4: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V3 ) @ ( plus_plus_nat @ U3 @ Z4 ) ) )
% 7.78/3.99 @ ( rep_Integ @ X4 )
% 7.78/3.99 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4178_less__eq__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re717283939379294677_int_o @ pcr_int
% 7.78/3.99 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 7.78/3.99 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 7.78/3.99 @ ord_less_eq_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4179_less__eq__int_Oabs__eq,axiom,
% 7.78/3.99 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) )
% 7.78/3.99 @ Xa2
% 7.78/3.99 @ X2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4180_int__ge__less__than2__def,axiom,
% 7.78/3.99 ( int_ge_less_than2
% 7.78/3.99 = ( ^ [D3: int] :
% 7.78/3.99 ( collec213857154873943460nt_int
% 7.78/3.99 @ ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [Z6: int,Z4: int] :
% 7.78/3.99 ( ( ord_less_eq_int @ D3 @ Z4 )
% 7.78/3.99 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4181_int__ge__less__than__def,axiom,
% 7.78/3.99 ( int_ge_less_than
% 7.78/3.99 = ( ^ [D3: int] :
% 7.78/3.99 ( collec213857154873943460nt_int
% 7.78/3.99 @ ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [Z6: int,Z4: int] :
% 7.78/3.99 ( ( ord_less_eq_int @ D3 @ Z6 )
% 7.78/3.99 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4182_less__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re717283939379294677_int_o @ pcr_int
% 7.78/3.99 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 7.78/3.99 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 7.78/3.99 @ ord_less_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4183_minus__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) )
% 7.78/3.99 @ minus_minus_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4184_plus__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) )
% 7.78/3.99 @ plus_plus_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4185_nat_Oabs__eq,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( nat2 @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4186_nat_Otransfer,axiom,
% 7.78/3.99 ( bNF_re4555766996558763186at_nat @ pcr_int
% 7.78/3.99 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.99 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 7.78/3.99 @ nat2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4187_uminus__int_Oabs__eq,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( abs_Integ
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 )
% 7.78/3.99 @ X2 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4188_uminus__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 7.78/3.99 @ uminus_uminus_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4189_times__int_Oabs__eq,axiom,
% 7.78/3.99 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( abs_Integ
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) )
% 7.78/3.99 @ Xa2
% 7.78/3.99 @ X2 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4190_plus__int_Oabs__eq,axiom,
% 7.78/3.99 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( abs_Integ
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) )
% 7.78/3.99 @ Xa2
% 7.78/3.99 @ X2 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4191_minus__int_Oabs__eq,axiom,
% 7.78/3.99 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( abs_Integ
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) )
% 7.78/3.99 @ Xa2
% 7.78/3.99 @ X2 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4192_times__int_Otransfer,axiom,
% 7.78/3.99 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) )
% 7.78/3.99 @ times_times_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4193_less__int_Oabs__eq,axiom,
% 7.78/3.99 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 7.78/3.99 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 7.78/3.99 = ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) )
% 7.78/3.99 @ Xa2
% 7.78/3.99 @ X2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4194_uminus__int__def,axiom,
% 7.78/3.99 ( uminus_uminus_int
% 7.78/3.99 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4195_times__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4196_nat__def,axiom,
% 7.78/3.99 ( nat2
% 7.78/3.99 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4197_minus__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4198_plus__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4199_less__eq__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re4202695980764964119_nat_o @ intrel
% 7.78/3.99 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 7.78/3.99 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4200_uminus__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 7.78/3.99 @ ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4201_nat_Orsp,axiom,
% 7.78/3.99 ( bNF_re8246922863344978751at_nat @ intrel
% 7.78/3.99 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.99 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 7.78/3.99 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4202_intrel__def,axiom,
% 7.78/3.99 ( intrel
% 7.78/3.99 = ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] :
% 7.78/3.99 ( ( plus_plus_nat @ X4 @ V3 )
% 7.78/3.99 = ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4203_less__int_Orsp,axiom,
% 7.78/3.99 ( bNF_re4202695980764964119_nat_o @ intrel
% 7.78/3.99 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 7.78/3.99 @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4204_times__int__def,axiom,
% 7.78/3.99 ( times_times_int
% 7.78/3.99 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y5 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y5 @ U3 ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4205_minus__int__def,axiom,
% 7.78/3.99 ( minus_minus_int
% 7.78/3.99 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y5 @ U3 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4206_plus__int__def,axiom,
% 7.78/3.99 ( plus_plus_int
% 7.78/3.99 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 7.78/3.99 @ ( produc27273713700761075at_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y5 @ V3 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4207_rat__less__code,axiom,
% 7.78/3.99 ( ord_less_rat
% 7.78/3.99 = ( ^ [P3: rat,Q3: rat] :
% 7.78/3.99 ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( ord_less_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) )
% 7.78/3.99 @ ( quotient_of @ Q3 ) )
% 7.78/3.99 @ ( quotient_of @ P3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4208_rat__less__eq__code,axiom,
% 7.78/3.99 ( ord_less_eq_rat
% 7.78/3.99 = ( ^ [P3: rat,Q3: rat] :
% 7.78/3.99 ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4947309494688390418_int_o
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) )
% 7.78/3.99 @ ( quotient_of @ Q3 ) )
% 7.78/3.99 @ ( quotient_of @ P3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4209_rat__uminus__code,axiom,
% 7.78/3.99 ! [P: rat] :
% 7.78/3.99 ( ( quotient_of @ ( uminus_uminus_rat @ P ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4210_less__int__def,axiom,
% 7.78/3.99 ( ord_less_int
% 7.78/3.99 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4211_less__eq__int__def,axiom,
% 7.78/3.99 ( ord_less_eq_int
% 7.78/3.99 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 7.78/3.99 @ ( produc8739625826339149834_nat_o
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] :
% 7.78/3.99 ( produc6081775807080527818_nat_o
% 7.78/3.99 @ ^ [U3: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U3 @ Y5 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4212_rat__minus__code,axiom,
% 7.78/3.99 ! [P: rat,Q: rat] :
% 7.78/3.99 ( ( quotient_of @ ( minus_minus_rat @ P @ Q ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 7.78/3.99 @ ( quotient_of @ Q ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4213_rat__plus__code,axiom,
% 7.78/3.99 ! [P: rat,Q: rat] :
% 7.78/3.99 ( ( quotient_of @ ( plus_plus_rat @ P @ Q ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D3 ) ) )
% 7.78/3.99 @ ( quotient_of @ Q ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4214_rat__divide__code,axiom,
% 7.78/3.99 ! [P: rat,Q: rat] :
% 7.78/3.99 ( ( quotient_of @ ( divide_divide_rat @ P @ Q ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D3 ) @ ( times_times_int @ C4 @ B4 ) ) )
% 7.78/3.99 @ ( quotient_of @ Q ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4215_rat__times__code,axiom,
% 7.78/3.99 ! [P: rat,Q: rat] :
% 7.78/3.99 ( ( quotient_of @ ( times_times_rat @ P @ Q ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int,C4: int] :
% 7.78/3.99 ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [B4: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C4 @ D3 ) ) )
% 7.78/3.99 @ ( quotient_of @ Q ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4216_pcr__int__def,axiom,
% 7.78/3.99 ( pcr_int
% 7.78/3.99 = ( relcom8911704206367525917at_int
% 7.78/3.99 @ ( basic_5328504652464829177at_nat
% 7.78/3.99 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
% 7.78/3.99 @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 7.78/3.99 @ cr_int ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4217_UNIV__unit,axiom,
% 7.78/3.99 ( top_to1996260823553986621t_unit
% 7.78/3.99 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4218_top__unit__def,axiom,
% 7.78/3.99 top_top_Product_unit = product_Unity ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4219_uminus__unit__def,axiom,
% 7.78/3.99 ( uminus2952777764628376836t_unit
% 7.78/3.99 = ( ^ [Uu2: product_unit] : product_Unity ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4220_inf__unit__def,axiom,
% 7.78/3.99 ( inf_inf_Product_unit
% 7.78/3.99 = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4221_old_Ounit_Oexhaust,axiom,
% 7.78/3.99 ! [Y3: product_unit] : ( Y3 = product_Unity ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4222_Inf__unit__def,axiom,
% 7.78/3.99 ( comple2584293577114468500t_unit
% 7.78/3.99 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4223_Sup__unit__def,axiom,
% 7.78/3.99 ( comple4687483117567863418t_unit
% 7.78/3.99 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4224_sup__unit__def,axiom,
% 7.78/3.99 ( sup_sup_Product_unit
% 7.78/3.99 = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4225_bot__unit__def,axiom,
% 7.78/3.99 bot_bot_Product_unit = product_Unity ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4226_default__unit__def,axiom,
% 7.78/3.99 defaul566961228789861419t_unit = product_Unity ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4227_Gcd__eq__Max,axiom,
% 7.78/3.99 ! [M: set_nat] :
% 7.78/3.99 ( ( finite_finite_nat @ M )
% 7.78/3.99 => ( ( M != bot_bot_set_nat )
% 7.78/3.99 => ( ~ ( member_nat @ zero_zero_nat @ M )
% 7.78/3.99 => ( ( gcd_Gcd_nat @ M )
% 7.78/3.99 = ( lattic8265883725875713057ax_nat
% 7.78/3.99 @ ( comple7806235888213564991et_nat
% 7.78/3.99 @ ( image_nat_set_nat
% 7.78/3.99 @ ^ [M5: nat] :
% 7.78/3.99 ( collect_nat
% 7.78/3.99 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ M5 ) )
% 7.78/3.99 @ M ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4228_Gcd__int__eq,axiom,
% 7.78/3.99 ! [N: set_nat] :
% 7.78/3.99 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N ) )
% 7.78/3.99 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4229_Gcd__int__def,axiom,
% 7.78/3.99 ( gcd_Gcd_int
% 7.78/3.99 = ( ^ [K3: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K3 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4230_Gcd__nat__abs__eq,axiom,
% 7.78/3.99 ! [K4: set_int] :
% 7.78/3.99 ( ( gcd_Gcd_nat
% 7.78/3.99 @ ( image_int_nat
% 7.78/3.99 @ ^ [K5: int] : ( nat2 @ ( abs_abs_int @ K5 ) )
% 7.78/3.99 @ K4 ) )
% 7.78/3.99 = ( nat2 @ ( gcd_Gcd_int @ K4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4231_range__abs__Nats,axiom,
% 7.78/3.99 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 7.78/3.99 = semiring_1_Nats_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4232_Gcd__abs__eq,axiom,
% 7.78/3.99 ! [K4: set_int] :
% 7.78/3.99 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K4 ) )
% 7.78/3.99 = ( gcd_Gcd_int @ K4 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4233_int__in__range__abs,axiom,
% 7.78/3.99 ! [N3: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N3 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4234_measure__function__int,axiom,
% 7.78/3.99 fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4235_rat__abs__code,axiom,
% 7.78/3.99 ! [P: rat] :
% 7.78/3.99 ( ( quotient_of @ ( abs_abs_rat @ P ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4236_surj__int__encode,axiom,
% 7.78/3.99 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4237_surj__int__decode,axiom,
% 7.78/3.99 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 7.78/3.99 = top_top_set_int ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4238_Lcm__abs__eq,axiom,
% 7.78/3.99 ! [K4: set_int] :
% 7.78/3.99 ( ( gcd_Lcm_int @ ( image_int_int @ abs_abs_int @ K4 ) )
% 7.78/3.99 = ( gcd_Lcm_int @ K4 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4239_Lcm__int__def,axiom,
% 7.78/3.99 ( gcd_Lcm_int
% 7.78/3.99 = ( ^ [K3: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K3 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4240_Lcm__int__eq,axiom,
% 7.78/3.99 ! [N: set_nat] :
% 7.78/3.99 ( ( gcd_Lcm_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N ) )
% 7.78/3.99 = ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ N ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4241_Lcm__nat__abs__eq,axiom,
% 7.78/3.99 ! [K4: set_int] :
% 7.78/3.99 ( ( gcd_Lcm_nat
% 7.78/3.99 @ ( image_int_nat
% 7.78/3.99 @ ^ [K5: int] : ( nat2 @ ( abs_abs_int @ K5 ) )
% 7.78/3.99 @ K4 ) )
% 7.78/3.99 = ( nat2 @ ( gcd_Lcm_int @ K4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4242_rat__inverse__code,axiom,
% 7.78/3.99 ! [P: rat] :
% 7.78/3.99 ( ( quotient_of @ ( inverse_inverse_rat @ P ) )
% 7.78/3.99 = ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 7.78/3.99 @ ( quotient_of @ P ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4243_euclidean__size__int__def,axiom,
% 7.78/3.99 ( euclid4774559944035922753ze_int
% 7.78/3.99 = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4244_Unity__def,axiom,
% 7.78/3.99 ( product_Unity
% 7.78/3.99 = ( product_Abs_unit @ $true ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4245_prod__encode__def,axiom,
% 7.78/3.99 ( nat_prod_encode
% 7.78/3.99 = ( produc6842872674320459806at_nat
% 7.78/3.99 @ ^ [M5: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M5 @ N4 ) ) @ M5 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4246_Abs__unit__cases,axiom,
% 7.78/3.99 ! [X2: product_unit] :
% 7.78/3.99 ~ ! [Y: $o] :
% 7.78/3.99 ( ( X2
% 7.78/3.99 = ( product_Abs_unit @ Y ) )
% 7.78/3.99 => ~ ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4247_Abs__unit__induct,axiom,
% 7.78/3.99 ! [P2: product_unit > $o,X2: product_unit] :
% 7.78/3.99 ( ! [Y: $o] :
% 7.78/3.99 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ( P2 @ ( product_Abs_unit @ Y ) ) )
% 7.78/3.99 => ( P2 @ X2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4248_Abs__unit__inject,axiom,
% 7.78/3.99 ! [X2: $o,Y3: $o] :
% 7.78/3.99 ( ( member_o @ X2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ( ( ( product_Abs_unit @ X2 )
% 7.78/3.99 = ( product_Abs_unit @ Y3 ) )
% 7.78/3.99 = ( X2 = Y3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4249_surj__prod__encode,axiom,
% 7.78/3.99 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4250_type__definition__unit,axiom,
% 7.78/3.99 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4251_Rep__unit__inject,axiom,
% 7.78/3.99 ! [X2: product_unit,Y3: product_unit] :
% 7.78/3.99 ( ( ( product_Rep_unit @ X2 )
% 7.78/3.99 = ( product_Rep_unit @ Y3 ) )
% 7.78/3.99 = ( X2 = Y3 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4252_Rep__unit__induct,axiom,
% 7.78/3.99 ! [Y3: $o,P2: $o > $o] :
% 7.78/3.99 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ( ! [X: product_unit] : ( P2 @ ( product_Rep_unit @ X ) )
% 7.78/3.99 => ( P2 @ Y3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4253_Rep__unit__cases,axiom,
% 7.78/3.99 ! [Y3: $o] :
% 7.78/3.99 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ~ ! [X: product_unit] :
% 7.78/3.99 ( Y3
% 7.78/3.99 = ( ~ ( product_Rep_unit @ X ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4254_Rep__unit,axiom,
% 7.78/3.99 ! [X2: product_unit] : ( member_o @ ( product_Rep_unit @ X2 ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4255_Rep__unit__inverse,axiom,
% 7.78/3.99 ! [X2: product_unit] :
% 7.78/3.99 ( ( product_Abs_unit @ ( product_Rep_unit @ X2 ) )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4256_Abs__unit__inverse,axiom,
% 7.78/3.99 ! [Y3: $o] :
% 7.78/3.99 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 7.78/3.99 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y3 ) )
% 7.78/3.99 = Y3 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4257_surj__prod__decode,axiom,
% 7.78/3.99 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 7.78/3.99 = top_to4669805908274784177at_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4258_pair__less__def,axiom,
% 7.78/3.99 ( fun_pair_less
% 7.78/3.99 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4259_list__decode_Oelims,axiom,
% 7.78/3.99 ! [X2: nat,Y3: list_nat] :
% 7.78/3.99 ( ( ( nat_list_decode @ X2 )
% 7.78/3.99 = Y3 )
% 7.78/3.99 => ( ( ( X2 = zero_zero_nat )
% 7.78/3.99 => ( Y3 != nil_nat ) )
% 7.78/3.99 => ~ ! [N2: nat] :
% 7.78/3.99 ( ( X2
% 7.78/3.99 = ( suc @ N2 ) )
% 7.78/3.99 => ( Y3
% 7.78/3.99 != ( produc2761476792215241774st_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 7.78/3.99 @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4260_nat__to__rat__surj__def,axiom,
% 7.78/3.99 ( nat_to_rat_surj
% 7.78/3.99 = ( ^ [N4: nat] :
% 7.78/3.99 ( produc6207742614233964070at_rat
% 7.78/3.99 @ ^ [A5: nat,B4: nat] : ( fract @ ( nat_int_decode @ A5 ) @ ( nat_int_decode @ B4 ) )
% 7.78/3.99 @ ( nat_prod_decode @ N4 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4261_list__decode_Osimps_I2_J,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( nat_list_decode @ ( suc @ N3 ) )
% 7.78/3.99 = ( produc2761476792215241774st_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 7.78/3.99 @ ( nat_prod_decode @ N3 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4262_list__decode_Opelims,axiom,
% 7.78/3.99 ! [X2: nat,Y3: list_nat] :
% 7.78/3.99 ( ( ( nat_list_decode @ X2 )
% 7.78/3.99 = Y3 )
% 7.78/3.99 => ( ( accp_nat @ nat_list_decode_rel @ X2 )
% 7.78/3.99 => ( ( ( X2 = zero_zero_nat )
% 7.78/3.99 => ( ( Y3 = nil_nat )
% 7.78/3.99 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 7.78/3.99 => ~ ! [N2: nat] :
% 7.78/3.99 ( ( X2
% 7.78/3.99 = ( suc @ N2 ) )
% 7.78/3.99 => ( ( Y3
% 7.78/3.99 = ( produc2761476792215241774st_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 7.78/3.99 @ ( nat_prod_decode @ N2 ) ) )
% 7.78/3.99 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4263_surj__list__decode,axiom,
% 7.78/3.99 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 7.78/3.99 = top_top_set_list_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4264_list__decode_Opsimps_I2_J,axiom,
% 7.78/3.99 ! [N3: nat] :
% 7.78/3.99 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 7.78/3.99 => ( ( nat_list_decode @ ( suc @ N3 ) )
% 7.78/3.99 = ( produc2761476792215241774st_nat
% 7.78/3.99 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 7.78/3.99 @ ( nat_prod_decode @ N3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4265_surj__sum__encode,axiom,
% 7.78/3.99 ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4266_surj__list__encode,axiom,
% 7.78/3.99 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 7.78/3.99 = top_top_set_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4267_surj__sum__decode,axiom,
% 7.78/3.99 ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 7.78/3.99 = top_to6661820994512907621at_nat ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4268_divmod__step__int__def,axiom,
% 7.78/3.99 ( unique5024387138958732305ep_int
% 7.78/3.99 = ( ^ [L3: num] :
% 7.78/3.99 ( produc4245557441103728435nt_int
% 7.78/3.99 @ ^ [Q3: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4269_divmod__step__nat__def,axiom,
% 7.78/3.99 ( unique5026877609467782581ep_nat
% 7.78/3.99 = ( ^ [L3: num] :
% 7.78/3.99 ( produc2626176000494625587at_nat
% 7.78/3.99 @ ^ [Q3: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4270_divmod__step__integer__def,axiom,
% 7.78/3.99 ( unique4921790084139445826nteger
% 7.78/3.99 = ( ^ [L3: num] :
% 7.78/3.99 ( produc6916734918728496179nteger
% 7.78/3.99 @ ^ [Q3: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4271_nat__of__integer__code,axiom,
% 7.78/3.99 ( code_nat_of_integer
% 7.78/3.99 = ( ^ [K5: code_integer] :
% 7.78/3.99 ( if_nat @ ( ord_le3102999989581377725nteger @ K5 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 7.78/3.99 @ ( produc1555791787009142072er_nat
% 7.78/3.99 @ ^ [L3: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 7.78/3.99 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4272_num__of__integer__code,axiom,
% 7.78/3.99 ( code_num_of_integer
% 7.78/3.99 = ( ^ [K5: code_integer] :
% 7.78/3.99 ( if_num @ ( ord_le3102999989581377725nteger @ K5 @ one_one_Code_integer ) @ one
% 7.78/3.99 @ ( produc7336495610019696514er_num
% 7.78/3.99 @ ^ [L3: code_integer,J: code_integer] : ( if_num @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 7.78/3.99 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4273_divmod__integer__code,axiom,
% 7.78/3.99 ( code_divmod_integer
% 7.78/3.99 = ( ^ [K5: code_integer,L3: code_integer] :
% 7.78/3.99 ( if_Pro6119634080678213985nteger @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K5 ) @ ( code_divmod_abs @ K5 @ L3 )
% 7.78/3.99 @ ( produc6916734918728496179nteger
% 7.78/3.99 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L3 @ S ) ) )
% 7.78/3.99 @ ( code_divmod_abs @ K5 @ L3 ) ) )
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K5 )
% 7.78/3.99 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K5 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K5 @ L3 )
% 7.78/3.99 @ ( produc6916734918728496179nteger
% 7.78/3.99 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L3 ) @ S ) ) )
% 7.78/3.99 @ ( code_divmod_abs @ K5 @ L3 ) ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4274_int__of__integer__code,axiom,
% 7.78/3.99 ( code_int_of_integer
% 7.78/3.99 = ( ^ [K5: code_integer] :
% 7.78/3.99 ( if_int @ ( ord_le6747313008572928689nteger @ K5 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K5 ) ) )
% 7.78/3.99 @ ( if_int @ ( K5 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 7.78/3.99 @ ( produc1553301316500091796er_int
% 7.78/3.99 @ ^ [L3: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 7.78/3.99 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4275_Code__Numeral_Onegative__def,axiom,
% 7.78/3.99 ( code_negative
% 7.78/3.99 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4276_bit__cut__integer__code,axiom,
% 7.78/3.99 ( code_bit_cut_integer
% 7.78/3.99 = ( ^ [K5: code_integer] :
% 7.78/3.99 ( if_Pro5737122678794959658eger_o @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 7.78/3.99 @ ( produc9125791028180074456eger_o
% 7.78/3.99 @ ^ [R5: code_integer,S: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K5 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S ) ) @ ( S = one_one_Code_integer ) )
% 7.78/3.99 @ ( code_divmod_abs @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4277_divmod__integer__eq__cases,axiom,
% 7.78/3.99 ( code_divmod_integer
% 7.78/3.99 = ( ^ [K5: code_integer,L3: code_integer] :
% 7.78/3.99 ( if_Pro6119634080678213985nteger @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K5 )
% 7.78/3.99 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 7.78/3.99 @ ( if_Pro6119634080678213985nteger
% 7.78/3.99 @ ( ( sgn_sgn_Code_integer @ K5 )
% 7.78/3.99 = ( sgn_sgn_Code_integer @ L3 ) )
% 7.78/3.99 @ ( code_divmod_abs @ K5 @ L3 )
% 7.78/3.99 @ ( produc6916734918728496179nteger
% 7.78/3.99 @ ^ [R5: code_integer,S: code_integer] : ( if_Pro6119634080678213985nteger @ ( S = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L3 ) @ S ) ) )
% 7.78/3.99 @ ( code_divmod_abs @ K5 @ L3 ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4278_UNIV__char__of__nat,axiom,
% 7.78/3.99 ( top_top_set_char
% 7.78/3.99 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4279_num__of__integer__def,axiom,
% 7.78/3.99 ( code_num_of_integer
% 7.78/3.99 = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4280_range__nat__of__char,axiom,
% 7.78/3.99 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 7.78/3.99 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4281_num__of__integer_Orsp,axiom,
% 7.78/3.99 ( bNF_re7626690874201225453um_num
% 7.78/3.99 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.99 @ ^ [Y2: num,Z: num] : ( Y2 = Z )
% 7.78/3.99 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 7.78/3.99 @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4282_num__of__integer_Otransfer,axiom,
% 7.78/3.99 ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 7.78/3.99 @ ^ [Y2: num,Z: num] : ( Y2 = Z )
% 7.78/3.99 @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 7.78/3.99 @ code_num_of_integer ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4283_pcr__integer__def,axiom,
% 7.78/3.99 ( code_pcr_integer
% 7.78/3.99 = ( relcom967497705283160040nteger
% 7.78/3.99 @ ^ [Y2: int,Z: int] : ( Y2 = Z )
% 7.78/3.99 @ code_cr_integer ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4284_Random__Pred_Onot__randompred__def,axiom,
% 7.78/3.99 ( random6974930770145893639ompred
% 7.78/3.99 = ( ^ [P4: produc7822875418678951345atural > produc4675096598859438275atural,S: produc7822875418678951345atural] :
% 7.78/3.99 ( produc6665183775751917029atural
% 7.78/3.99 @ ^ [P5: pred_Product_unit,S7: produc7822875418678951345atural] : ( if_Pro3444522238938527101atural @ ( eval_Product_unit @ P5 @ product_Unity ) @ ( produc5069803637994805237atural @ bot_bo2717538794563056311t_unit @ S7 ) @ ( produc5069803637994805237atural @ ( single_Product_unit @ product_Unity ) @ S7 ) )
% 7.78/3.99 @ ( P4 @ S ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4285_rat__floor__code,axiom,
% 7.78/3.99 ( archim3151403230148437115or_rat
% 7.78/3.99 = ( ^ [P3: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P3 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4286_Divides_Oadjust__div__def,axiom,
% 7.78/3.99 ( adjust_div
% 7.78/3.99 = ( produc8211389475949308722nt_int
% 7.78/3.99 @ ^ [Q3: int,R5: int] : ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4287_take__bit__num__code,axiom,
% 7.78/3.99 ( bit_take_bit_num
% 7.78/3.99 = ( ^ [N4: nat,M5: num] :
% 7.78/3.99 ( produc478579273971653890on_num
% 7.78/3.99 @ ^ [A5: nat,X4: num] :
% 7.78/3.99 ( case_nat_option_num @ none_num
% 7.78/3.99 @ ^ [O: nat] :
% 7.78/3.99 ( case_num_option_num @ ( some_num @ one )
% 7.78/3.99 @ ^ [P3: num] :
% 7.78/3.99 ( case_o6005452278849405969um_num @ none_num
% 7.78/3.99 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 7.78/3.99 @ ( bit_take_bit_num @ O @ P3 ) )
% 7.78/3.99 @ ^ [P3: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P3 ) ) )
% 7.78/3.99 @ X4 )
% 7.78/3.99 @ A5 )
% 7.78/3.99 @ ( product_Pair_nat_num @ N4 @ M5 ) ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(fact_4288_list__ex__iff__not__all__inverval__nat,axiom,
% 7.78/3.99 ! [P2: nat > $o,I: nat,J4: nat] :
% 7.78/3.99 ( ( list_ex_nat @ P2 @ ( upt @ I @ J4 ) )
% 7.78/3.99 = ( ~ ( all_interval_nat @ ( comp_o_o_nat @ (~) @ P2 ) @ I @ J4 ) ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 7.78/3.99 ! [X2: int,Y3: int] :
% 7.78/3.99 ( ( if_int @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 7.78/3.99 ! [X2: int,Y3: int] :
% 7.78/3.99 ( ( if_int @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 7.78/3.99 ! [X2: nat,Y3: nat] :
% 7.78/3.99 ( ( if_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 7.78/3.99 ! [X2: nat,Y3: nat] :
% 7.78/3.99 ( ( if_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 7.78/3.99 ! [X2: num,Y3: num] :
% 7.78/3.99 ( ( if_num @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 7.78/3.99 ! [X2: num,Y3: num] :
% 7.78/3.99 ( ( if_num @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 7.78/3.99 ! [X2: rat,Y3: rat] :
% 7.78/3.99 ( ( if_rat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 7.78/3.99 ! [X2: rat,Y3: rat] :
% 7.78/3.99 ( ( if_rat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 7.78/3.99 ! [X2: set_o,Y3: set_o] :
% 7.78/3.99 ( ( if_set_o @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 7.78/3.99 ! [X2: set_o,Y3: set_o] :
% 7.78/3.99 ( ( if_set_o @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Ounit_T,axiom,
% 7.78/3.99 ! [X2: product_unit,Y3: product_unit] :
% 7.78/3.99 ( ( if_Product_unit @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Ounit_T,axiom,
% 7.78/3.99 ! [X2: product_unit,Y3: product_unit] :
% 7.78/3.99 ( ( if_Product_unit @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 7.78/3.99 ! [X2: code_integer,Y3: code_integer] :
% 7.78/3.99 ( ( if_Code_integer @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 7.78/3.99 ! [X2: code_integer,Y3: code_integer] :
% 7.78/3.99 ( ( if_Code_integer @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 7.78/3.99 ! [X2: set_nat,Y3: set_nat] :
% 7.78/3.99 ( ( if_set_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 7.78/3.99 ! [X2: set_nat,Y3: set_nat] :
% 7.78/3.99 ( ( if_set_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 7.78/3.99 ! [X2: set_Product_unit,Y3: set_Product_unit] :
% 7.78/3.99 ( ( if_set_Product_unit @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 7.78/3.99 ! [X2: set_Product_unit,Y3: set_Product_unit] :
% 7.78/3.99 ( ( if_set_Product_unit @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Heap____Monad__OHeap_It__Heap__Oref_Itf__a_J_J_T,axiom,
% 7.78/3.99 ! [X2: heap_Heap_ref_a,Y3: heap_Heap_ref_a] :
% 7.78/3.99 ( ( if_Heap_Heap_ref_a @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Heap____Monad__OHeap_It__Heap__Oref_Itf__a_J_J_T,axiom,
% 7.78/3.99 ! [X2: heap_Heap_ref_a,Y3: heap_Heap_ref_a] :
% 7.78/3.99 ( ( if_Heap_Heap_ref_a @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 7.78/3.99 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 7.78/3.99 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 7.78/3.99 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 7.78/3.99 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.78/3.99 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 7.78/3.99 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.78/3.99 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 7.78/3.99 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 7.78/3.99 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 7.78/3.99 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 7.78/3.99 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 7.78/3.99 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 7.78/3.99 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 7.78/3.99 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 7.78/3.99 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 7.78/3.99 ! [X2: produc859450856879609959at_nat,Y3: produc859450856879609959at_nat] :
% 7.78/3.99 ( ( if_Pro4507677147265585453at_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 7.78/3.99 ! [X2: produc859450856879609959at_nat,Y3: produc859450856879609959at_nat] :
% 7.78/3.99 ( ( if_Pro4507677147265585453at_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 7.78/3.99 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 7.78/3.99 ( ( if_set1508868558775481357at_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 7.78/3.99 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 7.78/3.99 ( ( if_set1508868558775481357at_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 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,
% 7.78/3.99 ! [X2: produc4675096598859438275atural,Y3: produc4675096598859438275atural] :
% 7.78/3.99 ( ( if_Pro3444522238938527101atural @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 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,
% 7.78/3.99 ! [X2: produc4675096598859438275atural,Y3: produc4675096598859438275atural] :
% 7.78/3.99 ( ( if_Pro3444522238938527101atural @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_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_T,axiom,
% 7.78/3.99 ! [X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( if_Pro3594990065127090477at_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_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_T,axiom,
% 7.78/3.99 ! [X2: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
% 7.78/3.99 ( ( if_Pro3594990065127090477at_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_3_1_If_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_T,axiom,
% 7.78/3.99 ! [P2: $o] :
% 7.78/3.99 ( ( P2 = $true )
% 7.78/3.99 | ( P2 = $false ) ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_2_1_If_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_T,axiom,
% 7.78/3.99 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( ( if_set3208018901896979469at_nat @ $false @ X2 @ Y3 )
% 7.78/3.99 = Y3 ) ).
% 7.78/3.99
% 7.78/3.99 thf(help_If_1_1_If_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_T,axiom,
% 7.78/3.99 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 7.78/3.99 ( ( if_set3208018901896979469at_nat @ $true @ X2 @ Y3 )
% 7.78/3.99 = X2 ) ).
% 7.78/3.99
% 7.78/3.99 thf(conj_0,hypothesis,
% 7.78/3.99 $true ).
% 7.78/3.99
% 7.78/3.99 thf(conj_1,conjecture,
% 7.78/3.99 thesis ).
% 7.78/3.99 ------------------------
% 7.98/4.24 % (15203)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_14919 for (2997ds/27Mi)
% 7.98/4.24 % (15202)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_14919 for (2997ds/4Mi)
% 7.98/4.24 % (15201)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/183Mi)
% 7.98/4.24 % (15204)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/2Mi)
% 7.98/4.24 % (15205)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_14919 for (2997ds/2Mi)
% 7.98/4.24 % (15206)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_14919 for (2997ds/275Mi)
% 7.98/4.25 % (15204)Instruction limit reached!
% 7.98/4.25 % (15204)------------------------------
% 7.98/4.25 % (15204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.25 % (15204)Termination reason: Unknown
% 7.98/4.25 % (15204)Termination phase: shuffling
% 7.98/4.25
% 7.98/4.25 % (15204)Memory used [KB]: 8955
% 7.98/4.25 % (15204)Time elapsed: 0.002 s
% 7.98/4.25 % (15204)Instructions burned: 2 (million)
% 7.98/4.25 % (15204)------------------------------
% 7.98/4.25 % (15204)------------------------------
% 7.98/4.25 % (15205)Instruction limit reached!
% 7.98/4.25 % (15205)------------------------------
% 7.98/4.25 % (15205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.25 % (15205)Termination reason: Unknown
% 7.98/4.25 % (15205)Termination phase: shuffling
% 7.98/4.25
% 7.98/4.25 % (15205)Memory used [KB]: 8955
% 7.98/4.25 % (15205)Time elapsed: 0.002 s
% 7.98/4.25 % (15205)Instructions burned: 2 (million)
% 7.98/4.25 % (15205)------------------------------
% 7.98/4.25 % (15205)------------------------------
% 7.98/4.25 % (15202)Instruction limit reached!
% 7.98/4.25 % (15202)------------------------------
% 7.98/4.25 % (15202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.25 % (15202)Termination reason: Unknown
% 7.98/4.25 % (15202)Termination phase: shuffling
% 7.98/4.25
% 7.98/4.25 % (15202)Memory used [KB]: 9210
% 7.98/4.25 % (15202)Time elapsed: 0.004 s
% 7.98/4.25 % (15202)Instructions burned: 4 (million)
% 7.98/4.25 % (15202)------------------------------
% 7.98/4.25 % (15202)------------------------------
% 7.98/4.25 % (15207)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/18Mi)
% 7.98/4.26 % (15208)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/3Mi)
% 7.98/4.26 % (15209)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_14919 for (2997ds/37Mi)
% 7.98/4.26 % (15203)Instruction limit reached!
% 7.98/4.26 % (15203)------------------------------
% 7.98/4.26 % (15203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.26 % (15210)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_14919 for (2997ds/15Mi)
% 7.98/4.26 % (15203)Termination reason: Unknown
% 7.98/4.26 % (15203)Termination phase: shuffling
% 7.98/4.26
% 7.98/4.26 % (15203)Memory used [KB]: 9722
% 7.98/4.26 % (15203)Time elapsed: 0.015 s
% 7.98/4.26 % (15203)Instructions burned: 29 (million)
% 7.98/4.26 % (15203)------------------------------
% 7.98/4.26 % (15203)------------------------------
% 7.98/4.26 % (15208)Instruction limit reached!
% 7.98/4.26 % (15208)------------------------------
% 7.98/4.26 % (15208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.26 % (15208)Termination reason: Unknown
% 7.98/4.26 % (15208)Termination phase: shuffling
% 7.98/4.26
% 7.98/4.26 % (15208)Memory used [KB]: 9083
% 7.98/4.26 % (15208)Time elapsed: 0.004 s
% 7.98/4.26 % (15208)Instructions burned: 3 (million)
% 7.98/4.26 % (15208)------------------------------
% 7.98/4.26 % (15208)------------------------------
% 7.98/4.26 % (15207)Instruction limit reached!
% 7.98/4.26 % (15207)------------------------------
% 7.98/4.26 % (15207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.26 % (15207)Termination reason: Unknown
% 7.98/4.26 % (15207)Termination phase: shuffling
% 7.98/4.26
% 7.98/4.26 % (15207)Memory used [KB]: 9594
% 7.98/4.26 % (15207)Time elapsed: 0.016 s
% 7.98/4.26 % (15207)Instructions burned: 19 (million)
% 7.98/4.26 % (15207)------------------------------
% 7.98/4.26 % (15207)------------------------------
% 7.98/4.27 % (15210)Instruction limit reached!
% 7.98/4.27 % (15210)------------------------------
% 7.98/4.27 % (15210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.27 % (15210)Termination reason: Unknown
% 7.98/4.27 % (15210)Termination phase: shuffling
% 7.98/4.27
% 7.98/4.27 % (15210)Memory used [KB]: 9594
% 7.98/4.27 % (15210)Time elapsed: 0.010 s
% 7.98/4.27 % (15210)Instructions burned: 16 (million)
% 7.98/4.27 % (15210)------------------------------
% 7.98/4.27 % (15210)------------------------------
% 7.98/4.27 % (15211)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_14919 for (2997ds/3Mi)
% 7.98/4.27 % (15212)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_14919 for (2997ds/1041Mi)
% 7.98/4.27 % (15209)Instruction limit reached!
% 7.98/4.27 % (15209)------------------------------
% 7.98/4.27 % (15209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.27 % (15209)Termination reason: Unknown
% 7.98/4.27 % (15209)Termination phase: shuffling
% 7.98/4.27
% 7.98/4.27 % (15209)Memory used [KB]: 9978
% 7.98/4.27 % (15209)Time elapsed: 0.016 s
% 7.98/4.27 % (15209)Instructions burned: 37 (million)
% 7.98/4.27 % (15209)------------------------------
% 7.98/4.27 % (15209)------------------------------
% 7.98/4.27 % (15211)Instruction limit reached!
% 7.98/4.27 % (15211)------------------------------
% 7.98/4.27 % (15211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.27 % (15211)Termination reason: Unknown
% 7.98/4.27 % (15211)Termination phase: shuffling
% 7.98/4.27
% 7.98/4.27 % (15211)Memory used [KB]: 9083
% 7.98/4.27 % (15211)Time elapsed: 0.003 s
% 7.98/4.27 % (15211)Instructions burned: 3 (million)
% 7.98/4.27 % (15211)------------------------------
% 7.98/4.27 % (15211)------------------------------
% 7.98/4.27 % (15213)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/7Mi)
% 7.98/4.28 % (15214)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/16Mi)
% 7.98/4.28 % (15213)Instruction limit reached!
% 7.98/4.28 % (15213)------------------------------
% 7.98/4.28 % (15213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.28 % (15213)Termination reason: Unknown
% 7.98/4.28 % (15213)Termination phase: shuffling
% 7.98/4.28
% 7.98/4.28 % (15213)Memory used [KB]: 9466
% 7.98/4.28 % (15213)Time elapsed: 0.007 s
% 7.98/4.28 % (15213)Instructions burned: 8 (million)
% 7.98/4.28 % (15213)------------------------------
% 7.98/4.28 % (15213)------------------------------
% 7.98/4.28 % (15215)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_14919 for (2997ds/3Mi)
% 7.98/4.28 % (15216)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_14919 for (2997ds/3Mi)
% 7.98/4.28 % (15215)Instruction limit reached!
% 7.98/4.28 % (15215)------------------------------
% 7.98/4.28 % (15215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.28 % (15215)Termination reason: Unknown
% 7.98/4.28 % (15215)Termination phase: shuffling
% 7.98/4.28
% 7.98/4.28 % (15215)Memory used [KB]: 9083
% 7.98/4.28 % (15215)Time elapsed: 0.004 s
% 7.98/4.28 % (15215)Instructions burned: 3 (million)
% 7.98/4.28 % (15215)------------------------------
% 7.98/4.28 % (15215)------------------------------
% 7.98/4.28 % (15216)Instruction limit reached!
% 7.98/4.28 % (15216)------------------------------
% 7.98/4.28 % (15216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.28 % (15216)Termination reason: Unknown
% 7.98/4.28 % (15216)Termination phase: shuffling
% 7.98/4.28
% 7.98/4.28 % (15216)Memory used [KB]: 9083
% 7.98/4.28 % (15216)Time elapsed: 0.004 s
% 7.98/4.28 % (15216)Instructions burned: 3 (million)
% 7.98/4.28 % (15216)------------------------------
% 7.98/4.28 % (15216)------------------------------
% 7.98/4.29 % (15214)Instruction limit reached!
% 7.98/4.29 % (15214)------------------------------
% 7.98/4.29 % (15214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.98/4.29 % (15214)Termination reason: Unknown
% 7.98/4.29 % (15214)Termination phase: shuffling
% 7.98/4.29
% 7.98/4.29 % (15214)Memory used [KB]: 9594
% 7.98/4.29 % (15214)Time elapsed: 0.011 s
% 7.98/4.29 % (15214)Instructions burned: 18 (million)
% 7.98/4.29 % (15214)------------------------------
% 7.98/4.29 % (15214)------------------------------
% 7.98/4.29 % (15217)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/7Mi)
% 7.98/4.29 % (15218)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/3Mi)
% 7.98/4.29 % (15219)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/4Mi)
% 8.22/4.30 % (15218)Instruction limit reached!
% 8.22/4.30 % (15218)------------------------------
% 8.22/4.30 % (15218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.30 % (15218)Termination reason: Unknown
% 8.22/4.30 % (15218)Termination phase: shuffling
% 8.22/4.30
% 8.22/4.30 % (15218)Memory used [KB]: 9083
% 8.22/4.30 % (15218)Time elapsed: 0.004 s
% 8.22/4.30 % (15218)Instructions burned: 3 (million)
% 8.22/4.30 % (15218)------------------------------
% 8.22/4.30 % (15218)------------------------------
% 8.22/4.30 % (15217)Instruction limit reached!
% 8.22/4.30 % (15217)------------------------------
% 8.22/4.30 % (15217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.30 % (15217)Termination reason: Unknown
% 8.22/4.30 % (15217)Termination phase: shuffling
% 8.22/4.30
% 8.22/4.30 % (15217)Memory used [KB]: 9466
% 8.22/4.30 % (15217)Time elapsed: 0.008 s
% 8.22/4.30 % (15217)Instructions burned: 8 (million)
% 8.22/4.30 % (15217)------------------------------
% 8.22/4.30 % (15217)------------------------------
% 8.22/4.30 % (15220)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/18Mi)
% 8.22/4.30 % (15219)Instruction limit reached!
% 8.22/4.30 % (15219)------------------------------
% 8.22/4.30 % (15219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.30 % (15219)Termination reason: Unknown
% 8.22/4.30 % (15219)Termination phase: shuffling
% 8.22/4.30
% 8.22/4.30 % (15219)Memory used [KB]: 9210
% 8.22/4.30 % (15219)Time elapsed: 0.005 s
% 8.22/4.30 % (15219)Instructions burned: 4 (million)
% 8.22/4.30 % (15219)------------------------------
% 8.22/4.30 % (15219)------------------------------
% 8.22/4.31 % (15220)Instruction limit reached!
% 8.22/4.31 % (15220)------------------------------
% 8.22/4.31 % (15220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.31 % (15220)Termination reason: Unknown
% 8.22/4.31 % (15220)Termination phase: shuffling
% 8.22/4.31
% 8.22/4.31 % (15220)Memory used [KB]: 9594
% 8.22/4.31 % (15220)Time elapsed: 0.012 s
% 8.22/4.31 % (15220)Instructions burned: 20 (million)
% 8.22/4.31 % (15220)------------------------------
% 8.22/4.31 % (15220)------------------------------
% 8.22/4.31 % (15224)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/710Mi)
% 8.22/4.31 % (15225)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14919 for (2997ds/6Mi)
% 8.22/4.31 % (15226)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_14919 for (2997ds/902Mi)
% 8.22/4.31 % (15201)Instruction limit reached!
% 8.22/4.31 % (15201)------------------------------
% 8.22/4.31 % (15201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.31 % (15201)Termination reason: Unknown
% 8.22/4.31 % (15201)Termination phase: shuffling
% 8.22/4.31
% 8.22/4.31 % (15201)Memory used [KB]: 13048
% 8.22/4.31 % (15201)Time elapsed: 0.068 s
% 8.22/4.31 % (15201)Instructions burned: 185 (million)
% 8.22/4.31 % (15201)------------------------------
% 8.22/4.31 % (15201)------------------------------
% 8.22/4.31 % (15225)Instruction limit reached!
% 8.22/4.31 % (15225)------------------------------
% 8.22/4.31 % (15225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.31 % (15225)Termination reason: Unknown
% 8.22/4.31 % (15225)Termination phase: shuffling
% 8.22/4.31
% 8.22/4.31 % (15225)Memory used [KB]: 9338
% 8.22/4.31 % (15225)Time elapsed: 0.006 s
% 8.22/4.31 % (15225)Instructions burned: 6 (million)
% 8.22/4.31 % (15225)------------------------------
% 8.22/4.31 % (15225)------------------------------
% 8.22/4.32 % (15234)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_14919 for (2996ds/21Mi)
% 8.22/4.32 % (15237)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/5Mi)
% 8.22/4.32 % (15239)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_14919 for (2996ds/6Mi)
% 8.22/4.33 % (15237)Instruction limit reached!
% 8.22/4.33 % (15237)------------------------------
% 8.22/4.33 % (15237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.33 % (15237)Termination reason: Unknown
% 8.22/4.33 % (15237)Termination phase: shuffling
% 8.22/4.33
% 8.22/4.33 % (15237)Memory used [KB]: 9210
% 8.22/4.33 % (15237)Time elapsed: 0.005 s
% 8.22/4.33 % (15237)Instructions burned: 5 (million)
% 8.22/4.33 % (15237)------------------------------
% 8.22/4.33 % (15237)------------------------------
% 8.22/4.33 % (15239)Instruction limit reached!
% 8.22/4.33 % (15239)------------------------------
% 8.22/4.33 % (15239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.33 % (15239)Termination reason: Unknown
% 8.22/4.33 % (15239)Termination phase: shuffling
% 8.22/4.33
% 8.22/4.33 % (15239)Memory used [KB]: 9338
% 8.22/4.33 % (15239)Time elapsed: 0.006 s
% 8.22/4.33 % (15239)Instructions burned: 6 (million)
% 8.22/4.33 % (15239)------------------------------
% 8.22/4.33 % (15239)------------------------------
% 8.22/4.33 % (15234)Instruction limit reached!
% 8.22/4.33 % (15234)------------------------------
% 8.22/4.33 % (15234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.33 % (15234)Termination reason: Unknown
% 8.22/4.33 % (15234)Termination phase: shuffling
% 8.22/4.33
% 8.22/4.33 % (15234)Memory used [KB]: 9594
% 8.22/4.33 % (15234)Time elapsed: 0.012 s
% 8.22/4.33 % (15234)Instructions burned: 22 (million)
% 8.22/4.33 % (15234)------------------------------
% 8.22/4.33 % (15234)------------------------------
% 8.22/4.34 % (15250)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/377Mi)
% 8.22/4.34 % (15252)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_14919 for (2996ds/779Mi)
% 8.22/4.34 % (15254)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_14919 for (2996ds/19Mi)
% 8.22/4.34 % (15206)Instruction limit reached!
% 8.22/4.34 % (15206)------------------------------
% 8.22/4.34 % (15206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.34 % (15206)Termination reason: Unknown
% 8.22/4.34 % (15206)Termination phase: shuffling
% 8.22/4.34
% 8.22/4.34 % (15206)Memory used [KB]: 14200
% 8.22/4.34 % (15206)Time elapsed: 0.100 s
% 8.22/4.34 % (15206)Instructions burned: 277 (million)
% 8.22/4.34 % (15206)------------------------------
% 8.22/4.34 % (15206)------------------------------
% 8.22/4.35 % (15254)Instruction limit reached!
% 8.22/4.35 % (15254)------------------------------
% 8.22/4.35 % (15254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.35 % (15254)Termination reason: Unknown
% 8.22/4.35 % (15254)Termination phase: shuffling
% 8.22/4.35
% 8.22/4.35 % (15254)Memory used [KB]: 9594
% 8.22/4.35 % (15254)Time elapsed: 0.011 s
% 8.22/4.35 % (15254)Instructions burned: 22 (million)
% 8.22/4.35 % (15254)------------------------------
% 8.22/4.35 % (15254)------------------------------
% 8.22/4.36 % (15269)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/879Mi)
% 8.22/4.36 % (15271)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/17Mi)
% 8.22/4.37 % (15271)Instruction limit reached!
% 8.22/4.37 % (15271)------------------------------
% 8.22/4.37 % (15271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.37 % (15271)Termination reason: Unknown
% 8.22/4.37 % (15271)Termination phase: shuffling
% 8.22/4.37
% 8.22/4.37 % (15271)Memory used [KB]: 9594
% 8.22/4.37 % (15271)Time elapsed: 0.011 s
% 8.22/4.37 % (15271)Instructions burned: 19 (million)
% 8.22/4.37 % (15271)------------------------------
% 8.22/4.37 % (15271)------------------------------
% 8.22/4.38 % (15286)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/3Mi)
% 8.22/4.39 % (15286)Instruction limit reached!
% 8.22/4.39 % (15286)------------------------------
% 8.22/4.39 % (15286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/4.39 % (15286)Termination reason: Unknown
% 8.22/4.39 % (15286)Termination phase: shuffling
% 8.22/4.39
% 8.22/4.39 % (15286)Memory used [KB]: 9083
% 8.22/4.39 % (15286)Time elapsed: 0.003 s
% 8.22/4.39 % (15286)Instructions burned: 3 (million)
% 8.22/4.39 % (15286)------------------------------
% 8.22/4.39 % (15286)------------------------------
% 8.60/4.40 % (15295)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14919 for (2996ds/30Mi)
% 8.60/4.41 % (15295)Instruction limit reached!
% 8.60/4.41 % (15295)------------------------------
% 8.60/4.41 % (15295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/4.41 % (15295)Termination reason: Unknown
% 8.60/4.41 % (15295)Termination phase: shuffling
% 8.60/4.41
% 8.60/4.41 % (15295)Memory used [KB]: 9722
% 8.60/4.41 % (15295)Time elapsed: 0.015 s
% 8.60/4.41 % (15295)Instructions burned: 31 (million)
% 8.60/4.41 % (15295)------------------------------
% 8.60/4.41 % (15295)------------------------------
% 8.60/4.42 % (15319)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14919 for (2995ds/127Mi)
% 8.60/4.47 % (15319)Instruction limit reached!
% 8.60/4.47 % (15319)------------------------------
% 8.60/4.47 % (15319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/4.47 % (15319)Termination reason: Unknown
% 8.60/4.47 % (15319)Termination phase: shuffling
% 8.60/4.47
% 8.60/4.47 % (15319)Memory used [KB]: 12153
% 8.60/4.47 % (15319)Time elapsed: 0.046 s
% 8.60/4.47 % (15319)Instructions burned: 127 (million)
% 8.60/4.47 % (15319)------------------------------
% 8.60/4.47 % (15319)------------------------------
% 8.60/4.47 % (15250)Instruction limit reached!
% 8.60/4.47 % (15250)------------------------------
% 8.60/4.47 % (15250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/4.47 % (15250)Termination reason: Unknown
% 8.60/4.47 % (15250)Termination phase: shuffling
% 8.60/4.47
% 8.60/4.47 % (15250)Memory used [KB]: 15351
% 8.60/4.47 % (15250)Time elapsed: 0.131 s
% 8.60/4.47 % (15250)Instructions burned: 378 (million)
% 8.60/4.47 % (15250)------------------------------
% 8.60/4.47 % (15250)------------------------------
% 8.60/4.48 % (15370)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14919 for (2995ds/100Mi)
% 8.60/4.48 % (15373)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_14919 for (2995ds/3Mi)
% 8.60/4.48 % (15373)Instruction limit reached!
% 8.60/4.48 % (15373)------------------------------
% 8.60/4.48 % (15373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/4.48 % (15373)Termination reason: Unknown
% 8.60/4.48 % (15373)Termination phase: shuffling
% 8.60/4.48
% 8.60/4.48 % (15373)Memory used [KB]: 9083
% 8.60/4.48 % (15373)Time elapsed: 0.004 s
% 8.60/4.48 % (15373)Instructions burned: 3 (million)
% 8.60/4.48 % (15373)------------------------------
% 8.60/4.48 % (15373)------------------------------
% 8.60/4.49 % (15381)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_14919 for (2995ds/20Mi)
% 8.84/4.50 % (15381)Instruction limit reached!
% 8.84/4.50 % (15381)------------------------------
% 8.84/4.50 % (15381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.50 % (15381)Termination reason: Unknown
% 8.84/4.50 % (15381)Termination phase: shuffling
% 8.84/4.50
% 8.84/4.50 % (15381)Memory used [KB]: 9594
% 8.84/4.50 % (15381)Time elapsed: 0.012 s
% 8.84/4.50 % (15381)Instructions burned: 20 (million)
% 8.84/4.50 % (15381)------------------------------
% 8.84/4.50 % (15381)------------------------------
% 8.84/4.51 % (15370)Instruction limit reached!
% 8.84/4.51 % (15370)------------------------------
% 8.84/4.51 % (15370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.51 % (15370)Termination reason: Unknown
% 8.84/4.51 % (15370)Termination phase: shuffling
% 8.84/4.51
% 8.84/4.51 % (15370)Memory used [KB]: 11897
% 8.84/4.51 % (15370)Time elapsed: 0.033 s
% 8.84/4.51 % (15370)Instructions burned: 100 (million)
% 8.84/4.51 % (15370)------------------------------
% 8.84/4.51 % (15370)------------------------------
% 8.84/4.51 % (15393)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_14919 for (2994ds/86Mi)
% 8.84/4.52 % (15396)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_14919 for (2994ds/107Mi)
% 8.84/4.54 % (15224)Instruction limit reached!
% 8.84/4.54 % (15224)------------------------------
% 8.84/4.54 % (15224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.54 % (15224)Termination reason: Unknown
% 8.84/4.54 % (15224)Termination phase: Property scanning
% 8.84/4.54
% 8.84/4.54 % (15224)Memory used [KB]: 17014
% 8.84/4.54 % (15224)Time elapsed: 0.232 s
% 8.84/4.54 % (15224)Instructions burned: 712 (million)
% 8.84/4.54 % (15224)------------------------------
% 8.84/4.54 % (15224)------------------------------
% 8.84/4.54 % (15393)Instruction limit reached!
% 8.84/4.54 % (15393)------------------------------
% 8.84/4.54 % (15393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.54 % (15393)Termination reason: Unknown
% 8.84/4.54 % (15393)Termination phase: shuffling
% 8.84/4.54
% 8.84/4.54 % (15393)Memory used [KB]: 10746
% 8.84/4.54 % (15393)Time elapsed: 0.033 s
% 8.84/4.54 % (15393)Instructions burned: 88 (million)
% 8.84/4.54 % (15393)------------------------------
% 8.84/4.54 % (15393)------------------------------
% 8.84/4.55 % (15414)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_14919 for (2994ds/39Mi)
% 8.84/4.56 % (15416)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_14919 for (2994ds/448Mi)
% 8.84/4.56 % (15396)Instruction limit reached!
% 8.84/4.56 % (15396)------------------------------
% 8.84/4.56 % (15396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.56 % (15396)Termination reason: Unknown
% 8.84/4.56 % (15396)Termination phase: shuffling
% 8.84/4.56
% 8.84/4.56 % (15396)Memory used [KB]: 11001
% 8.84/4.56 % (15396)Time elapsed: 0.041 s
% 8.84/4.56 % (15396)Instructions burned: 107 (million)
% 8.84/4.56 % (15396)------------------------------
% 8.84/4.56 % (15396)------------------------------
% 8.84/4.57 % (15414)Instruction limit reached!
% 8.84/4.57 % (15414)------------------------------
% 8.84/4.57 % (15414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.57 % (15414)Termination reason: Unknown
% 8.84/4.57 % (15414)Termination phase: shuffling
% 8.84/4.57
% 8.84/4.57 % (15414)Memory used [KB]: 9978
% 8.84/4.57 % (15414)Time elapsed: 0.018 s
% 8.84/4.57 % (15414)Instructions burned: 42 (million)
% 8.84/4.57 % (15414)------------------------------
% 8.84/4.57 % (15414)------------------------------
% 8.84/4.57 % (15252)Instruction limit reached!
% 8.84/4.57 % (15252)------------------------------
% 8.84/4.57 % (15252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.57 % (15252)Termination reason: Unknown
% 8.84/4.57 % (15252)Termination phase: shuffling
% 8.84/4.57
% 8.84/4.57 % (15252)Memory used [KB]: 23666
% 8.84/4.57 % (15252)Time elapsed: 0.232 s
% 8.84/4.57 % (15252)Instructions burned: 781 (million)
% 8.84/4.57 % (15252)------------------------------
% 8.84/4.57 % (15252)------------------------------
% 8.84/4.57 % (15426)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_14919 for (2994ds/46Mi)
% 8.84/4.57 % (15212)Instruction limit reached!
% 8.84/4.57 % (15212)------------------------------
% 8.84/4.57 % (15212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.57 % (15212)Termination reason: Unknown
% 8.84/4.57 % (15212)Termination phase: Property scanning
% 8.84/4.57
% 8.84/4.57 % (15212)Memory used [KB]: 28912
% 8.84/4.57 % (15212)Time elapsed: 0.304 s
% 8.84/4.57 % (15212)Instructions burned: 1043 (million)
% 8.84/4.57 % (15212)------------------------------
% 8.84/4.57 % (15212)------------------------------
% 8.84/4.58 % (15432)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_14919 for (2994ds/98Mi)
% 8.84/4.58 % (15433)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_14919 for (2994ds/507Mi)
% 8.84/4.59 % (15437)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_14919 for (2994ds/149Mi)
% 8.84/4.59 % (15426)Instruction limit reached!
% 8.84/4.59 % (15426)------------------------------
% 8.84/4.59 % (15426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/4.59 % (15426)Termination reason: Unknown
% 8.84/4.59 % (15426)Termination phase: shuffling
% 8.84/4.59
% 8.84/4.59 % (15426)Memory used [KB]: 9978
% 8.84/4.59 % (15426)Time elapsed: 0.021 s
% 8.84/4.59 % (15426)Instructions burned: 47 (million)
% 8.84/4.59 % (15426)------------------------------
% 8.84/4.59 % (15426)------------------------------
% 9.87/4.60 % (15450)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14919 for (2994ds/39Mi)
% 9.87/4.61 % (15226)Instruction limit reached!
% 9.87/4.61 % (15226)------------------------------
% 9.87/4.61 % (15226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.61 % (15226)Termination reason: Unknown
% 9.87/4.61 % (15226)Termination phase: Preprocessing 3
% 9.87/4.61
% 9.87/4.61 % (15226)Memory used [KB]: 20084
% 9.87/4.61 % (15226)Time elapsed: 0.298 s
% 9.87/4.61 % (15226)Instructions burned: 904 (million)
% 9.87/4.61 % (15226)------------------------------
% 9.87/4.61 % (15226)------------------------------
% 9.87/4.61 % (15432)Instruction limit reached!
% 9.87/4.61 % (15432)------------------------------
% 9.87/4.61 % (15432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.61 % (15432)Termination reason: Unknown
% 9.87/4.61 % (15432)Termination phase: shuffling
% 9.87/4.61
% 9.87/4.61 % (15432)Memory used [KB]: 11897
% 9.87/4.61 % (15432)Time elapsed: 0.034 s
% 9.87/4.61 % (15432)Instructions burned: 99 (million)
% 9.87/4.61 % (15432)------------------------------
% 9.87/4.61 % (15432)------------------------------
% 9.87/4.62 % (15468)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_14919 for (2993ds/6Mi)
% 9.87/4.62 % (15450)Instruction limit reached!
% 9.87/4.62 % (15450)------------------------------
% 9.87/4.62 % (15450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.62 % (15450)Termination reason: Unknown
% 9.87/4.62 % (15450)Termination phase: shuffling
% 9.87/4.62
% 9.87/4.62 % (15450)Memory used [KB]: 9978
% 9.87/4.62 % (15450)Time elapsed: 0.018 s
% 9.87/4.62 % (15450)Instructions burned: 40 (million)
% 9.87/4.62 % (15450)------------------------------
% 9.87/4.62 % (15450)------------------------------
% 9.87/4.62 % (15468)Instruction limit reached!
% 9.87/4.62 % (15468)------------------------------
% 9.87/4.62 % (15468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.62 % (15468)Termination reason: Unknown
% 9.87/4.62 % (15468)Termination phase: shuffling
% 9.87/4.62
% 9.87/4.62 % (15468)Memory used [KB]: 9338
% 9.87/4.62 % (15468)Time elapsed: 0.006 s
% 9.87/4.62 % (15468)Instructions burned: 6 (million)
% 9.87/4.62 % (15468)------------------------------
% 9.87/4.62 % (15468)------------------------------
% 9.87/4.62 % (15473)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_14919 for (2993ds/1087Mi)
% 9.87/4.63 % (15477)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14919 for (2993ds/47Mi)
% 9.87/4.63 % (15480)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_14919 for (2993ds/44Mi)
% 9.87/4.64 % (15437)Instruction limit reached!
% 9.87/4.64 % (15437)------------------------------
% 9.87/4.64 % (15437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.64 % (15437)Termination reason: Unknown
% 9.87/4.64 % (15437)Termination phase: shuffling
% 9.87/4.64
% 9.87/4.64 % (15437)Memory used [KB]: 12537
% 9.87/4.64 % (15437)Time elapsed: 0.055 s
% 9.87/4.64 % (15437)Instructions burned: 151 (million)
% 9.87/4.64 % (15437)------------------------------
% 9.87/4.64 % (15437)------------------------------
% 9.87/4.64 % (15269)Instruction limit reached!
% 9.87/4.64 % (15269)------------------------------
% 9.87/4.64 % (15269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.64 % (15269)Termination reason: Unknown
% 9.87/4.64 % (15269)Termination phase: SInE selection
% 9.87/4.64
% 9.87/4.64 % (15269)Memory used [KB]: 17270
% 9.87/4.64 % (15269)Time elapsed: 0.288 s
% 9.87/4.64 % (15269)Instructions burned: 879 (million)
% 9.87/4.64 % (15269)------------------------------
% 9.87/4.64 % (15269)------------------------------
% 9.87/4.65 % (15480)Instruction limit reached!
% 9.87/4.65 % (15480)------------------------------
% 9.87/4.65 % (15480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.65 % (15477)Instruction limit reached!
% 9.87/4.65 % (15477)------------------------------
% 9.87/4.65 % (15477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.65 % (15477)Termination reason: Unknown
% 9.87/4.65 % (15480)Termination reason: Unknown
% 9.87/4.65 % (15477)Termination phase: shuffling
% 9.87/4.65 % (15480)Termination phase: shuffling
% 9.87/4.65
% 9.87/4.65
% 9.87/4.65 % (15477)Memory used [KB]: 10106
% 9.87/4.65 % (15480)Memory used [KB]: 10106
% 9.87/4.65 % (15477)Time elapsed: 0.021 s
% 9.87/4.65 % (15480)Time elapsed: 0.019 s
% 9.87/4.65 % (15477)Instructions burned: 48 (million)
% 9.87/4.65 % (15480)Instructions burned: 46 (million)
% 9.87/4.65 % (15477)------------------------------
% 9.87/4.65 % (15477)------------------------------
% 9.87/4.65 % (15480)------------------------------
% 9.87/4.65 % (15480)------------------------------
% 9.87/4.65 % (15483)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_14919 for (2993ds/432Mi)
% 9.87/4.65 % (15484)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14919 for (2993ds/62Mi)
% 9.87/4.66 % (15485)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_14919 for (2993ds/31Mi)
% 9.87/4.66 % (15486)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14919 for (2993ds/96Mi)
% 9.87/4.68 % (15485)Instruction limit reached!
% 9.87/4.68 % (15485)------------------------------
% 9.87/4.68 % (15485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.68 % (15485)Termination reason: Unknown
% 9.87/4.68 % (15485)Termination phase: shuffling
% 9.87/4.68
% 9.87/4.68 % (15485)Memory used [KB]: 9850
% 9.87/4.68 % (15485)Time elapsed: 0.016 s
% 9.87/4.68 % (15485)Instructions burned: 33 (million)
% 9.87/4.68 % (15485)------------------------------
% 9.87/4.68 % (15485)------------------------------
% 9.87/4.68 % (15484)Instruction limit reached!
% 9.87/4.68 % (15484)------------------------------
% 9.87/4.68 % (15484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.68 % (15484)Termination reason: Unknown
% 9.87/4.68 % (15484)Termination phase: shuffling
% 9.87/4.68
% 9.87/4.68 % (15484)Memory used [KB]: 11257
% 9.87/4.68 % (15484)Time elapsed: 0.023 s
% 9.87/4.68 % (15484)Instructions burned: 62 (million)
% 9.87/4.68 % (15484)------------------------------
% 9.87/4.68 % (15484)------------------------------
% 9.87/4.69 % (15487)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_14919 for (2993ds/453Mi)
% 9.87/4.69 % (15488)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_14919 for (2993ds/71Mi)
% 9.87/4.69 % (15416)Instruction limit reached!
% 9.87/4.69 % (15416)------------------------------
% 9.87/4.69 % (15416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/4.69 % (15416)Termination reason: Unknown
% 9.87/4.69 % (15416)Termination phase: shuffling
% 9.87/4.69
% 9.87/4.69 % (15416)Memory used [KB]: 19061
% 9.87/4.69 % (15416)Time elapsed: 0.136 s
% 9.87/4.69 % (15416)Instructions burned: 449 (million)
% 9.87/4.69 % (15416)------------------------------
% 9.87/4.69 % (15416)------------------------------
% 10.90/4.70 % (15486)Instruction limit reached!
% 10.90/4.70 % (15486)------------------------------
% 10.90/4.70 % (15486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.70 % (15486)Termination reason: Unknown
% 10.90/4.70 % (15486)Termination phase: shuffling
% 10.90/4.70
% 10.90/4.70 % (15486)Memory used [KB]: 10874
% 10.90/4.70 % (15486)Time elapsed: 0.037 s
% 10.90/4.70 % (15486)Instructions burned: 98 (million)
% 10.90/4.70 % (15486)------------------------------
% 10.90/4.70 % (15486)------------------------------
% 10.90/4.70 % (15489)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14919 for (2993ds/83Mi)
% 10.90/4.71 % (15490)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14919 for (2993ds/11Mi)
% 10.90/4.71 % (15488)Instruction limit reached!
% 10.90/4.71 % (15488)------------------------------
% 10.90/4.71 % (15488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.71 % (15488)Termination reason: Unknown
% 10.90/4.71 % (15488)Termination phase: shuffling
% 10.90/4.71
% 10.90/4.71 % (15488)Memory used [KB]: 10490
% 10.90/4.71 % (15488)Time elapsed: 0.028 s
% 10.90/4.71 % (15488)Instructions burned: 71 (million)
% 10.90/4.71 % (15488)------------------------------
% 10.90/4.71 % (15488)------------------------------
% 10.90/4.71 % (15490)Instruction limit reached!
% 10.90/4.71 % (15490)------------------------------
% 10.90/4.71 % (15490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.71 % (15490)Termination reason: Unknown
% 10.90/4.71 % (15490)Termination phase: shuffling
% 10.90/4.71
% 10.90/4.71 % (15490)Memory used [KB]: 9466
% 10.90/4.71 % (15490)Time elapsed: 0.009 s
% 10.90/4.71 % (15490)Instructions burned: 12 (million)
% 10.90/4.71 % (15490)------------------------------
% 10.90/4.71 % (15490)------------------------------
% 10.90/4.72 % (15491)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_14919 for (2992ds/41Mi)
% 10.90/4.73 % (15492)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14919 for (2992ds/6Mi)
% 10.90/4.73 % (15492)Instruction limit reached!
% 10.90/4.73 % (15492)------------------------------
% 10.90/4.73 % (15492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.73 % (15492)Termination reason: Unknown
% 10.90/4.73 % (15492)Termination phase: shuffling
% 10.90/4.73
% 10.90/4.73 % (15492)Memory used [KB]: 9338
% 10.90/4.73 % (15492)Time elapsed: 0.006 s
% 10.90/4.73 % (15492)Instructions burned: 6 (million)
% 10.90/4.73 % (15492)------------------------------
% 10.90/4.73 % (15492)------------------------------
% 10.90/4.73 % (15489)Instruction limit reached!
% 10.90/4.73 % (15489)------------------------------
% 10.90/4.73 % (15489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.73 % (15489)Termination reason: Unknown
% 10.90/4.73 % (15489)Termination phase: shuffling
% 10.90/4.73
% 10.90/4.73 % (15489)Memory used [KB]: 10618
% 10.90/4.73 % (15489)Time elapsed: 0.031 s
% 10.90/4.73 % (15489)Instructions burned: 83 (million)
% 10.90/4.73 % (15489)------------------------------
% 10.90/4.73 % (15489)------------------------------
% 10.90/4.74 % (15491)Instruction limit reached!
% 10.90/4.74 % (15491)------------------------------
% 10.90/4.74 % (15491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.74 % (15491)Termination reason: Unknown
% 10.90/4.74 % (15491)Termination phase: shuffling
% 10.90/4.74
% 10.90/4.74 % (15491)Memory used [KB]: 9978
% 10.90/4.74 % (15491)Time elapsed: 0.017 s
% 10.90/4.74 % (15491)Instructions burned: 41 (million)
% 10.90/4.74 % (15491)------------------------------
% 10.90/4.74 % (15491)------------------------------
% 10.90/4.74 % (15493)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14919 for (2992ds/150Mi)
% 10.90/4.74 % (15494)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14919 for (2992ds/343Mi)
% 10.90/4.75 % (15495)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_14919 for (2992ds/109Mi)
% 10.90/4.76 % (15433)Instruction limit reached!
% 10.90/4.76 % (15433)------------------------------
% 10.90/4.76 % (15433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.76 % (15433)Termination reason: Unknown
% 10.90/4.76 % (15433)Termination phase: shuffling
% 10.90/4.76
% 10.90/4.76 % (15433)Memory used [KB]: 16758
% 10.90/4.76 % (15433)Time elapsed: 0.175 s
% 10.90/4.76 % (15433)Instructions burned: 507 (million)
% 10.90/4.76 % (15433)------------------------------
% 10.90/4.76 % (15433)------------------------------
% 10.90/4.77 % (15496)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_14919 for (2992ds/253Mi)
% 10.90/4.78 % (15483)Instruction limit reached!
% 10.90/4.78 % (15483)------------------------------
% 10.90/4.78 % (15483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.78 % (15483)Termination reason: Unknown
% 10.90/4.78 % (15483)Termination phase: shuffling
% 10.90/4.78
% 10.90/4.78 % (15483)Memory used [KB]: 18933
% 10.90/4.78 % (15483)Time elapsed: 0.129 s
% 10.90/4.78 % (15483)Instructions burned: 435 (million)
% 10.90/4.78 % (15483)------------------------------
% 10.90/4.78 % (15483)------------------------------
% 10.90/4.79 % (15495)Instruction limit reached!
% 10.90/4.79 % (15495)------------------------------
% 10.90/4.79 % (15495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.79 % (15495)Termination reason: Unknown
% 10.90/4.79 % (15495)Termination phase: shuffling
% 10.90/4.79
% 10.90/4.79 % (15495)Memory used [KB]: 11001
% 10.90/4.79 % (15495)Time elapsed: 0.040 s
% 10.90/4.79 % (15495)Instructions burned: 109 (million)
% 10.90/4.79 % (15495)------------------------------
% 10.90/4.79 % (15495)------------------------------
% 10.90/4.79 % (15497)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14919 for (2992ds/140Mi)
% 10.90/4.79 % (15493)Instruction limit reached!
% 10.90/4.79 % (15493)------------------------------
% 10.90/4.79 % (15493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/4.79 % (15493)Termination reason: Unknown
% 10.90/4.79 % (15493)Termination phase: shuffling
% 10.90/4.79
% 10.90/4.79 % (15493)Memory used [KB]: 12537
% 10.90/4.79 % (15493)Time elapsed: 0.055 s
% 10.90/4.79 % (15493)Instructions burned: 152 (million)
% 10.90/4.79 % (15493)------------------------------
% 10.90/4.79 % (15493)------------------------------
% 11.51/4.80 % (15498)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_14919 for (2992ds/614Mi)
% 11.51/4.80 % (15499)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_14919 for (2991ds/202Mi)
% 11.51/4.82 % (15487)Instruction limit reached!
% 11.51/4.82 % (15487)------------------------------
% 11.51/4.82 % (15487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.51/4.82 % (15487)Termination reason: Unknown
% 11.51/4.82 % (15487)Termination phase: shuffling
% 11.51/4.82
% 11.51/4.82 % (15487)Memory used [KB]: 19189
% 11.51/4.82 % (15487)Time elapsed: 0.134 s
% 11.51/4.82 % (15487)Instructions burned: 456 (million)
% 11.51/4.82 % (15487)------------------------------
% 11.51/4.82 % (15487)------------------------------
% 11.51/4.83 % (15500)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_14919 for (2991ds/339Mi)
% 11.51/4.84 % (15497)Instruction limit reached!
% 11.51/4.84 % (15497)------------------------------
% 11.51/4.84 % (15497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.51/4.84 % (15497)Termination reason: Unknown
% 11.51/4.84 % (15497)Termination phase: shuffling
% 11.51/4.84
% 11.51/4.84 % (15497)Memory used [KB]: 12409
% 11.51/4.84 % (15497)Time elapsed: 0.050 s
% 11.51/4.84 % (15497)Instructions burned: 140 (million)
% 11.51/4.84 % (15497)------------------------------
% 11.51/4.84 % (15497)------------------------------
% 11.51/4.85 % (15501)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_14919 for (2991ds/283Mi)
% 11.51/4.86 % (15496)Instruction limit reached!
% 11.51/4.86 % (15496)------------------------------
% 11.51/4.86 % (15496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.51/4.86 % (15496)Termination reason: Unknown
% 11.51/4.86 % (15496)Termination phase: shuffling
% 11.51/4.86
% 11.51/4.86 % (15496)Memory used [KB]: 13944
% 11.51/4.86 % (15496)Time elapsed: 0.088 s
% 11.51/4.86 % (15496)Instructions burned: 253 (million)
% 11.51/4.86 % (15496)------------------------------
% 11.51/4.86 % (15496)------------------------------
% 11.51/4.86 % (15494)Instruction limit reached!
% 11.51/4.86 % (15494)------------------------------
% 11.51/4.86 % (15494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.51/4.86 % (15494)Termination reason: Unknown
% 11.51/4.86 % (15494)Termination phase: shuffling
% 11.51/4.86
% 11.51/4.86 % (15494)Memory used [KB]: 14967
% 11.51/4.86 % (15494)Time elapsed: 0.118 s
% 11.51/4.86 % (15494)Instructions burned: 344 (million)
% 11.51/4.86 % (15494)------------------------------
% 11.51/4.86 % (15494)------------------------------
% 11.51/4.87 % (15502)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14919 for (2991ds/134Mi)
% 11.51/4.87 % (15503)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14919 for (2991ds/298Mi)
% 11.51/4.87 % (15499)Instruction limit reached!
% 11.51/4.87 % (15499)------------------------------
% 11.51/4.87 % (15499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.51/4.87 % (15499)Termination reason: Unknown
% 11.51/4.87 % (15499)Termination phase: shuffling
% 11.51/4.87
% 11.51/4.87 % (15499)Memory used [KB]: 13176
% 11.51/4.87 % (15499)Time elapsed: 0.071 s
% 11.51/4.87 % (15499)Instructions burned: 202 (million)
% 11.51/4.87 % (15499)------------------------------
% 11.51/4.87 % (15499)------------------------------
% 11.51/4.89 % (15504)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14919 for (2991ds/192Mi)
% 12.02/4.91 % (15502)Instruction limit reached!
% 12.02/4.91 % (15502)------------------------------
% 12.02/4.91 % (15502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.91 % (15502)Termination reason: Unknown
% 12.02/4.91 % (15502)Termination phase: shuffling
% 12.02/4.91
% 12.02/4.91 % (15502)Memory used [KB]: 12281
% 12.02/4.91 % (15502)Time elapsed: 0.049 s
% 12.02/4.91 % (15502)Instructions burned: 134 (million)
% 12.02/4.91 % (15502)------------------------------
% 12.02/4.91 % (15502)------------------------------
% 12.02/4.92 % (15473)Refutation not found, incomplete strategy
% 12.02/4.92 % (15473)------------------------------
% 12.02/4.92 % (15473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.92 % (15473)Termination reason: Refutation not found, incomplete strategy
% 12.02/4.92
% 12.02/4.92
% 12.02/4.92 % (15473)Memory used [KB]: 21875
% 12.02/4.92 % (15473)Time elapsed: 0.298 s
% 12.02/4.92 % (15473)Instructions burned: 930 (million)
% 12.02/4.92 % (15473)------------------------------
% 12.02/4.92 % (15473)------------------------------
% 12.02/4.93 % (15505)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_14919 for (2990ds/258Mi)
% 12.02/4.93 % (15506)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_14919 for (2990ds/90Mi)
% 12.02/4.94 % (15501)Instruction limit reached!
% 12.02/4.94 % (15501)------------------------------
% 12.02/4.94 % (15501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.94 % (15501)Termination reason: Unknown
% 12.02/4.94 % (15501)Termination phase: shuffling
% 12.02/4.94
% 12.02/4.94 % (15501)Memory used [KB]: 14711
% 12.02/4.94 % (15501)Time elapsed: 0.085 s
% 12.02/4.94 % (15501)Instructions burned: 284 (million)
% 12.02/4.94 % (15501)------------------------------
% 12.02/4.94 % (15501)------------------------------
% 12.02/4.95 % (15507)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_14919 for (2990ds/231Mi)
% 12.02/4.95 % (15500)Instruction limit reached!
% 12.02/4.95 % (15500)------------------------------
% 12.02/4.95 % (15500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.95 % (15500)Termination reason: Unknown
% 12.02/4.95 % (15500)Termination phase: shuffling
% 12.02/4.95
% 12.02/4.95 % (15500)Memory used [KB]: 14839
% 12.02/4.95 % (15500)Time elapsed: 0.117 s
% 12.02/4.95 % (15500)Instructions burned: 339 (million)
% 12.02/4.95 % (15500)------------------------------
% 12.02/4.95 % (15500)------------------------------
% 12.02/4.95 % (15504)Instruction limit reached!
% 12.02/4.95 % (15504)------------------------------
% 12.02/4.95 % (15504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.95 % (15504)Termination reason: Unknown
% 12.02/4.95 % (15504)Termination phase: shuffling
% 12.02/4.95
% 12.02/4.95 % (15504)Memory used [KB]: 13176
% 12.02/4.95 % (15504)Time elapsed: 0.069 s
% 12.02/4.95 % (15504)Instructions burned: 194 (million)
% 12.02/4.95 % (15504)------------------------------
% 12.02/4.95 % (15504)------------------------------
% 12.02/4.96 % (15508)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_14919 for (2990ds/458Mi)
% 12.02/4.96 % (15503)Instruction limit reached!
% 12.02/4.96 % (15503)------------------------------
% 12.02/4.96 % (15503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.96 % (15503)Termination reason: Unknown
% 12.02/4.96 % (15503)Termination phase: shuffling
% 12.02/4.96
% 12.02/4.96 % (15503)Memory used [KB]: 14967
% 12.02/4.96 % (15503)Time elapsed: 0.090 s
% 12.02/4.96 % (15503)Instructions burned: 298 (million)
% 12.02/4.96 % (15503)------------------------------
% 12.02/4.96 % (15503)------------------------------
% 12.02/4.97 % (15509)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_14919 for (2990ds/31Mi)
% 12.02/4.97 % (15506)Instruction limit reached!
% 12.02/4.97 % (15506)------------------------------
% 12.02/4.97 % (15506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.97 % (15506)Termination reason: Unknown
% 12.02/4.97 % (15506)Termination phase: shuffling
% 12.02/4.97
% 12.02/4.97 % (15506)Memory used [KB]: 10746
% 12.02/4.97 % (15506)Time elapsed: 0.035 s
% 12.02/4.97 % (15506)Instructions burned: 91 (million)
% 12.02/4.97 % (15506)------------------------------
% 12.02/4.97 % (15506)------------------------------
% 12.02/4.97 % (15510)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_14919 for (2990ds/297Mi)
% 12.02/4.98 % (15511)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_14919 for (2990ds/987Mi)
% 12.02/4.98 % (15509)Instruction limit reached!
% 12.02/4.98 % (15509)------------------------------
% 12.02/4.98 % (15509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/4.98 % (15509)Termination reason: Unknown
% 12.02/4.98 % (15509)Termination phase: shuffling
% 12.02/4.98
% 12.02/4.98 % (15509)Memory used [KB]: 9850
% 12.02/4.98 % (15509)Time elapsed: 0.015 s
% 12.02/4.98 % (15509)Instructions burned: 31 (million)
% 12.02/4.98 % (15509)------------------------------
% 12.02/4.98 % (15509)------------------------------
% 12.02/4.99 % (15512)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_14919 for (2990ds/182Mi)
% 12.02/5.00 % (15498)Instruction limit reached!
% 12.02/5.00 % (15498)------------------------------
% 12.02/5.00 % (15498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/5.00 % (15498)Termination reason: Unknown
% 12.02/5.00 % (15498)Termination phase: Property scanning
% 12.02/5.00
% 12.02/5.00 % (15498)Memory used [KB]: 17142
% 12.02/5.00 % (15498)Time elapsed: 0.205 s
% 12.02/5.00 % (15498)Instructions burned: 615 (million)
% 12.02/5.00 % (15498)------------------------------
% 12.02/5.00 % (15498)------------------------------
% 13.37/5.01 % (15513)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_14919 for (2989ds/182Mi)
% 13.37/5.02 % (15505)Instruction limit reached!
% 13.37/5.02 % (15505)------------------------------
% 13.37/5.02 % (15505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.02 % (15505)Termination reason: Unknown
% 13.37/5.02 % (15505)Termination phase: shuffling
% 13.37/5.02
% 13.37/5.02 % (15505)Memory used [KB]: 13944
% 13.37/5.02 % (15505)Time elapsed: 0.092 s
% 13.37/5.02 % (15505)Instructions burned: 259 (million)
% 13.37/5.02 % (15505)------------------------------
% 13.37/5.02 % (15505)------------------------------
% 13.37/5.02 % (15507)Instruction limit reached!
% 13.37/5.02 % (15507)------------------------------
% 13.37/5.02 % (15507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.02 % (15507)Termination reason: Unknown
% 13.37/5.02 % (15507)Termination phase: shuffling
% 13.37/5.02
% 13.37/5.02 % (15507)Memory used [KB]: 13944
% 13.37/5.02 % (15507)Time elapsed: 0.072 s
% 13.37/5.02 % (15507)Instructions burned: 233 (million)
% 13.37/5.02 % (15507)------------------------------
% 13.37/5.02 % (15507)------------------------------
% 13.37/5.03 % (15514)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_14919 for (2989ds/154Mi)
% 13.37/5.03 % (15515)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_14919 for (2989ds/79Mi)
% 13.37/5.06 % (15512)Instruction limit reached!
% 13.37/5.06 % (15512)------------------------------
% 13.37/5.06 % (15512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.06 % (15512)Termination reason: Unknown
% 13.37/5.06 % (15512)Termination phase: shuffling
% 13.37/5.06
% 13.37/5.06 % (15512)Memory used [KB]: 13048
% 13.37/5.06 % (15512)Time elapsed: 0.065 s
% 13.37/5.06 % (15512)Instructions burned: 182 (million)
% 13.37/5.06 % (15512)------------------------------
% 13.37/5.06 % (15512)------------------------------
% 13.37/5.06 % (15515)Instruction limit reached!
% 13.37/5.06 % (15515)------------------------------
% 13.37/5.06 % (15515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.06 % (15515)Termination reason: Unknown
% 13.37/5.06 % (15515)Termination phase: shuffling
% 13.37/5.06
% 13.37/5.06 % (15515)Memory used [KB]: 10618
% 13.37/5.06 % (15515)Time elapsed: 0.030 s
% 13.37/5.06 % (15515)Instructions burned: 79 (million)
% 13.37/5.06 % (15515)------------------------------
% 13.37/5.06 % (15515)------------------------------
% 13.37/5.06 % (15510)Instruction limit reached!
% 13.37/5.06 % (15510)------------------------------
% 13.37/5.06 % (15510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.06 % (15510)Termination reason: Unknown
% 13.37/5.06 % (15510)Termination phase: shuffling
% 13.37/5.06
% 13.37/5.06 % (15510)Memory used [KB]: 17014
% 13.37/5.06 % (15510)Time elapsed: 0.090 s
% 13.37/5.06 % (15510)Instructions burned: 299 (million)
% 13.37/5.06 % (15510)------------------------------
% 13.37/5.06 % (15510)------------------------------
% 13.37/5.07 % (15516)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_14919 for (2989ds/216Mi)
% 13.37/5.07 % (15517)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14919 for (2989ds/114Mi)
% 13.37/5.07 % (15518)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_14919 for (2989ds/922Mi)
% 13.37/5.08 % (15514)Instruction limit reached!
% 13.37/5.08 % (15514)------------------------------
% 13.37/5.08 % (15514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.08 % (15514)Termination reason: Unknown
% 13.37/5.08 % (15514)Termination phase: shuffling
% 13.37/5.08
% 13.37/5.08 % (15514)Memory used [KB]: 12792
% 13.37/5.08 % (15514)Time elapsed: 0.048 s
% 13.37/5.08 % (15514)Instructions burned: 154 (million)
% 13.37/5.08 % (15514)------------------------------
% 13.37/5.08 % (15514)------------------------------
% 13.37/5.08 % (15513)Instruction limit reached!
% 13.37/5.08 % (15513)------------------------------
% 13.37/5.08 % (15513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.08 % (15513)Termination reason: Unknown
% 13.37/5.08 % (15513)Termination phase: shuffling
% 13.37/5.08
% 13.37/5.08 % (15513)Memory used [KB]: 13048
% 13.37/5.08 % (15513)Time elapsed: 0.065 s
% 13.37/5.08 % (15513)Instructions burned: 184 (million)
% 13.37/5.08 % (15513)------------------------------
% 13.37/5.08 % (15513)------------------------------
% 13.37/5.09 % (15519)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_14919 for (2989ds/182Mi)
% 13.37/5.09 % (15520)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_14919 for (2989ds/164Mi)
% 13.37/5.11 % (15517)Instruction limit reached!
% 13.37/5.11 % (15517)------------------------------
% 13.37/5.11 % (15517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/5.11 % (15517)Termination reason: Unknown
% 13.37/5.11 % (15517)Termination phase: shuffling
% 13.37/5.11
% 13.37/5.11 % (15517)Memory used [KB]: 11001
% 13.37/5.11 % (15517)Time elapsed: 0.042 s
% 13.37/5.11 % (15517)Instructions burned: 115 (million)
% 13.37/5.11 % (15517)------------------------------
% 13.37/5.11 % (15517)------------------------------
% 13.95/5.12 % (15508)Instruction limit reached!
% 13.95/5.12 % (15508)------------------------------
% 13.95/5.12 % (15508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.12 % (15508)Termination reason: Unknown
% 13.95/5.12 % (15508)Termination phase: shuffling
% 13.95/5.12
% 13.95/5.12 % (15508)Memory used [KB]: 16375
% 13.95/5.12 % (15508)Time elapsed: 0.157 s
% 13.95/5.12 % (15508)Instructions burned: 460 (million)
% 13.95/5.12 % (15508)------------------------------
% 13.95/5.12 % (15508)------------------------------
% 13.95/5.12 % (15521)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_14919 for (2988ds/50Mi)
% 13.95/5.13 % (15522)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14919 for (2988ds/368Mi)
% 13.95/5.13 % (15516)Instruction limit reached!
% 13.95/5.13 % (15516)------------------------------
% 13.95/5.13 % (15516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.13 % (15516)Termination reason: Unknown
% 13.95/5.13 % (15516)Termination phase: shuffling
% 13.95/5.13
% 13.95/5.13 % (15516)Memory used [KB]: 13816
% 13.95/5.13 % (15516)Time elapsed: 0.066 s
% 13.95/5.13 % (15516)Instructions burned: 217 (million)
% 13.95/5.13 % (15516)------------------------------
% 13.95/5.13 % (15516)------------------------------
% 13.95/5.14 % (15521)Instruction limit reached!
% 13.95/5.14 % (15521)------------------------------
% 13.95/5.14 % (15521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.14 % (15521)Termination reason: Unknown
% 13.95/5.14 % (15521)Termination phase: shuffling
% 13.95/5.14
% 13.95/5.14 % (15521)Memory used [KB]: 10106
% 13.95/5.14 % (15521)Time elapsed: 0.019 s
% 13.95/5.14 % (15521)Instructions burned: 52 (million)
% 13.95/5.14 % (15521)------------------------------
% 13.95/5.14 % (15521)------------------------------
% 13.95/5.14 % (15520)Instruction limit reached!
% 13.95/5.14 % (15520)------------------------------
% 13.95/5.14 % (15520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.14 % (15520)Termination reason: Unknown
% 13.95/5.14 % (15520)Termination phase: shuffling
% 13.95/5.14
% 13.95/5.14 % (15520)Memory used [KB]: 13048
% 13.95/5.14 % (15520)Time elapsed: 0.052 s
% 13.95/5.14 % (15520)Instructions burned: 167 (million)
% 13.95/5.14 % (15520)------------------------------
% 13.95/5.14 % (15520)------------------------------
% 13.95/5.14 % (15519)Instruction limit reached!
% 13.95/5.14 % (15519)------------------------------
% 13.95/5.14 % (15519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.14 % (15519)Termination reason: Unknown
% 13.95/5.14 % (15519)Termination phase: shuffling
% 13.95/5.14
% 13.95/5.14 % (15519)Memory used [KB]: 13304
% 13.95/5.14 % (15519)Time elapsed: 0.056 s
% 13.95/5.14 % (15519)Instructions burned: 182 (million)
% 13.95/5.14 % (15519)------------------------------
% 13.95/5.14 % (15519)------------------------------
% 13.95/5.14 % (15523)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_14919 for (2988ds/1021Mi)
% 13.95/5.15 % (15524)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_14919 for (2988ds/267Mi)
% 13.95/5.15 % (15525)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_14919 for (2988ds/204Mi)
% 13.95/5.15 % (15526)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_14919 for (2988ds/26Mi)
% 13.95/5.16 % (15526)Instruction limit reached!
% 13.95/5.16 % (15526)------------------------------
% 13.95/5.16 % (15526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.16 % (15526)Termination reason: Unknown
% 13.95/5.16 % (15526)Termination phase: shuffling
% 13.95/5.16
% 13.95/5.16 % (15526)Memory used [KB]: 9722
% 13.95/5.16 % (15526)Time elapsed: 0.013 s
% 13.95/5.16 % (15526)Instructions burned: 26 (million)
% 13.95/5.16 % (15526)------------------------------
% 13.95/5.16 % (15526)------------------------------
% 13.95/5.18 % (15527)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_14919 for (2988ds/53Mi)
% 13.95/5.19 % (15527)Instruction limit reached!
% 13.95/5.19 % (15527)------------------------------
% 13.95/5.19 % (15527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/5.19 % (15527)Termination reason: Unknown
% 13.95/5.19 % (15527)Termination phase: shuffling
% 13.95/5.19
% 13.95/5.19 % (15527)Memory used [KB]: 10234
% 13.95/5.19 % (15527)Time elapsed: 0.020 s
% 13.95/5.19 % (15527)Instructions burned: 54 (million)
% 13.95/5.19 % (15527)------------------------------
% 13.95/5.19 % (15527)------------------------------
% 14.34/5.21 % (15528)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_14919 for (2988ds/4436Mi)
% 14.34/5.22 % (15525)Instruction limit reached!
% 14.34/5.22 % (15525)------------------------------
% 14.34/5.22 % (15525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/5.22 % (15525)Termination reason: Unknown
% 14.34/5.22 % (15525)Termination phase: shuffling
% 14.34/5.22
% 14.34/5.22 % (15525)Memory used [KB]: 13304
% 14.34/5.22 % (15525)Time elapsed: 0.073 s
% 14.34/5.22 % (15525)Instructions burned: 206 (million)
% 14.34/5.22 % (15525)------------------------------
% 14.34/5.22 % (15525)------------------------------
% 14.34/5.23 % (15524)Instruction limit reached!
% 14.34/5.23 % (15524)------------------------------
% 14.34/5.23 % (15524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/5.23 % (15524)Termination reason: Unknown
% 14.34/5.23 % (15524)Termination phase: shuffling
% 14.34/5.23
% 14.34/5.23 % (15524)Memory used [KB]: 14456
% 14.34/5.23 % (15524)Time elapsed: 0.081 s
% 14.34/5.23 % (15524)Instructions burned: 267 (million)
% 14.34/5.23 % (15524)------------------------------
% 14.34/5.23 % (15524)------------------------------
% 14.34/5.23 % (15529)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_14919 for (2987ds/1539Mi)
% 14.34/5.24 % (15530)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_14919 for (2987ds/408Mi)
% 14.34/5.25 % (15522)Instruction limit reached!
% 14.34/5.25 % (15522)------------------------------
% 14.34/5.25 % (15522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/5.25 % (15522)Termination reason: Unknown
% 14.34/5.25 % (15522)Termination phase: shuffling
% 14.34/5.25
% 14.34/5.25 % (15522)Memory used [KB]: 15223
% 14.34/5.25 % (15522)Time elapsed: 0.128 s
% 14.34/5.25 % (15522)Instructions burned: 370 (million)
% 14.34/5.25 % (15522)------------------------------
% 14.34/5.25 % (15522)------------------------------
% 14.34/5.26 % (15531)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_14919 for (2987ds/5205Mi)
% 14.34/5.26 % (15511)Instruction limit reached!
% 14.34/5.26 % (15511)------------------------------
% 14.34/5.26 % (15511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/5.26 % (15511)Termination reason: Unknown
% 14.34/5.26 % (15511)Termination phase: Property scanning
% 14.34/5.26
% 14.34/5.26 % (15511)Memory used [KB]: 28912
% 14.34/5.26 % (15511)Time elapsed: 0.287 s
% 14.34/5.26 % (15511)Instructions burned: 989 (million)
% 14.34/5.26 % (15511)------------------------------
% 14.34/5.26 % (15511)------------------------------
% 14.34/5.28 % (15532)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_14919 for (2987ds/1913Mi)
% 14.73/5.37 % (15518)Instruction limit reached!
% 14.73/5.37 % (15518)------------------------------
% 14.73/5.37 % (15518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/5.37 % (15518)Termination reason: Unknown
% 14.73/5.37 % (15518)Termination phase: Saturation
% 14.73/5.37
% 14.73/5.37 % (15518)Memory used [KB]: 22131
% 14.73/5.37 % (15518)Time elapsed: 0.297 s
% 14.73/5.37 % (15518)Instructions burned: 924 (million)
% 14.73/5.37 % (15518)------------------------------
% 14.73/5.37 % (15518)------------------------------
% 14.73/5.38 % (15530)Instruction limit reached!
% 14.73/5.38 % (15530)------------------------------
% 14.73/5.38 % (15530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/5.38 % (15530)Termination reason: Unknown
% 14.73/5.38 % (15530)Termination phase: shuffling
% 14.73/5.38
% 14.73/5.38 % (15530)Memory used [KB]: 15735
% 14.73/5.38 % (15530)Time elapsed: 0.140 s
% 14.73/5.38 % (15530)Instructions burned: 410 (million)
% 14.73/5.38 % (15530)------------------------------
% 14.73/5.38 % (15530)------------------------------
% 14.73/5.38 % (15533)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_14919 for (2986ds/4350Mi)
% 14.73/5.39 % (15534)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_14919 for (2986ds/68Mi)
% 15.19/5.41 % (15534)Instruction limit reached!
% 15.19/5.41 % (15534)------------------------------
% 15.19/5.41 % (15534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/5.41 % (15534)Termination reason: Unknown
% 15.19/5.41 % (15534)Termination phase: shuffling
% 15.19/5.41
% 15.19/5.41 % (15534)Memory used [KB]: 10490
% 15.19/5.41 % (15534)Time elapsed: 0.028 s
% 15.19/5.41 % (15534)Instructions burned: 71 (million)
% 15.19/5.41 % (15534)------------------------------
% 15.19/5.41 % (15534)------------------------------
% 15.19/5.43 % (15535)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_14919 for (2985ds/358Mi)
% 15.19/5.47 % (15523)Instruction limit reached!
% 15.19/5.47 % (15523)------------------------------
% 15.19/5.47 % (15523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/5.47 % (15523)Termination reason: Unknown
% 15.19/5.47 % (15523)Termination phase: Preprocessing 3
% 15.19/5.47
% 15.19/5.47 % (15523)Memory used [KB]: 20724
% 15.19/5.47 % (15523)Time elapsed: 0.330 s
% 15.19/5.47 % (15523)Instructions burned: 1021 (million)
% 15.19/5.47 % (15523)------------------------------
% 15.19/5.47 % (15523)------------------------------
% 15.19/5.48 % (15536)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_14919 for (2985ds/31Mi)
% 15.57/5.50 % (15536)Instruction limit reached!
% 15.57/5.50 % (15536)------------------------------
% 15.57/5.50 % (15536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.57/5.50 % (15536)Termination reason: Unknown
% 15.57/5.50 % (15536)Termination phase: shuffling
% 15.57/5.50
% 15.57/5.50 % (15536)Memory used [KB]: 9850
% 15.57/5.50 % (15536)Time elapsed: 0.015 s
% 15.57/5.50 % (15536)Instructions burned: 32 (million)
% 15.57/5.50 % (15536)------------------------------
% 15.57/5.50 % (15536)------------------------------
% 15.57/5.50 % (15528)Refutation not found, incomplete strategy
% 15.57/5.50 % (15528)------------------------------
% 15.57/5.50 % (15528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.57/5.50 % (15528)Termination reason: Refutation not found, incomplete strategy
% 15.57/5.50
% 15.57/5.50
% 15.57/5.50 % (15528)Memory used [KB]: 21875
% 15.57/5.50 % (15528)Time elapsed: 0.296 s
% 15.57/5.50 % (15528)Instructions burned: 931 (million)
% 15.57/5.50 % (15528)------------------------------
% 15.57/5.50 % (15528)------------------------------
% 15.57/5.51 % (15537)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14919 for (2984ds/279Mi)
% 15.57/5.51 % (15538)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14919 for (2984ds/258Mi)
% 15.57/5.55 % (15535)Instruction limit reached!
% 15.57/5.55 % (15535)------------------------------
% 15.57/5.55 % (15535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.57/5.55 % (15535)Termination reason: Unknown
% 15.57/5.55 % (15535)Termination phase: shuffling
% 15.57/5.55
% 15.57/5.55 % (15535)Memory used [KB]: 15095
% 15.57/5.55 % (15535)Time elapsed: 0.123 s
% 15.57/5.55 % (15535)Instructions burned: 359 (million)
% 15.57/5.55 % (15535)------------------------------
% 15.57/5.55 % (15535)------------------------------
% 15.57/5.56 % (15539)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_14919 for (2984ds/26Mi)
% 15.57/5.57 % (15539)Instruction limit reached!
% 15.57/5.57 % (15539)------------------------------
% 15.57/5.57 % (15539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.57/5.57 % (15539)Termination reason: Unknown
% 15.57/5.57 % (15539)Termination phase: shuffling
% 15.57/5.57
% 15.57/5.57 % (15539)Memory used [KB]: 9722
% 15.57/5.57 % (15539)Time elapsed: 0.013 s
% 15.57/5.57 % (15539)Instructions burned: 28 (million)
% 15.57/5.57 % (15539)------------------------------
% 15.57/5.57 % (15539)------------------------------
% 15.57/5.58 % (15540)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_14919 for (2984ds/995Mi)
% 15.57/5.59 % (15537)Instruction limit reached!
% 15.57/5.59 % (15537)------------------------------
% 15.57/5.59 % (15537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.57/5.59 % (15537)Termination reason: Unknown
% 15.57/5.59 % (15537)Termination phase: shuffling
% 15.57/5.59
% 15.57/5.59 % (15537)Memory used [KB]: 14711
% 15.57/5.59 % (15537)Time elapsed: 0.086 s
% 15.57/5.59 % (15537)Instructions burned: 282 (million)
% 15.57/5.59 % (15537)------------------------------
% 15.57/5.59 % (15537)------------------------------
% 16.16/5.60 % (15538)Instruction limit reached!
% 16.16/5.60 % (15538)------------------------------
% 16.16/5.60 % (15538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/5.60 % (15538)Termination reason: Unknown
% 16.16/5.60 % (15538)Termination phase: shuffling
% 16.16/5.60
% 16.16/5.60 % (15538)Memory used [KB]: 13944
% 16.16/5.60 % (15538)Time elapsed: 0.091 s
% 16.16/5.60 % (15538)Instructions burned: 259 (million)
% 16.16/5.60 % (15538)------------------------------
% 16.16/5.60 % (15538)------------------------------
% 16.16/5.60 % (15541)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_14919 for (2983ds/373Mi)
% 16.16/5.62 % (15542)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_14919 for (2983ds/253Mi)
% 16.16/5.67 % (15533)Refutation not found, incomplete strategy
% 16.16/5.67 % (15533)------------------------------
% 16.16/5.67 % (15533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/5.67 % (15533)Termination reason: Refutation not found, incomplete strategy
% 16.16/5.67
% 16.16/5.67
% 16.16/5.67 % (15533)Memory used [KB]: 21875
% 16.16/5.67 % (15533)Time elapsed: 0.291 s
% 16.16/5.67 % (15533)Instructions burned: 908 (million)
% 16.16/5.67 % (15533)------------------------------
% 16.16/5.67 % (15533)------------------------------
% 16.16/5.68 % (15543)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_14919 for (2983ds/832Mi)
% 16.16/5.69 % (15542)Instruction limit reached!
% 16.16/5.69 % (15542)------------------------------
% 16.16/5.69 % (15542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/5.69 % (15542)Termination reason: Unknown
% 16.16/5.69 % (15542)Termination phase: shuffling
% 16.16/5.69
% 16.16/5.69 % (15542)Memory used [KB]: 14328
% 16.16/5.69 % (15542)Time elapsed: 0.078 s
% 16.16/5.69 % (15542)Instructions burned: 255 (million)
% 16.16/5.69 % (15542)------------------------------
% 16.16/5.69 % (15542)------------------------------
% 16.65/5.70 % (15544)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_14919 for (2982ds/668Mi)
% 16.65/5.72 % (15529)Instruction limit reached!
% 16.65/5.72 % (15529)------------------------------
% 16.65/5.72 % (15529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.65/5.72 % (15529)Termination reason: Unknown
% 16.65/5.72 % (15529)Termination phase: Function definition elimination
% 16.65/5.72
% 16.65/5.72 % (15529)Memory used [KB]: 25585
% 16.65/5.72 % (15529)Time elapsed: 0.483 s
% 16.65/5.72 % (15529)Instructions burned: 1541 (million)
% 16.65/5.72 % (15529)------------------------------
% 16.65/5.72 % (15529)------------------------------
% 16.65/5.73 % (15545)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_14919 for (2982ds/40Mi)
% 16.65/5.73 % (15541)Instruction limit reached!
% 16.65/5.73 % (15541)------------------------------
% 16.65/5.73 % (15541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.65/5.73 % (15541)Termination reason: Unknown
% 16.65/5.73 % (15541)Termination phase: shuffling
% 16.65/5.73
% 16.65/5.73 % (15541)Memory used [KB]: 15223
% 16.65/5.73 % (15541)Time elapsed: 0.130 s
% 16.65/5.73 % (15541)Instructions burned: 373 (million)
% 16.65/5.73 % (15541)------------------------------
% 16.65/5.73 % (15541)------------------------------
% 16.65/5.74 % (15545)Instruction limit reached!
% 16.65/5.74 % (15545)------------------------------
% 16.65/5.74 % (15545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.65/5.74 % (15545)Termination reason: Unknown
% 16.65/5.74 % (15545)Termination phase: shuffling
% 16.65/5.74
% 16.65/5.74 % (15545)Memory used [KB]: 9978
% 16.65/5.74 % (15545)Time elapsed: 0.017 s
% 16.65/5.74 % (15545)Instructions burned: 41 (million)
% 16.65/5.74 % (15545)------------------------------
% 16.65/5.74 % (15545)------------------------------
% 16.65/5.75 % (15546)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_14919 for (2982ds/294Mi)
% 16.65/5.76 % (15547)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_14919 for (2982ds/187Mi)
% 17.31/5.82 % (15547)Instruction limit reached!
% 17.31/5.82 % (15547)------------------------------
% 17.31/5.82 % (15547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.31/5.82 % (15547)Termination reason: Unknown
% 17.31/5.82 % (15547)Termination phase: shuffling
% 17.31/5.82
% 17.31/5.82 % (15547)Memory used [KB]: 13048
% 17.31/5.82 % (15547)Time elapsed: 0.067 s
% 17.31/5.82 % (15547)Instructions burned: 189 (million)
% 17.31/5.82 % (15547)------------------------------
% 17.31/5.82 % (15547)------------------------------
% 17.31/5.83 % (15546)Instruction limit reached!
% 17.31/5.83 % (15546)------------------------------
% 17.31/5.83 % (15546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.31/5.83 % (15546)Termination reason: Unknown
% 17.31/5.83 % (15546)Termination phase: shuffling
% 17.31/5.83
% 17.31/5.83 % (15546)Memory used [KB]: 14839
% 17.31/5.83 % (15546)Time elapsed: 0.087 s
% 17.31/5.83 % (15546)Instructions burned: 294 (million)
% 17.31/5.83 % (15546)------------------------------
% 17.31/5.83 % (15546)------------------------------
% 17.31/5.83 % (15548)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14919 for (2981ds/371Mi)
% 17.31/5.84 % (15549)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14919 for (2981ds/1827Mi)
% 17.31/5.87 % (15540)Instruction limit reached!
% 17.31/5.87 % (15540)------------------------------
% 17.31/5.87 % (15540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.31/5.87 % (15540)Termination reason: Unknown
% 17.31/5.87 % (15540)Termination phase: Property scanning
% 17.31/5.87
% 17.31/5.87 % (15540)Memory used [KB]: 28912
% 17.31/5.87 % (15540)Time elapsed: 0.293 s
% 17.31/5.87 % (15540)Instructions burned: 996 (million)
% 17.31/5.87 % (15540)------------------------------
% 17.31/5.87 % (15540)------------------------------
% 17.31/5.89 % (15532)Instruction limit reached!
% 17.31/5.89 % (15532)------------------------------
% 17.31/5.89 % (15532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.31/5.89 % (15532)Termination reason: Unknown
% 17.31/5.89 % (15532)Termination phase: Saturation
% 17.31/5.89
% 17.31/5.89 % (15532)Memory used [KB]: 18293
% 17.31/5.89 % (15532)Time elapsed: 0.609 s
% 17.31/5.89 % (15532)Instructions burned: 1915 (million)
% 17.31/5.89 % (15532)------------------------------
% 17.31/5.89 % (15532)------------------------------
% 17.31/5.89 % (15550)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_14919 for (2981ds/70Mi)
% 18.41/5.90 % (15551)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_14919 for (2981ds/316Mi)
% 18.41/5.90 % (15544)Instruction limit reached!
% 18.41/5.90 % (15544)------------------------------
% 18.41/5.90 % (15544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.41/5.90 % (15544)Termination reason: Unknown
% 18.41/5.90 % (15544)Termination phase: shuffling
% 18.41/5.90
% 18.41/5.90 % (15544)Memory used [KB]: 22131
% 18.41/5.90 % (15544)Time elapsed: 0.199 s
% 18.41/5.90 % (15544)Instructions burned: 670 (million)
% 18.41/5.90 % (15544)------------------------------
% 18.41/5.90 % (15544)------------------------------
% 18.41/5.91 % (15550)Instruction limit reached!
% 18.41/5.91 % (15550)------------------------------
% 18.41/5.91 % (15550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.41/5.91 % (15550)Termination reason: Unknown
% 18.41/5.91 % (15550)Termination phase: shuffling
% 18.41/5.91
% 18.41/5.91 % (15550)Memory used [KB]: 11385
% 18.41/5.91 % (15550)Time elapsed: 0.025 s
% 18.41/5.91 % (15550)Instructions burned: 71 (million)
% 18.41/5.91 % (15550)------------------------------
% 18.41/5.91 % (15550)------------------------------
% 18.41/5.91 % (15552)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_14919 for (2980ds/932Mi)
% 18.41/5.92 % (15553)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_14919 for (2980ds/4714Mi)
% 18.41/5.95 % (15543)Instruction limit reached!
% 18.41/5.95 % (15543)------------------------------
% 18.41/5.95 % (15543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.41/5.95 % (15543)Termination reason: Unknown
% 18.41/5.95 % (15543)Termination phase: Preprocessing 1
% 18.41/5.95
% 18.41/5.95 % (15543)Memory used [KB]: 17654
% 18.41/5.95 % (15543)Time elapsed: 0.268 s
% 18.41/5.95 % (15543)Instructions burned: 834 (million)
% 18.41/5.95 % (15543)------------------------------
% 18.41/5.95 % (15543)------------------------------
% 18.41/5.96 % (15548)Instruction limit reached!
% 18.41/5.96 % (15548)------------------------------
% 18.41/5.96 % (15548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.41/5.96 % (15548)Termination reason: Unknown
% 18.41/5.96 % (15548)Termination phase: shuffling
% 18.41/5.96
% 18.41/5.96 % (15548)Memory used [KB]: 15351
% 18.41/5.96 % (15548)Time elapsed: 0.129 s
% 18.41/5.96 % (15548)Instructions burned: 372 (million)
% 18.41/5.96 % (15548)------------------------------
% 18.41/5.96 % (15548)------------------------------
% 18.41/5.96 % (15554)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_14919 for (2980ds/8250Mi)
% 18.41/5.97 % (15555)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_14919 for (2980ds/770Mi)
% 18.41/5.99 % (15551)Instruction limit reached!
% 18.41/5.99 % (15551)------------------------------
% 18.41/5.99 % (15551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.41/5.99 % (15551)Termination reason: Unknown
% 18.41/5.99 % (15551)Termination phase: shuffling
% 18.41/5.99
% 18.41/5.99 % (15551)Memory used [KB]: 17270
% 18.41/5.99 % (15551)Time elapsed: 0.095 s
% 18.41/5.99 % (15551)Instructions burned: 317 (million)
% 18.41/5.99 % (15551)------------------------------
% 18.41/5.99 % (15551)------------------------------
% 18.41/6.00 % (15556)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_14919 for (2980ds/794Mi)
% 21.09/6.18 % (15552)Instruction limit reached!
% 21.09/6.18 % (15552)------------------------------
% 21.09/6.18 % (15552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/6.18 % (15552)Termination reason: Unknown
% 21.09/6.18 % (15552)Termination phase: Property scanning
% 21.09/6.18
% 21.09/6.18 % (15552)Memory used [KB]: 28912
% 21.09/6.18 % (15552)Time elapsed: 0.271 s
% 21.09/6.18 % (15552)Instructions burned: 933 (million)
% 21.09/6.18 % (15552)------------------------------
% 21.09/6.18 % (15552)------------------------------
% 21.67/6.20 % (15557)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_14919 for (2978ds/464Mi)
% 21.67/6.22 % (15555)Instruction limit reached!
% 21.67/6.22 % (15555)------------------------------
% 21.67/6.22 % (15555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/6.22 % (15555)Termination reason: Unknown
% 21.67/6.22 % (15555)Termination phase: Property scanning
% 21.67/6.22
% 21.67/6.22 % (15555)Memory used [KB]: 18038
% 21.67/6.22 % (15555)Time elapsed: 0.246 s
% 21.67/6.22 % (15555)Instructions burned: 770 (million)
% 21.67/6.22 % (15555)------------------------------
% 21.67/6.22 % (15555)------------------------------
% 21.67/6.23 % (15558)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_14919 for (2977ds/1376Mi)
% 21.67/6.25 % (15556)Instruction limit reached!
% 21.67/6.25 % (15556)------------------------------
% 21.67/6.25 % (15556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/6.25 % (15556)Termination reason: Unknown
% 21.67/6.25 % (15556)Termination phase: Property scanning
% 21.67/6.25
% 21.67/6.25 % (15556)Memory used [KB]: 17142
% 21.67/6.25 % (15556)Time elapsed: 0.248 s
% 21.67/6.25 % (15556)Instructions burned: 795 (million)
% 21.67/6.25 % (15556)------------------------------
% 21.67/6.25 % (15556)------------------------------
% 21.67/6.26 % (15559)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_14919 for (2977ds/906Mi)
% 22.18/6.36 % (15557)Instruction limit reached!
% 22.18/6.36 % (15557)------------------------------
% 22.18/6.36 % (15557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.18/6.36 % (15557)Termination reason: Unknown
% 22.18/6.36 % (15557)Termination phase: shuffling
% 22.18/6.36
% 22.18/6.36 % (15557)Memory used [KB]: 16502
% 22.18/6.36 % (15557)Time elapsed: 0.163 s
% 22.18/6.36 % (15557)Instructions burned: 466 (million)
% 22.18/6.36 % (15557)------------------------------
% 22.18/6.36 % (15557)------------------------------
% 22.18/6.37 % (15560)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_14919 for (2976ds/434Mi)
% 22.18/6.39 % (15549)Instruction limit reached!
% 22.18/6.39 % (15549)------------------------------
% 22.18/6.39 % (15549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.18/6.39 % (15549)Termination reason: Unknown
% 22.18/6.39 % (15549)Termination phase: Saturation
% 22.18/6.39
% 22.18/6.39 % (15549)Memory used [KB]: 30191
% 22.18/6.39 % (15549)Time elapsed: 0.551 s
% 22.18/6.39 % (15549)Instructions burned: 1827 (million)
% 22.18/6.39 % (15549)------------------------------
% 22.18/6.39 % (15549)------------------------------
% 22.77/6.41 % (15561)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_14919 for (2975ds/865Mi)
% 23.07/6.52 % (15560)Instruction limit reached!
% 23.07/6.52 % (15560)------------------------------
% 23.07/6.52 % (15560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.07/6.52 % (15560)Termination reason: Unknown
% 23.07/6.52 % (15560)Termination phase: shuffling
% 23.07/6.52
% 23.07/6.52 % (15560)Memory used [KB]: 16119
% 23.07/6.52 % (15560)Time elapsed: 0.148 s
% 23.07/6.52 % (15560)Instructions burned: 435 (million)
% 23.07/6.52 % (15560)------------------------------
% 23.07/6.52 % (15560)------------------------------
% 23.07/6.53 % (15562)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_14919 for (2974ds/593Mi)
% 23.07/6.55 % (15559)Instruction limit reached!
% 23.07/6.55 % (15559)------------------------------
% 23.07/6.55 % (15559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.07/6.55 % (15559)Termination reason: Unknown
% 23.07/6.55 % (15559)Termination phase: Preprocessing 3
% 23.07/6.55
% 23.07/6.55 % (15559)Memory used [KB]: 19829
% 23.07/6.55 % (15559)Time elapsed: 0.292 s
% 23.07/6.55 % (15559)Instructions burned: 907 (million)
% 23.07/6.55 % (15559)------------------------------
% 23.07/6.55 % (15559)------------------------------
% 23.07/6.56 % (15563)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_14919 for (2974ds/443Mi)
% 23.83/6.61 % (15558)Instruction limit reached!
% 23.83/6.61 % (15558)------------------------------
% 23.83/6.61 % (15558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.83/6.61 % (15558)Termination reason: Unknown
% 23.83/6.61 % (15558)Termination phase: Property scanning
% 23.83/6.61
% 23.83/6.61 % (15558)Memory used [KB]: 29040
% 23.83/6.61 % (15558)Time elapsed: 0.387 s
% 23.83/6.61 % (15558)Instructions burned: 1379 (million)
% 23.83/6.61 % (15558)------------------------------
% 23.83/6.61 % (15558)------------------------------
% 23.83/6.63 % (15564)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_14919 for (2973ds/594Mi)
% 23.83/6.65 % (15561)Instruction limit reached!
% 23.83/6.65 % (15561)------------------------------
% 23.83/6.65 % (15561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.83/6.65 % (15561)Termination reason: Unknown
% 23.83/6.65 % (15561)Termination phase: shuffling
% 23.83/6.65
% 23.83/6.65 % (15561)Memory used [KB]: 28784
% 23.83/6.65 % (15561)Time elapsed: 0.249 s
% 23.83/6.65 % (15561)Instructions burned: 865 (million)
% 23.83/6.65 % (15561)------------------------------
% 23.83/6.65 % (15561)------------------------------
% 23.83/6.67 % (15565)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_14919 for (2973ds/327Mi)
% 24.79/6.70 % (15562)Instruction limit reached!
% 24.79/6.70 % (15562)------------------------------
% 24.79/6.70 % (15562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/6.70 % (15562)Termination reason: Unknown
% 24.79/6.70 % (15562)Termination phase: shuffling
% 24.79/6.70
% 24.79/6.70 % (15562)Memory used [KB]: 20980
% 24.79/6.70 % (15562)Time elapsed: 0.172 s
% 24.79/6.70 % (15562)Instructions burned: 594 (million)
% 24.79/6.70 % (15562)------------------------------
% 24.79/6.70 % (15562)------------------------------
% 24.79/6.71 % (15563)Instruction limit reached!
% 24.79/6.71 % (15563)------------------------------
% 24.79/6.71 % (15563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/6.71 % (15563)Termination reason: Unknown
% 24.79/6.71 % (15563)Termination phase: shuffling
% 24.79/6.71 % (15566)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_14919 for (2972ds/5411Mi)
% 24.79/6.71
% 24.79/6.71 % (15563)Memory used [KB]: 16119
% 24.79/6.71 % (15563)Time elapsed: 0.150 s
% 24.79/6.71 % (15563)Instructions burned: 445 (million)
% 24.79/6.71 % (15563)------------------------------
% 24.79/6.71 % (15563)------------------------------
% 24.79/6.72 % (15567)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_14919 for (2972ds/1762Mi)
% 24.79/6.73 % (15531)Instruction limit reached!
% 24.79/6.73 % (15531)------------------------------
% 24.79/6.73 % (15531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/6.73 % (15531)Termination reason: Unknown
% 24.79/6.73 % (15531)Termination phase: Saturation
% 24.79/6.73
% 24.79/6.73 % (15531)Memory used [KB]: 43112
% 24.79/6.73 % (15531)Time elapsed: 1.463 s
% 24.79/6.73 % (15531)Instructions burned: 5207 (million)
% 24.79/6.73 % (15531)------------------------------
% 24.79/6.73 % (15531)------------------------------
% 24.79/6.74 % (15568)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_14919 for (2972ds/96Mi)
% 24.79/6.77 % (15568)Instruction limit reached!
% 24.79/6.77 % (15568)------------------------------
% 24.79/6.77 % (15568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/6.77 % (15568)Termination reason: Unknown
% 24.79/6.77 % (15568)Termination phase: shuffling
% 24.79/6.77
% 24.79/6.77 % (15568)Memory used [KB]: 11897
% 24.79/6.77 % (15568)Time elapsed: 0.032 s
% 24.79/6.77 % (15568)Instructions burned: 96 (million)
% 24.79/6.77 % (15568)------------------------------
% 24.79/6.77 % (15568)------------------------------
% 24.79/6.78 % (15565)Instruction limit reached!
% 24.79/6.78 % (15565)------------------------------
% 24.79/6.78 % (15565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/6.78 % (15565)Termination reason: Unknown
% 24.79/6.78 % (15565)Termination phase: shuffling
% 24.79/6.78
% 24.79/6.78 % (15565)Memory used [KB]: 14711
% 24.79/6.78 % (15565)Time elapsed: 0.113 s
% 24.79/6.78 % (15565)Instructions burned: 328 (million)
% 24.79/6.78 % (15565)------------------------------
% 24.79/6.78 % (15565)------------------------------
% 24.79/6.78 % (15569)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_14919 for (2972ds/503Mi)
% 24.79/6.79 % (15570)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_14919 for (2972ds/90Mi)
% 25.54/6.82 % (15564)Instruction limit reached!
% 25.54/6.82 % (15564)------------------------------
% 25.54/6.82 % (15564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.54/6.82 % (15564)Termination reason: Unknown
% 25.54/6.82 % (15564)Termination phase: Property scanning
% 25.54/6.82
% 25.54/6.82 % (15564)Memory used [KB]: 17142
% 25.54/6.82 % (15564)Time elapsed: 0.196 s
% 25.54/6.82 % (15564)Instructions burned: 597 (million)
% 25.54/6.82 % (15564)------------------------------
% 25.54/6.82 % (15564)------------------------------
% 25.54/6.82 % (15570)Instruction limit reached!
% 25.54/6.82 % (15570)------------------------------
% 25.54/6.82 % (15570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.54/6.82 % (15570)Termination reason: Unknown
% 25.54/6.82 % (15570)Termination phase: shuffling
% 25.54/6.82
% 25.54/6.82 % (15570)Memory used [KB]: 10746
% 25.54/6.82 % (15570)Time elapsed: 0.035 s
% 25.54/6.82 % (15570)Instructions burned: 92 (million)
% 25.54/6.82 % (15570)------------------------------
% 25.54/6.82 % (15570)------------------------------
% 25.54/6.83 % (15572)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_14919 for (2971ds/1512Mi)
% 25.54/6.83 % (15571)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_14919 for (2971ds/593Mi)
% 25.99/6.96 % (15569)Instruction limit reached!
% 25.99/6.96 % (15569)------------------------------
% 25.99/6.96 % (15569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.99/6.96 % (15569)Termination reason: Unknown
% 25.99/6.96 % (15569)Termination phase: shuffling
% 25.99/6.96
% 25.99/6.96 % (15569)Memory used [KB]: 16886
% 25.99/6.96 % (15569)Time elapsed: 0.175 s
% 25.99/6.96 % (15569)Instructions burned: 503 (million)
% 25.99/6.96 % (15569)------------------------------
% 25.99/6.96 % (15569)------------------------------
% 25.99/6.97 % (15573)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_14919 for (2970ds/569Mi)
% 25.99/7.00 % (15566)Refutation not found, incomplete strategy
% 25.99/7.00 % (15566)------------------------------
% 25.99/7.00 % (15566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.99/7.00 % (15566)Termination reason: Refutation not found, incomplete strategy
% 25.99/7.00
% 25.99/7.00
% 25.99/7.00 % (15566)Memory used [KB]: 21875
% 25.99/7.00 % (15566)Time elapsed: 0.292 s
% 25.99/7.00 % (15566)Instructions burned: 886 (million)
% 25.99/7.00 % (15566)------------------------------
% 25.99/7.00 % (15566)------------------------------
% 27.39/7.02 % (15574)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_14919 for (2969ds/501Mi)
% 27.39/7.03 % (15571)Instruction limit reached!
% 27.39/7.03 % (15571)------------------------------
% 27.39/7.03 % (15571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.39/7.03 % (15571)Termination reason: Unknown
% 27.39/7.03 % (15571)Termination phase: Property scanning
% 27.39/7.03
% 27.39/7.03 % (15571)Memory used [KB]: 17142
% 27.39/7.03 % (15571)Time elapsed: 0.201 s
% 27.39/7.03 % (15571)Instructions burned: 595 (million)
% 27.39/7.03 % (15571)------------------------------
% 27.39/7.03 % (15571)------------------------------
% 27.39/7.05 % (15575)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_14919 for (2969ds/562Mi)
% 27.92/7.12 % (15553)Refutation not found, incomplete strategy
% 27.92/7.12 % (15553)------------------------------
% 27.92/7.12 % (15553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.92/7.12 % (15553)Termination reason: Refutation not found, incomplete strategy
% 27.92/7.12
% 27.92/7.12
% 27.92/7.12 % (15553)Memory used [KB]: 46438
% 27.92/7.12 % (15553)Time elapsed: 1.197 s
% 27.92/7.12 % (15553)Instructions burned: 4171 (million)
% 27.92/7.12 % (15553)------------------------------
% 27.92/7.12 % (15553)------------------------------
% 27.92/7.13 % (15576)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_14919 for (2968ds/406Mi)
% 27.92/7.13 % (15573)Instruction limit reached!
% 27.92/7.13 % (15573)------------------------------
% 27.92/7.13 % (15573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.92/7.13 % (15573)Termination reason: Unknown
% 27.92/7.13 % (15573)Termination phase: shuffling
% 27.92/7.13
% 27.92/7.13 % (15573)Memory used [KB]: 20724
% 27.92/7.13 % (15573)Time elapsed: 0.167 s
% 27.92/7.13 % (15573)Instructions burned: 570 (million)
% 27.92/7.13 % (15573)------------------------------
% 27.92/7.13 % (15573)------------------------------
% 27.92/7.15 % (15577)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_14919 for (2968ds/582Mi)
% 27.92/7.19 % (15574)Instruction limit reached!
% 27.92/7.19 % (15574)------------------------------
% 27.92/7.19 % (15574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.92/7.19 % (15574)Termination reason: Unknown
% 27.92/7.19 % (15574)Termination phase: shuffling
% 27.92/7.19
% 27.92/7.19 % (15574)Memory used [KB]: 16758
% 27.92/7.19 % (15574)Time elapsed: 0.171 s
% 27.92/7.19 % (15574)Instructions burned: 502 (million)
% 27.92/7.19 % (15574)------------------------------
% 27.92/7.19 % (15574)------------------------------
% 28.44/7.20 % (15578)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_14919 for (2968ds/456Mi)
% 28.44/7.21 % (15554)First to succeed.
% 28.44/7.21 % (15575)Instruction limit reached!
% 28.44/7.21 % (15575)------------------------------
% 28.44/7.21 % (15575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.44/7.21 % (15575)Termination reason: Unknown
% 28.44/7.21 % (15575)Termination phase: shuffling
% 28.44/7.21
% 28.44/7.21 % (15575)Memory used [KB]: 20596
% 28.44/7.21 % (15575)Time elapsed: 0.165 s
% 28.44/7.21 % (15575)Instructions burned: 563 (million)
% 28.44/7.21 % (15575)------------------------------
% 28.44/7.21 % (15575)------------------------------
% 28.44/7.22 % (15567)Instruction limit reached!
% 28.44/7.22 % (15567)------------------------------
% 28.44/7.22 % (15567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.44/7.22 % (15567)Termination reason: Unknown
% 28.44/7.22 % (15567)Termination phase: Property scanning
% 28.44/7.22
% 28.44/7.22 % (15567)Memory used [KB]: 29679
% 28.44/7.22 % (15567)Time elapsed: 0.493 s
% 28.44/7.22 % (15567)Instructions burned: 1764 (million)
% 28.44/7.22 % (15567)------------------------------
% 28.44/7.22 % (15567)------------------------------
% 28.44/7.22 % (15579)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_14919 for (2967ds/393Mi)
% 28.44/7.23 % (15554)Refutation found. Thanks to Tanya!
% 28.44/7.23 % SZS status Theorem for DTF2THF_14919
% 28.44/7.23 % SZS output start Proof for DTF2THF_14919
% 28.44/7.23 thf(type_def_5, type, rat: $tType).
% 28.44/7.23 thf(type_def_6, type, int: $tType).
% 28.44/7.23 thf(type_def_8, type, set_int: $tType).
% 28.44/7.23 thf(type_def_9, type, set_Pr958786334691620121nt_int: $tType).
% 28.44/7.23 thf(type_def_10, type, set_nat: $tType).
% 28.44/7.23 thf(type_def_11, type, set_Pr1261947904930325089at_nat: $tType).
% 28.44/7.23 thf(type_def_12, type, set_se7855581050983116737at_nat: $tType).
% 28.44/7.23 thf(type_def_13, type, set_Pr4329608150637261639at_nat: $tType).
% 28.44/7.23 thf(type_def_14, type, set_se5479201105039950375at_nat: $tType).
% 28.44/7.23 thf(type_def_15, type, set_Pr7459493094073627847at_nat: $tType).
% 28.44/7.23 thf(type_def_16, type, code_integer: $tType).
% 28.44/7.23 thf(type_def_17, type, nat: $tType).
% 28.44/7.23 thf(type_def_18, type, set_o: $tType).
% 28.44/7.23 thf(type_def_19, type, set_Product_prod_o_o: $tType).
% 28.44/7.23 thf(type_def_20, type, set_Pr3448869479623346877nt_nat: $tType).
% 28.44/7.23 thf(type_def_21, type, set_Pr7995236796853374141at_int: $tType).
% 28.44/7.23 thf(type_def_22, type, num: $tType).
% 28.44/7.23 thf(type_def_23, type, set_Pr6200539531224447659at_num: $tType).
% 28.44/7.23 thf(type_def_24, type, set_Pr4105333604307423337at_rat: $tType).
% 28.44/7.23 thf(type_def_25, type, set_num: $tType).
% 28.44/7.23 thf(type_def_26, type, set_Pr8218934625190621173um_num: $tType).
% 28.44/7.23 thf(type_def_27, type, set_Co4375521073081744395nteger: $tType).
% 28.44/7.23 thf(type_def_28, type, produc8923325533196201883nteger: $tType).
% 28.44/7.23 thf(type_def_29, type, set_Co726186806682698383nteger: $tType).
% 28.44/7.23 thf(type_def_30, type, set_int_int: $tType).
% 28.44/7.23 thf(type_def_31, type, set_int_nat: $tType).
% 28.44/7.23 thf(type_def_32, type, set_int_num: $tType).
% 28.44/7.23 thf(type_def_33, type, set_in6154042108061588260nt_int: $tType).
% 28.44/7.23 thf(type_def_34, type, product_prod_int_int: $tType).
% 28.44/7.23 thf(type_def_35, type, set_in7748886932685137004at_nat: $tType).
% 28.44/7.23 thf(type_def_36, type, product_prod_nat_nat: $tType).
% 28.44/7.23 thf(type_def_37, type, set_in3169746454734514176um_num: $tType).
% 28.44/7.23 thf(type_def_38, type, product_prod_num_num: $tType).
% 28.44/7.23 thf(type_def_39, type, set_li2168235667650531768at_nat: $tType).
% 28.44/7.23 thf(type_def_40, type, list_nat: $tType).
% 28.44/7.23 thf(type_def_41, type, set_nat_o: $tType).
% 28.44/7.23 thf(type_def_42, type, set_nat_nat: $tType).
% 28.44/7.23 thf(type_def_43, type, set_na7251125088705586816nt_int: $tType).
% 28.44/7.23 thf(type_def_44, type, set_na8845969913329135560at_nat: $tType).
% 28.44/7.23 thf(type_def_45, type, set_ra518564293221149304nt_int: $tType).
% 28.44/7.23 thf(type_def_46, type, set_ra2113409117844698048at_nat: $tType).
% 28.44/7.23 thf(type_def_47, type, set_ch6383161263842509759nt_int: $tType).
% 28.44/7.23 thf(type_def_48, type, char: $tType).
% 28.44/7.23 thf(type_def_49, type, set_ch7978006088466058503at_nat: $tType).
% 28.44/7.23 thf(type_def_50, type, product_unit: $tType).
% 28.44/7.23 thf(type_def_51, type, set_Code_integer: $tType).
% 28.44/7.23 thf(type_def_52, type, set_ref_a: $tType).
% 28.44/7.23 thf(type_def_53, type, ref_a: $tType).
% 28.44/7.23 thf(type_def_54, type, heap_e7401611519738050253t_unit: $tType).
% 28.44/7.23 thf(type_def_55, type, set_list_nat: $tType).
% 28.44/7.23 thf(type_def_56, type, set_Pr1133966238863718811t_unit: $tType).
% 28.44/7.23 thf(type_def_57, type, produc7812382424243267045t_unit: $tType).
% 28.44/7.23 thf(type_def_58, type, set_rat: $tType).
% 28.44/7.23 thf(type_def_59, type, set_char: $tType).
% 28.44/7.23 thf(type_def_60, type, produc101387210554329899nteger: $tType).
% 28.44/7.23 thf(type_def_61, type, product_prod_o_o: $tType).
% 28.44/7.23 thf(type_def_62, type, product_prod_o_nat: $tType).
% 28.44/7.23 thf(type_def_63, type, product_prod_nat_o: $tType).
% 28.44/7.23 thf(type_def_64, type, product_prod_num_nat: $tType).
% 28.44/7.23 thf(type_def_65, type, produc723880050079548563nteger: $tType).
% 28.44/7.23 thf(type_def_66, type, product_prod_int_nat: $tType).
% 28.44/7.23 thf(type_def_67, type, product_prod_nat_int: $tType).
% 28.44/7.23 thf(type_def_68, type, product_prod_nat_num: $tType).
% 28.44/7.23 thf(type_def_69, type, product_prod_num_o: $tType).
% 28.44/7.23 thf(type_def_70, type, produc3843707927480180839at_nat: $tType).
% 28.44/7.23 thf(type_def_71, type, set_Pr8415741480598773322nteger: $tType).
% 28.44/7.23 thf(type_def_72, type, produc2963269191615333738nteger: $tType).
% 28.44/7.23 thf(type_def_73, type, set_Pr49084382684228242at_int: $tType).
% 28.44/7.23 thf(type_def_74, type, produc859450856879609959at_nat: $tType).
% 28.44/7.23 thf(type_def_75, type, produc4196048018000912732at_int: $tType).
% 28.44/7.23 thf(type_def_76, type, set_o_o: $tType).
% 28.44/7.23 thf(type_def_77, type, set_o_nat: $tType).
% 28.44/7.23 thf(type_def_78, type, set_Product_unit: $tType).
% 28.44/7.23 thf(type_def_79, type, set_o_Product_unit: $tType).
% 28.44/7.23 thf(type_def_80, type, set_int_rat: $tType).
% 28.44/7.23 thf(type_def_81, type, set_nat_int: $tType).
% 28.44/7.23 thf(type_def_82, type, set_rat_o: $tType).
% 28.44/7.23 thf(type_def_83, type, set_rat_nat: $tType).
% 28.44/7.23 thf(type_def_84, type, set_rat_Product_unit: $tType).
% 28.44/7.23 thf(type_def_85, type, set_char_o: $tType).
% 28.44/7.23 thf(type_def_86, type, set_char_nat: $tType).
% 28.44/7.23 thf(type_def_87, type, set_ch7814610555394875923t_unit: $tType).
% 28.44/7.23 thf(type_def_88, type, produc1319942482725812455at_nat: $tType).
% 28.44/7.23 thf(type_def_89, type, set_he8644174446132254637t_unit: $tType).
% 28.44/7.23 thf(type_def_90, type, option_num: $tType).
% 28.44/7.23 thf(type_def_91, type, produc6271795597528267376eger_o: $tType).
% 28.44/7.23 thf(type_def_92, type, set_int_int_o: $tType).
% 28.44/7.23 thf(type_def_93, type, set_int_o: $tType).
% 28.44/7.23 thf(type_def_94, type, set_nat_nat_o: $tType).
% 28.44/7.23 thf(type_def_95, type, set_nat_num_o: $tType).
% 28.44/7.23 thf(type_def_96, type, set_Pr8049984349381595834_int_o: $tType).
% 28.44/7.23 thf(type_def_97, type, set_Pr5582243495563764594_nat_o: $tType).
% 28.44/7.23 thf(type_def_98, type, set_Pr7010166363911110284_nat_o: $tType).
% 28.44/7.23 thf(type_def_99, type, set_se9180647916752606350_nat_o: $tType).
% 28.44/7.23 thf(type_def_100, type, set_se7255092946006855566_nat_o: $tType).
% 28.44/7.23 thf(type_def_101, type, set_set_o: $tType).
% 28.44/7.23 thf(type_def_102, type, set_set_int: $tType).
% 28.44/7.23 thf(type_def_103, type, set_set_nat: $tType).
% 28.44/7.23 thf(type_def_104, type, set_se6260736226359567993nt_int: $tType).
% 28.44/7.23 thf(type_def_105, type, set_se4826145725398303499at_num: $tType).
% 28.44/7.23 thf(type_def_106, type, set_se6425085446898223655at_nat: $tType).
% 28.44/7.23 thf(type_def_107, type, set_Pr8693737435421807431at_nat: $tType).
% 28.44/7.23 thf(type_def_108, type, set_se7592288975875140775at_nat: $tType).
% 28.44/7.23 thf(type_def_109, type, set_set_Product_unit: $tType).
% 28.44/7.23 thf(type_def_110, type, set_set_rat: $tType).
% 28.44/7.23 thf(type_def_111, type, set_set_char: $tType).
% 28.44/7.23 thf(type_def_112, type, set_se4612898379794543757t_unit: $tType).
% 28.44/7.23 thf(type_def_113, type, produc8126358835630522215t_unit: $tType).
% 28.44/7.23 thf(type_def_114, type, produc5288414631154139675_ref_a: $tType).
% 28.44/7.23 thf(type_def_115, type, product_prod_o_int: $tType).
% 28.44/7.23 thf(type_def_116, type, product_prod_o_num: $tType).
% 28.44/7.23 thf(type_def_117, type, produc1799199577659733785_ref_a: $tType).
% 28.44/7.23 thf(type_def_118, type, set_Pr4111642102156807771nteger: $tType).
% 28.44/7.23 thf(type_def_119, type, set_Pr4811707699266497531nteger: $tType).
% 28.44/7.23 thf(type_def_120, type, set_Pr3280342998896498603um_nat: $tType).
% 28.44/7.23 thf(type_def_121, type, set_Pr5564308138774400199at_nat: $tType).
% 28.44/7.23 thf(type_def_122, type, heap_Heap_ref_a: $tType).
% 28.44/7.23 thf(type_def_123, type, heap_H6156071679106078628t_unit: $tType).
% 28.44/7.23 thf(type_def_124, type, heap_Heap_a: $tType).
% 28.44/7.23 thf(type_def_125, type, a: $tType).
% 28.44/7.23 thf(type_def_126, type, literal: $tType).
% 28.44/7.23 thf(type_def_127, type, produc4675096598859438275atural: $tType).
% 28.44/7.23 thf(type_def_128, type, set_Pr2101469702781467981_o_nat: $tType).
% 28.44/7.23 thf(type_def_129, type, set_Pr6671815714118170108t_unit: $tType).
% 28.44/7.23 thf(type_def_130, type, set_Pr3149072824959771635_nat_o: $tType).
% 28.44/7.23 thf(type_def_131, type, set_Pr4334478416066269672t_unit: $tType).
% 28.44/7.23 thf(type_def_132, type, set_Pr5464989305201766866unit_o: $tType).
% 28.44/7.23 thf(type_def_133, type, set_Pr1763845938948868674it_nat: $tType).
% 28.44/7.23 thf(type_def_134, type, set_Pr5094982260447487303t_unit: $tType).
% 28.44/7.23 thf(type_def_135, type, sum_sum_nat_nat: $tType).
% 28.44/7.23 thf(type_def_136, type, set_Pr2560585780119916871nt_int: $tType).
% 28.44/7.23 thf(type_def_137, type, pred_Product_unit: $tType).
% 28.44/7.23 thf(type_def_138, type, set_Pr3798168094891919931at_nat: $tType).
% 28.44/7.23 thf(type_def_139, type, set_int_char: $tType).
% 28.44/7.23 thf(type_def_140, type, set_nat_rat: $tType).
% 28.44/7.23 thf(type_def_141, type, set_nat_char: $tType).
% 28.44/7.23 thf(type_def_142, type, set_rat_rat: $tType).
% 28.44/7.23 thf(type_def_143, type, set_rat_char: $tType).
% 28.44/7.23 thf(type_def_144, type, set_char_rat: $tType).
% 28.44/7.23 thf(type_def_145, type, set_char_char: $tType).
% 28.44/7.23 thf(type_def_146, type, set_Pr2926629348867340898t_char: $tType).
% 28.44/7.23 thf(type_def_147, type, set_Pr3594552606344371909at_int: $tType).
% 28.44/7.23 thf(type_def_148, type, set_Pr6084635751276098665at_nat: $tType).
% 28.44/7.23 thf(type_def_149, type, set_Pr8928021450653196913at_rat: $tType).
% 28.44/7.23 thf(type_def_150, type, set_Pr8263365689940771946t_char: $tType).
% 28.44/7.23 thf(type_def_151, type, set_Pr8146363407509552702ar_int: $tType).
% 28.44/7.23 thf(type_def_152, type, set_Pr1413074515586503650ar_nat: $tType).
% 28.44/7.23 thf(type_def_153, type, set_Pr4256460214963601898ar_rat: $tType).
% 28.44/7.23 thf(type_def_154, type, set_Pr3309569728657787619r_char: $tType).
% 28.44/7.23 thf(type_def_155, type, set_Sum_sum_nat_nat: $tType).
% 28.44/7.23 thf(type_def_156, type, produc3788275437394581276t_unit: $tType).
% 28.44/7.23 thf(type_def_157, type, product_prod_int_o: $tType).
% 28.44/7.23 thf(type_def_158, type, produc6865911496949736918t_unit: $tType).
% 28.44/7.23 thf(type_def_159, type, product_prod_int_rat: $tType).
% 28.44/7.23 thf(type_def_160, type, produc526117512892780850t_unit: $tType).
% 28.44/7.23 thf(type_def_161, type, product_prod_nat_rat: $tType).
% 28.44/7.23 thf(type_def_162, type, produc7822875418678951345atural: $tType).
% 28.44/7.23 thf(type_def_163, type, produc1219242969750017639nt_int: $tType).
% 28.44/7.23 thf(type_def_164, type, produc349518998152878311at_nat: $tType).
% 28.44/7.23 thf(type_def_165, type, produc1906917888121415911at_nat: $tType).
% 28.44/7.23 thf(type_def_166, type, produc7485711547916492274unit_o: $tType).
% 28.44/7.23 thf(type_def_167, type, produc600557818389255820it_nat: $tType).
% 28.44/7.23 thf(type_def_168, type, produc8459935480633519975t_unit: $tType).
% 28.44/7.23 thf(type_def_169, type, produc6315701296850634900it_rat: $tType).
% 28.44/7.23 thf(type_def_170, type, product_prod_rat_int: $tType).
% 28.44/7.23 thf(type_def_171, type, product_prod_rat_nat: $tType).
% 28.44/7.23 thf(type_def_172, type, product_prod_rat_rat: $tType).
% 28.44/7.23 thf(type_def_173, type, set_Pr8834758594704517033_o_int: $tType).
% 28.44/7.23 thf(type_def_174, type, set_Pr903927857289325719_int_o: $tType).
% 28.44/7.23 thf(type_def_175, type, set_Pr5889264611543340172t_unit: $tType).
% 28.44/7.23 thf(type_def_176, type, set_Pr6292255179000445125nt_rat: $tType).
% 28.44/7.23 thf(type_def_177, type, set_Pr6123067485828015636nt_int: $tType).
% 28.44/7.23 thf(type_def_178, type, set_Pr7717912310451564380at_nat: $tType).
% 28.44/7.23 thf(type_def_179, type, set_Pr2543308735921124078nt_nat: $tType).
% 28.44/7.23 thf(type_def_180, type, set_Pr4155430604743465615at_nat: $tType).
% 28.44/7.23 thf(type_def_181, type, set_Pr6558897299634722526_nat_o: $tType).
% 28.44/7.23 thf(type_def_182, type, set_Pr2539167527615954998at_nat: $tType).
% 28.44/7.23 thf(type_def_183, type, set_Pr7098892610798258687nt_int: $tType).
% 28.44/7.23 thf(type_def_184, type, set_Pr4607231638325966922it_rat: $tType).
% 28.44/7.23 thf(type_def_185, type, produc3969062480670737046t_unit: $tType).
% 28.44/7.23 thf(type_def_186, type, produc8483956148555600810_a_int: $tType).
% 28.44/7.23 thf(type_def_187, type, produc5066145461314735602t_unit: $tType).
% 28.44/7.23 thf(type_def_188, type, produc3438435131210021710_a_nat: $tType).
% 28.44/7.23 thf(type_def_189, type, produc4146679068158859416_a_num: $tType).
% 28.44/7.23 thf(type_def_190, type, produc3629471303718939987t_unit: $tType).
% 28.44/7.23 thf(type_def_191, type, produc5561445381605014009at_nat: $tType).
% 28.44/7.23 thf(type_def_192, type, produc2296667697112141421t_unit: $tType).
% 28.44/7.23 thf(type_def_193, type, produc4041253808165279839at_nat: $tType).
% 28.44/7.23 thf(type_def_194, type, produc3922234789054302210ar_nat: $tType).
% 28.44/7.23 thf(type_def_195, type, produc414006230660905482ar_rat: $tType).
% 28.44/7.23 thf(type_def_196, type, produc143505574896075907r_char: $tType).
% 28.44/7.23 thf(type_def_197, type, produc8967755806399881310ar_int: $tType).
% 28.44/7.23 thf(type_def_198, type, produc3346328345660746739nteger: $tType).
% 28.44/7.23 thf(type_def_199, type, produc6945250483304103390nt_int: $tType).
% 28.44/7.23 thf(type_def_200, type, produc7248412053542808358at_nat: $tType).
% 28.44/7.23 thf(type_def_201, type, produc1709102135585200056nt_nat: $tType).
% 28.44/7.23 thf(type_def_202, type, produc1522404539988722607at_nat: $tType).
% 28.44/7.23 thf(type_def_203, type, produc8373899037510109440at_nat: $tType).
% 28.44/7.23 thf(type_def_204, type, produc556289286640904991nt_int: $tType).
% 28.44/7.23 thf(type_def_205, type, produc652263959640188542_nat_o: $tType).
% 28.44/7.23 thf(type_def_206, type, ref_ref_a: $tType).
% 28.44/7.23 thf(type_def_207, type, set_Pr553994874890374343at_nat: $tType).
% 28.44/7.23 thf(type_def_208, type, set_Pr5908833319024110760_num_o: $tType).
% 28.44/7.23 thf(type_def_209, type, set_Pr7669914128964046860_nat_o: $tType).
% 28.44/7.23 thf(func_def_0, type, set_se7592288975875140775at_nat: $tType).
% 28.44/7.23 thf(func_def_1, type, set_Pr7669914128964046860_nat_o: $tType).
% 28.44/7.23 thf(func_def_2, type, set_Pr7459493094073627847at_nat: $tType).
% 28.44/7.23 thf(func_def_3, type, set_se7255092946006855566_nat_o: $tType).
% 28.44/7.23 thf(func_def_4, type, produc1319942482725812455at_nat: $tType).
% 28.44/7.23 thf(func_def_5, type, produc101387210554329899nteger: $tType).
% 28.44/7.23 thf(func_def_6, type, set_Pr5564308138774400199at_nat: $tType).
% 28.44/7.23 thf(func_def_7, type, produc1906917888121415911at_nat: $tType).
% 28.44/7.23 thf(func_def_8, type, set_Pr553994874890374343at_nat: $tType).
% 28.44/7.23 thf(func_def_9, type, produc349518998152878311at_nat: $tType).
% 28.44/7.23 thf(func_def_10, type, produc2296667697112141421t_unit: $tType).
% 28.44/7.23 thf(func_def_11, type, produc4041253808165279839at_nat: $tType).
% 28.44/7.23 thf(func_def_12, type, set_se5479201105039950375at_nat: $tType).
% 28.44/7.23 thf(func_def_13, type, set_Pr7010166363911110284_nat_o: $tType).
% 28.44/7.23 thf(func_def_14, type, set_Pr4111642102156807771nteger: $tType).
% 28.44/7.23 thf(func_def_15, type, set_Pr4329608150637261639at_nat: $tType).
% 28.44/7.23 thf(func_def_16, type, set_se9180647916752606350_nat_o: $tType).
% 28.44/7.23 thf(func_def_17, type, set_se6425085446898223655at_nat: $tType).
% 28.44/7.23 thf(func_def_18, type, produc3843707927480180839at_nat: $tType).
% 28.44/7.23 thf(func_def_19, type, produc4675096598859438275atural: $tType).
% 28.44/7.23 thf(func_def_20, type, produc723880050079548563nteger: $tType).
% 28.44/7.23 thf(func_def_21, type, produc3629471303718939987t_unit: $tType).
% 28.44/7.23 thf(func_def_22, type, set_Pr8693737435421807431at_nat: $tType).
% 28.44/7.23 thf(func_def_23, type, set_Pr7098892610798258687nt_int: $tType).
% 28.44/7.23 thf(func_def_24, type, set_Pr4155430604743465615at_nat: $tType).
% 28.44/7.23 thf(func_def_25, type, set_Pr2560585780119916871nt_int: $tType).
% 28.44/7.23 thf(func_def_26, type, produc3346328345660746739nteger: $tType).
% 28.44/7.23 thf(func_def_27, type, produc8126358835630522215t_unit: $tType).
% 28.44/7.23 thf(func_def_28, type, produc859450856879609959at_nat: $tType).
% 28.44/7.23 thf(func_def_29, type, produc556289286640904991nt_int: $tType).
% 28.44/7.23 thf(func_def_30, type, produc1522404539988722607at_nat: $tType).
% 28.44/7.23 thf(func_def_31, type, produc1219242969750017639nt_int: $tType).
% 28.44/7.23 thf(func_def_32, type, set_Pr3798168094891919931at_nat: $tType).
% 28.44/7.23 thf(func_def_33, type, set_Pr1133966238863718811t_unit: $tType).
% 28.44/7.23 thf(func_def_34, type, produc5561445381605014009at_nat: $tType).
% 28.44/7.23 thf(func_def_35, type, set_Co4375521073081744395nteger: $tType).
% 28.44/7.23 thf(func_def_36, type, set_Pr2539167527615954998at_nat: $tType).
% 28.44/7.23 thf(func_def_37, type, set_Pr49084382684228242at_int: $tType).
% 28.44/7.23 thf(func_def_38, type, set_Pr2543308735921124078nt_nat: $tType).
% 28.44/7.23 thf(func_def_39, type, set_Pr7717912310451564380at_nat: $tType).
% 28.44/7.23 thf(func_def_40, type, set_Pr6123067485828015636nt_int: $tType).
% 28.44/7.23 thf(func_def_41, type, set_li2168235667650531768at_nat: $tType).
% 28.44/7.23 thf(func_def_42, type, produc7812382424243267045t_unit: $tType).
% 28.44/7.23 thf(func_def_43, type, produc1799199577659733785_ref_a: $tType).
% 28.44/7.23 thf(func_def_44, type, set_Pr6558897299634722526_nat_o: $tType).
% 28.44/7.23 thf(func_def_45, type, set_Pr4811707699266497531nteger: $tType).
% 28.44/7.23 thf(func_def_46, type, produc5066145461314735602t_unit: $tType).
% 28.44/7.23 thf(func_def_47, type, produc3969062480670737046t_unit: $tType).
% 28.44/7.23 thf(func_def_48, type, produc8373899037510109440at_nat: $tType).
% 28.44/7.23 thf(func_def_49, type, produc4196048018000912732at_int: $tType).
% 28.44/7.23 thf(func_def_50, type, produc1709102135585200056nt_nat: $tType).
% 28.44/7.23 thf(func_def_51, type, produc7248412053542808358at_nat: $tType).
% 28.44/7.23 thf(func_def_52, type, produc6945250483304103390nt_int: $tType).
% 28.44/7.23 thf(func_def_53, type, set_Pr5094982260447487303t_unit: $tType).
% 28.44/7.23 thf(func_def_54, type, set_ch7978006088466058503at_nat: $tType).
% 28.44/7.23 thf(func_def_55, type, set_ch6383161263842509759nt_int: $tType).
% 28.44/7.23 thf(func_def_56, type, set_ra2113409117844698048at_nat: $tType).
% 28.44/7.23 thf(func_def_57, type, set_ra518564293221149304nt_int: $tType).
% 28.44/7.23 thf(func_def_58, type, set_na8845969913329135560at_nat: $tType).
% 28.44/7.23 thf(func_def_59, type, set_na7251125088705586816nt_int: $tType).
% 28.44/7.23 thf(func_def_60, type, set_in3169746454734514176um_num: $tType).
% 28.44/7.23 thf(func_def_61, type, set_in7748886932685137004at_nat: $tType).
% 28.44/7.23 thf(func_def_62, type, set_in6154042108061588260nt_int: $tType).
% 28.44/7.23 thf(func_def_63, type, set_se4612898379794543757t_unit: $tType).
% 28.44/7.23 thf(func_def_64, type, produc652263959640188542_nat_o: $tType).
% 28.44/7.23 thf(func_def_65, type, set_se4826145725398303499at_num: $tType).
% 28.44/7.23 thf(func_def_66, type, set_se7855581050983116737at_nat: $tType).
% 28.44/7.23 thf(func_def_67, type, set_se6260736226359567993nt_int: $tType).
% 28.44/7.23 thf(func_def_68, type, set_Pr8415741480598773322nteger: $tType).
% 28.44/7.23 thf(func_def_69, type, produc7822875418678951345atural: $tType).
% 28.44/7.23 thf(func_def_70, type, produc8923325533196201883nteger: $tType).
% 28.44/7.23 thf(func_def_71, type, set_Pr4607231638325966922it_rat: $tType).
% 28.44/7.23 thf(func_def_72, type, set_Pr1763845938948868674it_nat: $tType).
% 28.44/7.23 thf(func_def_73, type, set_Pr4334478416066269672t_unit: $tType).
% 28.44/7.23 thf(func_def_74, type, set_Pr5889264611543340172t_unit: $tType).
% 28.44/7.23 thf(func_def_75, type, set_Pr5908833319024110760_num_o: $tType).
% 28.44/7.23 thf(func_def_76, type, set_Pr5582243495563764594_nat_o: $tType).
% 28.44/7.23 thf(func_def_77, type, set_Pr8049984349381595834_int_o: $tType).
% 28.44/7.23 thf(func_def_78, type, set_Co726186806682698383nteger: $tType).
% 28.44/7.23 thf(func_def_79, type, produc8459935480633519975t_unit: $tType).
% 28.44/7.23 thf(func_def_80, type, set_Pr3309569728657787619r_char: $tType).
% 28.44/7.23 thf(func_def_81, type, set_Pr4256460214963601898ar_rat: $tType).
% 28.44/7.23 thf(func_def_82, type, set_Pr1413074515586503650ar_nat: $tType).
% 28.44/7.23 thf(func_def_83, type, set_Pr8146363407509552702ar_int: $tType).
% 28.44/7.23 thf(func_def_84, type, set_Pr8263365689940771946t_char: $tType).
% 28.44/7.23 thf(func_def_85, type, set_Pr5464989305201766866unit_o: $tType).
% 28.44/7.23 thf(func_def_86, type, set_Pr2926629348867340898t_char: $tType).
% 28.44/7.23 thf(func_def_87, type, set_Pr6671815714118170108t_unit: $tType).
% 28.44/7.23 thf(func_def_88, type, produc5288414631154139675_ref_a: $tType).
% 28.44/7.23 thf(func_def_89, type, set_he8644174446132254637t_unit: $tType).
% 28.44/7.23 thf(func_def_90, type, set_Pr8928021450653196913at_rat: $tType).
% 28.44/7.23 thf(func_def_91, type, set_Pr6084635751276098665at_nat: $tType).
% 28.44/7.23 thf(func_def_92, type, set_Pr3594552606344371909at_int: $tType).
% 28.44/7.23 thf(func_def_93, type, set_Pr8218934625190621173um_num: $tType).
% 28.44/7.23 thf(func_def_94, type, set_Pr3280342998896498603um_nat: $tType).
% 28.44/7.23 thf(func_def_95, type, set_Pr4105333604307423337at_rat: $tType).
% 28.44/7.23 thf(func_def_96, type, set_Pr6200539531224447659at_num: $tType).
% 28.44/7.23 thf(func_def_97, type, set_Pr1261947904930325089at_nat: $tType).
% 28.44/7.23 thf(func_def_98, type, set_Pr7995236796853374141at_int: $tType).
% 28.44/7.23 thf(func_def_99, type, set_Pr6292255179000445125nt_rat: $tType).
% 28.44/7.23 thf(func_def_100, type, set_Pr3448869479623346877nt_nat: $tType).
% 28.44/7.23 thf(func_def_101, type, set_Pr958786334691620121nt_int: $tType).
% 28.44/7.23 thf(func_def_102, type, produc2963269191615333738nteger: $tType).
% 28.44/7.23 thf(func_def_103, type, produc6315701296850634900it_rat: $tType).
% 28.44/7.23 thf(func_def_104, type, produc600557818389255820it_nat: $tType).
% 28.44/7.23 thf(func_def_105, type, produc526117512892780850t_unit: $tType).
% 28.44/7.23 thf(func_def_106, type, produc6865911496949736918t_unit: $tType).
% 28.44/7.23 thf(func_def_107, type, set_ch7814610555394875923t_unit: $tType).
% 28.44/7.23 thf(func_def_108, type, set_Sum_sum_nat_nat: $tType).
% 28.44/7.23 thf(func_def_109, type, produc4146679068158859416_a_num: $tType).
% 28.44/7.23 thf(func_def_110, type, produc3438435131210021710_a_nat: $tType).
% 28.44/7.23 thf(func_def_111, type, produc8483956148555600810_a_int: $tType).
% 28.44/7.23 thf(func_def_112, type, set_rat_Product_unit: $tType).
% 28.44/7.23 thf(func_def_113, type, set_nat_num_o: $tType).
% 28.44/7.23 thf(func_def_114, type, set_nat_nat_o: $tType).
% 28.44/7.23 thf(func_def_115, type, set_int_int_o: $tType).
% 28.44/7.23 thf(func_def_116, type, produc143505574896075907r_char: $tType).
% 28.44/7.23 thf(func_def_117, type, set_Pr3149072824959771635_nat_o: $tType).
% 28.44/7.23 thf(func_def_118, type, set_Pr903927857289325719_int_o: $tType).
% 28.44/7.23 thf(func_def_119, type, set_Pr2101469702781467981_o_nat: $tType).
% 28.44/7.23 thf(func_def_120, type, set_Pr8834758594704517033_o_int: $tType).
% 28.44/7.23 thf(func_def_121, type, produc6271795597528267376eger_o: $tType).
% 28.44/7.23 thf(func_def_122, type, produc414006230660905482ar_rat: $tType).
% 28.44/7.23 thf(func_def_123, type, produc3922234789054302210ar_nat: $tType).
% 28.44/7.23 thf(func_def_124, type, produc8967755806399881310ar_int: $tType).
% 28.44/7.23 thf(func_def_125, type, produc7485711547916492274unit_o: $tType).
% 28.44/7.23 thf(func_def_126, type, produc3788275437394581276t_unit: $tType).
% 28.44/7.23 thf(func_def_127, type, set_char_char: $tType).
% 28.44/7.23 thf(func_def_128, type, set_set_Product_unit: $tType).
% 28.44/7.23 thf(func_def_129, type, heap_e7401611519738050253t_unit: $tType).
% 28.44/7.23 thf(func_def_130, type, product_prod_rat_rat: $tType).
% 28.44/7.23 thf(func_def_131, type, product_prod_rat_nat: $tType).
% 28.44/7.23 thf(func_def_132, type, product_prod_rat_int: $tType).
% 28.44/7.23 thf(func_def_133, type, product_prod_num_num: $tType).
% 28.44/7.23 thf(func_def_134, type, product_prod_num_nat: $tType).
% 28.44/7.23 thf(func_def_135, type, product_prod_nat_rat: $tType).
% 28.44/7.23 thf(func_def_136, type, product_prod_nat_num: $tType).
% 28.44/7.23 thf(func_def_137, type, product_prod_nat_nat: $tType).
% 28.44/7.23 thf(func_def_138, type, product_prod_nat_int: $tType).
% 28.44/7.23 thf(func_def_139, type, product_prod_int_rat: $tType).
% 28.44/7.23 thf(func_def_140, type, product_prod_int_nat: $tType).
% 28.44/7.23 thf(func_def_141, type, product_prod_int_int: $tType).
% 28.44/7.23 thf(func_def_142, type, set_char_rat: $tType).
% 28.44/7.23 thf(func_def_143, type, set_char_nat: $tType).
% 28.44/7.23 thf(func_def_144, type, set_rat_char: $tType).
% 28.44/7.23 thf(func_def_145, type, set_nat_char: $tType).
% 28.44/7.23 thf(func_def_146, type, set_int_char: $tType).
% 28.44/7.23 thf(func_def_147, type, set_o_Product_unit: $tType).
% 28.44/7.23 thf(func_def_148, type, set_Product_prod_o_o: $tType).
% 28.44/7.23 thf(func_def_149, type, heap_H6156071679106078628t_unit: $tType).
% 28.44/7.23 thf(func_def_150, type, sum_sum_nat_nat: $tType).
% 28.44/7.23 thf(func_def_151, type, set_rat_rat: $tType).
% 28.44/7.23 thf(func_def_152, type, set_rat_nat: $tType).
% 28.44/7.23 thf(func_def_153, type, set_nat_rat: $tType).
% 28.44/7.23 thf(func_def_154, type, set_nat_nat: $tType).
% 28.44/7.23 thf(func_def_155, type, set_nat_int: $tType).
% 28.44/7.23 thf(func_def_156, type, set_int_rat: $tType).
% 28.44/7.23 thf(func_def_157, type, set_int_num: $tType).
% 28.44/7.23 thf(func_def_158, type, set_int_nat: $tType).
% 28.44/7.23 thf(func_def_159, type, set_int_int: $tType).
% 28.44/7.23 thf(func_def_160, type, heap_Heap_ref_a: $tType).
% 28.44/7.23 thf(func_def_161, type, set_set_char: $tType).
% 28.44/7.23 thf(func_def_162, type, pred_Product_unit: $tType).
% 28.44/7.23 thf(func_def_163, type, set_list_nat: $tType).
% 28.44/7.23 thf(func_def_164, type, product_prod_num_o: $tType).
% 28.44/7.23 thf(func_def_165, type, product_prod_nat_o: $tType).
% 28.44/7.23 thf(func_def_166, type, product_prod_int_o: $tType).
% 28.44/7.23 thf(func_def_167, type, product_prod_o_num: $tType).
% 28.44/7.23 thf(func_def_168, type, product_prod_o_nat: $tType).
% 28.44/7.23 thf(func_def_169, type, product_prod_o_int: $tType).
% 28.44/7.23 thf(func_def_170, type, set_char_o: $tType).
% 28.44/7.23 thf(func_def_171, type, set_set_rat: $tType).
% 28.44/7.23 thf(func_def_172, type, set_set_nat: $tType).
% 28.44/7.23 thf(func_def_173, type, set_set_int: $tType).
% 28.44/7.23 thf(func_def_174, type, set_Code_integer: $tType).
% 28.44/7.23 thf(func_def_175, type, set_Product_unit: $tType).
% 28.44/7.23 thf(func_def_176, type, set_rat_o: $tType).
% 28.44/7.23 thf(func_def_177, type, set_nat_o: $tType).
% 28.44/7.23 thf(func_def_178, type, set_int_o: $tType).
% 28.44/7.23 thf(func_def_179, type, set_o_nat: $tType).
% 28.44/7.23 thf(func_def_180, type, ref_ref_a: $tType).
% 28.44/7.23 thf(func_def_181, type, set_ref_a: $tType).
% 28.44/7.23 thf(func_def_182, type, product_prod_o_o: $tType).
% 28.44/7.23 thf(func_def_183, type, set_set_o: $tType).
% 28.44/7.23 thf(func_def_184, type, option_num: $tType).
% 28.44/7.23 thf(func_def_185, type, set_char: $tType).
% 28.44/7.23 thf(func_def_186, type, set_o_o: $tType).
% 28.44/7.23 thf(func_def_187, type, heap_Heap_a: $tType).
% 28.44/7.23 thf(func_def_188, type, list_nat: $tType).
% 28.44/7.23 thf(func_def_189, type, set_rat: $tType).
% 28.44/7.23 thf(func_def_190, type, set_num: $tType).
% 28.44/7.23 thf(func_def_191, type, set_nat: $tType).
% 28.44/7.23 thf(func_def_192, type, set_int: $tType).
% 28.44/7.23 thf(func_def_193, type, code_integer: $tType).
% 28.44/7.23 thf(func_def_194, type, product_unit: $tType).
% 28.44/7.23 thf(func_def_195, type, ref_a: $tType).
% 28.44/7.23 thf(func_def_196, type, literal: $tType).
% 28.44/7.23 thf(func_def_197, type, set_o: $tType).
% 28.44/7.23 thf(func_def_198, type, char: $tType).
% 28.44/7.23 thf(func_def_199, type, rat: $tType).
% 28.44/7.23 thf(func_def_200, type, num: $tType).
% 28.44/7.23 thf(func_def_201, type, nat: $tType).
% 28.44/7.23 thf(func_def_202, type, int: $tType).
% 28.44/7.23 thf(func_def_203, type, a: $tType).
% 28.44/7.23 thf(func_def_204, type, archim3151403230148437115or_rat: rat > int).
% 28.44/7.23 thf(func_def_205, type, bNF_Ca5157130669891357211al_int: set_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_206, type, bNF_Ca5159621140400407487al_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_207, type, bNF_Ca8448034394003515314at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_208, type, bNF_Ca6037544080215331608at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_209, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_210, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_211, type, bNF_Ca402612664642806191nteger: set_Pr958786334691620121nt_int > (int > code_integer) > $o).
% 28.44/7.23 thf(func_def_212, type, bNF_Ca1965613569405424510nt_int: set_Pr958786334691620121nt_int > (int > int) > $o).
% 28.44/7.23 thf(func_def_213, type, bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > (int > nat) > $o).
% 28.44/7.23 thf(func_def_214, type, bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > (int > rat) > $o).
% 28.44/7.23 thf(func_def_215, type, bNF_Ca30959104405961555nteger: set_Pr1261947904930325089at_nat > (nat > code_integer) > $o).
% 28.44/7.23 thf(func_def_216, type, bNF_Ca966259857504369954at_int: set_Pr1261947904930325089at_nat > (nat > int) > $o).
% 28.44/7.23 thf(func_def_217, type, bNF_Ca968750328013420230at_nat: set_Pr1261947904930325089at_nat > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_218, type, bNF_Ca333620267926924494at_rat: set_Pr1261947904930325089at_nat > (nat > rat) > $o).
% 28.44/7.23 thf(func_def_219, type, bNF_Ca4946600973702282345at_int: set_Pr4329608150637261639at_nat > (set_Pr1261947904930325089at_nat > int) > $o).
% 28.44/7.23 thf(func_def_220, type, bNF_Ca4949091444211332621at_nat: set_Pr4329608150637261639at_nat > (set_Pr1261947904930325089at_nat > nat) > $o).
% 28.44/7.23 thf(func_def_221, type, bNF_Gr_o_o: set_o > ($o > $o) > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_222, type, bNF_Gr_int_int: set_int > (int > int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_223, type, bNF_Gr_int_nat: set_int > (int > nat) > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_224, type, bNF_Gr_nat_int: set_nat > (nat > int) > set_Pr7995236796853374141at_int).
% 28.44/7.23 thf(func_def_225, type, bNF_Gr_nat_nat: set_nat > (nat > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_226, type, bNF_Gr_nat_num: set_nat > (nat > num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_227, type, bNF_Gr_nat_rat: set_nat > (nat > rat) > set_Pr4105333604307423337at_rat).
% 28.44/7.23 thf(func_def_228, type, bNF_Gr_num_num: set_num > (num > num) > set_Pr8218934625190621173um_num).
% 28.44/7.23 thf(func_def_229, type, bNF_Gr1527221351080490466at_nat: set_se7855581050983116737at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_230, type, bNF_Gr7888059597227825506at_nat: set_se5479201105039950375at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_231, type, bNF_Gr1453458339979195462nteger: set_Co4375521073081744395nteger > ((code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_232, type, bNF_Gr4092539093814444494nteger: set_Co726186806682698383nteger > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_233, type, bNF_Gr2243168462153404386nt_nat: set_int_int > ((int > int) > int > nat) > (int > int) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_234, type, bNF_Gr6763702254253555408nt_num: set_int_nat > ((int > nat) > int > num) > (int > nat) > (int > num) > $o).
% 28.44/7.23 thf(func_def_235, type, bNF_Gr318824752125099290nt_num: set_int_num > ((int > num) > int > num) > (int > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_236, type, bNF_Gr952524912132828525nt_int: set_in6154042108061588260nt_int > ((int > product_prod_int_int) > int > int) > (int > product_prod_int_int) > (int > int) > $o).
% 28.44/7.23 thf(func_def_237, type, bNF_Gr1462982377596425817nt_nat: set_in7748886932685137004at_nat > ((int > product_prod_nat_nat) > int > nat) > (int > product_prod_nat_nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_238, type, bNF_Gr5590197745039885111nt_num: set_in3169746454734514176um_num > ((int > product_prod_num_num) > int > num) > (int > product_prod_num_num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_239, type, bNF_Gr1532745923208276441at_nat: set_li2168235667650531768at_nat > ((list_nat > product_prod_nat_nat) > list_nat > nat) > (list_nat > product_prod_nat_nat) > (list_nat > nat) > $o).
% 28.44/7.23 thf(func_def_240, type, bNF_Grp_nat_o_nat_o: set_nat_o > ((nat > $o) > nat > $o) > (nat > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_241, type, bNF_Gr3847987472475283150at_nat: set_nat_nat > ((nat > nat) > nat > nat) > (nat > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_242, type, bNF_Gr2878093617000900205at_int: set_na7251125088705586816nt_int > ((nat > product_prod_int_int) > nat > int) > (nat > product_prod_int_int) > (nat > int) > $o).
% 28.44/7.23 thf(func_def_243, type, bNF_Gr3388551082464497497at_nat: set_na8845969913329135560at_nat > ((nat > product_prod_nat_nat) > nat > nat) > (nat > product_prod_nat_nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_244, type, bNF_Gr6858100456814184557at_int: set_ra518564293221149304nt_int > ((rat > product_prod_int_int) > rat > int) > (rat > product_prod_int_int) > (rat > int) > $o).
% 28.44/7.23 thf(func_def_245, type, bNF_Gr7368557922277781849at_nat: set_ra2113409117844698048at_nat > ((rat > product_prod_nat_nat) > rat > nat) > (rat > product_prod_nat_nat) > (rat > nat) > $o).
% 28.44/7.23 thf(func_def_246, type, bNF_Gr6947267152677263533ar_int: set_ch6383161263842509759nt_int > ((char > product_prod_int_int) > char > int) > (char > product_prod_int_int) > (char > int) > $o).
% 28.44/7.23 thf(func_def_247, type, bNF_Gr1779741795384719769ar_nat: set_ch7978006088466058503at_nat > ((char > product_prod_nat_nat) > char > nat) > (char > product_prod_nat_nat) > (char > nat) > $o).
% 28.44/7.23 thf(func_def_248, type, bNF_Grp_o_o: set_o > ($o > $o) > $o > $o > $o).
% 28.44/7.23 thf(func_def_249, type, bNF_Gr395642070819736771t_unit: set_o > ($o > product_unit) > $o > product_unit > $o).
% 28.44/7.23 thf(func_def_250, type, bNF_Grp_o_rat: set_o > ($o > rat) > $o > rat > $o).
% 28.44/7.23 thf(func_def_251, type, bNF_Grp_o_char: set_o > ($o > char) > $o > char > $o).
% 28.44/7.23 thf(func_def_252, type, bNF_Gr6045950513751025625er_int: set_Code_integer > (code_integer > int) > code_integer > int > $o).
% 28.44/7.23 thf(func_def_253, type, bNF_Gr6510375311308651680t_unit: set_ref_a > (ref_a > heap_e7401611519738050253t_unit) > ref_a > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_254, type, bNF_Gr6684649993275963353nteger: set_int > (int > code_integer) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_255, type, bNF_Grp_int_int: set_int > (int > int) > int > int > $o).
% 28.44/7.23 thf(func_def_256, type, bNF_Grp_int_nat: set_int > (int > nat) > int > nat > $o).
% 28.44/7.23 thf(func_def_257, type, bNF_Grp_int_num: set_int > (int > num) > int > num > $o).
% 28.44/7.23 thf(func_def_258, type, bNF_Gr6591314147588017797at_nat: set_int > (int > product_prod_nat_nat) > int > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_259, type, bNF_Grp_int_rat: set_int > (int > rat) > int > rat > $o).
% 28.44/7.23 thf(func_def_260, type, bNF_Grp_int_char: set_int > (int > char) > int > char > $o).
% 28.44/7.23 thf(func_def_261, type, bNF_Grp_list_nat_int: set_list_nat > (list_nat > int) > list_nat > int > $o).
% 28.44/7.23 thf(func_def_262, type, bNF_Gr600725020315365264st_nat: set_list_nat > (list_nat > list_nat) > list_nat > list_nat > $o).
% 28.44/7.23 thf(func_def_263, type, bNF_Gr4119388860389678161at_nat: set_list_nat > (list_nat > product_prod_nat_nat) > list_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_264, type, bNF_Grp_nat_o: set_nat > (nat > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_265, type, bNF_Grp_nat_int: set_nat > (nat > int) > nat > int > $o).
% 28.44/7.23 thf(func_def_266, type, bNF_Grp_nat_nat: set_nat > (nat > nat) > nat > nat > $o).
% 28.44/7.23 thf(func_def_267, type, bNF_Grp_nat_num: set_nat > (nat > num) > nat > num > $o).
% 28.44/7.23 thf(func_def_268, type, bNF_Gr3553472063123884001at_nat: set_nat > (nat > product_prod_nat_nat) > nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_269, type, bNF_Gr1993012052113314029t_unit: set_nat > (nat > product_unit) > nat > product_unit > $o).
% 28.44/7.23 thf(func_def_270, type, bNF_Grp_nat_rat: set_nat > (nat > rat) > nat > rat > $o).
% 28.44/7.23 thf(func_def_271, type, bNF_Grp_nat_char: set_nat > (nat > char) > nat > char > $o).
% 28.44/7.23 thf(func_def_272, type, bNF_Grp_num_num: set_num > (num > num) > num > num > $o).
% 28.44/7.23 thf(func_def_273, type, bNF_Gr5237703264515865432t_unit: set_Pr1133966238863718811t_unit > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_274, type, bNF_Gr5964920315653434322_ref_a: set_Pr1133966238863718811t_unit > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > ref_a > $o).
% 28.44/7.23 thf(func_def_275, type, bNF_Gr2749509334501985047nt_int: set_Pr958786334691620121nt_int > (product_prod_int_int > int) > product_prod_int_int > int > $o).
% 28.44/7.23 thf(func_def_276, type, bNF_Gr8532703628021589765nt_num: set_Pr958786334691620121nt_int > (product_prod_int_int > num) > product_prod_int_int > num > $o).
% 28.44/7.23 thf(func_def_277, type, bNF_Gr8859634586176591525_nat_o: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o > $o).
% 28.44/7.23 thf(func_def_278, type, bNF_Gr190934199572118623at_int: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > int) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_279, type, bNF_Gr193424670081168899at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat) > product_prod_nat_nat > nat > $o).
% 28.44/7.23 thf(func_def_280, type, bNF_Gr5974128493091723341at_num: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > num) > product_prod_nat_nat > num > $o).
% 28.44/7.23 thf(func_def_281, type, bNF_Gr7275288873855648526at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_282, type, bNF_Grp_rat_int: set_rat > (rat > int) > rat > int > $o).
% 28.44/7.23 thf(func_def_283, type, bNF_Grp_rat_nat: set_rat > (rat > nat) > rat > nat > $o).
% 28.44/7.23 thf(func_def_284, type, bNF_Gr6883301533820405721at_nat: set_rat > (rat > product_prod_nat_nat) > rat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_285, type, bNF_Grp_rat_rat: set_rat > (rat > rat) > rat > rat > $o).
% 28.44/7.23 thf(func_def_286, type, bNF_Grp_rat_char: set_rat > (rat > char) > rat > char > $o).
% 28.44/7.23 thf(func_def_287, type, bNF_Gr6677838525845560078at_nat: set_se7855581050983116737at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_288, type, bNF_Grp_char_int: set_char > (char > int) > char > int > $o).
% 28.44/7.23 thf(func_def_289, type, bNF_Grp_char_nat: set_char > (char > nat) > char > nat > $o).
% 28.44/7.23 thf(func_def_290, type, bNF_Gr8982933507515605408at_nat: set_char > (char > product_prod_nat_nat) > char > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_291, type, bNF_Grp_char_rat: set_char > (char > rat) > char > rat > $o).
% 28.44/7.23 thf(func_def_292, type, bNF_Grp_char_char: set_char > (char > char) > char > char > $o).
% 28.44/7.23 thf(func_def_293, type, bNF_co1764293801198077070nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > produc101387210554329899nteger).
% 28.44/7.23 thf(func_def_294, type, bNF_convol_o_o_o: ($o > $o) > ($o > $o) > $o > product_prod_o_o).
% 28.44/7.23 thf(func_def_295, type, bNF_convol_o_o_nat: ($o > $o) > ($o > nat) > $o > product_prod_o_nat).
% 28.44/7.23 thf(func_def_296, type, bNF_convol_o_nat_o: ($o > nat) > ($o > $o) > $o > product_prod_nat_o).
% 28.44/7.23 thf(func_def_297, type, bNF_convol_o_nat_nat: ($o > nat) > ($o > nat) > $o > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_298, type, bNF_convol_o_num_nat: ($o > num) > ($o > nat) > $o > product_prod_num_nat).
% 28.44/7.23 thf(func_def_299, type, bNF_co6169604788974073338nteger: (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > code_integer > produc723880050079548563nteger).
% 28.44/7.23 thf(func_def_300, type, bNF_co3156833790671340178nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > produc101387210554329899nteger).
% 28.44/7.23 thf(func_def_301, type, bNF_co2174166945328636015nt_int: (int > int) > (int > int) > int > product_prod_int_int).
% 28.44/7.23 thf(func_def_302, type, bNF_co2176657415837686291nt_nat: (int > int) > (int > nat) > int > product_prod_int_nat).
% 28.44/7.23 thf(func_def_303, type, bNF_co1174813233427581459at_int: (int > nat) > (int > int) > int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_304, type, bNF_co1177303703936631735at_nat: (int > nat) > (int > nat) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_305, type, bNF_co6958007526947186177at_num: (int > nat) > (int > num) > int > product_prod_nat_num).
% 28.44/7.23 thf(func_def_306, type, bNF_co8531006144098876929um_nat: (int > num) > (int > nat) > int > product_prod_num_nat).
% 28.44/7.23 thf(func_def_307, type, bNF_co5088337930254655563um_num: (int > num) > (int > num) > int > product_prod_num_num).
% 28.44/7.23 thf(func_def_308, type, bNF_convol_nat_o_o: (nat > $o) > (nat > $o) > nat > product_prod_o_o).
% 28.44/7.23 thf(func_def_309, type, bNF_convol_nat_o_nat: (nat > $o) > (nat > nat) > nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_310, type, bNF_convol_nat_nat_o: (nat > nat) > (nat > $o) > nat > product_prod_nat_o).
% 28.44/7.23 thf(func_def_311, type, bNF_co805650143699787099at_nat: (nat > nat) > (nat > nat) > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_312, type, bNF_convol_nat_num_o: (nat > num) > (nat > $o) > nat > product_prod_num_o).
% 28.44/7.23 thf(func_def_313, type, bNF_co8159352583862032293um_nat: (nat > num) > (nat > nat) > nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_314, type, bNF_co4716684370017810927um_num: (nat > num) > (nat > num) > nat > product_prod_num_num).
% 28.44/7.23 thf(func_def_315, type, bNF_convol_num_o_nat: (num > $o) > (num > nat) > num > product_prod_o_nat).
% 28.44/7.23 thf(func_def_316, type, bNF_co7969830008525221797at_nat: (num > nat) > (num > nat) > num > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_317, type, bNF_co6100160411832691183um_nat: (num > num) > (num > nat) > num > product_prod_num_nat).
% 28.44/7.23 thf(func_def_318, type, bNF_co6607689160745551784nt_int: (produc7812382424243267045t_unit > int) > (produc7812382424243267045t_unit > int) > produc7812382424243267045t_unit > product_prod_int_int).
% 28.44/7.23 thf(func_def_319, type, bNF_co5610825919353547504at_nat: (produc7812382424243267045t_unit > nat) > (produc7812382424243267045t_unit > nat) > produc7812382424243267045t_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_320, type, bNF_co3748779267718262122nt_int: (product_prod_int_int > int) > (product_prod_int_int > int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_321, type, bNF_co2751916026326257842at_nat: (product_prod_int_int > nat) > (product_prod_int_int > nat) > product_prod_int_int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_322, type, bNF_co49787548815638194nt_int: (product_prod_nat_nat > int) > (product_prod_nat_nat > int) > product_prod_nat_nat > product_prod_int_int).
% 28.44/7.23 thf(func_def_323, type, bNF_co8276296344278409722at_nat: (product_prod_nat_nat > nat) > (product_prod_nat_nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_324, type, bNF_co147202357524637304at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_325, type, bNF_cs4943907971211754724nteger: set_Pr8415741480598773322nteger > (product_prod_int_int > int) > (produc2963269191615333738nteger > int) > (produc2963269191615333738nteger > product_prod_int_int) > (produc2963269191615333738nteger > produc2963269191615333738nteger) > $o).
% 28.44/7.23 thf(func_def_326, type, bNF_cs7194553038297458973at_int: set_Pr49084382684228242at_int > (produc859450856879609959at_nat > product_prod_nat_nat) > (produc4196048018000912732at_int > product_prod_nat_nat) > (produc4196048018000912732at_int > produc859450856879609959at_nat) > (produc4196048018000912732at_int > produc4196048018000912732at_int) > $o).
% 28.44/7.23 thf(func_def_327, type, bNF_fs409234558581511823t_unit: (ref_a > heap_e7401611519738050253t_unit > $o) > (heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o) > produc7812382424243267045t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_328, type, bNF_fs4543836202474805097nteger: (int > int > $o) > (int > code_integer > $o) > produc2963269191615333738nteger > product_prod_int_int).
% 28.44/7.23 thf(func_def_329, type, bNF_fs8167890477030535480nt_int: (int > int > $o) > (int > int > $o) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_330, type, bNF_fs6799373675401686564at_nat: (nat > nat > $o) > (nat > nat > $o) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_331, type, bNF_fs6342258632037972510at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > produc4196048018000912732at_int > produc859450856879609959at_nat).
% 28.44/7.23 thf(func_def_332, type, bNF_fs1946732770515719151at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_333, type, bNF_pi4515785505327359899nteger: (int > int > $o) > (int > code_integer > $o) > int > code_integer > int).
% 28.44/7.23 thf(func_def_334, type, bNF_pi770922605693484880at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_335, type, bNF_re6580757339198446453_nat_o: (($o > $o) > ($o > $o) > $o) > (((nat > $o) > nat > $o) > ((nat > $o) > nat > $o) > $o) > (($o > $o) > (nat > $o) > nat > $o) > (($o > $o) > (nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_336, type, bNF_re7413876800493218871nt_nat: (($o > $o) > (int > nat) > $o) > (((nat > $o) > nat > $o) > ((int > int) > int > nat) > $o) > (($o > $o) > (nat > $o) > nat > $o) > ((int > nat) > (int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_337, type, bNF_re1515921786380824775at_nat: (($o > $o) > (nat > nat) > $o) > (((nat > $o) > nat > $o) > ((nat > nat) > nat > nat) > $o) > (($o > $o) > (nat > $o) > nat > $o) > ((nat > nat) > (nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_338, type, bNF_re7387973359137000979nt_num: (($o > $o) > (nat > num) > $o) > (((nat > $o) > nat > $o) > ((int > nat) > int > num) > $o) > (($o > $o) > (nat > $o) > nat > $o) > ((nat > num) > (int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_339, type, bNF_re2961086658867094474nt_num: ((int > int) > (int > code_integer) > $o) > ((int > num) > (int > num) > $o) > ((int > int) > int > num) > ((int > code_integer) > int > num) > $o).
% 28.44/7.23 thf(func_def_340, type, bNF_re2034674868506727813nt_nat: ((int > int) > (int > int) > $o) > ((int > nat) > (int > nat) > $o) > ((int > int) > int > nat) > ((int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_341, type, bNF_re7492190849051111027nt_num: ((int > int) > (int > nat) > $o) > ((int > nat) > (int > num) > $o) > ((int > int) > int > nat) > ((int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_342, type, bNF_re5502197115626545091er_num: ((int > nat) > (code_integer > nat) > $o) > ((int > num) > (code_integer > num) > $o) > ((int > nat) > int > num) > ((code_integer > nat) > code_integer > num) > $o).
% 28.44/7.23 thf(func_def_343, type, bNF_re3642433447925381491nt_nat: ((int > nat) > (int > int) > $o) > ((int > num) > (int > nat) > $o) > ((int > nat) > int > num) > ((int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_344, type, bNF_re6307232852808291833nt_nat: ((int > nat) > (int > nat) > $o) > (((int > int) > int > nat) > ((int > int) > int > nat) > $o) > ((int > nat) > (int > int) > int > nat) > ((int > nat) > (int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_345, type, bNF_re4099335476084980305nt_nat: ((int > nat) > (int > nat) > $o) > (((product_prod_nat_nat > int) > product_prod_nat_nat > nat) > ((int > int) > int > nat) > $o) > ((int > nat) > (product_prod_nat_nat > int) > product_prod_nat_nat > nat) > ((int > nat) > (int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_346, type, bNF_re9099949428469764705nt_num: ((int > nat) > (int > nat) > $o) > ((int > num) > (int > num) > $o) > ((int > nat) > int > num) > ((int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_347, type, bNF_re7435575058205011731_nat_o: ((int > nat) > (nat > $o) > $o) > ((int > num) > (nat > $o) > $o) > ((int > nat) > int > num) > ((nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_348, type, bNF_re717418264989850719at_nat: ((int > nat) > (nat > nat) > $o) > ((int > num) > (nat > nat) > $o) > ((int > nat) > int > num) > ((nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_349, type, bNF_re4310571189260822741nt_num: ((int > nat) > (nat > num) > $o) > (((int > int) > int > nat) > ((int > nat) > int > num) > $o) > ((int > nat) > (int > int) > int > nat) > ((nat > num) > (int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_350, type, bNF_re7839584876883444355nt_num: ((int > num) > (code_integer > num) > $o) > (((int > int) > int > num) > ((int > code_integer) > int > num) > $o) > ((int > num) > (int > int) > int > num) > ((code_integer > num) > (int > code_integer) > int > num) > $o).
% 28.44/7.23 thf(func_def_351, type, bNF_re6292805115969292119er_num: ((int > num) > (code_integer > num) > $o) > ((int > num) > (code_integer > num) > $o) > ((int > num) > int > num) > ((code_integer > num) > code_integer > num) > $o).
% 28.44/7.23 thf(func_def_352, type, bNF_re4768042542643474933nt_num: ((int > num) > (int > num) > $o) > ((int > num) > (int > num) > $o) > ((int > num) > int > num) > ((int > num) > int > num) > $o).
% 28.44/7.23 thf(func_def_353, type, bNF_re1982657550219213441nt_nat: ((nat > $o) > (int > int) > $o) > ((nat > $o) > (int > nat) > $o) > ((nat > $o) > nat > $o) > ((int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_354, type, bNF_re4102725726183926567nt_num: ((nat > $o) > (int > nat) > $o) > ((nat > $o) > (int > num) > $o) > ((nat > $o) > nat > $o) > ((int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_355, type, bNF_re2697311982885662685_nat_o: ((nat > $o) > (nat > $o) > $o) > ((nat > $o) > (nat > $o) > $o) > ((nat > $o) > nat > $o) > ((nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_356, type, bNF_re2144779315220482269at_nat: ((nat > $o) > (nat > nat) > $o) > ((nat > $o) > (nat > nat) > $o) > ((nat > $o) > nat > $o) > ((nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_357, type, bNF_re3930744952143938759_nat_o: ((nat > nat) > ($o > $o) > $o) > (((nat > nat) > nat > nat) > ((nat > $o) > nat > $o) > $o) > ((nat > nat) > (nat > nat) > nat > nat) > (($o > $o) > (nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_358, type, bNF_re8622501330148003679nt_num: ((nat > nat) > (int > nat) > $o) > ((nat > nat) > (int > num) > $o) > ((nat > nat) > nat > nat) > ((int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_359, type, bNF_re7744223787735169245_nat_o: ((nat > nat) > (nat > $o) > $o) > ((nat > nat) > (nat > $o) > $o) > ((nat > nat) > nat > nat) > ((nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_360, type, bNF_re3262823321055862553at_nat: ((nat > nat) > (nat > nat) > $o) > (((nat > nat) > nat > nat) > ((nat > nat) > nat > nat) > $o) > ((nat > nat) > (nat > nat) > nat > nat) > ((nat > nat) > (nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_361, type, bNF_re1160762158786734233nt_nat: ((nat > nat) > (nat > nat) > $o) > (((product_prod_nat_nat > nat) > product_prod_nat_nat > nat) > ((int > nat) > int > nat) > $o) > ((nat > nat) > (product_prod_nat_nat > nat) > product_prod_nat_nat > nat) > ((nat > nat) > (int > nat) > int > nat) > $o).
% 28.44/7.23 thf(func_def_362, type, bNF_re239970166668089693at_nat: ((nat > nat) > (nat > nat) > $o) > ((nat > nat) > (nat > nat) > $o) > ((nat > nat) > nat > nat) > ((nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_363, type, bNF_re584878643992547173nt_num: ((nat > nat) > (nat > num) > $o) > (((nat > nat) > nat > nat) > ((int > nat) > int > num) > $o) > ((nat > nat) > (nat > nat) > nat > nat) > ((nat > num) > (int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_364, type, bNF_re3931674169038344211_nat_o: ((nat > num) > ($o > $o) > $o) > (((int > nat) > int > num) > ((nat > $o) > nat > $o) > $o) > ((nat > num) > (int > nat) > int > num) > (($o > $o) > (nat > $o) > nat > $o) > $o).
% 28.44/7.23 thf(func_def_365, type, bNF_re5843449549409830101nt_nat: ((nat > num) > (int > nat) > $o) > (((int > nat) > int > num) > ((int > int) > int > nat) > $o) > ((nat > num) > (int > nat) > int > num) > ((int > nat) > (int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_366, type, bNF_re6524732562925676389at_nat: ((nat > num) > (nat > nat) > $o) > (((int > nat) > int > num) > ((nat > nat) > nat > nat) > $o) > ((nat > num) > (int > nat) > int > num) > ((nat > nat) > (nat > nat) > nat > nat) > $o).
% 28.44/7.23 thf(func_def_367, type, bNF_re2655444144887082515er_num: ((nat > num) > (nat > num) > $o) > (((int > nat) > int > num) > ((code_integer > nat) > code_integer > num) > $o) > ((nat > num) > (int > nat) > int > num) > ((nat > num) > (code_integer > nat) > code_integer > num) > $o).
% 28.44/7.23 thf(func_def_368, type, bNF_re3846787885862361009nt_num: ((nat > num) > (nat > num) > $o) > (((int > nat) > int > num) > ((int > nat) > int > num) > $o) > ((nat > num) > (int > nat) > int > num) > ((nat > num) > (int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_369, type, bNF_re2742285375668209089nt_num: ((nat > num) > (nat > num) > $o) > (((product_prod_nat_nat > nat) > product_prod_nat_nat > num) > ((int > nat) > int > num) > $o) > ((nat > num) > (product_prod_nat_nat > nat) > product_prod_nat_nat > num) > ((nat > num) > (int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_370, type, bNF_re4105200416192800571er_num: ((num > num) > (num > num) > $o) > (((int > num) > int > num) > ((code_integer > num) > code_integer > num) > $o) > ((num > num) > (int > num) > int > num) > ((num > num) > (code_integer > num) > code_integer > num) > $o).
% 28.44/7.23 thf(func_def_371, type, bNF_re5446066262214944985nt_num: ((num > num) > (num > num) > $o) > (((int > num) > int > num) > ((int > num) > int > num) > $o) > ((num > num) > (int > num) > int > num) > ((num > num) > (int > num) > int > num) > $o).
% 28.44/7.23 thf(func_def_372, type, bNF_re3284331099615978085nt_nat: ((product_prod_nat_nat > int) > (int > int) > $o) > ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((product_prod_nat_nat > int) > product_prod_nat_nat > nat) > ((int > int) > int > nat) > $o).
% 28.44/7.23 thf(func_def_373, type, bNF_re8419181437172746013nt_nat: ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((product_prod_nat_nat > nat) > product_prod_nat_nat > nat) > ((int > nat) > int > nat) > $o).
% 28.44/7.23 thf(func_def_374, type, bNF_re2682547871993127601nt_num: ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((product_prod_nat_nat > num) > (int > num) > $o) > ((product_prod_nat_nat > nat) > product_prod_nat_nat > num) > ((int > nat) > int > num) > $o).
% 28.44/7.23 thf(func_def_375, type, bNF_rel_fun_o_o_o_o: ($o > $o > $o) > ($o > $o > $o) > ($o > $o) > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_376, type, bNF_re4895681925607069953_o_nat: ($o > int > $o) > ($o > nat > $o) > ($o > $o) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_377, type, bNF_re4209105892566519389_o_nat: ($o > nat > $o) > ($o > nat > $o) > ($o > $o) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_378, type, bNF_re766437678722298023_o_num: ($o > nat > $o) > ($o > num > $o) > ($o > $o) > (nat > num) > $o).
% 28.44/7.23 thf(func_def_379, type, bNF_re1181178334029315097nteger: (code_integer > code_integer > $o) > ((code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (code_integer > code_integer > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_380, type, bNF_re40212662316476751um_num: (code_integer > code_integer > $o) > (num > num > $o) > (code_integer > num) > (code_integer > num) > $o).
% 28.44/7.23 thf(func_def_381, type, bNF_re8313794964846168862um_num: (code_integer > int > $o) > (num > num > $o) > (code_integer > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_382, type, bNF_re1366391616432607057unit_o: (ref_a > heap_e7401611519738050253t_unit > $o) > ((ref_a > $o) > (heap_e7401611519738050253t_unit > $o) > $o) > (ref_a > ref_a > $o) > (heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o) > $o).
% 28.44/7.23 thf(func_def_383, type, bNF_re5775369113877777_int_o: (ref_a > heap_e7401611519738050253t_unit > $o) > ((int > $o) > (int > $o) > $o) > (ref_a > int > $o) > (heap_e7401611519738050253t_unit > int > $o) > $o).
% 28.44/7.23 thf(func_def_384, type, bNF_re9202112420002600977_nat_o: (ref_a > heap_e7401611519738050253t_unit > $o) > ((nat > $o) > (nat > $o) > $o) > (ref_a > nat > $o) > (heap_e7401611519738050253t_unit > nat > $o) > $o).
% 28.44/7.23 thf(func_def_385, type, bNF_re1850668159662942673it_o_o: (ref_a > heap_e7401611519738050253t_unit > $o) > ($o > $o > $o) > (ref_a > $o) > (heap_e7401611519738050253t_unit > $o) > $o).
% 28.44/7.23 thf(func_def_386, type, bNF_re3379532845092657523nteger: (int > code_integer > $o) > (int > code_integer > $o) > (int > int) > (code_integer > code_integer) > $o).
% 28.44/7.23 thf(func_def_387, type, bNF_re2807294637932363402at_nat: (int > code_integer > $o) > (nat > nat > $o) > (int > nat) > (code_integer > nat) > $o).
% 28.44/7.23 thf(func_def_388, type, bNF_re6718328864250387230um_num: (int > code_integer > $o) > (num > num > $o) > (int > num) > (code_integer > num) > $o).
% 28.44/7.23 thf(func_def_389, type, bNF_re2828929484557863493at_int: (int > code_integer > $o) > (product_prod_nat_nat > int > $o) > (int > product_prod_nat_nat) > (code_integer > int) > $o).
% 28.44/7.23 thf(func_def_390, type, bNF_re5404797796594736747unit_o: (int > int > $o) > ((ref_a > $o) > (heap_e7401611519738050253t_unit > $o) > $o) > (int > ref_a > $o) > (int > heap_e7401611519738050253t_unit > $o) > $o).
% 28.44/7.23 thf(func_def_391, type, bNF_re3403563459893282935_int_o: (int > int > $o) > ((int > $o) > (int > $o) > $o) > (int > int > $o) > (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_392, type, bNF_re3376528473927230327_nat_o: (int > int > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (int > nat > $o) > $o).
% 28.44/7.23 thf(func_def_393, type, bNF_re5089333283451836215nt_o_o: (int > int > $o) > ($o > $o > $o) > (int > $o) > (int > $o) > $o).
% 28.44/7.23 thf(func_def_394, type, bNF_re982302072995117890nteger: (int > int > $o) > (int > code_integer > $o) > (int > int) > (int > code_integer) > $o).
% 28.44/7.23 thf(func_def_395, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 28.44/7.23 thf(func_def_396, type, bNF_re4715010359784256181nt_nat: (int > int > $o) > (int > nat > $o) > (int > int) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_397, type, bNF_re3713166177374151349at_int: (int > int > $o) > (nat > int > $o) > (int > nat) > (int > int) > $o).
% 28.44/7.23 thf(func_def_398, type, bNF_re3715656647883201625at_nat: (int > int > $o) > (nat > nat > $o) > (int > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_399, type, bNF_re272988434038980259at_num: (int > int > $o) > (nat > num > $o) > (int > nat) > (int > num) > $o).
% 28.44/7.23 thf(func_def_400, type, bNF_re1845987051190671011um_nat: (int > int > $o) > (num > nat > $o) > (int > num) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_401, type, bNF_re7626690874201225453um_num: (int > int > $o) > (num > num > $o) > (int > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_402, type, bNF_re8766404587435608311at_nat: (int > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > product_prod_nat_nat) > (int > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_403, type, bNF_re4914077030771115051_nat_o: (int > nat > $o) > (nat > $o > $o) > (int > nat) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_404, type, bNF_re3344003087646356989at_nat: (int > nat > $o) > (nat > nat > $o) > (int > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_405, type, bNF_re9124706910656911431at_num: (int > nat > $o) > (nat > num > $o) > (int > nat) > (nat > num) > $o).
% 28.44/7.23 thf(func_def_406, type, bNF_re3760060065607074657_num_o: (int > nat > $o) > (num > $o > $o) > (int > num) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_407, type, bNF_re1474333490953826375um_nat: (int > nat > $o) > (num > nat > $o) > (int > num) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_408, type, bNF_re4629543205785817921at_nat: (list_nat > list_nat > $o) > (nat > nat > $o) > (list_nat > nat) > (list_nat > nat) > $o).
% 28.44/7.23 thf(func_def_409, type, bNF_re439150893885221597_nat_o: (nat > $o > $o) > (nat > $o > $o) > (nat > nat) > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_410, type, bNF_re8508505965575957011_num_o: (nat > $o > $o) > (num > $o > $o) > (nat > num) > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_411, type, bNF_re8207659476513966505_o_int: (nat > int > $o) > ($o > int > $o) > (nat > $o) > (int > int) > $o).
% 28.44/7.23 thf(func_def_412, type, bNF_re8210149947023016781_o_nat: (nat > int > $o) > ($o > nat > $o) > (nat > $o) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_413, type, bNF_re4767481733178795415_o_num: (nat > int > $o) > ($o > num > $o) > (nat > $o) > (int > num) > $o).
% 28.44/7.23 thf(func_def_414, type, bNF_re6025474579976152573at_nat: (nat > int > $o) > (nat > nat > $o) > (nat > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_415, type, bNF_re2582806366131931207at_num: (nat > int > $o) > (nat > num > $o) > (nat > nat) > (int > num) > $o).
% 28.44/7.23 thf(func_def_416, type, bNF_re4155804983283621959um_nat: (nat > int > $o) > (num > nat > $o) > (nat > num) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_417, type, bNF_re5655699643857186083unit_o: (nat > nat > $o) > ((ref_a > $o) > (heap_e7401611519738050253t_unit > $o) > $o) > (nat > ref_a > $o) > (nat > heap_e7401611519738050253t_unit > $o) > $o).
% 28.44/7.23 thf(func_def_418, type, bNF_re605504016728627135_int_o: (nat > nat > $o) > ((int > $o) > (int > $o) > $o) > (nat > int > $o) > (nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_419, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_420, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_421, type, bNF_re7523573913982466217_o_nat: (nat > nat > $o) > ($o > nat > $o) > (nat > $o) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_422, type, bNF_re6650684261131312217nt_int: (nat > nat > $o) > (int > int > $o) > (nat > int) > (nat > int) > $o).
% 28.44/7.23 thf(func_def_423, type, bNF_re1402873238235875719_nat_o: (nat > nat > $o) > (nat > $o > $o) > (nat > nat) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_424, type, bNF_re5653821019739307937at_nat: (nat > nat > $o) > (nat > nat > $o) > (nat > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_425, type, bNF_re2211152805895086571at_num: (nat > nat > $o) > (nat > num > $o) > (nat > nat) > (nat > num) > $o).
% 28.44/7.23 thf(func_def_426, type, bNF_re3784151423046777323um_nat: (nat > nat > $o) > (num > nat > $o) > (nat > num) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_427, type, bNF_re341483209202555957um_num: (nat > nat > $o) > (num > num > $o) > (nat > num) > (nat > num) > $o).
% 28.44/7.23 thf(func_def_428, type, bNF_re4702136315717946289at_rat: (nat > nat > $o) > (rat > rat > $o) > (nat > rat) > (nat > rat) > $o).
% 28.44/7.23 thf(func_def_429, type, bNF_re4736500879113541833um_num: (num > num > $o) > (num > num > $o) > (num > num) > (num > num) > $o).
% 28.44/7.23 thf(func_def_430, 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).
% 28.44/7.23 thf(func_def_431, 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).
% 28.44/7.23 thf(func_def_432, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 28.44/7.23 thf(func_def_433, type, bNF_re6202762543029211035nteger: (product_prod_nat_nat > int > $o) > (int > code_integer > $o) > (product_prod_nat_nat > int) > (int > code_integer) > $o).
% 28.44/7.23 thf(func_def_434, type, bNF_re5552630237950767466nt_int: (product_prod_nat_nat > int > $o) > (int > int > $o) > (product_prod_nat_nat > int) > (int > int) > $o).
% 28.44/7.23 thf(func_def_435, type, bNF_re4555766996558763186at_nat: (product_prod_nat_nat > int > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_436, type, bNF_re8466801222876787014um_num: (product_prod_nat_nat > int > $o) > (num > num > $o) > (product_prod_nat_nat > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_437, 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).
% 28.44/7.23 thf(func_def_438, 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).
% 28.44/7.23 thf(func_def_439, 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).
% 28.44/7.23 thf(func_def_440, 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).
% 28.44/7.23 thf(func_def_441, type, bNF_re20414067882207223nt_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > (product_prod_nat_nat > int) > (product_prod_nat_nat > int) > $o).
% 28.44/7.23 thf(func_def_442, 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).
% 28.44/7.23 thf(func_def_443, 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).
% 28.44/7.23 thf(func_def_444, type, bNF_re1865807574169326223at_o_o: (rat > rat > $o) > ($o > $o > $o) > (rat > $o) > (rat > $o) > $o).
% 28.44/7.23 thf(func_def_445, type, bNF_re7554818335971813481nt_int: (rat > rat > $o) > (int > int > $o) > (rat > int) > (rat > int) > $o).
% 28.44/7.23 thf(func_def_446, type, bNF_re6557955094579809201at_nat: (rat > rat > $o) > (nat > nat > $o) > (rat > nat) > (rat > nat) > $o).
% 28.44/7.23 thf(func_def_447, type, bNF_re1692451286490762625ar_o_o: (char > char > $o) > ($o > $o > $o) > (char > $o) > (char > $o) > $o).
% 28.44/7.23 thf(func_def_448, type, bNF_re4780507660726531203_o_int: (char > char > $o) > ($o > int > $o) > (char > $o) > (char > int) > $o).
% 28.44/7.23 thf(func_def_449, type, bNF_re4782998131235581479_o_nat: (char > char > $o) > ($o > nat > $o) > (char > $o) > (char > nat) > $o).
% 28.44/7.23 thf(func_def_450, type, bNF_re6064627146911078825_int_o: (char > char > $o) > (int > $o > $o) > (char > int) > (char > $o) > $o).
% 28.44/7.23 thf(func_def_451, type, bNF_re4731199128827642459nt_int: (char > char > $o) > (int > int > $o) > (char > int) > (char > int) > $o).
% 28.44/7.23 thf(func_def_452, type, bNF_re4733689599336692735nt_nat: (char > char > $o) > (int > nat > $o) > (char > int) > (char > nat) > $o).
% 28.44/7.23 thf(func_def_453, type, bNF_re7885669492343766789_nat_o: (char > char > $o) > (nat > $o > $o) > (char > nat) > (char > $o) > $o).
% 28.44/7.23 thf(func_def_454, type, bNF_re3731845416926587903at_int: (char > char > $o) > (nat > int > $o) > (char > nat) > (char > int) > $o).
% 28.44/7.23 thf(func_def_455, type, bNF_re3734335887435638179at_nat: (char > char > $o) > (nat > nat > $o) > (char > nat) > (char > nat) > $o).
% 28.44/7.23 thf(func_def_456, type, bNF_sn8323453914685745821t_unit: (ref_a > ref_a > $o) > (ref_a > heap_e7401611519738050253t_unit > $o) > produc7812382424243267045t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_457, type, bNF_sn8000174127721201323nteger: (int > int > $o) > (int > code_integer > $o) > produc2963269191615333738nteger > produc2963269191615333738nteger).
% 28.44/7.23 thf(func_def_458, type, bNF_sn1062102010912252026nt_int: (int > int > $o) > (int > int > $o) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_459, type, bNF_sn8916957246138178918at_nat: (nat > nat > $o) > (nat > nat > $o) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_460, type, bNF_sn649997494946348640at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > produc4196048018000912732at_int > produc4196048018000912732at_int).
% 28.44/7.23 thf(func_def_461, type, bNF_sn1857951156667551021at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_462, type, bNF_vi7828673959370436579_int_o: (ref_a > int) > (heap_e7401611519738050253t_unit > int) > (int > int > $o) > ref_a > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_463, type, bNF_vi4623496019404053219_nat_o: (ref_a > nat) > (heap_e7401611519738050253t_unit > nat) > (nat > nat > $o) > ref_a > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_464, type, bNF_vi699694178825965831eger_o: (int > int) > (code_integer > code_integer) > (int > code_integer > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_465, type, bNF_vi2125572119366604152_int_o: (int > int) > (code_integer > int) > (int > int > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_466, type, bNF_vi3884084463199473129_int_o: (int > int) > (int > int) > (int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_467, type, bNF_vi3197508430158922565_int_o: (int > int) > (nat > int) > (int > int > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_468, type, bNF_vi5018550775591610529_nat_o: (int > int) > (nat > nat) > (int > nat > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_469, type, bNF_vi1281217848275042457_rat_o: (int > int) > (nat > rat) > (int > rat > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_470, type, bNF_vi9149698133064535136char_o: (int > int) > (nat > char) > (int > char > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_471, type, bNF_vi2193923016096921761_nat_o: (int > nat) > (int > nat) > (nat > nat > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_472, type, bNF_vi7769575839906753835_rat_o: (int > nat) > (num > rat) > (nat > rat > $o) > int > num > $o).
% 28.44/7.23 thf(func_def_473, type, bNF_vi1300075849944819442char_o: (int > nat) > (num > char) > (nat > char > $o) > int > num > $o).
% 28.44/7.23 thf(func_def_474, type, bNF_vi2326032003723069084_num_o: (int > num) > (code_integer > num) > (num > num > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_475, type, bNF_vi2107963681178519309_num_o: (int > num) > (int > num) > (num > num > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_476, type, bNF_vi2881549544236934259_int_o: (int > product_prod_nat_nat) > (code_integer > int) > (product_prod_nat_nat > int > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_477, type, bNF_vi1204582724742824157_nat_o: (int > product_prod_nat_nat) > (int > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_478, type, bNF_vi467646977814820164_int_o: (list_nat > int) > (code_integer > int) > (int > int > $o) > list_nat > code_integer > $o).
% 28.44/7.23 thf(func_def_479, type, bNF_vi5202502398764838569_nat_o: (list_nat > product_prod_nat_nat) > (int > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > $o) > list_nat > int > $o).
% 28.44/7.23 thf(func_def_480, type, bNF_vi5856767400800367702unit_o: (nat > $o) > ($o > product_unit) > ($o > product_unit > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_481, type, bNF_vi3868162310295888627_rat_o: (nat > $o) > ($o > rat) > ($o > rat > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_482, type, bNF_vi8816436626763797690char_o: (nat > $o) > ($o > char) > ($o > char > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_483, type, bNF_vi7331807916455492308_int_o: (nat > int) > (code_integer > int) > (int > int > $o) > nat > code_integer > $o).
% 28.44/7.23 thf(func_def_484, type, bNF_vi8357618154448083105_int_o: (nat > int) > (nat > int) > (int > int > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_485, type, bNF_vi1731478210338170163_nat_o: (nat > int) > (num > nat) > (int > nat > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_486, type, bNF_vi6818137723729380987_o_o_o: (nat > nat) > ($o > $o) > (nat > $o > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_487, type, bNF_vi1443435967014148806unit_o: (nat > nat) > ($o > product_unit) > (nat > product_unit > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_488, type, bNF_vi6667456707345531737_nat_o: (nat > nat) > (nat > nat) > (nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_489, type, bNF_vi2930123780028963665_rat_o: (nat > nat) > (nat > rat) > (nat > rat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_490, type, bNF_vi8943400373106913048char_o: (nat > nat) > (nat > char) > (nat > char > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_491, type, bNF_vi190728152058600505_nat_o: (nat > product_prod_nat_nat) > (int > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > $o) > nat > int > $o).
% 28.44/7.23 thf(func_def_492, type, bNF_vi1633389952966819264_nat_o: (product_prod_int_int > int) > (num > nat) > (int > nat > $o) > product_prod_int_int > num > $o).
% 28.44/7.23 thf(func_def_493, type, bNF_vi5082502771524357669nt_o_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_494, type, bNF_vi8966365312794588230_int_o: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_495, type, bNF_vi33923956287962137eger_o: (product_prod_nat_nat > int) > (int > code_integer) > (int > code_integer > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_496, type, bNF_vi9094538908245281400_nat_o: (product_prod_nat_nat > int) > (num > nat) > (int > nat > $o) > product_prod_nat_nat > num > $o).
% 28.44/7.23 thf(func_def_497, type, bNF_vi2682369418337388893_int_o: (product_prod_nat_nat > int) > (product_prod_nat_nat > int) > (int > int > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_498, type, bNF_vi9025507403824386624_o_o_o: (product_prod_nat_nat > nat) > ($o > $o) > (nat > $o > $o) > product_prod_nat_nat > $o > $o).
% 28.44/7.23 thf(func_def_499, type, bNF_vi5493721401438417730_nat_o: (product_prod_nat_nat > nat) > (int > nat) > (nat > nat > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_500, type, bNF_vi5426221348228882691_int_o: (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_501, type, bNF_vi763171854521451549_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) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_502, type, bNF_vi508398028314858188_int_o: (rat > int) > (code_integer > int) > (int > int > $o) > rat > code_integer > $o).
% 28.44/7.23 thf(func_def_503, type, bNF_vi2997284877290766385_nat_o: (rat > product_prod_nat_nat) > (int > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > $o) > rat > int > $o).
% 28.44/7.23 thf(func_def_504, type, bNF_vi7262943168399475603_int_o: (char > int) > (code_integer > int) > (int > int > $o) > char > code_integer > $o).
% 28.44/7.23 thf(func_def_505, type, bNF_vi728936465572800120_nat_o: (char > product_prod_nat_nat) > (int > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > $o) > char > int > $o).
% 28.44/7.23 thf(func_def_506, type, bNF_Gr2943678036615987864nt_int: set_o > ($o > int) > ($o > int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_507, type, bNF_Gr1946814795223983584at_nat: set_o > ($o > nat) > ($o > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_508, type, bNF_Gr7727518618234538026at_num: set_o > ($o > nat) > ($o > num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_509, type, bNF_Gr8686673574714534880nt_int: set_int > (int > int) > (int > int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_510, type, bNF_Gr7689810333322530600at_nat: set_int > (int > nat) > (int > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_511, type, bNF_Gr4247142119478309234at_num: set_int > (int > nat) > (int > num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_512, type, bNF_Gr8315020014477690244nt_int: set_nat > (nat > int) > (nat > int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_513, type, bNF_Gr7318156773085685964at_nat: set_nat > (nat > nat) > (nat > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_514, type, bNF_Gr3875488559241464598at_num: set_nat > (nat > nat) > (nat > num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_515, type, bNF_Gr5511461681843259283at_num: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat) > (product_prod_nat_nat > num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_516, type, bNF_Gr166583433173494904er_num: (int > num) > (code_integer > num) > (int > code_integer > $o) > num > num > $o).
% 28.44/7.23 thf(func_def_517, type, bNF_Gr7020624548710275655nt_num: (int > num) > (int > num) > (int > int > $o) > num > num > $o).
% 28.44/7.23 thf(func_def_518, type, bNF_Gr364077372107685167_int_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 28.44/7.23 thf(func_def_519, type, bNF_Gr1354378531936274772nt_int: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 28.44/7.23 thf(func_def_520, type, bNF_Gr6955563364113978072nt_nat: (product_prod_nat_nat > nat) > (int > nat) > (product_prod_nat_nat > int > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_521, type, bNF_We7690717809131995284nc_o_o: set_o > set_o > set_o_o).
% 28.44/7.23 thf(func_def_522, type, bNF_We6830391624356636116_o_nat: set_o > set_nat > set_o_nat).
% 28.44/7.23 thf(func_def_523, type, bNF_We8730861560085513481t_unit: set_o > set_Product_unit > set_o_Product_unit).
% 28.44/7.23 thf(func_def_524, type, bNF_We8537379975951060974nt_int: set_int > set_int > set_int_int).
% 28.44/7.23 thf(func_def_525, type, bNF_We8539870446460111250nt_nat: set_int > set_nat > set_int_nat).
% 28.44/7.23 thf(func_def_526, type, bNF_We7904740386373615514nt_rat: set_int > set_rat > set_int_rat).
% 28.44/7.23 thf(func_def_527, type, bNF_We7538026264050006418at_int: set_nat > set_int > set_nat_int).
% 28.44/7.23 thf(func_def_528, type, bNF_We7540516734559056694at_nat: set_nat > set_nat > set_nat_nat).
% 28.44/7.23 thf(func_def_529, type, bNF_We6195730058148253354_rat_o: set_rat > set_o > set_rat_o).
% 28.44/7.23 thf(func_def_530, type, bNF_We7223962090624190782at_nat: set_rat > set_nat > set_rat_nat).
% 28.44/7.23 thf(func_def_531, type, bNF_We8564238559827753503t_unit: set_rat > set_Product_unit > set_rat_Product_unit).
% 28.44/7.23 thf(func_def_532, type, bNF_We6174688282833725809char_o: set_char > set_o > set_char_o).
% 28.44/7.23 thf(func_def_533, type, bNF_We935846424581991991ar_nat: set_char > set_nat > set_char_nat).
% 28.44/7.23 thf(func_def_534, type, bNF_We7396736742984212070t_unit: set_char > set_Product_unit > set_ch7814610555394875923t_unit).
% 28.44/7.23 thf(func_def_535, type, bNF_We2264329196211740764nt_int: set_int > (int > int) > (int > int) > (int > int) > int > int).
% 28.44/7.23 thf(func_def_536, type, bNF_We2266819666720791040nt_nat: set_int > (int > int) > (int > nat) > (nat > int) > int > int).
% 28.44/7.23 thf(func_def_537, type, bNF_We1264975484310686208at_int: set_int > (int > nat) > (int > int) > (int > int) > int > nat).
% 28.44/7.23 thf(func_def_538, type, bNF_We1267465954819736484at_nat: set_int > (int > nat) > (int > nat) > (nat > int) > int > nat).
% 28.44/7.23 thf(func_def_539, type, bNF_We1892675635974896128nt_int: set_int > (nat > int) > (int > int) > (int > nat) > int > int).
% 28.44/7.23 thf(func_def_540, type, bNF_We1895166106483946404nt_nat: set_int > (nat > int) > (int > nat) > (nat > nat) > int > int).
% 28.44/7.23 thf(func_def_541, type, bNF_We893321924073841572at_int: set_int > (nat > nat) > (int > int) > (int > nat) > int > nat).
% 28.44/7.23 thf(func_def_542, type, bNF_We895812394582891848at_nat: set_int > (nat > nat) > (int > nat) > (nat > nat) > int > nat).
% 28.44/7.23 thf(func_def_543, type, bNF_We576767280138975660at_int: set_int > (nat > rat) > (int > int) > (int > nat) > int > rat).
% 28.44/7.23 thf(func_def_544, type, bNF_We579257750648025936at_nat: set_int > (nat > rat) > (int > nat) > (nat > nat) > int > rat).
% 28.44/7.23 thf(func_def_545, type, bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_546, type, basic_1872990034501187214nt_int: (int > nat) > (int > nat) > product_prod_int_int > nat).
% 28.44/7.23 thf(func_def_547, type, basic_1875480505010237490nt_nat: (int > nat) > (nat > nat) > product_prod_int_nat > nat).
% 28.44/7.23 thf(func_def_548, type, basic_873636322600132658at_int: (nat > nat) > (int > nat) > product_prod_nat_int > nat).
% 28.44/7.23 thf(func_def_549, type, basic_876126793109182934at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_550, type, basic_685971451221398055t_unit: produc7812382424243267045t_unit > set_ref_a).
% 28.44/7.23 thf(func_def_551, type, basic_fsts_int_int: product_prod_int_int > set_int).
% 28.44/7.23 thf(func_def_552, type, basic_fsts_nat_nat: product_prod_nat_nat > set_nat).
% 28.44/7.23 thf(func_def_553, type, basic_fsts_nat_num: product_prod_nat_num > set_nat).
% 28.44/7.23 thf(func_def_554, type, basic_3661821009137050567at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_555, type, basic_1274512288150691911at_nat: produc1319942482725812455at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_556, type, basic_5328504652464829177at_nat: (nat > nat > $o) > (nat > nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_557, type, basic_1496934909540232809t_unit: produc7812382424243267045t_unit > set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_558, type, basic_snds_int_int: product_prod_int_int > set_int).
% 28.44/7.23 thf(func_def_559, type, basic_snds_nat_nat: product_prod_nat_nat > set_nat).
% 28.44/7.23 thf(func_def_560, type, basic_snds_nat_num: product_prod_nat_num > set_num).
% 28.44/7.23 thf(func_def_561, type, basic_484852565060450053at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_562, type, basic_5713354656523905413at_nat: produc1319942482725812455at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_563, type, bit_take_bit_num: nat > num > option_num).
% 28.44/7.23 thf(func_def_564, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 28.44/7.23 thf(func_def_565, type, code_cr_integer: int > code_integer > $o).
% 28.44/7.23 thf(func_def_566, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_567, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_568, type, code_int_of_integer: code_integer > int).
% 28.44/7.23 thf(func_def_569, type, code_nat_of_integer: code_integer > nat).
% 28.44/7.23 thf(func_def_570, type, code_negative: num > code_integer).
% 28.44/7.23 thf(func_def_571, type, code_num_of_integer: code_integer > num).
% 28.44/7.23 thf(func_def_572, type, code_pcr_integer: int > code_integer > $o).
% 28.44/7.23 thf(func_def_573, type, complete_Inf_Inf_o_o: set_o_o > $o > $o).
% 28.44/7.23 thf(func_def_574, type, comple5770381748412298549_int_o: set_int_int_o > int > int > $o).
% 28.44/7.23 thf(func_def_575, type, comple4393433247856107946_int_o: set_int_o > int > $o).
% 28.44/7.23 thf(func_def_576, type, comple1675732732025788397_nat_o: set_nat_nat_o > nat > nat > $o).
% 28.44/7.23 thf(func_def_577, type, comple2433913294995299363_num_o: set_nat_num_o > nat > num > $o).
% 28.44/7.23 thf(func_def_578, type, comple6214475593288795910_nat_o: set_nat_o > nat > $o).
% 28.44/7.23 thf(func_def_579, type, comple4707286699709038525_int_o: set_Pr8049984349381595834_int_o > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_580, type, comple6265855634338933877_nat_o: set_Pr5582243495563764594_nat_o > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_581, type, comple8183010123678664591_nat_o: set_Pr7010166363911110284_nat_o > produc3843707927480180839at_nat > $o).
% 28.44/7.23 thf(func_def_582, type, comple8322679762649017525_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_583, type, comple5307621999477653941_nat_o: set_se7255092946006855566_nat_o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_584, type, complete_Inf_Inf_o: set_o > $o).
% 28.44/7.23 thf(func_def_585, type, complete_Inf_Inf_int: set_int > int).
% 28.44/7.23 thf(func_def_586, type, complete_Inf_Inf_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_587, type, comple2584293577114468500t_unit: set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_588, type, comple3063163877087187839_set_o: set_set_o > set_o).
% 28.44/7.23 thf(func_def_589, type, comple3628384868704368283et_int: set_set_int > set_int).
% 28.44/7.23 thf(func_def_590, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 28.44/7.23 thf(func_def_591, type, comple1626965760690514720nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_592, type, comple1930127330929219688at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_593, type, comple6868718957223342258at_num: set_se4826145725398303499at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_594, type, comple6332534001959699150at_nat: set_se6425085446898223655at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_595, type, comple6751905152567503566at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_596, type, comple4403251139954110286at_nat: set_se7592288975875140775at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_597, type, comple7216939928495492468t_unit: set_set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_598, type, comple4298007329820168263et_rat: set_set_rat > set_rat).
% 28.44/7.23 thf(func_def_599, type, comple7965528767983648192t_char: set_set_char > set_char).
% 28.44/7.23 thf(func_def_600, type, complete_Sup_Sup_o_o: set_o_o > $o > $o).
% 28.44/7.23 thf(func_def_601, type, comple7687260386943045147_int_o: set_int_int_o > int > int > $o).
% 28.44/7.23 thf(func_def_602, type, comple6496622788309502864_int_o: set_int_o > int > $o).
% 28.44/7.23 thf(func_def_603, type, comple3592611370556534995_nat_o: set_nat_nat_o > nat > nat > $o).
% 28.44/7.23 thf(func_def_604, type, comple4350791933526045961_num_o: set_nat_num_o > nat > num > $o).
% 28.44/7.23 thf(func_def_605, type, comple8317665133742190828_nat_o: set_nat_o > nat > $o).
% 28.44/7.23 thf(func_def_606, type, comple342879659800731223_int_o: set_Pr8049984349381595834_int_o > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_607, type, comple1901448594430626575_nat_o: set_Pr5582243495563764594_nat_o > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_608, type, comple1177764198577243945_nat_o: set_Pr7010166363911110284_nat_o > produc3843707927480180839at_nat > $o).
% 28.44/7.23 thf(func_def_609, type, comple493620192902636699_nat_o: set_se9180647916752606350_nat_o > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_610, type, comple4502628867940267931_nat_o: set_se7255092946006855566_nat_o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_611, type, complete_Sup_Sup_o: set_o > $o).
% 28.44/7.23 thf(func_def_612, type, complete_Sup_Sup_int: set_int > int).
% 28.44/7.23 thf(func_def_613, type, complete_Sup_Sup_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_614, type, comple4687483117567863418t_unit: set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_615, type, comple90263536869209701_set_o: set_set_o > set_o).
% 28.44/7.23 thf(func_def_616, type, comple6989579708249578522t_unit: set_se4612898379794543757t_unit > set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_617, type, comple3221217463730067765et_int: set_set_int > set_int).
% 28.44/7.23 thf(func_def_618, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 28.44/7.23 thf(func_def_619, type, comple5382143125604098054nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_620, type, comple5685304695842803022at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_621, type, comple1400524285282149784at_num: set_se4826145725398303499at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_622, type, comple2748534634209756852at_nat: set_se6425085446898223655at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_623, type, comple4364388969068068532at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_624, type, comple7342073961973170484at_nat: set_se7592288975875140775at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_625, type, comple3349607820504768346t_unit: set_set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_626, type, comple3890839924845867745et_rat: set_set_rat > set_rat).
% 28.44/7.23 thf(func_def_627, type, comple4338141846124676698t_char: set_set_char > set_char).
% 28.44/7.23 thf(func_def_628, type, condit5488710616941104124bove_o: set_o > $o).
% 28.44/7.23 thf(func_def_629, type, condit1118808407379112185nteger: set_Code_integer > $o).
% 28.44/7.23 thf(func_def_630, type, condit2212336002400062152ve_int: set_int > $o).
% 28.44/7.23 thf(func_def_631, type, condit2214826472909112428ve_nat: set_nat > $o).
% 28.44/7.23 thf(func_def_632, type, condit2080475194861589617t_unit: set_Product_unit > $o).
% 28.44/7.23 thf(func_def_633, type, condit1579696412822616692ve_rat: set_rat > $o).
% 28.44/7.23 thf(func_def_634, type, condit5477540289124974626et_nat: set_set_nat > $o).
% 28.44/7.23 thf(func_def_635, type, condit5413489452508810728elow_o: set_o > $o).
% 28.44/7.23 thf(func_def_636, type, condit4933233095834890765nteger: set_Code_integer > $o).
% 28.44/7.23 thf(func_def_637, type, condit1735850657277959132ow_int: set_int > $o).
% 28.44/7.23 thf(func_def_638, type, condit1738341127787009408ow_nat: set_nat > $o).
% 28.44/7.23 thf(func_def_639, type, condit9161856309968323677t_unit: set_Product_unit > $o).
% 28.44/7.23 thf(func_def_640, type, condit1103211067700513672ow_rat: set_rat > $o).
% 28.44/7.23 thf(func_def_641, type, condit68592940725977398et_nat: set_set_nat > $o).
% 28.44/7.23 thf(func_def_642, type, nat_to_rat_surj: nat > rat).
% 28.44/7.23 thf(func_def_643, type, adjust_div: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_644, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_645, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_646, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_647, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_648, type, euclid4774559944035922753ze_int: int > nat).
% 28.44/7.23 thf(func_def_649, type, inverse_inverse_rat: rat > rat).
% 28.44/7.23 thf(func_def_650, type, finite_Fpow_int: set_int > set_set_int).
% 28.44/7.23 thf(func_def_651, type, finite_Fpow_nat: set_nat > set_set_nat).
% 28.44/7.23 thf(func_def_652, type, finite_Fpow_rat: set_rat > set_set_rat).
% 28.44/7.23 thf(func_def_653, type, finite_card_int: set_int > nat).
% 28.44/7.23 thf(func_def_654, type, finite_card_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_655, type, finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_656, type, finite_card_rat: set_rat > nat).
% 28.44/7.23 thf(func_def_657, type, finite6756937295472016048nteger: set_Co726186806682698383nteger > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_658, type, finite7905178416053733328on_o_o: set_o > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_659, type, finite4703585013658510744_o_nat: set_o > ($o > nat > nat) > $o).
% 28.44/7.23 thf(func_def_660, type, finite366418920864469932nteger: set_Code_integer > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_661, type, finite5985214029334008090_int_o: set_int > (int > $o > $o) > $o).
% 28.44/7.23 thf(func_def_662, type, finite4582259249640653518nt_nat: set_int > (int > nat > nat) > $o).
% 28.44/7.23 thf(func_def_663, type, finite7806256374766696054_nat_o: set_nat > (nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_664, type, finite3582905537739598962at_nat: set_nat > (nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_665, type, finite1496024664758132007_nat_o: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_666, type, finite2110315540964234241at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_667, type, finite2818816984019561153_nat_o: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_668, type, finite8619596206551965927at_nat: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_669, type, finite954763878425697269nteger: set_Co726186806682698383nteger > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_670, type, finite2426395113773319005_o_nat: set_o > ($o > nat > nat) > $o).
% 28.44/7.23 thf(func_def_671, type, finite917065715488314481nteger: set_Code_integer > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_672, type, finite8981753823465611337nt_nat: set_int > (int > nat > nat) > $o).
% 28.44/7.23 thf(func_def_673, type, finite7982400111564556781at_nat: set_nat > (nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_674, type, finite5150387867909132486at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_675, type, finite352855791390415404at_nat: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > nat > nat) > $o).
% 28.44/7.23 thf(func_def_676, type, finite_finite_o: set_o > $o).
% 28.44/7.23 thf(func_def_677, type, finite_finite_int: set_int > $o).
% 28.44/7.23 thf(func_def_678, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 28.44/7.23 thf(func_def_679, type, finite_finite_nat: set_nat > $o).
% 28.44/7.23 thf(func_def_680, type, finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_681, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_682, type, finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_683, type, finite4290736615968046902t_unit: set_Product_unit > $o).
% 28.44/7.23 thf(func_def_684, type, finite_finite_rat: set_rat > $o).
% 28.44/7.23 thf(func_def_685, type, finite_finite_char: set_char > $o).
% 28.44/7.23 thf(func_def_686, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 28.44/7.23 thf(func_def_687, type, comp_C2822359487432382964nteger: ((code_integer > code_integer) > code_integer > code_integer) > (code_integer > code_integer > code_integer) > code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_688, type, comp_C3983183376822107068nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > code_integer > code_integer) > (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_689, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_690, type, comp_C7826480081638475456nteger: ((code_integer > code_integer) > code_integer) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer).
% 28.44/7.23 thf(func_def_691, type, comp_C6484513282182537548nteger: ((code_integer > code_integer) > produc101387210554329899nteger) > (code_integer > code_integer > code_integer) > code_integer > produc101387210554329899nteger).
% 28.44/7.23 thf(func_def_692, type, comp_P3928908779438215820nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_693, type, comp_o_o_o: ($o > $o) > ($o > $o) > $o > $o).
% 28.44/7.23 thf(func_def_694, type, comp_o_o_int: ($o > $o) > (int > $o) > int > $o).
% 28.44/7.23 thf(func_def_695, type, comp_o_o_nat: ($o > $o) > (nat > $o) > nat > $o).
% 28.44/7.23 thf(func_def_696, type, comp_o_o_num: ($o > $o) > (num > $o) > num > $o).
% 28.44/7.23 thf(func_def_697, type, comp_o_int_nat: ($o > int) > (nat > $o) > nat > int).
% 28.44/7.23 thf(func_def_698, type, comp_o_nat_o: ($o > nat) > ($o > $o) > $o > nat).
% 28.44/7.23 thf(func_def_699, type, comp_o_nat_int: ($o > nat) > (int > $o) > int > nat).
% 28.44/7.23 thf(func_def_700, type, comp_o_nat_nat: ($o > nat) > (nat > $o) > nat > nat).
% 28.44/7.23 thf(func_def_701, type, comp_o_num_o: ($o > num) > ($o > $o) > $o > num).
% 28.44/7.23 thf(func_def_702, type, comp_o_num_int: ($o > num) > (int > $o) > int > num).
% 28.44/7.23 thf(func_def_703, type, comp_o_num_nat: ($o > num) > (nat > $o) > nat > num).
% 28.44/7.23 thf(func_def_704, type, comp_o_num_num: ($o > num) > (num > $o) > num > num).
% 28.44/7.23 thf(func_def_705, type, comp_o7658611401268416066_o_nat: ($o > product_prod_o_o) > (nat > $o) > nat > product_prod_o_o).
% 28.44/7.23 thf(func_def_706, type, comp_o6895741221744486154t_unit: ($o > set_o) > (product_unit > $o) > product_unit > set_o).
% 28.44/7.23 thf(func_def_707, type, comp_o_set_int_nat: ($o > set_int) > (nat > $o) > nat > set_int).
% 28.44/7.23 thf(func_def_708, type, comp_o1521574261646630388t_unit: ($o > set_int) > (product_unit > $o) > product_unit > set_int).
% 28.44/7.23 thf(func_def_709, type, comp_o_set_nat_nat: ($o > set_nat) > (nat > $o) > nat > set_nat).
% 28.44/7.23 thf(func_def_710, type, comp_o9190160103024335696t_unit: ($o > set_nat) > (product_unit > $o) > product_unit > set_nat).
% 28.44/7.23 thf(func_def_711, type, comp_o2254869825208929t_unit: ($o > set_Pr1261947904930325089at_nat) > (product_unit > $o) > product_unit > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_712, type, comp_o4913564575355137019t_unit: ($o > set_Pr4329608150637261639at_nat) > (product_unit > $o) > product_unit > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_713, type, comp_o_set_rat_nat: ($o > set_rat) > (nat > $o) > nat > set_rat).
% 28.44/7.23 thf(func_def_714, type, comp_o_char_o: ($o > char) > ($o > $o) > $o > char).
% 28.44/7.23 thf(func_def_715, type, comp_C2931745410781319416nteger: (code_integer > code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_716, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_717, type, comp_C7449957260575251196nteger: (code_integer > code_integer) > (code_integer > code_integer) > code_integer > code_integer).
% 28.44/7.23 thf(func_def_718, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 28.44/7.23 thf(func_def_719, type, comp_C1043215000170864188nteger: (code_integer > code_integer) > (produc8923325533196201883nteger > code_integer) > produc8923325533196201883nteger > code_integer).
% 28.44/7.23 thf(func_def_720, type, comp_C2177396528461469320um_int: (code_integer > num) > (int > code_integer) > int > num).
% 28.44/7.23 thf(func_def_721, type, comp_C8580465762518603278nteger: (code_integer > num) > (produc2963269191615333738nteger > code_integer) > produc2963269191615333738nteger > num).
% 28.44/7.23 thf(func_def_722, type, comp_h4837689053573563144t_unit: (heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit) > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_723, type, comp_h7449592329096033597t_unit: (heap_e7401611519738050253t_unit > int) > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > int).
% 28.44/7.23 thf(func_def_724, type, comp_h8354993580257045729t_unit: (heap_e7401611519738050253t_unit > nat) > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > nat).
% 28.44/7.23 thf(func_def_725, type, comp_h5940001671827863714t_unit: (heap_e7401611519738050253t_unit > produc8126358835630522215t_unit) > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > produc8126358835630522215t_unit).
% 28.44/7.23 thf(func_def_726, type, comp_r3604920825623061426t_unit: (ref_a > heap_e7401611519738050253t_unit) > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_727, type, comp_r2143332150499412868t_unit: (ref_a > ref_a) > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_728, type, comp_r7249815618783853587t_unit: (ref_a > int) > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > int).
% 28.44/7.23 thf(func_def_729, type, comp_r8155216869944865719t_unit: (ref_a > nat) > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > nat).
% 28.44/7.23 thf(func_def_730, type, comp_r6154141770783548544t_unit: (ref_a > produc5288414631154139675_ref_a) > (produc7812382424243267045t_unit > ref_a) > produc7812382424243267045t_unit > produc5288414631154139675_ref_a).
% 28.44/7.23 thf(func_def_731, type, comp_i653165354545908656at_int: (int > int > $o) > (produc4196048018000912732at_int > int) > produc4196048018000912732at_int > int > $o).
% 28.44/7.23 thf(func_def_732, type, comp_i4519014998770822500at_int: (int > int > int) > (produc4196048018000912732at_int > int) > produc4196048018000912732at_int > int > int).
% 28.44/7.23 thf(func_def_733, type, comp_int_o_o: (int > $o) > ($o > int) > $o > $o).
% 28.44/7.23 thf(func_def_734, type, comp_int_o_int: (int > $o) > (int > int) > int > $o).
% 28.44/7.23 thf(func_def_735, type, comp_int_o_nat: (int > $o) > (nat > int) > nat > $o).
% 28.44/7.23 thf(func_def_736, type, comp_i1585864551200866970er_int: (int > code_integer) > (int > int) > int > code_integer).
% 28.44/7.23 thf(func_def_737, type, comp_int_int_o: (int > int) > ($o > int) > $o > int).
% 28.44/7.23 thf(func_def_738, type, comp_i2224564030725804698nteger: (int > int) > (code_integer > int) > code_integer > int).
% 28.44/7.23 thf(func_def_739, type, comp_int_int_int: (int > int) > (int > int) > int > int).
% 28.44/7.23 thf(func_def_740, type, comp_int_int_nat: (int > int) > (nat > int) > nat > int).
% 28.44/7.23 thf(func_def_741, type, comp_i4330622015127193916nt_int: (int > int) > (product_prod_int_int > int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_742, type, comp_int_int_rat: (int > int) > (rat > int) > rat > int).
% 28.44/7.23 thf(func_def_743, type, comp_int_int_char: (int > int) > (char > int) > char > int).
% 28.44/7.23 thf(func_def_744, type, comp_int_nat_o: (int > nat) > ($o > int) > $o > nat).
% 28.44/7.23 thf(func_def_745, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 28.44/7.23 thf(func_def_746, type, comp_int_nat_nat: (int > nat) > (nat > int) > nat > nat).
% 28.44/7.23 thf(func_def_747, type, comp_i1292779930663060120nt_int: (int > nat) > (product_prod_int_int > int) > product_prod_int_int > nat).
% 28.44/7.23 thf(func_def_748, type, comp_i4471277238271202272at_nat: (int > nat) > (product_prod_nat_nat > int) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_749, type, comp_i5627883460353289149at_int: (int > nat) > (produc4196048018000912732at_int > int) > produc4196048018000912732at_int > nat).
% 28.44/7.23 thf(func_def_750, type, comp_int_nat_rat: (int > nat) > (rat > int) > rat > nat).
% 28.44/7.23 thf(func_def_751, type, comp_int_nat_char: (int > nat) > (char > int) > char > nat).
% 28.44/7.23 thf(func_def_752, type, comp_int_num_int: (int > num) > (int > int) > int > num).
% 28.44/7.23 thf(func_def_753, type, comp_int_num_nat: (int > num) > (nat > int) > nat > num).
% 28.44/7.23 thf(func_def_754, type, comp_int_num_num: (int > num) > (num > int) > num > num).
% 28.44/7.23 thf(func_def_755, type, comp_i3846818780818535807nteger: (int > num) > (produc2963269191615333738nteger > int) > produc2963269191615333738nteger > num).
% 28.44/7.23 thf(func_def_756, type, comp_i7231038107349025742nt_int: (int > num) > (product_prod_int_int > int) > product_prod_int_int > num).
% 28.44/7.23 thf(func_def_757, type, comp_i1186163378102392086at_nat: (int > num) > (product_prod_nat_nat > int) > product_prod_nat_nat > num).
% 28.44/7.23 thf(func_def_758, type, comp_i1108739374719436894at_int: (int > product_prod_nat_nat) > (int > int) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_759, type, comp_int_rat_nat: (int > rat) > (nat > int) > nat > rat).
% 28.44/7.23 thf(func_def_760, type, comp_int_set_nat_int: (int > set_nat) > (int > int) > int > set_nat).
% 28.44/7.23 thf(func_def_761, type, comp_nat_o_o: (nat > $o) > ($o > nat) > $o > $o).
% 28.44/7.23 thf(func_def_762, type, comp_nat_o_int: (nat > $o) > (int > nat) > int > $o).
% 28.44/7.23 thf(func_def_763, type, comp_nat_o_nat: (nat > $o) > (nat > nat) > nat > $o).
% 28.44/7.23 thf(func_def_764, type, comp_n1662990198670838940at_nat: (nat > $o) > (product_prod_nat_nat > nat) > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_765, type, comp_nat_int_o: (nat > int) > ($o > nat) > $o > int).
% 28.44/7.23 thf(func_def_766, type, comp_nat_int_int: (nat > int) > (int > nat) > int > int).
% 28.44/7.23 thf(func_def_767, type, comp_nat_int_nat: (nat > int) > (nat > nat) > nat > int).
% 28.44/7.23 thf(func_def_768, type, comp_nat_int_num: (nat > int) > (num > nat) > num > int).
% 28.44/7.23 thf(func_def_769, type, comp_n5749082658982224864at_nat: (nat > int) > (product_prod_nat_nat > nat) > product_prod_nat_nat > int).
% 28.44/7.23 thf(func_def_770, type, comp_nat_int_rat: (nat > int) > (rat > nat) > rat > int).
% 28.44/7.23 thf(func_def_771, type, comp_nat_int_char: (nat > int) > (char > nat) > char > int).
% 28.44/7.23 thf(func_def_772, type, comp_nat_nat_o: (nat > nat) > ($o > nat) > $o > nat).
% 28.44/7.23 thf(func_def_773, type, comp_nat_nat_int: (nat > nat) > (int > nat) > int > nat).
% 28.44/7.23 thf(func_def_774, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 28.44/7.23 thf(func_def_775, type, comp_nat_nat_num: (nat > nat) > (num > nat) > num > nat).
% 28.44/7.23 thf(func_def_776, type, comp_n2711240574518091068at_nat: (nat > nat) > (product_prod_nat_nat > nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_777, type, comp_nat_nat_rat: (nat > nat) > (rat > nat) > rat > nat).
% 28.44/7.23 thf(func_def_778, type, comp_nat_nat_char: (nat > nat) > (char > nat) > char > nat).
% 28.44/7.23 thf(func_def_779, type, comp_n2103536230552569900nteger: (nat > num) > (code_integer > nat) > code_integer > num).
% 28.44/7.23 thf(func_def_780, type, comp_nat_num_int: (nat > num) > (int > nat) > int > num).
% 28.44/7.23 thf(func_def_781, type, comp_nat_num_nat: (nat > num) > (nat > nat) > nat > num).
% 28.44/7.23 thf(func_def_782, type, comp_nat_num_num: (nat > num) > (num > nat) > num > num).
% 28.44/7.23 thf(func_def_783, type, comp_n8649498751204056690at_nat: (nat > num) > (product_prod_nat_nat > nat) > product_prod_nat_nat > num).
% 28.44/7.23 thf(func_def_784, type, comp_n8574565218330151774at_nat: (nat > product_prod_nat_nat) > (nat > nat) > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_785, type, comp_n8531277669757933902um_int: (nat > product_prod_num_num) > (int > nat) > int > product_prod_num_num).
% 28.44/7.23 thf(func_def_786, type, comp_nat_rat_int: (nat > rat) > (int > nat) > int > rat).
% 28.44/7.23 thf(func_def_787, type, comp_nat_rat_nat: (nat > rat) > (nat > nat) > nat > rat).
% 28.44/7.23 thf(func_def_788, type, comp_nat_rat_rat: (nat > rat) > (rat > nat) > rat > rat).
% 28.44/7.23 thf(func_def_789, type, comp_nat_rat_char: (nat > rat) > (char > nat) > char > rat).
% 28.44/7.23 thf(func_def_790, type, comp_nat_set_nat_int: (nat > set_nat) > (int > nat) > int > set_nat).
% 28.44/7.23 thf(func_def_791, type, comp_nat_set_nat_nat: (nat > set_nat) > (nat > nat) > nat > set_nat).
% 28.44/7.23 thf(func_def_792, type, comp_nat_set_rat_int: (nat > set_rat) > (int > nat) > int > set_rat).
% 28.44/7.23 thf(func_def_793, type, comp_nat_set_rat_nat: (nat > set_rat) > (nat > nat) > nat > set_rat).
% 28.44/7.23 thf(func_def_794, type, comp_nat_char_char: (nat > char) > (char > nat) > char > char).
% 28.44/7.23 thf(func_def_795, type, comp_num_o_o: (num > $o) > ($o > num) > $o > $o).
% 28.44/7.23 thf(func_def_796, type, comp_num_o_int: (num > $o) > (int > num) > int > $o).
% 28.44/7.23 thf(func_def_797, type, comp_num_o_nat: (num > $o) > (nat > num) > nat > $o).
% 28.44/7.23 thf(func_def_798, type, comp_num_o_num: (num > $o) > (num > num) > num > $o).
% 28.44/7.23 thf(func_def_799, type, comp_num_nat_int: (num > nat) > (int > num) > int > nat).
% 28.44/7.23 thf(func_def_800, type, comp_num_nat_nat: (num > nat) > (nat > num) > nat > nat).
% 28.44/7.23 thf(func_def_801, type, comp_num_nat_num: (num > nat) > (num > num) > num > nat).
% 28.44/7.23 thf(func_def_802, type, comp_num_num_o: (num > num) > ($o > num) > $o > num).
% 28.44/7.23 thf(func_def_803, type, comp_n8557746072492896886nteger: (num > num) > (code_integer > num) > code_integer > num).
% 28.44/7.23 thf(func_def_804, type, comp_num_num_int: (num > num) > (int > num) > int > num).
% 28.44/7.23 thf(func_def_805, type, comp_num_num_nat: (num > num) > (nat > num) > nat > num).
% 28.44/7.23 thf(func_def_806, type, comp_num_num_num: (num > num) > (num > num) > num > num).
% 28.44/7.23 thf(func_def_807, type, comp_num_set_int_int: (num > set_int) > (int > num) > int > set_int).
% 28.44/7.23 thf(func_def_808, type, comp_num_set_nat_int: (num > set_nat) > (int > num) > int > set_nat).
% 28.44/7.23 thf(func_def_809, type, comp_num_set_rat_int: (num > set_rat) > (int > num) > int > set_rat).
% 28.44/7.23 thf(func_def_810, type, comp_P8564252314792299288nteger: (produc723880050079548563nteger > produc101387210554329899nteger) > (code_integer > produc723880050079548563nteger) > code_integer > produc101387210554329899nteger).
% 28.44/7.23 thf(func_def_811, type, comp_P2137996956111167876_o_o_o: (product_prod_o_o > $o) > ($o > product_prod_o_o) > $o > $o).
% 28.44/7.23 thf(func_def_812, type, comp_P551574746845053877_o_o_o: (product_prod_o_o > product_prod_o_o) > ($o > product_prod_o_o) > $o > product_prod_o_o).
% 28.44/7.23 thf(func_def_813, type, comp_P7034811116587396339_o_nat: (product_prod_o_o > product_prod_o_o) > (nat > product_prod_o_o) > nat > product_prod_o_o).
% 28.44/7.23 thf(func_def_814, type, comp_P4785046977597218846at_nat: (product_prod_o_o > product_prod_o_o) > (product_prod_nat_nat > product_prod_o_o) > product_prod_nat_nat > product_prod_o_o).
% 28.44/7.23 thf(func_def_815, type, comp_P1471321874221585045at_o_o: (product_prod_o_o > product_prod_nat_o) > ($o > product_prod_o_o) > $o > product_prod_nat_o).
% 28.44/7.23 thf(func_def_816, type, comp_P465755969289462830at_int: (product_prod_o_int > product_prod_o_nat) > (product_prod_nat_int > product_prod_o_int) > product_prod_nat_int > product_prod_o_nat).
% 28.44/7.23 thf(func_def_817, type, comp_P1422407636550552773_nat_o: (product_prod_o_nat > product_prod_o_nat) > ($o > product_prod_o_nat) > $o > product_prod_o_nat).
% 28.44/7.23 thf(func_def_818, type, comp_P1391661485614827491at_nat: (product_prod_o_nat > product_prod_o_nat) > (nat > product_prod_o_nat) > nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_819, type, comp_P4962864564169660718at_nat: (product_prod_o_nat > product_prod_o_nat) > (product_prod_nat_nat > product_prod_o_nat) > product_prod_nat_nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_820, type, comp_P9057111047297513408at_int: (product_prod_o_nat > product_prod_o_num) > (product_prod_nat_int > product_prod_o_nat) > product_prod_nat_int > product_prod_o_num).
% 28.44/7.23 thf(func_def_821, type, comp_P196761593691424337_nat_o: (product_prod_o_nat > product_prod_nat_nat) > ($o > product_prod_o_nat) > $o > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_822, type, comp_P972951341003599239_nat_o: (product_prod_o_nat > product_prod_num_nat) > ($o > product_prod_o_nat) > $o > product_prod_num_nat).
% 28.44/7.23 thf(func_def_823, type, comp_P3428181540658402820nteger: (produc8923325533196201883nteger > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > code_integer).
% 28.44/7.23 thf(func_def_824, type, comp_P8237986404257982958t_unit: (produc8126358835630522215t_unit > heap_e7401611519738050253t_unit) > (produc7812382424243267045t_unit > produc8126358835630522215t_unit) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_825, type, comp_P3239167524078694454t_unit: (produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit) > (produc7812382424243267045t_unit > produc1799199577659733785_ref_a) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_826, type, comp_P1287623958910499840t_unit: (produc1799199577659733785_ref_a > ref_a) > (produc7812382424243267045t_unit > produc1799199577659733785_ref_a) > produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_827, type, comp_P2006160480335490974_ref_a: (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > (produc1799199577659733785_ref_a > produc7812382424243267045t_unit) > produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_828, type, comp_P8019343326919024234t_unit: (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > (produc7812382424243267045t_unit > produc7812382424243267045t_unit) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_829, type, comp_P6390991081591698364at_nat: (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > (product_prod_nat_nat > produc7812382424243267045t_unit) > product_prod_nat_nat > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_830, type, comp_P7254561687666694144_ref_a: (produc7812382424243267045t_unit > ref_a) > (produc1799199577659733785_ref_a > produc7812382424243267045t_unit) > produc1799199577659733785_ref_a > ref_a).
% 28.44/7.23 thf(func_def_831, type, comp_P4044372497395451596t_unit: (produc7812382424243267045t_unit > ref_a) > (produc7812382424243267045t_unit > produc7812382424243267045t_unit) > produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_832, type, comp_P7986581389989349338at_nat: (produc7812382424243267045t_unit > ref_a) > (product_prod_nat_nat > produc7812382424243267045t_unit) > product_prod_nat_nat > ref_a).
% 28.44/7.23 thf(func_def_833, type, comp_P9134237804721252988t_unit: (produc5288414631154139675_ref_a > ref_a) > (produc7812382424243267045t_unit > produc5288414631154139675_ref_a) > produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_834, type, comp_P9034173210191959223nt_int: (product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_835, type, comp_P6651465171681656048nt_int: (product_prod_int_int > int) > (int > product_prod_int_int) > int > int).
% 28.44/7.23 thf(func_def_836, type, comp_P6653955642190706324nt_nat: (product_prod_int_int > int) > (nat > product_prod_int_int) > nat > int).
% 28.44/7.23 thf(func_def_837, type, comp_P5356232565778667509nt_int: (product_prod_int_int > int) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_838, type, comp_P6018825582104210588nt_rat: (product_prod_int_int > int) > (rat > product_prod_int_int) > rat > int).
% 28.44/7.23 thf(func_def_839, type, comp_P4161745170962941589t_char: (product_prod_int_int > int) > (char > product_prod_int_int) > char > int).
% 28.44/7.23 thf(func_def_840, type, comp_P2318390481314533713nt_int: (product_prod_int_int > nat) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > nat).
% 28.44/7.23 thf(func_def_841, type, comp_P2788356708182965334nt_int: (product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_842, type, comp_P2134349925370910487at_int: (product_prod_int_int > product_prod_nat_nat) > (int > product_prod_int_int) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_843, type, comp_P3488689526429045841nt_nat: (product_prod_int_nat > nat) > (product_prod_int_nat > product_prod_int_nat) > product_prod_int_nat > nat).
% 28.44/7.23 thf(func_def_844, type, comp_P1145193044942399421um_int: (product_prod_int_nat > product_prod_nat_num) > (int > product_prod_int_nat) > int > product_prod_nat_num).
% 28.44/7.23 thf(func_def_845, type, comp_P5799945282029801519_o_nat: (product_prod_nat_o > product_prod_nat_o) > (nat > product_prod_nat_o) > nat > product_prod_nat_o).
% 28.44/7.23 thf(func_def_846, type, comp_P8901546994122883554at_nat: (product_prod_nat_o > product_prod_nat_o) > (product_prod_nat_nat > product_prod_nat_o) > product_prod_nat_nat > product_prod_nat_o).
% 28.44/7.23 thf(func_def_847, type, comp_P6576135029341976421_o_nat: (product_prod_nat_o > product_prod_num_o) > (nat > product_prod_nat_o) > nat > product_prod_num_o).
% 28.44/7.23 thf(func_def_848, type, comp_P5807473265676440968nt_nat: (product_prod_nat_o > product_prod_num_o) > (product_prod_int_nat > product_prod_nat_o) > product_prod_int_nat > product_prod_num_o).
% 28.44/7.23 thf(func_def_849, type, comp_P397146161216181329at_int: (product_prod_nat_int > nat) > (product_prod_nat_int > product_prod_nat_int) > product_prod_nat_int > nat).
% 28.44/7.23 thf(func_def_850, type, comp_P8376639181999047357at_int: (product_prod_nat_int > product_prod_num_nat) > (int > product_prod_nat_int) > int > product_prod_num_nat).
% 28.44/7.23 thf(func_def_851, type, comp_P3772045228931366376nt_int: (product_prod_nat_int > product_prod_num_nat) > (product_prod_int_int > product_prod_nat_int) > product_prod_int_int > product_prod_num_nat).
% 28.44/7.23 thf(func_def_852, type, comp_P2002127591014248037at_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).
% 28.44/7.23 thf(func_def_853, type, comp_P7900071416159368952at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (produc4196048018000912732at_int > product_prod_nat_nat) > produc4196048018000912732at_int > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_854, type, comp_P3913276677246710332at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_855, type, comp_P4524073163769703009at_int: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (produc4196048018000912732at_int > product_prod_nat_nat) > produc4196048018000912732at_int > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_856, type, comp_P4605287290794827253at_nat: (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > int).
% 28.44/7.23 thf(func_def_857, type, comp_P1953119740877977564at_int: (product_prod_nat_nat > nat) > (int > product_prod_nat_nat) > int > nat).
% 28.44/7.23 thf(func_def_858, type, comp_P5292260908303971472st_nat: (product_prod_nat_nat > nat) > (list_nat > product_prod_nat_nat) > list_nat > nat).
% 28.44/7.23 thf(func_def_859, type, comp_P1955610211387027840at_nat: (product_prod_nat_nat > nat) > (nat > product_prod_nat_nat) > nat > nat).
% 28.44/7.23 thf(func_def_860, type, comp_P1567445206330693457at_nat: (product_prod_nat_nat > nat) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_861, type, comp_P8635049891247748876at_int: (product_prod_nat_nat > nat) > (produc4196048018000912732at_int > product_prod_nat_nat) > produc4196048018000912732at_int > nat).
% 28.44/7.23 thf(func_def_862, type, comp_P1320480151300532104at_rat: (product_prod_nat_nat > nat) > (rat > product_prod_nat_nat) > rat > nat).
% 28.44/7.23 thf(func_def_863, type, comp_P1491501995297412481t_char: (product_prod_nat_nat > nat) > (char > product_prod_nat_nat) > char > nat).
% 28.44/7.23 thf(func_def_864, type, comp_P7428279379633703887at_int: (product_prod_nat_nat > product_prod_nat_nat) > (int > product_prod_nat_nat) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_865, type, comp_P7430769850142754163at_nat: (product_prod_nat_nat > product_prod_nat_nat) > (nat > product_prod_nat_nat) > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_866, type, comp_P6334688330072917552at_int: (product_prod_nat_nat > product_prod_nat_num) > (product_prod_nat_int > product_prod_nat_nat) > product_prod_nat_int > product_prod_nat_num).
% 28.44/7.23 thf(func_def_867, type, comp_P5371577678113413053at_nat: (product_prod_nat_nat > product_prod_num_nat) > (nat > product_prod_nat_nat) > nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_868, type, comp_P5124699952429557552nt_nat: (product_prod_nat_nat > product_prod_num_nat) > (product_prod_int_nat > product_prod_nat_nat) > product_prod_int_nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_869, type, comp_P7387482301570536291um_int: (product_prod_nat_nat > product_prod_num_num) > (int > product_prod_nat_nat) > int > product_prod_num_num).
% 28.44/7.23 thf(func_def_870, type, comp_P9218946435557410242nt_int: (product_prod_nat_nat > product_prod_num_num) > (product_prod_int_int > product_prod_nat_nat) > product_prod_int_int > product_prod_num_num).
% 28.44/7.23 thf(func_def_871, type, comp_P8336958949797789649um_nat: (product_prod_nat_num > nat) > (product_prod_num_nat > product_prod_nat_num) > product_prod_num_nat > nat).
% 28.44/7.23 thf(func_def_872, type, comp_P5051845089628979463um_nat: (product_prod_nat_num > num) > (product_prod_num_nat > product_prod_nat_num) > product_prod_num_nat > num).
% 28.44/7.23 thf(func_def_873, type, comp_P3192427084145116251at_num: (product_prod_num_nat > product_prod_o_nat) > (num > product_prod_num_nat) > num > product_prod_o_nat).
% 28.44/7.23 thf(func_def_874, type, comp_P2539519431309506803at_num: (product_prod_num_nat > product_prod_nat_nat) > (num > product_prod_num_nat) > num > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_875, type, comp_P480327259280165693at_num: (product_prod_num_nat > product_prod_num_nat) > (num > product_prod_num_nat) > num > product_prod_num_nat).
% 28.44/7.23 thf(func_def_876, type, comp_P4305060815297604026um_int: (product_prod_num_num > num) > (int > product_prod_num_num) > int > num).
% 28.44/7.23 thf(func_def_877, type, comp_P864883071962432936um_num: (product_prod_num_num > num) > (num > product_prod_num_num) > num > num).
% 28.44/7.23 thf(func_def_878, type, comp_P4974406650942564362at_nat: (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > (produc3843707927480180839at_nat > produc3843707927480180839at_nat) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_879, type, comp_P4528037747288561284at_nat: (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > (set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_880, type, comp_P3728553842126764068at_nat: (produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat) > (produc1319942482725812455at_nat > produc1319942482725812455at_nat) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_881, type, comp_P8235817900121468292at_nat: (produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat) > (set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_882, type, comp_P5156358013004227690it_o_o: (product_unit > $o) > ($o > product_unit) > $o > $o).
% 28.44/7.23 thf(func_def_883, type, comp_P4985893458130756478_o_nat: (product_unit > $o) > (nat > product_unit) > nat > $o).
% 28.44/7.23 thf(func_def_884, type, comp_rat_o_o: (rat > $o) > ($o > rat) > $o > $o).
% 28.44/7.23 thf(func_def_885, type, comp_rat_o_nat: (rat > $o) > (nat > rat) > nat > $o).
% 28.44/7.23 thf(func_def_886, type, comp_rat_int_int: (rat > int) > (int > rat) > int > int).
% 28.44/7.23 thf(func_def_887, type, comp_rat_int_nat: (rat > int) > (nat > rat) > nat > int).
% 28.44/7.23 thf(func_def_888, type, comp_rat_int_char: (rat > int) > (char > rat) > char > int).
% 28.44/7.23 thf(func_def_889, type, comp_rat_nat_o: (rat > nat) > ($o > rat) > $o > nat).
% 28.44/7.23 thf(func_def_890, type, comp_rat_nat_int: (rat > nat) > (int > rat) > int > nat).
% 28.44/7.23 thf(func_def_891, type, comp_rat_nat_nat: (rat > nat) > (nat > rat) > nat > nat).
% 28.44/7.23 thf(func_def_892, type, comp_rat_nat_rat: (rat > nat) > (rat > rat) > rat > nat).
% 28.44/7.23 thf(func_def_893, type, comp_rat_nat_char: (rat > nat) > (char > rat) > char > nat).
% 28.44/7.23 thf(func_def_894, type, comp_rat_num_nat: (rat > num) > (nat > rat) > nat > num).
% 28.44/7.23 thf(func_def_895, type, comp_rat_num_num: (rat > num) > (num > rat) > num > num).
% 28.44/7.23 thf(func_def_896, type, comp_rat_rat_nat: (rat > rat) > (nat > rat) > nat > rat).
% 28.44/7.23 thf(func_def_897, type, comp_rat_rat_char: (rat > rat) > (char > rat) > char > rat).
% 28.44/7.23 thf(func_def_898, type, comp_rat_char_char: (rat > char) > (char > rat) > char > char).
% 28.44/7.23 thf(func_def_899, type, comp_s4786119426940707554nteger: (set_Co726186806682698383nteger > set_Code_integer) > (set_Pr4111642102156807771nteger > set_Co726186806682698383nteger) > set_Pr4111642102156807771nteger > set_Code_integer).
% 28.44/7.23 thf(func_def_900, type, comp_s9189197539837705563_set_o: (set_o > set_nat) > (set_o > set_o) > set_o > set_nat).
% 28.44/7.23 thf(func_def_901, type, comp_s7717450105097109807et_nat: (set_int > set_int) > (set_nat > set_int) > set_nat > set_int).
% 28.44/7.23 thf(func_def_902, type, comp_s2487324123861929025et_int: (set_int > set_int) > (set_set_int > set_int) > set_set_int > set_int).
% 28.44/7.23 thf(func_def_903, type, comp_s5712175470073906149et_int: (set_int > set_nat) > (set_set_int > set_int) > set_set_int > set_nat).
% 28.44/7.23 thf(func_def_904, type, comp_s7011316712748663051_int_o: (set_nat > set_int) > ($o > set_nat) > $o > set_int).
% 28.44/7.23 thf(func_def_905, type, comp_s5617672292595496825nt_int: (set_nat > set_int) > (int > set_nat) > int > set_int).
% 28.44/7.23 thf(func_def_906, type, comp_s5620162763104547101nt_nat: (set_nat > set_int) > (nat > set_nat) > nat > set_int).
% 28.44/7.23 thf(func_def_907, type, comp_s6458263553158497821et_num: (set_nat > set_int) > (set_num > set_nat) > set_num > set_int).
% 28.44/7.23 thf(func_def_908, type, comp_s3768223441818958217et_nat: (set_nat > set_int) > (set_set_nat > set_nat) > set_set_nat > set_int).
% 28.44/7.23 thf(func_def_909, type, comp_s33089643564333159_nat_o: (set_nat > set_nat) > ($o > set_nat) > $o > set_nat).
% 28.44/7.23 thf(func_def_910, type, comp_s3430750717902475037at_int: (set_nat > set_nat) > (int > set_nat) > int > set_nat).
% 28.44/7.23 thf(func_def_911, type, comp_s3433241188411525313at_nat: (set_nat > set_nat) > (nat > set_nat) > nat > set_nat).
% 28.44/7.23 thf(func_def_912, type, comp_s8964582002068861047et_nat: (set_nat > set_nat) > (set_nat > set_nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_913, type, comp_s6993074788030935341et_nat: (set_nat > set_nat) > (set_set_nat > set_nat) > set_set_nat > set_nat).
% 28.44/7.23 thf(func_def_914, type, comp_s8507027185284273247_rat_o: (set_nat > set_rat) > ($o > set_nat) > $o > set_rat).
% 28.44/7.23 thf(func_def_915, type, comp_s8253438564248248613at_int: (set_nat > set_rat) > (int > set_nat) > int > set_rat).
% 28.44/7.23 thf(func_def_916, type, comp_s8255929034757298889at_nat: (set_nat > set_rat) > (nat > set_nat) > nat > set_rat).
% 28.44/7.23 thf(func_def_917, type, comp_s6435139744279249717et_nat: (set_nat > set_rat) > (set_set_nat > set_nat) > set_set_nat > set_rat).
% 28.44/7.23 thf(func_def_918, type, comp_s7355055891894327172at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_919, type, comp_s8709038167382007543et_int: (set_set_int > set_int) > (set_set_int > set_set_int) > set_set_int > set_int).
% 28.44/7.23 thf(func_def_920, type, comp_s1975749275458958491et_nat: (set_set_int > set_int) > (set_set_nat > set_set_int) > set_set_nat > set_int).
% 28.44/7.23 thf(func_def_921, type, comp_s6907669228194913343et_int: (set_set_nat > set_nat) > (set_set_int > set_set_nat) > set_set_int > set_nat).
% 28.44/7.23 thf(func_def_922, type, comp_s174380336271864291et_nat: (set_set_nat > set_nat) > (set_set_nat > set_set_nat) > set_set_nat > set_nat).
% 28.44/7.23 thf(func_def_923, type, comp_s703482200030188019et_nat: (set_set_rat > set_rat) > (set_set_nat > set_set_rat) > set_set_nat > set_rat).
% 28.44/7.23 thf(func_def_924, type, comp_char_o_o: (char > $o) > ($o > char) > $o > $o).
% 28.44/7.23 thf(func_def_925, type, comp_char_o_char: (char > $o) > (char > char) > char > $o).
% 28.44/7.23 thf(func_def_926, type, comp_char_int_char: (char > int) > (char > char) > char > int).
% 28.44/7.23 thf(func_def_927, type, comp_char_nat_int: (char > nat) > (int > char) > int > nat).
% 28.44/7.23 thf(func_def_928, type, comp_char_nat_nat: (char > nat) > (nat > char) > nat > nat).
% 28.44/7.23 thf(func_def_929, type, comp_char_nat_char: (char > nat) > (char > char) > char > nat).
% 28.44/7.23 thf(func_def_930, type, comp_char_num_nat: (char > num) > (nat > char) > nat > num).
% 28.44/7.23 thf(func_def_931, type, comp_char_num_num: (char > num) > (num > char) > num > num).
% 28.44/7.23 thf(func_def_932, type, comp_char_num_char: (char > num) > (char > char) > char > num).
% 28.44/7.23 thf(func_def_933, type, comp_char_rat_char: (char > rat) > (char > char) > char > rat).
% 28.44/7.23 thf(func_def_934, type, comp_char_set_int_o: (char > set_int) > ($o > char) > $o > set_int).
% 28.44/7.23 thf(func_def_935, type, comp_c3102392033783471720nt_nat: (char > set_int) > (nat > char) > nat > set_int).
% 28.44/7.23 thf(func_def_936, type, comp_c8883095856794026162nt_num: (char > set_int) > (num > char) > num > set_int).
% 28.44/7.23 thf(func_def_937, type, comp_char_set_nat_o: (char > set_nat) > ($o > char) > $o > set_nat).
% 28.44/7.23 thf(func_def_938, type, comp_c912979988581399656at_int: (char > set_nat) > (int > char) > int > set_nat).
% 28.44/7.23 thf(func_def_939, type, comp_c915470459090449932at_nat: (char > set_nat) > (nat > char) > nat > set_nat).
% 28.44/7.23 thf(func_def_940, type, comp_c6696174282101004374at_num: (char > set_nat) > (num > char) > num > set_nat).
% 28.44/7.23 thf(func_def_941, type, comp_char_set_rat_o: (char > set_rat) > ($o > char) > $o > set_rat).
% 28.44/7.23 thf(func_def_942, type, comp_c5735667834927173232at_int: (char > set_rat) > (int > char) > int > set_rat).
% 28.44/7.23 thf(func_def_943, type, comp_c5738158305436223508at_nat: (char > set_rat) > (nat > char) > nat > set_rat).
% 28.44/7.23 thf(func_def_944, type, comp_c2295490091592002142at_num: (char > set_rat) > (num > char) > num > set_rat).
% 28.44/7.23 thf(func_def_945, type, comp_char_char_char: (char > char) > (char > char) > char > char).
% 28.44/7.23 thf(func_def_946, type, fun_upd_o_o: ($o > $o) > $o > $o > $o > $o).
% 28.44/7.23 thf(func_def_947, type, fun_upd_o_nat: ($o > nat) > $o > nat > $o > nat).
% 28.44/7.23 thf(func_def_948, type, fun_up846054379331416818t_unit: ($o > product_unit) > $o > product_unit > $o > product_unit).
% 28.44/7.23 thf(func_def_949, type, fun_upd_o_set_o: ($o > set_o) > $o > set_o > $o > set_o).
% 28.44/7.23 thf(func_def_950, type, fun_up4718931970374059986t_unit: ($o > set_Product_unit) > $o > set_Product_unit > $o > set_Product_unit).
% 28.44/7.23 thf(func_def_951, type, fun_up8056716234270145717nteger: (code_integer > code_integer > code_integer) > code_integer > (code_integer > code_integer) > code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_952, type, fun_up8139772397987072257nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > (produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_953, type, fun_upd_int_o: (int > $o) > int > $o > int > $o).
% 28.44/7.23 thf(func_def_954, type, fun_upd_int_int: (int > int) > int > int > int > int).
% 28.44/7.23 thf(func_def_955, type, fun_upd_int_nat: (int > nat) > int > nat > int > nat).
% 28.44/7.23 thf(func_def_956, type, fun_upd_int_num: (int > num) > int > num > int > num).
% 28.44/7.23 thf(func_def_957, type, fun_up2220634978854545698t_unit: (int > product_unit) > int > product_unit > int > product_unit).
% 28.44/7.23 thf(func_def_958, type, fun_upd_int_set_o: (int > set_o) > int > set_o > int > set_o).
% 28.44/7.23 thf(func_def_959, type, fun_upd_int_set_nat: (int > set_nat) > int > set_nat > int > set_nat).
% 28.44/7.23 thf(func_def_960, type, fun_up5054257004045450754t_unit: (int > set_Product_unit) > int > set_Product_unit > int > set_Product_unit).
% 28.44/7.23 thf(func_def_961, type, fun_upd_nat_o: (nat > $o) > nat > $o > nat > $o).
% 28.44/7.23 thf(func_def_962, type, fun_upd_nat_int: (nat > int) > nat > int > nat > int).
% 28.44/7.23 thf(func_def_963, type, fun_upd_nat_nat: (nat > nat) > nat > nat > nat > nat).
% 28.44/7.23 thf(func_def_964, type, fun_upd_nat_rat: (nat > rat) > nat > rat > nat > rat).
% 28.44/7.23 thf(func_def_965, type, fun_upd_nat_set_o: (nat > set_o) > nat > set_o > nat > set_o).
% 28.44/7.23 thf(func_def_966, type, fun_up1220017903161424222t_unit: (nat > set_Product_unit) > nat > set_Product_unit > nat > set_Product_unit).
% 28.44/7.23 thf(func_def_967, type, fun_up5432024876597553480unit_o: (product_unit > $o) > product_unit > $o > product_unit > $o).
% 28.44/7.23 thf(func_def_968, type, fun_up6473050886840373792it_nat: (product_unit > nat) > product_unit > nat > product_unit > nat).
% 28.44/7.23 thf(func_def_969, type, fun_up6875000483049295805t_unit: (product_unit > product_unit) > product_unit > product_unit > product_unit > product_unit).
% 28.44/7.23 thf(func_def_970, type, fun_up1762901246852280360_set_o: (product_unit > set_o) > product_unit > set_o > product_unit > set_o).
% 28.44/7.23 thf(func_def_971, type, fun_up4569834200710200790et_nat: (product_unit > set_nat) > product_unit > set_nat > product_unit > set_nat).
% 28.44/7.23 thf(func_def_972, type, fun_up488859312337516701t_unit: (product_unit > set_Product_unit) > product_unit > set_Product_unit > product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_973, type, id_nat_o: (nat > $o) > nat > $o).
% 28.44/7.23 thf(func_def_974, type, id_nat_nat: (nat > nat) > nat > nat).
% 28.44/7.23 thf(func_def_975, type, id_Pro496765588584934260nteger: (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_976, type, id_o: $o > $o).
% 28.44/7.23 thf(func_def_977, type, id_Code_integer: code_integer > code_integer).
% 28.44/7.23 thf(func_def_978, type, id_int: int > int).
% 28.44/7.23 thf(func_def_979, type, id_list_nat: list_nat > list_nat).
% 28.44/7.23 thf(func_def_980, type, id_nat: nat > nat).
% 28.44/7.23 thf(func_def_981, type, id_num: num > num).
% 28.44/7.23 thf(func_def_982, type, id_Pro2309048762231606924nteger: produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_983, type, id_Pro4381231610383771306nt_int: product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_984, type, id_Pro7559728917991913458at_nat: product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_985, type, id_Pro8267972854940751164at_num: product_prod_nat_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_986, type, id_Pro8722402698821300696at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_987, type, id_Pro6043886709289754456at_nat: produc1319942482725812455at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_988, type, id_Product_unit: product_unit > product_unit).
% 28.44/7.23 thf(func_def_989, type, id_rat: rat > rat).
% 28.44/7.23 thf(func_def_990, type, id_set_o: set_o > set_o).
% 28.44/7.23 thf(func_def_991, type, id_set_int: set_int > set_int).
% 28.44/7.23 thf(func_def_992, type, id_set_nat: set_nat > set_nat).
% 28.44/7.23 thf(func_def_993, type, id_set_num: set_num > set_num).
% 28.44/7.23 thf(func_def_994, type, id_set2334057505560298834at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_995, type, id_set7849613212452405432at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_996, type, id_char: char > char).
% 28.44/7.23 thf(func_def_997, type, inj_on5500977043710295017nteger: ((code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Co4375521073081744395nteger > $o).
% 28.44/7.23 thf(func_def_998, type, inj_on3998011822705705585nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Co726186806682698383nteger > $o).
% 28.44/7.23 thf(func_def_999, type, inj_on856898432580761861nt_nat: ((int > int) > int > nat) > set_int_int > $o).
% 28.44/7.23 thf(func_def_1000, type, inj_on7039184780174133295nt_int: ((int > int) > set_Pr958786334691620121nt_int) > set_int_int > $o).
% 28.44/7.23 thf(func_def_1001, type, inj_on5377432224680912883nt_num: ((int > nat) > int > num) > set_int_nat > $o).
% 28.44/7.23 thf(func_def_1002, type, inj_on_nat_o_nat_o: ((nat > $o) > nat > $o) > set_nat_o > $o).
% 28.44/7.23 thf(func_def_1003, type, inj_on2461717442902640625at_nat: ((nat > nat) > nat > nat) > set_nat_nat > $o).
% 28.44/7.23 thf(func_def_1004, type, inj_on3412903767820855855at_nat: ((nat > nat) > set_Pr1261947904930325089at_nat) > set_nat_nat > $o).
% 28.44/7.23 thf(func_def_1005, type, inj_on_o_o: ($o > $o) > set_o > $o).
% 28.44/7.23 thf(func_def_1006, type, inj_on_o_int: ($o > int) > set_o > $o).
% 28.44/7.23 thf(func_def_1007, type, inj_on_o_nat: ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_1008, type, inj_on4268752236855399398t_unit: ($o > product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_1009, type, inj_on_o_rat: ($o > rat) > set_o > $o).
% 28.44/7.23 thf(func_def_1010, type, inj_on_o_char: ($o > char) > set_o > $o).
% 28.44/7.23 thf(func_def_1011, type, inj_on108595395805848489nteger: (code_integer > code_integer > code_integer) > set_Code_integer > $o).
% 28.44/7.23 thf(func_def_1012, type, inj_on7031512951821619701nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Code_integer > $o).
% 28.44/7.23 thf(func_def_1013, type, inj_on1158064722259180589nteger: (code_integer > code_integer) > set_Code_integer > $o).
% 28.44/7.23 thf(func_def_1014, type, inj_on_int_o: (int > $o) > set_int > $o).
% 28.44/7.23 thf(func_def_1015, type, inj_on_int_int: (int > int) > set_int > $o).
% 28.44/7.23 thf(func_def_1016, type, inj_on_int_nat: (int > nat) > set_int > $o).
% 28.44/7.23 thf(func_def_1017, type, inj_on_int_num: (int > num) > set_int > $o).
% 28.44/7.23 thf(func_def_1018, type, inj_on5397397550511676250nt_int: (int > product_prod_int_int) > set_int > $o).
% 28.44/7.23 thf(func_def_1019, type, inj_on8575894858119818402at_nat: (int > product_prod_nat_nat) > set_int > $o).
% 28.44/7.23 thf(func_def_1020, type, inj_on4178023183795006766t_unit: (int > product_unit) > set_int > $o).
% 28.44/7.23 thf(func_def_1021, type, inj_on3049792774292151987st_nat: (list_nat > list_nat) > set_list_nat > $o).
% 28.44/7.23 thf(func_def_1022, type, inj_on7574789179980466158at_nat: (list_nat > product_prod_nat_nat) > set_list_nat > $o).
% 28.44/7.23 thf(func_def_1023, type, inj_on_nat_o: (nat > $o) > set_nat > $o).
% 28.44/7.23 thf(func_def_1024, type, inj_on_nat_int: (nat > int) > set_nat > $o).
% 28.44/7.23 thf(func_def_1025, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 28.44/7.23 thf(func_def_1026, type, inj_on_nat_num: (nat > num) > set_nat > $o).
% 28.44/7.23 thf(func_def_1027, type, inj_on5538052773655684606at_nat: (nat > product_prod_nat_nat) > set_nat > $o).
% 28.44/7.23 thf(func_def_1028, type, inj_on6246296710604522312at_num: (nat > product_prod_nat_num) > set_nat > $o).
% 28.44/7.23 thf(func_def_1029, type, inj_on7061601236592826506t_unit: (nat > product_unit) > set_nat > $o).
% 28.44/7.23 thf(func_def_1030, type, inj_on_nat_rat: (nat > rat) > set_nat > $o).
% 28.44/7.23 thf(func_def_1031, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 28.44/7.23 thf(func_def_1032, type, inj_on_num_o: (num > $o) > set_num > $o).
% 28.44/7.23 thf(func_def_1033, type, inj_on_num_int: (num > int) > set_num > $o).
% 28.44/7.23 thf(func_def_1034, type, inj_on_num_nat: (num > nat) > set_num > $o).
% 28.44/7.23 thf(func_def_1035, type, inj_on20428373856169009nteger: (produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Pr4811707699266497531nteger > $o).
% 28.44/7.23 thf(func_def_1036, type, inj_on6454360653267994289nt_int: (product_prod_int_int > product_prod_int_int) > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_1037, type, inj_on2178005380612969504at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1038, type, inj_on8969904277767023793at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1039, type, inj_on2339680571444523825at_num: (product_prod_num_nat > product_prod_nat_num) > set_Pr3280342998896498603um_nat > $o).
% 28.44/7.23 thf(func_def_1040, type, inj_on991952103320416098_nat_o: (produc859450856879609959at_nat > $o) > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1041, type, inj_on490725545064285830at_nat: (produc859450856879609959at_nat > nat) > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1042, type, inj_on229527429751349963at_nat: (produc859450856879609959at_nat > product_prod_nat_nat) > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1043, type, inj_on1041401102088758999t_unit: (produc859450856879609959at_nat > product_unit) > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1044, type, inj_on8430303779476321073at_nat: (produc3843707927480180839at_nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1045, type, inj_on3108384905993948887t_unit: (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1046, type, inj_on3942866938762682161at_nat: (produc1319942482725812455at_nat > produc1319942482725812455at_nat) > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_1047, type, inj_on8854722734121536060unit_o: (product_unit > $o) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1048, type, inj_on8427948621271784584it_int: (product_unit > int) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1049, type, inj_on8430439091780834860it_nat: (product_unit > nat) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1050, type, inj_on8151373323710067377t_unit: (product_unit > product_unit) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1051, type, inj_on7795309031694339124it_rat: (product_unit > rat) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1052, type, inj_on1959294024837303853t_char: (product_unit > char) > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1053, type, inj_on_rat_o: (rat > $o) > set_rat > $o).
% 28.44/7.23 thf(func_def_1054, type, inj_on_rat_int: (rat > int) > set_rat > $o).
% 28.44/7.23 thf(func_def_1055, type, inj_on_rat_nat: (rat > nat) > set_rat > $o).
% 28.44/7.23 thf(func_def_1056, type, inj_on8867882244352206326at_nat: (rat > product_prod_nat_nat) > set_rat > $o).
% 28.44/7.23 thf(func_def_1057, type, inj_on_rat_rat: (rat > rat) > set_rat > $o).
% 28.44/7.23 thf(func_def_1058, type, inj_on6435365835345961783et_int: (set_int > set_int) > set_set_int > $o).
% 28.44/7.23 thf(func_def_1059, type, inj_on1389844818000382683et_nat: (set_int > set_nat) > set_set_int > $o).
% 28.44/7.23 thf(func_def_1060, type, inj_on426556184350386907et_int: (set_nat > set_int) > set_set_nat > $o).
% 28.44/7.23 thf(func_def_1061, type, inj_on4604407203859583615et_nat: (set_nat > set_nat) > set_set_nat > $o).
% 28.44/7.23 thf(func_def_1062, type, inj_on1096178645466186887et_rat: (set_nat > set_rat) > set_set_nat > $o).
% 28.44/7.23 thf(func_def_1063, type, inj_on699426629415580343at_nat: (set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat) > set_se7855581050983116737at_nat > $o).
% 28.44/7.23 thf(func_def_1064, type, inj_on1468925692805905105at_nat: (set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat) > set_se5479201105039950375at_nat > $o).
% 28.44/7.23 thf(func_def_1065, type, inj_on_char_o: (char > $o) > set_char > $o).
% 28.44/7.23 thf(func_def_1066, type, inj_on_char_int: (char > int) > set_char > $o).
% 28.44/7.23 thf(func_def_1067, type, inj_on_char_nat: (char > nat) > set_char > $o).
% 28.44/7.23 thf(func_def_1068, type, inj_on1021528964648911549at_nat: (char > product_prod_nat_nat) > set_char > $o).
% 28.44/7.23 thf(func_def_1069, type, inj_on_char_char: (char > char) > set_char > $o).
% 28.44/7.23 thf(func_def_1070, type, map_fu1227494855608507351um_num: (code_integer > int) > (num > num) > (int > num) > code_integer > num).
% 28.44/7.23 thf(func_def_1071, 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 > $o).
% 28.44/7.23 thf(func_def_1072, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 28.44/7.23 thf(func_def_1073, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 28.44/7.23 thf(func_def_1074, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 28.44/7.23 thf(func_def_1075, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 28.44/7.23 thf(func_def_1076, type, the_inv_into_o_o: set_o > ($o > $o) > $o > $o).
% 28.44/7.23 thf(func_def_1077, type, the_inv_into_o_int: set_o > ($o > int) > int > $o).
% 28.44/7.23 thf(func_def_1078, type, the_inv_into_o_nat: set_o > ($o > nat) > nat > $o).
% 28.44/7.23 thf(func_def_1079, type, the_inv_into_o_rat: set_o > ($o > rat) > rat > $o).
% 28.44/7.23 thf(func_def_1080, type, the_inv_into_o_char: set_o > ($o > char) > char > $o).
% 28.44/7.23 thf(func_def_1081, type, the_inv_into_int_o: set_int > (int > $o) > $o > int).
% 28.44/7.23 thf(func_def_1082, type, the_inv_into_int_int: set_int > (int > int) > int > int).
% 28.44/7.23 thf(func_def_1083, type, the_inv_into_int_nat: set_int > (int > nat) > nat > int).
% 28.44/7.23 thf(func_def_1084, type, the_inv_into_int_num: set_int > (int > num) > num > int).
% 28.44/7.23 thf(func_def_1085, type, the_inv_into_int_rat: set_int > (int > rat) > rat > int).
% 28.44/7.23 thf(func_def_1086, type, the_inv_into_nat_o: set_nat > (nat > $o) > $o > nat).
% 28.44/7.23 thf(func_def_1087, type, the_inv_into_nat_int: set_nat > (nat > int) > int > nat).
% 28.44/7.23 thf(func_def_1088, type, the_inv_into_nat_nat: set_nat > (nat > nat) > nat > nat).
% 28.44/7.23 thf(func_def_1089, type, the_inv_into_nat_num: set_nat > (nat > num) > num > nat).
% 28.44/7.23 thf(func_def_1090, type, the_inv_into_nat_rat: set_nat > (nat > rat) > rat > nat).
% 28.44/7.23 thf(func_def_1091, type, the_in9023905271258939222t_char: set_nat > (nat > char) > char > nat).
% 28.44/7.23 thf(func_def_1092, type, the_inv_into_num_o: set_num > (num > $o) > $o > num).
% 28.44/7.23 thf(func_def_1093, type, the_inv_into_num_int: set_num > (num > int) > int > num).
% 28.44/7.23 thf(func_def_1094, type, the_inv_into_num_nat: set_num > (num > nat) > nat > num).
% 28.44/7.23 thf(func_def_1095, type, the_in43325605794470270unit_o: set_Product_unit > (product_unit > $o) > $o > product_unit).
% 28.44/7.23 thf(func_def_1096, type, the_in3915408195775746418it_rat: set_Product_unit > (product_unit > rat) > rat > product_unit).
% 28.44/7.23 thf(func_def_1097, type, the_in3194898024646563179t_char: set_Product_unit > (product_unit > char) > char > product_unit).
% 28.44/7.23 thf(func_def_1098, type, the_inv_into_rat_o: set_rat > (rat > $o) > $o > rat).
% 28.44/7.23 thf(func_def_1099, type, the_inv_into_rat_nat: set_rat > (rat > nat) > nat > rat).
% 28.44/7.23 thf(func_def_1100, type, fun_in_rel_int_int: set_Pr958786334691620121nt_int > int > int > $o).
% 28.44/7.23 thf(func_def_1101, type, fun_in_rel_nat_nat: set_Pr1261947904930325089at_nat > nat > nat > $o).
% 28.44/7.23 thf(func_def_1102, type, fun_in_rel_nat_num: set_Pr6200539531224447659at_num > nat > num > $o).
% 28.44/7.23 thf(func_def_1103, type, fun_in8056734985859589634at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1104, type, fun_in6812141508599261570at_nat: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1105, type, fun_is_measure_int: (int > nat) > $o).
% 28.44/7.23 thf(func_def_1106, type, fun_max_strict: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1107, type, fun_max_weak: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1108, type, fun_min_strict: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1109, type, fun_min_weak: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1110, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1111, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1112, type, fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o).
% 28.44/7.23 thf(func_def_1113, type, fun_rp8445993449185644698at_nat: produc1319942482725812455at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1114, type, gcd_Gcd_int: set_int > int).
% 28.44/7.23 thf(func_def_1115, type, gcd_Gcd_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_1116, type, gcd_Lcm_int: set_int > int).
% 28.44/7.23 thf(func_def_1117, type, gcd_Lcm_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_1118, type, abs_abs_Code_integer: code_integer > code_integer).
% 28.44/7.23 thf(func_def_1119, type, abs_abs_int: int > int).
% 28.44/7.23 thf(func_def_1120, type, abs_abs_rat: rat > rat).
% 28.44/7.23 thf(func_def_1121, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_1122, type, minus_minus_int: int > int > int).
% 28.44/7.23 thf(func_def_1123, type, minus_minus_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_1124, type, minus_minus_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_1125, type, minus_minus_set_o: set_o > set_o > set_o).
% 28.44/7.23 thf(func_def_1126, type, minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 28.44/7.23 thf(func_def_1127, type, minus_minus_set_int: set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_1128, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_1129, type, minus_7052513330764642158od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1130, type, minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1131, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1132, type, minus_8321449233255521966at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1133, type, minus_8235382265540049710at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_1134, type, minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1135, type, minus_8674369445256047406at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1136, type, minus_6452836326544984404t_unit: set_Product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_1137, type, minus_minus_set_rat: set_rat > set_rat > set_rat).
% 28.44/7.23 thf(func_def_1138, type, minus_minus_set_char: set_char > set_char > set_char).
% 28.44/7.23 thf(func_def_1139, type, one_one_Code_integer: code_integer).
% 28.44/7.23 thf(func_def_1140, type, one_one_int: int).
% 28.44/7.23 thf(func_def_1141, type, one_one_nat: nat).
% 28.44/7.23 thf(func_def_1142, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_1143, type, plus_plus_int: int > int > int).
% 28.44/7.23 thf(func_def_1144, type, plus_plus_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_1145, type, plus_plus_num: num > num > num).
% 28.44/7.23 thf(func_def_1146, type, plus_plus_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_1147, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 28.44/7.23 thf(func_def_1148, type, sgn_sgn_int: int > int).
% 28.44/7.23 thf(func_def_1149, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_1150, type, times_times_int: int > int > int).
% 28.44/7.23 thf(func_def_1151, type, times_times_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_1152, type, times_times_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_1153, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 28.44/7.23 thf(func_def_1154, type, uminus_uminus_int: int > int).
% 28.44/7.23 thf(func_def_1155, type, uminus2952777764628376836t_unit: product_unit > product_unit).
% 28.44/7.23 thf(func_def_1156, type, uminus_uminus_rat: rat > rat).
% 28.44/7.23 thf(func_def_1157, type, zero_z3403309356797280102nteger: code_integer).
% 28.44/7.23 thf(func_def_1158, type, zero_zero_int: int).
% 28.44/7.23 thf(func_def_1159, type, zero_zero_nat: nat).
% 28.44/7.23 thf(func_def_1160, type, the_Pr5012129486825234846t_unit: (produc7812382424243267045t_unit > $o) > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1161, type, the_Pr4378521158711661632nt_int: (product_prod_int_int > $o) > product_prod_int_int).
% 28.44/7.23 thf(func_def_1162, type, the_Pr7557018466319803784at_nat: (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1163, type, the_Pr8265262403268641490at_num: (product_prod_nat_num > $o) > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1164, type, the_Pr4604535484834969198at_nat: (produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1165, type, the_Pr4877703158196064750at_nat: (produc1319942482725812455at_nat > $o) > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1166, type, defaul566961228789861419t_unit: product_unit).
% 28.44/7.23 thf(func_def_1167, type, lim_Product_unit: heap_e7401611519738050253t_unit > nat).
% 28.44/7.23 thf(func_def_1168, type, heap_b146640354529102224_ref_a: heap_Heap_ref_a > (ref_a > heap_Heap_ref_a) > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1169, type, heap_effect_ref_a: heap_Heap_ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > $o).
% 28.44/7.23 thf(func_def_1170, type, heap_e2830298082929533060t_unit: heap_H6156071679106078628t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > product_unit > $o).
% 28.44/7.23 thf(func_def_1171, type, heap_effect_a: heap_Heap_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > a > $o).
% 28.44/7.23 thf(func_def_1172, type, heap_guard_ref_a: (heap_e7401611519738050253t_unit > $o) > (heap_e7401611519738050253t_unit > produc7812382424243267045t_unit) > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1173, type, heap_heap_ref_a: (heap_e7401611519738050253t_unit > produc7812382424243267045t_unit) > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1174, type, heap_raise_ref_a: literal > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1175, type, heap_return_ref_a: ref_a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1176, type, heap_success_ref_a: heap_Heap_ref_a > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_1177, type, heap_tap_ref_a: (heap_e7401611519738050253t_unit > ref_a) > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1178, type, heap_tap_a: (heap_e7401611519738050253t_unit > a) > heap_Heap_a).
% 28.44/7.23 thf(func_def_1179, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 28.44/7.23 thf(func_def_1180, type, if_Heap_Heap_ref_a: $o > heap_Heap_ref_a > heap_Heap_ref_a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1181, type, if_int: $o > int > int > int).
% 28.44/7.23 thf(func_def_1182, type, if_nat: $o > nat > nat > nat).
% 28.44/7.23 thf(func_def_1183, type, if_num: $o > num > num > num).
% 28.44/7.23 thf(func_def_1184, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 28.44/7.23 thf(func_def_1185, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1186, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1187, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1188, type, if_Pro3444522238938527101atural: $o > produc4675096598859438275atural > produc4675096598859438275atural > produc4675096598859438275atural).
% 28.44/7.23 thf(func_def_1189, type, if_Pro4507677147265585453at_nat: $o > produc859450856879609959at_nat > produc859450856879609959at_nat > produc859450856879609959at_nat).
% 28.44/7.23 thf(func_def_1190, type, if_Pro3594990065127090477at_nat: $o > produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1191, type, if_Product_unit: $o > product_unit > product_unit > product_unit).
% 28.44/7.23 thf(func_def_1192, type, if_rat: $o > rat > rat > rat).
% 28.44/7.23 thf(func_def_1193, type, if_set_o: $o > set_o > set_o > set_o).
% 28.44/7.23 thf(func_def_1194, type, if_set_nat: $o > set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_1195, type, if_set1508868558775481357at_nat: $o > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1196, type, if_set3208018901896979469at_nat: $o > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1197, type, if_set_Product_unit: $o > set_Product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_1198, type, abs_Integ: product_prod_nat_nat > int).
% 28.44/7.23 thf(func_def_1199, type, rep_Integ: int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1200, type, cr_int: product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_1201, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1202, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1203, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1204, type, nat2: int > nat).
% 28.44/7.23 thf(func_def_1205, type, pcr_int: product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_1206, type, inf_inf_int_int_o: (int > int > $o) > (int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_1207, type, inf_inf_nat_nat_o: (nat > nat > $o) > (nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_1208, type, inf_inf_nat_num_o: (nat > num > $o) > (nat > num > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_1209, type, inf_in6124848772414083356_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1210, type, inf_in6969519006101653788_nat_o: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1211, type, inf_inf_int: int > int > int).
% 28.44/7.23 thf(func_def_1212, type, inf_inf_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_1213, type, inf_inf_Product_unit: product_unit > product_unit > product_unit).
% 28.44/7.23 thf(func_def_1214, type, inf_inf_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_1215, type, inf_inf_set_o: set_o > set_o > set_o).
% 28.44/7.23 thf(func_def_1216, type, inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 28.44/7.23 thf(func_def_1217, type, inf_inf_set_int: set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_1218, type, inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat).
% 28.44/7.23 thf(func_def_1219, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_1220, type, inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1221, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1222, type, inf_in7510916698018314649at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_1223, type, inf_in4302113700860409141at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1224, type, inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1225, type, inf_in2456762090751560885at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1226, type, inf_in4660618365625256667t_unit: set_Product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_1227, type, inf_inf_set_rat: set_rat > set_rat > set_rat).
% 28.44/7.23 thf(func_def_1228, type, inf_inf_set_char: set_char > set_char > set_char).
% 28.44/7.23 thf(func_def_1229, type, sup_su1544571744061072657eger_o: (int > code_integer > $o) > (int > code_integer > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_1230, type, sup_sup_int_int_o: (int > int > $o) > (int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_1231, type, sup_sup_nat_nat_o: (nat > nat > $o) > (nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_1232, type, sup_sup_nat_num_o: (nat > num > $o) > (nat > num > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_1233, type, sup_su5231854730092680051_int_o: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_1234, type, sup_su362511073950362882_nat_o: (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 > $o).
% 28.44/7.23 thf(func_def_1235, 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).
% 28.44/7.23 thf(func_def_1236, type, sup_su6164525874564267778_nat_o: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1237, type, sup_sup_int: int > int > int).
% 28.44/7.23 thf(func_def_1238, type, sup_sup_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_1239, type, sup_sup_Product_unit: product_unit > product_unit > product_unit).
% 28.44/7.23 thf(func_def_1240, type, sup_sup_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_1241, type, sup_sup_set_o: set_o > set_o > set_o).
% 28.44/7.23 thf(func_def_1242, type, sup_sup_set_int: set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_1243, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_1244, type, sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1245, type, sup_su8679140417860611193_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat).
% 28.44/7.23 thf(func_def_1246, type, sup_su4058753791541417424t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit).
% 28.44/7.23 thf(func_def_1247, type, sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1248, type, sup_su503371503184139039_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o).
% 28.44/7.23 thf(func_def_1249, type, sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1250, type, sup_su2042722026077122175at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_1251, type, sup_su4209953369189666580t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit).
% 28.44/7.23 thf(func_def_1252, type, sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1253, type, sup_su2851927382625014182unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o).
% 28.44/7.23 thf(func_def_1254, type, sup_su1639320892072265582it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat).
% 28.44/7.23 thf(func_def_1255, type, sup_su6481247232241170203t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit).
% 28.44/7.23 thf(func_def_1256, type, sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1257, type, sup_su5395584912770621083at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1258, type, sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_1259, type, sup_sup_set_rat: set_rat > set_rat > set_rat).
% 28.44/7.23 thf(func_def_1260, type, sup_sup_set_set_o: set_set_o > set_set_o > set_set_o).
% 28.44/7.23 thf(func_def_1261, type, sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat).
% 28.44/7.23 thf(func_def_1262, type, sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_1263, type, sup_su474284620922681339at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_1264, type, sup_su5975557051335651745t_unit: set_set_Product_unit > set_set_Product_unit > set_set_Product_unit).
% 28.44/7.23 thf(func_def_1265, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_1266, type, quotie9062115205763428814nteger: ((code_integer > code_integer) > (code_integer > code_integer) > $o) > ((code_integer > code_integer) > code_integer) > (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_1267, type, quotie8207154290130328982nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o) > $o).
% 28.44/7.23 thf(func_def_1268, type, quotie8803226531959296410nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer) > (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_1269, type, quotient_o_o: ($o > $o > $o) > ($o > $o) > ($o > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_1270, type, quotient_o_nat: ($o > $o > $o) > ($o > nat) > (nat > $o) > ($o > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1271, type, quotie2291698863146621601nteger: (int > int > $o) > (int > code_integer) > (code_integer > int) > (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_1272, type, quotient_int_int: (int > int > $o) > (int > int) > (int > int) > (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_1273, type, quotient_int_nat: (int > int > $o) > (int > nat) > (nat > int) > (int > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1274, type, quotient_int_num: (int > int > $o) > (int > num) > (num > int) > (int > num > $o) > $o).
% 28.44/7.23 thf(func_def_1275, type, quotient_nat_o: (nat > nat > $o) > (nat > $o) > ($o > nat) > (nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_1276, type, quotient_nat_int: (nat > nat > $o) > (nat > int) > (int > nat) > (nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_1277, type, quotient_nat_nat: (nat > nat > $o) > (nat > nat) > (nat > nat) > (nat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1278, type, quotient_nat_num: (nat > nat > $o) > (nat > num) > (num > nat) > (nat > num > $o) > $o).
% 28.44/7.23 thf(func_def_1279, type, quotient_nat_rat: (nat > nat > $o) > (nat > rat) > (rat > nat) > (nat > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1280, type, quotient_nat_char: (nat > nat > $o) > (nat > char) > (char > nat) > (nat > char > $o) > $o).
% 28.44/7.23 thf(func_def_1281, type, quotient_num_int: (num > num > $o) > (num > int) > (int > num) > (num > int > $o) > $o).
% 28.44/7.23 thf(func_def_1282, type, quotient_num_nat: (num > num > $o) > (num > nat) > (nat > num) > (num > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1283, type, quotie1194848508323700631at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int) > (int > product_prod_nat_nat) > (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_1284, type, quotie4166942682936818134at_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) > $o).
% 28.44/7.23 thf(func_def_1285, type, quotient_rat_int: (rat > rat > $o) > (rat > int) > (int > rat) > (rat > int > $o) > $o).
% 28.44/7.23 thf(func_def_1286, type, quotient_rat_nat: (rat > rat > $o) > (rat > nat) > (nat > rat) > (rat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1287, type, quotient_rat_rat: (rat > rat > $o) > (rat > rat) > (rat > rat) > (rat > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1288, type, quotient_rat_char: (rat > rat > $o) > (rat > char) > (char > rat) > (rat > char > $o) > $o).
% 28.44/7.23 thf(func_def_1289, type, quotient_char_int: (char > char > $o) > (char > int) > (int > char) > (char > int > $o) > $o).
% 28.44/7.23 thf(func_def_1290, type, quotient_char_nat: (char > char > $o) > (char > nat) > (nat > char) > (char > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1291, type, quotient_char_rat: (char > char > $o) > (char > rat) > (rat > char) > (char > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1292, type, quotient_char_char: (char > char > $o) > (char > char) > (char > char) > (char > char > $o) > $o).
% 28.44/7.23 thf(func_def_1293, type, all_interval_nat: (nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_1294, type, cons_nat: nat > list_nat > list_nat).
% 28.44/7.23 thf(func_def_1295, type, nil_nat: list_nat).
% 28.44/7.23 thf(func_def_1296, type, list_ex_nat: (nat > $o) > list_nat > $o).
% 28.44/7.23 thf(func_def_1297, type, upt: nat > nat > list_nat).
% 28.44/7.23 thf(func_def_1298, type, suc: nat > nat).
% 28.44/7.23 thf(func_def_1299, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 28.44/7.23 thf(func_def_1300, type, semiring_1_Nats_int: set_int).
% 28.44/7.23 thf(func_def_1301, type, semiri1314217659103216013at_int: nat > int).
% 28.44/7.23 thf(func_def_1302, type, nat_int_decode: nat > int).
% 28.44/7.23 thf(func_def_1303, type, nat_int_encode: int > nat).
% 28.44/7.23 thf(func_def_1304, type, nat_list_decode: nat > list_nat).
% 28.44/7.23 thf(func_def_1305, type, nat_list_decode_rel: nat > nat > $o).
% 28.44/7.23 thf(func_def_1306, type, nat_list_encode: list_nat > nat).
% 28.44/7.23 thf(func_def_1307, type, nat_prod_decode: nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1308, type, nat_prod_encode: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_1309, type, nat_sum_decode: nat > sum_sum_nat_nat).
% 28.44/7.23 thf(func_def_1310, type, nat_sum_encode: sum_sum_nat_nat > nat).
% 28.44/7.23 thf(func_def_1311, type, nat_triangle: nat > nat).
% 28.44/7.23 thf(func_def_1312, type, bit0: num > num).
% 28.44/7.23 thf(func_def_1313, type, bit1: num > num).
% 28.44/7.23 thf(func_def_1314, type, one: num).
% 28.44/7.23 thf(func_def_1315, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 28.44/7.23 thf(func_def_1316, type, num_of_nat: nat > num).
% 28.44/7.23 thf(func_def_1317, type, numera6620942414471956472nteger: num > code_integer).
% 28.44/7.23 thf(func_def_1318, type, numeral_numeral_int: num > int).
% 28.44/7.23 thf(func_def_1319, type, numeral_numeral_nat: num > nat).
% 28.44/7.23 thf(func_def_1320, type, none_num: option_num).
% 28.44/7.23 thf(func_def_1321, type, some_num: num > option_num).
% 28.44/7.23 thf(func_def_1322, type, case_option_num_num: num > (num > num) > option_num > num).
% 28.44/7.23 thf(func_def_1323, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 28.44/7.23 thf(func_def_1324, type, order_aboveS_int: set_Pr958786334691620121nt_int > int > set_int).
% 28.44/7.23 thf(func_def_1325, type, order_aboveS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 28.44/7.23 thf(func_def_1326, type, order_1761765819289301284nt_int: set_Pr2560585780119916871nt_int > product_prod_int_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1327, type, order_4940263126897443436at_nat: set_Pr8693737435421807431at_nat > product_prod_nat_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1328, type, order_4440095836999870412at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_1329, type, order_2442354982230848562at_nat: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_1330, type, order_6238756238976269133r_on_o: set_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1331, type, order_4471489696718655927on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_1332, type, order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1333, type, order_7480980593162297270at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1334, type, order_2711500226769404828at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_1335, type, order_888282469287196226t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_1336, type, order_5942792088423767318at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1337, type, order_1878278401035043452at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_1338, type, order_1960202971199294558of_int: (int > int > $o) > set_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1339, type, order_1962693441708344834of_nat: (nat > nat > $o) > set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1340, type, order_8809246210994205103at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1341, type, order_8308734813930759573at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1342, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 28.44/7.23 thf(func_def_1343, type, order_2615775362358406454r_on_o: set_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1344, type, order_2886507596567047182on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_1345, type, order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1346, type, order_8331247224601271455at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1347, type, order_2339240034117818117at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_1348, type, order_3164716736300062379t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_1349, type, order_1968183844437341695at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1350, type, order_423636163458052581at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_1351, type, bot_bo341146761387662761eger_o: int > code_integer > $o).
% 28.44/7.23 thf(func_def_1352, type, bot_bot_int_int_o: int > int > $o).
% 28.44/7.23 thf(func_def_1353, type, bot_bot_nat_nat_o: nat > nat > $o).
% 28.44/7.23 thf(func_def_1354, type, bot_bot_nat_num_o: nat > num > $o).
% 28.44/7.23 thf(func_def_1355, type, bot_bo5438875203632553179_int_o: product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_1356, type, bot_bo4898103413517107610_nat_o: product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1357, type, bot_bo394778441745866138_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1358, type, bot_bo3364206721330744218_nat_o: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1359, type, bot_bo2717538794563056311t_unit: pred_Product_unit).
% 28.44/7.23 thf(func_def_1360, type, bot_bot_Product_unit: product_unit).
% 28.44/7.23 thf(func_def_1361, type, bot_bot_set_o: set_o).
% 28.44/7.23 thf(func_def_1362, type, bot_bo3686245532977126937t_unit: set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_1363, type, bot_bot_set_ref_a: set_ref_a).
% 28.44/7.23 thf(func_def_1364, type, bot_bot_set_int: set_int).
% 28.44/7.23 thf(func_def_1365, type, bot_bot_set_nat: set_nat).
% 28.44/7.23 thf(func_def_1366, type, bot_bot_set_num: set_num).
% 28.44/7.23 thf(func_def_1367, type, bot_bo7073875226086086771od_o_o: set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1368, type, bot_bo66526543525301729_o_nat: set_Pr2101469702781467981_o_nat).
% 28.44/7.23 thf(func_def_1369, type, bot_bo4402188677660116584t_unit: set_Pr6671815714118170108t_unit).
% 28.44/7.23 thf(func_def_1370, type, bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1371, type, bot_bo1114129665703605383_nat_o: set_Pr3149072824959771635_nat_o).
% 28.44/7.23 thf(func_def_1372, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1373, type, bot_bo7038385379056416535at_num: set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_1374, type, bot_bo5043309098482578556t_unit: set_Pr4334478416066269672t_unit).
% 28.44/7.23 thf(func_def_1375, type, bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1376, type, bot_bo7193250159860175667at_nat: set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_1377, type, bot_bo3195362268743713342unit_o: set_Pr5464989305201766866unit_o).
% 28.44/7.23 thf(func_def_1378, type, bot_bo2472676621365177558it_nat: set_Pr1763845938948868674it_nat).
% 28.44/7.23 thf(func_def_1379, type, bot_bo6659885642593197735at_nat: set_Pr3798168094891919931at_nat).
% 28.44/7.23 thf(func_def_1380, type, bot_bo1654022762305692595t_unit: set_Pr5094982260447487303t_unit).
% 28.44/7.23 thf(func_def_1381, type, bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1382, type, bot_bo4948859079157340979at_nat: set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1383, type, bot_bo3957492148770167129t_unit: set_Product_unit).
% 28.44/7.23 thf(func_def_1384, type, bot_bot_set_rat: set_rat).
% 28.44/7.23 thf(func_def_1385, type, bot_bot_set_set_nat: set_set_nat).
% 28.44/7.23 thf(func_def_1386, type, bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_1387, type, bot_bo1534825418459847827at_nat: set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_1388, type, bot_bot_set_char: set_char).
% 28.44/7.23 thf(func_def_1389, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 28.44/7.23 thf(func_def_1390, type, ord_less_int: int > int > $o).
% 28.44/7.23 thf(func_def_1391, type, ord_less_nat: nat > nat > $o).
% 28.44/7.23 thf(func_def_1392, type, ord_less_rat: rat > rat > $o).
% 28.44/7.23 thf(func_def_1393, type, ord_le7522433683449569238eger_o: ((int > int) > (code_integer > code_integer) > $o) > ((int > int) > (code_integer > code_integer) > $o) > $o).
% 28.44/7.23 thf(func_def_1394, type, ord_le6931201860925936491_num_o: ((int > num) > (code_integer > num) > $o) > ((int > num) > (code_integer > num) > $o) > $o).
% 28.44/7.23 thf(func_def_1395, type, ord_le4541714130423454556_num_o: ((int > num) > (int > num) > $o) > ((int > num) > (int > num) > $o) > $o).
% 28.44/7.23 thf(func_def_1396, type, ord_le8615040745438789472_int_o: ((int > product_prod_nat_nat) > (code_integer > int) > $o) > ((int > product_prod_nat_nat) > (code_integer > int) > $o) > $o).
% 28.44/7.23 thf(func_def_1397, type, ord_le2932013042137311317nt_o_o: ((product_prod_nat_nat > $o) > (int > $o) > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > $o).
% 28.44/7.23 thf(func_def_1398, type, ord_le6141271677531915726eger_o: ((product_prod_nat_nat > int) > (int > code_integer) > $o) > ((product_prod_nat_nat > int) > (int > code_integer) > $o) > $o).
% 28.44/7.23 thf(func_def_1399, type, ord_le1714508135640884727_nat_o: ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((product_prod_nat_nat > nat) > (int > nat) > $o) > $o).
% 28.44/7.23 thf(func_def_1400, type, ord_le2484784447047653514_int_o: ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > $o).
% 28.44/7.23 thf(func_def_1401, type, ord_le3602516367967493612eger_o: (code_integer > code_integer > $o) > (code_integer > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_1402, type, ord_le996066559646421213eger_o: (int > code_integer > $o) > (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_1403, type, ord_le6741204236512500942_int_o: (int > int > $o) > (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_1404, type, ord_le8236914709048111138_rat_o: (int > rat > $o) > (int > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1405, type, ord_le7608100903186094441char_o: (int > char > $o) > (int > char > $o) > $o).
% 28.44/7.23 thf(func_def_1406, type, ord_le2646555220125990790_nat_o: (nat > nat > $o) > (nat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1407, type, ord_le3404735783095501756_num_o: (nat > num > $o) > (nat > num > $o) > $o).
% 28.44/7.23 thf(func_def_1408, type, ord_le1897120724991155070_rat_o: (nat > rat > $o) > (nat > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1409, type, ord_le4878496333587278021char_o: (nat > char > $o) > (nat > char > $o) > $o).
% 28.44/7.23 thf(func_def_1410, type, ord_le6124364862034508274_num_o: (num > num > $o) > (num > num > $o) > $o).
% 28.44/7.23 thf(func_def_1411, type, ord_le129227817499904167_int_o: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_1412, type, ord_le5604493270027003598_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_1413, type, ord_le3222257882335906850_int_o: (rat > int > $o) > (rat > int > $o) > $o).
% 28.44/7.23 thf(func_def_1414, type, ord_le5467402850006352766_nat_o: (rat > nat > $o) > (rat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1415, type, ord_le4717968354871517046_rat_o: (rat > rat > $o) > (rat > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1416, type, ord_le6546876390139131069char_o: (rat > char > $o) > (rat > char > $o) > $o).
% 28.44/7.23 thf(func_def_1417, type, ord_le3935385432712749774_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > $o).
% 28.44/7.23 thf(func_def_1418, type, ord_le3072208448688395470_nat_o: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > $o).
% 28.44/7.23 thf(func_def_1419, type, ord_le3396192186225775209_int_o: (char > int > $o) > (char > int > $o) > $o).
% 28.44/7.23 thf(func_def_1420, type, ord_le5641337153896221125_nat_o: (char > nat > $o) > (char > nat > $o) > $o).
% 28.44/7.23 thf(func_def_1421, type, ord_le4891902658761385405_rat_o: (char > rat > $o) > (char > rat > $o) > $o).
% 28.44/7.23 thf(func_def_1422, type, ord_le2540245887939449860char_o: (char > char > $o) > (char > char > $o) > $o).
% 28.44/7.23 thf(func_def_1423, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 28.44/7.23 thf(func_def_1424, type, ord_less_eq_int: int > int > $o).
% 28.44/7.23 thf(func_def_1425, type, ord_less_eq_nat: nat > nat > $o).
% 28.44/7.23 thf(func_def_1426, type, ord_le3221252021190050221t_unit: product_unit > product_unit > $o).
% 28.44/7.23 thf(func_def_1427, type, ord_less_eq_rat: rat > rat > $o).
% 28.44/7.23 thf(func_def_1428, type, ord_le348599935723844335nteger: set_Co726186806682698383nteger > set_Co726186806682698383nteger > $o).
% 28.44/7.23 thf(func_def_1429, type, ord_less_eq_set_o: set_o > set_o > $o).
% 28.44/7.23 thf(func_def_1430, type, ord_less_eq_set_int: set_int > set_int > $o).
% 28.44/7.23 thf(func_def_1431, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 28.44/7.23 thf(func_def_1432, type, ord_less_eq_set_num: set_num > set_num > $o).
% 28.44/7.23 thf(func_def_1433, type, ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1434, type, ord_le6472378536984071597_o_nat: set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat > $o).
% 28.44/7.23 thf(func_def_1435, type, ord_le518195775913581980t_unit: set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit > $o).
% 28.44/7.23 thf(func_def_1436, type, ord_le5525191956872776187t_unit: set_Pr1133966238863718811t_unit > set_Pr1133966238863718811t_unit > $o).
% 28.44/7.23 thf(func_def_1437, type, ord_le2638047946463454698nteger: set_Pr8415741480598773322nteger > set_Pr8415741480598773322nteger > $o).
% 28.44/7.23 thf(func_def_1438, type, ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_1439, type, ord_le5333435103577920093nt_nat: set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat > $o).
% 28.44/7.23 thf(func_def_1440, type, ord_le7519981659162375251_nat_o: set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o > $o).
% 28.44/7.23 thf(func_def_1441, type, ord_le656430383953171549at_int: set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int > $o).
% 28.44/7.23 thf(func_def_1442, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1443, type, ord_le8085105155179020875at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > $o).
% 28.44/7.23 thf(func_def_1444, type, ord_le1468274181084648008t_unit: set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit > $o).
% 28.44/7.23 thf(func_def_1445, type, ord_le5989899228261996553at_rat: set_Pr4105333604307423337at_rat > set_Pr4105333604307423337at_rat > $o).
% 28.44/7.23 thf(func_def_1446, type, ord_le5164908622851071819um_nat: set_Pr3280342998896498603um_nat > set_Pr3280342998896498603um_nat > $o).
% 28.44/7.23 thf(func_def_1447, type, ord_le880128212290418581um_num: set_Pr8218934625190621173um_num > set_Pr8218934625190621173um_num > $o).
% 28.44/7.23 thf(func_def_1448, type, ord_le4604737605482584818at_int: set_Pr49084382684228242at_int > set_Pr49084382684228242at_int > $o).
% 28.44/7.23 thf(func_def_1449, type, ord_le3000389064537975527at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1450, type, ord_le3091953645718357095at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_1451, type, ord_le8534741403851954546unit_o: set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o > $o).
% 28.44/7.23 thf(func_def_1452, type, ord_le8121013740822022818it_nat: set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat > $o).
% 28.44/7.23 thf(func_def_1453, type, ord_le8681960759543468507at_nat: set_Pr3798168094891919931at_nat > set_Pr3798168094891919931at_nat > $o).
% 28.44/7.23 thf(func_def_1454, type, ord_le930853871177014503t_unit: set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_1455, type, ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1456, type, ord_le5997549366648089703at_nat: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_1457, type, ord_le3507040750410214029t_unit: set_Product_unit > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_1458, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 28.44/7.23 thf(func_def_1459, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 28.44/7.23 thf(func_def_1460, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 28.44/7.23 thf(func_def_1461, type, ord_le2077887516847798113at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o).
% 28.44/7.23 thf(func_def_1462, type, ord_le7966958417815640519at_nat: set_se5479201105039950375at_nat > set_se5479201105039950375at_nat > $o).
% 28.44/7.23 thf(func_def_1463, type, ord_le513522071413781156et_rat: set_set_rat > set_set_rat > $o).
% 28.44/7.23 thf(func_def_1464, type, ord_less_eq_set_char: set_char > set_char > $o).
% 28.44/7.23 thf(func_def_1465, type, order_3677659787690696076nt_int: (int > int) > $o).
% 28.44/7.23 thf(func_def_1466, type, order_3680150258199746352nt_nat: (int > nat) > $o).
% 28.44/7.23 thf(func_def_1467, type, order_2678306075789641520at_int: (nat > int) > $o).
% 28.44/7.23 thf(func_def_1468, type, order_2680796546298691796at_nat: (nat > nat) > $o).
% 28.44/7.23 thf(func_def_1469, type, order_2045666486212196060at_rat: (nat > rat) > $o).
% 28.44/7.23 thf(func_def_1470, type, order_mono_o_int: ($o > int) > $o).
% 28.44/7.23 thf(func_def_1471, type, order_mono_o_nat: ($o > nat) > $o).
% 28.44/7.23 thf(func_def_1472, type, order_7782127260464396005t_unit: ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_1473, type, order_mono_int_int: (int > int) > $o).
% 28.44/7.23 thf(func_def_1474, type, order_mono_int_nat: (int > nat) > $o).
% 28.44/7.23 thf(func_def_1475, type, order_2843698775922903023t_unit: (int > product_unit) > $o).
% 28.44/7.23 thf(func_def_1476, type, order_mono_nat_int: (nat > int) > $o).
% 28.44/7.23 thf(func_def_1477, type, order_mono_nat_nat: (nat > nat) > $o).
% 28.44/7.23 thf(func_def_1478, type, order_5727276828720722763t_unit: (nat > product_unit) > $o).
% 28.44/7.23 thf(func_def_1479, type, order_mono_nat_rat: (nat > rat) > $o).
% 28.44/7.23 thf(func_def_1480, type, order_7093624213399680841it_int: (product_unit > int) > $o).
% 28.44/7.23 thf(func_def_1481, type, order_7096114683908731117it_nat: (product_unit > nat) > $o).
% 28.44/7.23 thf(func_def_1482, type, order_4454465170704313136t_unit: (product_unit > product_unit) > $o).
% 28.44/7.23 thf(func_def_1483, type, order_509894322932672675et_nat: (product_unit > set_nat) > $o).
% 28.44/7.23 thf(func_def_1484, type, order_7928700340835332885t_unit: (set_nat > product_unit) > $o).
% 28.44/7.23 thf(func_def_1485, type, order_1005506198798982270et_nat: (set_nat > set_nat) > $o).
% 28.44/7.23 thf(func_def_1486, type, order_6722886889984875411nt_int: (int > int) > $o).
% 28.44/7.23 thf(func_def_1487, type, order_6725377360493925687nt_nat: (int > nat) > $o).
% 28.44/7.23 thf(func_def_1488, type, order_6090247300407429951nt_rat: (int > rat) > $o).
% 28.44/7.23 thf(func_def_1489, type, order_5723533178083820855at_int: (nat > int) > $o).
% 28.44/7.23 thf(func_def_1490, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 28.44/7.23 thf(func_def_1491, type, order_5090893588506375395at_rat: (nat > rat) > $o).
% 28.44/7.23 thf(func_def_1492, type, order_5406978534148954943at_int: (rat > int) > $o).
% 28.44/7.23 thf(func_def_1493, type, order_5409469004658005219at_nat: (rat > nat) > $o).
% 28.44/7.23 thf(func_def_1494, type, order_4774338944571509483at_rat: (rat > rat) > $o).
% 28.44/7.23 thf(func_def_1495, type, top_top_int_int_o: int > int > $o).
% 28.44/7.23 thf(func_def_1496, type, top_top_nat_nat_o: nat > nat > $o).
% 28.44/7.23 thf(func_def_1497, type, top_top_nat_num_o: nat > num > $o).
% 28.44/7.23 thf(func_def_1498, type, top_to8903224817164384382_nat_o: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1499, type, top_to1326704617074743934_nat_o: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1500, type, top_top_Product_unit: product_unit).
% 28.44/7.23 thf(func_def_1501, type, top_to3639204395728341691nteger: set_Co4375521073081744395nteger).
% 28.44/7.23 thf(func_def_1502, type, top_to3804862627464599871nteger: set_Co726186806682698383nteger).
% 28.44/7.23 thf(func_def_1503, type, top_top_set_int_int: set_int_int).
% 28.44/7.23 thf(func_def_1504, type, top_top_set_int_nat: set_int_nat).
% 28.44/7.23 thf(func_def_1505, type, top_top_set_int_rat: set_int_rat).
% 28.44/7.23 thf(func_def_1506, type, top_top_set_int_char: set_int_char).
% 28.44/7.23 thf(func_def_1507, type, top_top_set_nat_o: set_nat_o).
% 28.44/7.23 thf(func_def_1508, type, top_top_set_nat_nat: set_nat_nat).
% 28.44/7.23 thf(func_def_1509, type, top_top_set_nat_rat: set_nat_rat).
% 28.44/7.23 thf(func_def_1510, type, top_top_set_nat_char: set_nat_char).
% 28.44/7.23 thf(func_def_1511, type, top_top_set_rat_nat: set_rat_nat).
% 28.44/7.23 thf(func_def_1512, type, top_top_set_rat_rat: set_rat_rat).
% 28.44/7.23 thf(func_def_1513, type, top_top_set_rat_char: set_rat_char).
% 28.44/7.23 thf(func_def_1514, type, top_top_set_char_nat: set_char_nat).
% 28.44/7.23 thf(func_def_1515, type, top_top_set_char_rat: set_char_rat).
% 28.44/7.23 thf(func_def_1516, type, top_to8079350907815874599r_char: set_char_char).
% 28.44/7.23 thf(func_def_1517, type, top_top_set_o: set_o).
% 28.44/7.23 thf(func_def_1518, type, top_to4645266643341252675nteger: set_Code_integer).
% 28.44/7.23 thf(func_def_1519, type, top_to3956321331435058429t_unit: set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_1520, type, top_top_set_ref_a: set_ref_a).
% 28.44/7.23 thf(func_def_1521, type, top_top_set_int: set_int).
% 28.44/7.23 thf(func_def_1522, type, top_top_set_list_nat: set_list_nat).
% 28.44/7.23 thf(func_def_1523, type, top_top_set_nat: set_nat).
% 28.44/7.23 thf(func_def_1524, type, top_top_set_num: set_num).
% 28.44/7.23 thf(func_def_1525, type, top_to2363841527343591755nteger: set_Pr4811707699266497531nteger).
% 28.44/7.23 thf(func_def_1526, type, top_to2503719809363509323t_unit: set_Pr1133966238863718811t_unit).
% 28.44/7.23 thf(func_def_1527, type, top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1528, type, top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1529, type, top_to385025497714130939at_num: set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_1530, type, top_to7513191607651882425at_rat: set_Pr4105333604307423337at_rat).
% 28.44/7.23 thf(func_def_1531, type, top_to7107842681480589234t_char: set_Pr2926629348867340898t_char).
% 28.44/7.23 thf(func_def_1532, type, top_to7002410609688830997at_int: set_Pr3594552606344371909at_int).
% 28.44/7.23 thf(func_def_1533, type, top_to269121717765781945at_nat: set_Pr6084635751276098665at_nat).
% 28.44/7.23 thf(func_def_1534, type, top_to3112507417142880193at_rat: set_Pr8928021450653196913at_rat).
% 28.44/7.23 thf(func_def_1535, type, top_to3221206985699244474t_char: set_Pr8263365689940771946t_char).
% 28.44/7.23 thf(func_def_1536, type, top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1537, type, top_to5281548843312042519at_nat: set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1538, type, top_to3104204703268025230ar_int: set_Pr8146363407509552702ar_int).
% 28.44/7.23 thf(func_def_1539, type, top_to5594287848199751986ar_nat: set_Pr1413074515586503650ar_nat).
% 28.44/7.23 thf(func_def_1540, type, top_to8437673547576850234ar_rat: set_Pr4256460214963601898ar_rat).
% 28.44/7.23 thf(func_def_1541, type, top_to1235241553633177651r_char: set_Pr3309569728657787619r_char).
% 28.44/7.23 thf(func_def_1542, type, top_to1996260823553986621t_unit: set_Product_unit).
% 28.44/7.23 thf(func_def_1543, type, top_top_set_rat: set_rat).
% 28.44/7.23 thf(func_def_1544, type, top_top_set_char: set_char).
% 28.44/7.23 thf(func_def_1545, type, top_to6661820994512907621at_nat: set_Sum_sum_nat_nat).
% 28.44/7.23 thf(func_def_1546, type, eval_Product_unit: pred_Product_unit > product_unit > $o).
% 28.44/7.23 thf(func_def_1547, type, single_Product_unit: product_unit > pred_Product_unit).
% 28.44/7.23 thf(func_def_1548, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 28.44/7.23 thf(func_def_1549, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 28.44/7.23 thf(func_def_1550, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1551, type, produc3901946521647900940t_unit: $o > product_unit > produc3788275437394581276t_unit).
% 28.44/7.23 thf(func_def_1552, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 28.44/7.23 thf(func_def_1553, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1554, type, produc8256076736985659095t_unit: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > produc8126358835630522215t_unit).
% 28.44/7.23 thf(func_def_1555, type, produc2564672488694626579_ref_a: heap_e7401611519738050253t_unit > ref_a > produc1799199577659733785_ref_a).
% 28.44/7.23 thf(func_def_1556, type, produc6544324848051098391t_unit: ref_a > heap_e7401611519738050253t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1557, type, produc1340070678782110931_ref_a: ref_a > ref_a > produc5288414631154139675_ref_a).
% 28.44/7.23 thf(func_def_1558, type, product_Pair_int_o: int > $o > product_prod_int_o).
% 28.44/7.23 thf(func_def_1559, type, product_Pair_int_int: int > int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1560, type, product_Pair_int_nat: int > nat > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1561, type, produc550872421827702152t_unit: int > product_unit > produc6865911496949736918t_unit).
% 28.44/7.23 thf(func_def_1562, type, product_Pair_int_rat: int > rat > product_prod_int_rat).
% 28.44/7.23 thf(func_def_1563, type, product_Pair_nat_o: nat > $o > product_prod_nat_o).
% 28.44/7.23 thf(func_def_1564, type, product_Pair_nat_int: nat > int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1565, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1566, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1567, type, produc3434450474625521892t_unit: nat > product_unit > produc526117512892780850t_unit).
% 28.44/7.23 thf(func_def_1568, type, product_Pair_nat_rat: nat > rat > product_prod_nat_rat).
% 28.44/7.23 thf(func_def_1569, type, product_Pair_num_nat: num > nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1570, type, product_Pair_num_num: num > num > product_prod_num_num).
% 28.44/7.23 thf(func_def_1571, type, produc5069803637994805237atural: pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural).
% 28.44/7.23 thf(func_def_1572, type, produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int).
% 28.44/7.23 thf(func_def_1573, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 28.44/7.23 thf(func_def_1574, type, produc4662710985925991255at_nat: produc859450856879609959at_nat > produc859450856879609959at_nat > produc349518998152878311at_nat).
% 28.44/7.23 thf(func_def_1575, type, produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat).
% 28.44/7.23 thf(func_def_1576, type, produc8487917018914037602unit_o: product_unit > $o > produc7485711547916492274unit_o).
% 28.44/7.23 thf(func_def_1577, type, produc4803288329813530246it_nat: product_unit > nat > produc600557818389255820it_nat).
% 28.44/7.23 thf(func_def_1578, type, produc5692694829384537815t_unit: product_unit > product_unit > produc8459935480633519975t_unit).
% 28.44/7.23 thf(func_def_1579, type, produc4168158269727034510it_rat: product_unit > rat > produc6315701296850634900it_rat).
% 28.44/7.23 thf(func_def_1580, type, product_Pair_rat_int: rat > int > product_prod_rat_int).
% 28.44/7.23 thf(func_def_1581, type, product_Pair_rat_nat: rat > nat > product_prod_rat_nat).
% 28.44/7.23 thf(func_def_1582, type, product_Pair_rat_rat: rat > rat > product_prod_rat_rat).
% 28.44/7.23 thf(func_def_1583, type, produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1584, type, produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1585, type, product_Sigma_o_o: set_o > ($o > set_o) > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1586, type, product_Sigma_o_int: set_o > ($o > set_int) > set_Pr8834758594704517033_o_int).
% 28.44/7.23 thf(func_def_1587, type, product_Sigma_o_nat: set_o > ($o > set_nat) > set_Pr2101469702781467981_o_nat).
% 28.44/7.23 thf(func_def_1588, type, produc411009820408249917t_unit: set_o > ($o > set_Product_unit) > set_Pr6671815714118170108t_unit).
% 28.44/7.23 thf(func_def_1589, type, produc5882431272649516420nteger: set_Code_integer > (code_integer > set_Code_integer) > set_Pr4811707699266497531nteger).
% 28.44/7.23 thf(func_def_1590, type, produc3946373962484743846t_unit: set_ref_a > (ref_a > set_he8644174446132254637t_unit) > set_Pr1133966238863718811t_unit).
% 28.44/7.23 thf(func_def_1591, type, product_Sigma_int_o: set_int > (int > set_o) > set_Pr903927857289325719_int_o).
% 28.44/7.23 thf(func_def_1592, type, produc1453890548195736866nt_int: set_int > (int > set_int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1593, type, produc1456381018704787142nt_nat: set_int > (int > set_nat) > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_1594, type, produc2622961094310184599t_unit: set_int > (int > set_Product_unit) > set_Pr5889264611543340172t_unit).
% 28.44/7.23 thf(func_def_1595, type, produc821250958618291406nt_rat: set_int > (int > set_rat) > set_Pr6292255179000445125nt_rat).
% 28.44/7.23 thf(func_def_1596, type, product_Sigma_nat_o: set_nat > (nat > set_o) > set_Pr3149072824959771635_nat_o).
% 28.44/7.23 thf(func_def_1597, type, produc454536836294682310at_int: set_nat > (nat > set_int) > set_Pr7995236796853374141at_int).
% 28.44/7.23 thf(func_def_1598, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1599, type, produc6237731129814287028at_num: set_nat > (nat > set_num) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_1600, type, produc7854212285064481439nt_int: set_nat > (nat > set_Pr958786334691620121nt_int) > set_Pr6123067485828015636nt_int).
% 28.44/7.23 thf(func_def_1601, type, produc1809337555817847783at_nat: set_nat > (nat > set_Pr1261947904930325089at_nat) > set_Pr7717912310451564380at_nat).
% 28.44/7.23 thf(func_def_1602, type, produc5506539147108004339t_unit: set_nat > (nat > set_Product_unit) > set_Pr4334478416066269672t_unit).
% 28.44/7.23 thf(func_def_1603, type, produc9045269283572012658at_rat: set_nat > (nat > set_rat) > set_Pr4105333604307423337at_rat).
% 28.44/7.23 thf(func_def_1604, type, produc4754187946284079723t_char: set_nat > (nat > set_char) > set_Pr2926629348867340898t_char).
% 28.44/7.23 thf(func_def_1605, type, produc7810729746965977780um_nat: set_num > (num > set_nat) > set_Pr3280342998896498603um_nat).
% 28.44/7.23 thf(func_def_1606, type, produc1007865297704999105nt_nat: set_Pr958786334691620121nt_int > (product_prod_int_int > set_nat) > set_Pr2543308735921124078nt_nat).
% 28.44/7.23 thf(func_def_1607, type, produc245848125267896712nt_int: set_Pr958786334691620121nt_int > (product_prod_int_int > set_Pr958786334691620121nt_int) > set_Pr2560585780119916871nt_int).
% 28.44/7.23 thf(func_def_1608, type, produc3424345432876038864at_nat: set_Pr958786334691620121nt_int > (product_prod_int_int > set_Pr1261947904930325089at_nat) > set_Pr4155430604743465615at_nat).
% 28.44/7.23 thf(func_def_1609, type, produc203973861852599583_nat_o: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_o) > set_Pr6558897299634722526_nat_o).
% 28.44/7.23 thf(func_def_1610, type, produc7672662199629908489at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_Pr2539167527615954998at_nat).
% 28.44/7.23 thf(func_def_1611, type, produc8806266479013559872nt_int: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_Pr958786334691620121nt_int) > set_Pr7098892610798258687nt_int).
% 28.44/7.23 thf(func_def_1612, type, produc2761391749766926216at_nat: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_Pr1261947904930325089at_nat) > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1613, type, produc4441300235185154312at_nat: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat) > set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_1614, type, produc4996980317674386579unit_o: set_Product_unit > (product_unit > set_o) > set_Pr5464989305201766866unit_o).
% 28.44/7.23 thf(func_def_1615, type, produc6875377002296012693it_nat: set_Product_unit > (product_unit > set_nat) > set_Pr1763845938948868674it_nat).
% 28.44/7.23 thf(func_def_1616, type, produc3904733337175673596at_nat: set_Product_unit > (product_unit > set_Pr1261947904930325089at_nat) > set_Pr3798168094891919931at_nat).
% 28.44/7.23 thf(func_def_1617, type, produc6121607364029222536t_unit: set_Product_unit > (product_unit > set_Product_unit) > set_Pr5094982260447487303t_unit).
% 28.44/7.23 thf(func_def_1618, type, produc6240246942209516957it_rat: set_Product_unit > (product_unit > set_rat) > set_Pr4607231638325966922it_rat).
% 28.44/7.23 thf(func_def_1619, type, produc137982192359816398at_int: set_rat > (rat > set_int) > set_Pr3594552606344371909at_int).
% 28.44/7.23 thf(func_def_1620, type, produc140472662868866674at_nat: set_rat > (rat > set_nat) > set_Pr6084635751276098665at_nat).
% 28.44/7.23 thf(func_def_1621, type, produc8728714639637146746at_rat: set_rat > (rat > set_rat) > set_Pr8928021450653196913at_rat).
% 28.44/7.23 thf(func_def_1622, type, produc1427039474575272051t_char: set_rat > (rat > set_char) > set_Pr8263365689940771946t_char).
% 28.44/7.23 thf(func_def_1623, type, produc7726050920695093128at_nat: set_se7855581050983116737at_nat > (set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1624, type, produc6258361011560675592at_nat: set_se5479201105039950375at_nat > (set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat) > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1625, type, produc1836876251250453959ar_int: set_char > (char > set_int) > set_Pr8146363407509552702ar_int).
% 28.44/7.23 thf(func_def_1626, type, produc1839366721759504235ar_nat: set_char > (char > set_nat) > set_Pr1413074515586503650ar_nat).
% 28.44/7.23 thf(func_def_1627, type, produc1204236661673008499ar_rat: set_char > (char > set_rat) > set_Pr4256460214963601898ar_rat).
% 28.44/7.23 thf(func_def_1628, type, produc2936396906406871148r_char: set_char > (char > set_char) > set_Pr3309569728657787619r_char).
% 28.44/7.23 thf(func_def_1629, type, product_Unity: product_unit).
% 28.44/7.23 thf(func_def_1630, type, produc3195571438000033749nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1631, type, produc4508741384315284437t_unit: (ref_a > ref_a) > produc7812382424243267045t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1632, type, produc5845103964736263686t_unit: (ref_a > int) > produc7812382424243267045t_unit > produc3969062480670737046t_unit).
% 28.44/7.23 thf(func_def_1633, type, produc6143945040009431475nt_int: (ref_a > int) > produc8483956148555600810_a_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1634, type, produc6942186945380262242t_unit: (ref_a > nat) > produc7812382424243267045t_unit > produc5066145461314735602t_unit).
% 28.44/7.23 thf(func_def_1635, type, produc5147081798617427195at_nat: (ref_a > nat) > produc3438435131210021710_a_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1636, type, produc1704413584773205829at_num: (ref_a > nat) > produc4146679068158859416_a_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1637, type, produc5323809043756447493t_unit: (ref_a > set_Pr1261947904930325089at_nat) > produc7812382424243267045t_unit > produc3629471303718939987t_unit).
% 28.44/7.23 thf(func_def_1638, type, produc4016808307611786905at_nat: (ref_a > set_Pr1261947904930325089at_nat) > produc5561445381605014009at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1639, type, produc5988837738927868575t_unit: (ref_a > set_Pr4329608150637261639at_nat) > produc7812382424243267045t_unit > produc2296667697112141421t_unit).
% 28.44/7.23 thf(func_def_1640, type, produc2316621926130398489at_nat: (ref_a > set_Pr4329608150637261639at_nat) > produc4041253808165279839at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1641, type, produc2355237562570658114nt_int: (int > int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1642, type, produc986720760941809198at_nat: (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1643, type, produc6767424583952363640at_num: (nat > nat) > product_prod_nat_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1644, type, produc5380969780118646373at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1645, type, produc6529295065807390923at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > produc1319942482725812455at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1646, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1647, type, produc3038839249364385243_ref_a: (heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1648, type, produc3558794870892339738_ref_a: (heap_e7401611519738050253t_unit > int) > produc7812382424243267045t_unit > produc8483956148555600810_a_int).
% 28.44/7.23 thf(func_def_1649, type, produc6768910348387636265nt_int: (heap_e7401611519738050253t_unit > int) > produc3969062480670737046t_unit > product_prod_int_int).
% 28.44/7.23 thf(func_def_1650, type, produc8366372614399963582_ref_a: (heap_e7401611519738050253t_unit > nat) > produc7812382424243267045t_unit > produc3438435131210021710_a_nat).
% 28.44/7.23 thf(func_def_1651, type, produc5772047106995631985at_nat: (heap_e7401611519738050253t_unit > nat) > produc5066145461314735602t_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1652, type, produc7633249859560231688_ref_a: (heap_e7401611519738050253t_unit > num) > produc7812382424243267045t_unit > produc4146679068158859416_a_num).
% 28.44/7.23 thf(func_def_1653, type, produc3902377510303101371um_nat: (heap_e7401611519738050253t_unit > num) > produc5066145461314735602t_unit > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1654, type, produc2928627021203296111_ref_a: (heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat) > produc7812382424243267045t_unit > produc5561445381605014009at_nat).
% 28.44/7.23 thf(func_def_1655, type, produc8705118745468743695at_nat: (heap_e7401611519738050253t_unit > set_Pr1261947904930325089at_nat) > produc3629471303718939987t_unit > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1656, type, produc5080965012319039829_ref_a: (heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat) > produc7812382424243267045t_unit > produc4041253808165279839at_nat).
% 28.44/7.23 thf(func_def_1657, type, produc5990651871820846223at_nat: (heap_e7401611519738050253t_unit > set_Pr4329608150637261639at_nat) > produc2296667697112141421t_unit > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1658, type, produc4463282112584876420nt_int: (int > int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1659, type, produc3094765310956027504at_nat: (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1660, type, produc1225095714263496890um_nat: (nat > num) > product_prod_nat_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1661, type, produc1035573138926686394at_nat: (num > nat) > product_prod_nat_num > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1662, type, produc8389275579088931588um_nat: (num > num) > product_prod_nat_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1663, type, produc6468969725218530979at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1664, type, produc8057050257526108681at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > produc1319942482725812455at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1665, type, produc175634133007206835_int_o: (product_prod_int_int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_1666, type, produc1016772743285680337nt_int: (product_prod_int_int > int) > int > int > int).
% 28.44/7.23 thf(func_def_1667, type, produc8249235968001453780nt_int: (product_prod_int_int > product_prod_int_int) > int > int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1668, type, produc3704529784387675049_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > nat > nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1669, type, produc3610074571335452306at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > nat > nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1670, type, produc1310100445399344235_nat_o: (product_prod_nat_nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_1671, type, produc156083480235303841_num_o: (product_prod_nat_num > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_1672, type, produc7820828192191229133_nat_o: (produc3843707927480180839at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1673, type, produc447603880154497357_nat_o: (produc1319942482725812455at_nat > $o) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1674, type, produc8005341501107743676_int_o: (int > int > $o) > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_1675, type, produc7926200574084438792nt_int: (int > int > int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_1676, type, produc297006045350968285nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1677, type, produc4780622933104268256_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1678, type, produc1854806715440696265at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1679, type, produc4724772261320961782nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > produc723880050079548563nteger > produc101387210554329899nteger).
% 28.44/7.23 thf(func_def_1680, type, produc1928436952130685430_o_o_o: ($o > $o) > ($o > $o) > product_prod_o_o > product_prod_o_o).
% 28.44/7.23 thf(func_def_1681, type, produc8070579729948654068nt_nat: ($o > $o) > (int > nat) > product_prod_o_int > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1682, type, produc7071226018047599512at_nat: ($o > $o) > (nat > nat) > product_prod_o_nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1683, type, produc3628557804203378146at_num: ($o > $o) > (nat > num) > product_prod_o_nat > product_prod_o_num).
% 28.44/7.23 thf(func_def_1684, type, produc9141321880750005618at_o_o: ($o > nat) > ($o > $o) > product_prod_o_o > product_prod_nat_o).
% 28.44/7.23 thf(func_def_1685, type, produc6587185857518356756at_nat: ($o > nat) > (nat > nat) > product_prod_o_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1686, type, produc4527993685489015646at_nat: ($o > num) > (nat > nat) > product_prod_o_nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1687, type, produc1802105962441033582nteger: (code_integer > code_integer) > (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1688, type, produc3456481717235892722t_unit: (ref_a > ref_a) > (heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1689, type, produc6036585564866528938nt_int: (int > int) > (int > int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1690, type, produc5039722323474524658at_nat: (int > int) > (nat > nat) > product_prod_int_nat > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1691, type, produc4404592263388028922at_rat: (int > int) > (nat > rat) > product_prod_int_nat > product_prod_int_rat).
% 28.44/7.23 thf(func_def_1692, type, produc5664932004629684302nt_int: (int > nat) > (int > int) > product_prod_int_int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1693, type, produc5667422475138734578nt_nat: (int > nat) > (int > nat) > product_prod_int_int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1694, type, produc2224754261294513212nt_num: (int > nat) > (int > num) > product_prod_int_int > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1695, type, produc8298419091753553490_nat_o: (int > nat) > (nat > $o) > product_prod_int_nat > product_prod_nat_o).
% 28.44/7.23 thf(func_def_1696, type, produc4665578292728629746at_int: (int > nat) > (nat > int) > product_prod_int_nat > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1697, type, produc4668068763237680022at_nat: (int > nat) > (nat > nat) > product_prod_int_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1698, type, produc1225400549393458656at_num: (int > nat) > (nat > num) > product_prod_int_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1699, type, produc4032938703151184286at_rat: (int > nat) > (nat > rat) > product_prod_int_nat > product_prod_nat_rat).
% 28.44/7.23 thf(func_def_1700, type, produc3608230303109393468nt_nat: (int > num) > (int > nat) > product_prod_int_int > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1701, type, produc165562089265172102nt_num: (int > num) > (int > num) > product_prod_int_int > product_prod_num_num).
% 28.44/7.23 thf(func_def_1702, type, produc9074608839065728392_nat_o: (int > num) > (nat > $o) > product_prod_int_nat > product_prod_num_o).
% 28.44/7.23 thf(func_def_1703, type, produc2608876591208338912at_nat: (int > num) > (nat > nat) > product_prod_int_nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1704, type, produc8248099538878400170nt_int: (nat > $o) > (int > int) > product_prod_nat_int > product_prod_o_int).
% 28.44/7.23 thf(func_def_1705, type, produc8250590009387450446nt_nat: (nat > $o) > (int > nat) > product_prod_nat_int > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1706, type, produc4807921795543229080nt_num: (nat > $o) > (int > num) > product_prod_nat_int > product_prod_o_num).
% 28.44/7.23 thf(func_def_1707, type, produc6957950696844810486_nat_o: (nat > $o) > (nat > $o) > product_prod_nat_nat > product_prod_o_o).
% 28.44/7.23 thf(func_def_1708, type, produc7251236297486395890at_nat: (nat > $o) > (nat > nat) > product_prod_nat_nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1709, type, produc8346403496959479886nt_int: (nat > int) > (int > int) > product_prod_nat_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1710, type, produc8348893967468530162nt_nat: (nat > int) > (int > nat) > product_prod_nat_int > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1711, type, produc7347049785058425330at_int: (nat > int) > (nat > int) > product_prod_nat_nat > product_prod_int_int).
% 28.44/7.23 thf(func_def_1712, type, produc5477380188365894716um_int: (nat > int) > (num > int) > product_prod_nat_num > product_prod_int_int).
% 28.44/7.23 thf(func_def_1713, type, produc2001155298098703512at_o_o: (nat > nat) > ($o > $o) > product_prod_nat_o > product_prod_nat_o).
% 28.44/7.23 thf(func_def_1714, type, produc7974749936722635250nt_int: (nat > nat) > (int > int) > product_prod_nat_int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1715, type, produc7977240407231685526nt_nat: (nat > nat) > (int > nat) > product_prod_nat_int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1716, type, produc4534572193387464160nt_num: (nat > nat) > (int > num) > product_prod_nat_int > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1717, type, produc4787215299218314158_nat_o: (nat > nat) > (nat > $o) > product_prod_nat_nat > product_prod_nat_o).
% 28.44/7.23 thf(func_def_1718, type, produc6977886695330630970at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1719, type, produc3535218481486409604at_num: (nat > nat) > (nat > num) > product_prod_nat_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1720, type, produc5108217098638100356um_nat: (nat > nat) > (num > nat) > product_prod_nat_num > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1721, type, produc1665548884793878990um_num: (nat > nat) > (num > num) > product_prod_nat_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1722, type, produc3264868786340801506um_o_o: (nat > num) > ($o > $o) > product_prod_nat_o > product_prod_num_o).
% 28.44/7.23 thf(func_def_1723, type, produc5918048235202344416nt_nat: (nat > num) > (int > nat) > product_prod_nat_int > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1724, type, produc4918694523301289860at_nat: (nat > num) > (nat > nat) > product_prod_nat_nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1725, type, produc1476026309457068494at_num: (nat > num) > (nat > num) > product_prod_nat_nat > product_prod_num_num).
% 28.44/7.23 thf(func_def_1726, type, produc8746822746284154874nt_int: (nat > rat) > (int > int) > product_prod_nat_int > product_prod_rat_int).
% 28.44/7.23 thf(func_def_1727, type, produc8749313216793205150nt_nat: (nat > rat) > (int > nat) > product_prod_nat_int > product_prod_rat_nat).
% 28.44/7.23 thf(func_def_1728, type, produc170006858110003436at_nat: (nat > set_Pr1261947904930325089at_nat) > (num > set_Pr1261947904930325089at_nat) > product_prod_nat_num > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1729, type, produc8319293927732033832at_nat: (num > $o) > (nat > nat) > product_prod_num_nat > product_prod_o_nat).
% 28.44/7.23 thf(func_def_1730, type, produc4208724500416182148at_nat: (num > nat) > (nat > nat) > product_prod_num_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1731, type, produc2149532328386841038at_nat: (num > num) > (nat > nat) > product_prod_num_nat > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1732, type, produc3932168101365401472at_num: (set_Pr1261947904930325089at_nat > nat) > (set_Pr1261947904930325089at_nat > num) > produc3843707927480180839at_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1733, type, produc1547070076189439812at_rat: (char > char) > (nat > rat) > produc3922234789054302210ar_nat > produc414006230660905482ar_rat).
% 28.44/7.23 thf(func_def_1734, type, produc8759894717825771837t_char: (char > char) > (nat > char) > produc3922234789054302210ar_nat > produc143505574896075907r_char).
% 28.44/7.23 thf(func_def_1735, type, produc1863155021832019360at_int: (char > char) > (rat > int) > produc414006230660905482ar_rat > produc8967755806399881310ar_int).
% 28.44/7.23 thf(func_def_1736, type, produc1865645492341069636at_nat: (char > char) > (rat > nat) > produc414006230660905482ar_rat > produc3922234789054302210ar_nat).
% 28.44/7.23 thf(func_def_1737, type, produc1230515432254573900at_rat: (char > char) > (rat > rat) > produc414006230660905482ar_rat > produc414006230660905482ar_rat).
% 28.44/7.23 thf(func_def_1738, type, produc5432746246116964165t_char: (char > char) > (rat > char) > produc414006230660905482ar_rat > produc143505574896075907r_char).
% 28.44/7.23 thf(func_def_1739, type, produc5842583022792146073ar_int: (char > char) > (char > int) > produc143505574896075907r_char > produc8967755806399881310ar_int).
% 28.44/7.23 thf(func_def_1740, type, produc5845073493301196349ar_nat: (char > char) > (char > nat) > produc143505574896075907r_char > produc3922234789054302210ar_nat).
% 28.44/7.23 thf(func_def_1741, type, produc5209943433214700613ar_rat: (char > char) > (char > rat) > produc143505574896075907r_char > produc414006230660905482ar_rat).
% 28.44/7.23 thf(func_def_1742, type, produc7830753070125841726r_char: (char > char) > (char > char) > produc143505574896075907r_char > produc143505574896075907r_char).
% 28.44/7.23 thf(func_def_1743, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 28.44/7.23 thf(func_def_1744, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 28.44/7.23 thf(func_def_1745, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 28.44/7.23 thf(func_def_1746, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 28.44/7.23 thf(func_def_1747, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1748, type, produc4281629032016041417nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > produc3346328345660746739nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1749, type, produc4426278547552487717t_unit: (heap_e7401611519738050253t_unit > ref_a > produc7812382424243267045t_unit) > produc1799199577659733785_ref_a > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1750, type, produc4924168586796184916unit_o: (ref_a > heap_e7401611519738050253t_unit > $o) > produc7812382424243267045t_unit > $o).
% 28.44/7.23 thf(func_def_1751, type, produc2552614499379209865t_unit: (ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit) > produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1752, type, produc4846201513286513633_ref_a: (ref_a > heap_e7401611519738050253t_unit > ref_a) > produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_1753, type, produc2058451029528183389_ref_a: (ref_a > heap_e7401611519738050253t_unit > produc1799199577659733785_ref_a) > produc7812382424243267045t_unit > produc1799199577659733785_ref_a).
% 28.44/7.23 thf(func_def_1754, type, produc540600059291021473eger_o: (int > code_integer > $o) > produc2963269191615333738nteger > $o).
% 28.44/7.23 thf(func_def_1755, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_1756, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_1757, type, produc8213879946458358998nt_nat: (int > int > nat) > product_prod_int_int > nat).
% 28.44/7.23 thf(func_def_1758, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1759, type, produc8423408460612925143nt_nat: (int > int > product_prod_int_nat) > product_prod_int_int > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1760, type, produc3246203729202673879at_int: (int > int > product_prod_nat_int) > product_prod_int_int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1761, type, produc4257766111578684402_set_o: (int > int > set_o) > product_prod_int_int > set_o).
% 28.44/7.23 thf(func_def_1762, type, produc73460835934605544et_int: (int > int > set_int) > product_prod_int_int > set_int).
% 28.44/7.23 thf(func_def_1763, type, produc4251311855443802252et_nat: (int > int > set_nat) > product_prod_int_int > set_nat).
% 28.44/7.23 thf(func_def_1764, type, produc5385566376148791347nt_nat: (int > nat > product_prod_int_nat) > product_prod_int_nat > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1765, type, produc1877337817755394619nt_rat: (int > nat > product_prod_int_rat) > product_prod_int_nat > product_prod_int_rat).
% 28.44/7.23 thf(func_def_1766, type, produc208361644738540083at_int: (int > nat > product_prod_nat_int) > product_prod_int_nat > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1767, type, produc877984105854340063at_rat: (int > nat > product_prod_nat_rat) > product_prod_int_nat > product_prod_nat_rat).
% 28.44/7.23 thf(func_def_1768, type, produc6663371796859813939nt_nat: (nat > int > product_prod_int_nat) > product_prod_nat_int > product_prod_int_nat).
% 28.44/7.23 thf(func_def_1769, type, produc1486167065449562675at_int: (nat > int > product_prod_nat_int) > product_prod_nat_int > product_prod_nat_int).
% 28.44/7.23 thf(func_def_1770, type, produc1169612421514696763at_int: (nat > int > product_prod_rat_int) > product_prod_nat_int > product_prod_rat_int).
% 28.44/7.23 thf(func_def_1771, type, produc5347463441023893471at_nat: (nat > int > product_prod_rat_nat) > product_prod_nat_int > product_prod_rat_nat).
% 28.44/7.23 thf(func_def_1772, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1773, 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).
% 28.44/7.23 thf(func_def_1774, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1775, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 28.44/7.23 thf(func_def_1776, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 28.44/7.23 thf(func_def_1777, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_1778, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1779, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 28.44/7.23 thf(func_def_1780, type, produc59986286002894506_set_o: (nat > nat > set_o) > product_prod_nat_nat > set_o).
% 28.44/7.23 thf(func_def_1781, type, produc2011625207790711856et_int: (nat > nat > set_int) > product_prod_nat_nat > set_int).
% 28.44/7.23 thf(func_def_1782, type, produc6189476227299908564et_nat: (nat > nat > set_nat) > product_prod_nat_nat > set_nat).
% 28.44/7.23 thf(func_def_1783, type, produc8197505143624133779at_nat: (nat > nat > set_Pr1261947904930325089at_nat) > product_prod_nat_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1784, type, produc4927758841916487424_num_o: (nat > num > $o) > product_prod_nat_num > $o).
% 28.44/7.23 thf(func_def_1785, type, produc4970712607118878916um_int: (nat > num > int) > product_prod_nat_num > int).
% 28.44/7.23 thf(func_def_1786, type, produc4973203077627929192um_nat: (nat > num > nat) > product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_1787, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 28.44/7.23 thf(func_def_1788, type, produc8564434177180591209at_nat: (nat > num > product_prod_nat_nat) > product_prod_nat_num > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1789, type, produc49306077274653107at_num: (nat > num > product_prod_nat_num) > product_prod_nat_num > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1790, type, produc836176033315069408_set_o: (nat > num > set_o) > product_prod_nat_num > set_o).
% 28.44/7.23 thf(func_def_1791, type, produc9175805072616146554et_int: (nat > num > set_int) > product_prod_nat_num > set_int).
% 28.44/7.23 thf(func_def_1792, type, produc4130284055270567454et_nat: (nat > num > set_nat) > product_prod_nat_num > set_nat).
% 28.44/7.23 thf(func_def_1793, type, produc859037500352796105at_nat: (nat > num > set_Pr1261947904930325089at_nat) > product_prod_nat_num > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1794, type, produc4306188689235752475_int_o: (nat > product_prod_int_int > $o) > produc6945250483304103390nt_int > $o).
% 28.44/7.23 thf(func_def_1795, type, produc5864757623865647827_nat_o: (nat > product_prod_nat_nat > $o) > produc7248412053542808358at_nat > $o).
% 28.44/7.23 thf(func_def_1796, type, produc6857965554392702720_nat_o: (num > nat > $o) > product_prod_num_nat > $o).
% 28.44/7.23 thf(func_def_1797, type, produc5219324331026901427at_num: (num > nat > product_prod_nat_num) > product_prod_num_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1798, type, produc5703948589228662326_num_o: (num > num > $o) > product_prod_num_num > $o).
% 28.44/7.23 thf(func_def_1799, type, produc6665183775751917029atural: (pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural) > produc4675096598859438275atural > produc4675096598859438275atural).
% 28.44/7.23 thf(func_def_1800, type, produc5441891513209881465_nat_o: (product_prod_int_int > nat > $o) > produc1709102135585200056nt_nat > $o).
% 28.44/7.23 thf(func_def_1801, type, produc1676490119946744748_int_o: (product_prod_int_int > product_prod_int_int > $o) > produc1219242969750017639nt_int > $o).
% 28.44/7.23 thf(func_def_1802, type, produc3235059054576640100_nat_o: (product_prod_int_int > product_prod_nat_nat > $o) > produc1522404539988722607at_nat > $o).
% 28.44/7.23 thf(func_def_1803, type, produc6937227050501860053_int_o: (product_prod_nat_nat > int > $o) > produc4196048018000912732at_int > $o).
% 28.44/7.23 thf(func_def_1804, type, produc8758269395934548017_nat_o: (product_prod_nat_nat > nat > $o) > produc8373899037510109440at_nat > $o).
% 28.44/7.23 thf(func_def_1805, type, produc5031841752791441652_int_o: (product_prod_nat_nat > product_prod_int_int > $o) > produc556289286640904991nt_int > $o).
% 28.44/7.23 thf(func_def_1806, type, produc6590410687421337004_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc859450856879609959at_nat > $o).
% 28.44/7.23 thf(func_def_1807, type, produc410239310623530412_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > $o).
% 28.44/7.23 thf(func_def_1808, type, produc7548845685434208379at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat) > produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1809, type, produc9020218426428501292_nat_o: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > produc1319942482725812455at_nat > $o).
% 28.44/7.23 thf(func_def_1810, type, produc5456455677105495163at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat) > produc1319942482725812455at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1811, type, product_fst_o_o: product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1812, type, product_fst_o_int: product_prod_o_int > $o).
% 28.44/7.23 thf(func_def_1813, type, product_fst_o_nat: product_prod_o_nat > $o).
% 28.44/7.23 thf(func_def_1814, type, produc5219655352205527288t_unit: produc3788275437394581276t_unit > $o).
% 28.44/7.23 thf(func_def_1815, type, produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer).
% 28.44/7.23 thf(func_def_1816, type, produc1861665112190112313nteger: produc3346328345660746739nteger > code_integer).
% 28.44/7.23 thf(func_def_1817, type, produc2762368996035445955t_unit: produc8126358835630522215t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1818, type, produc5717040794327095847_ref_a: produc1799199577659733785_ref_a > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1819, type, produc473321116828791851t_unit: produc7812382424243267045t_unit > ref_a).
% 28.44/7.23 thf(func_def_1820, type, produc6942380573175061695_ref_a: produc5288414631154139675_ref_a > ref_a).
% 28.44/7.23 thf(func_def_1821, type, product_fst_int_o: product_prod_int_o > int).
% 28.44/7.23 thf(func_def_1822, type, produc45500017171379470nteger: produc2963269191615333738nteger > int).
% 28.44/7.23 thf(func_def_1823, type, product_fst_int_int: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_1824, type, product_fst_int_nat: product_prod_int_nat > int).
% 28.44/7.23 thf(func_def_1825, type, produc917050878549155996t_unit: produc6865911496949736918t_unit > int).
% 28.44/7.23 thf(func_def_1826, type, product_fst_nat_o: product_prod_nat_o > nat).
% 28.44/7.23 thf(func_def_1827, type, product_fst_nat_int: product_prod_nat_int > nat).
% 28.44/7.23 thf(func_def_1828, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_1829, type, product_fst_nat_num: product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_1830, type, produc3800628931346975736t_unit: produc526117512892780850t_unit > nat).
% 28.44/7.23 thf(func_def_1831, type, product_fst_num_nat: product_prod_num_nat > num).
% 28.44/7.23 thf(func_def_1832, type, product_fst_num_num: product_prod_num_num > num).
% 28.44/7.23 thf(func_def_1833, type, produc6435950281062462810_nat_o: produc652263959640188542_nat_o > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1834, type, produc4619704898428564714at_int: produc4196048018000912732at_int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1835, type, produc3213797794245857475at_nat: produc859450856879609959at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1836, type, produc582253812616888142unit_o: produc7485711547916492274unit_o > product_unit).
% 28.44/7.23 thf(func_def_1837, type, produc5169466786534984090it_nat: produc600557818389255820it_nat > product_unit).
% 28.44/7.23 thf(func_def_1838, type, produc6963936691090040003t_unit: produc8459935480633519975t_unit > product_unit).
% 28.44/7.23 thf(func_def_1839, type, produc6011863565407846595at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1840, type, produc4486455499028916547at_nat: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1841, type, product_snd_o_o: product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1842, type, product_snd_o_int: product_prod_o_int > int).
% 28.44/7.23 thf(func_def_1843, type, product_snd_o_nat: product_prod_o_nat > nat).
% 28.44/7.23 thf(func_def_1844, type, produc2875488738488844090t_unit: produc3788275437394581276t_unit > product_unit).
% 28.44/7.23 thf(func_def_1845, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 28.44/7.23 thf(func_def_1846, type, produc7955729907432593271nteger: produc3346328345660746739nteger > produc8923325533196201883nteger).
% 28.44/7.23 thf(func_def_1847, type, produc1692618790031806469t_unit: produc8126358835630522215t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1848, type, produc6369869760173755749_ref_a: produc1799199577659733785_ref_a > ref_a).
% 28.44/7.23 thf(func_def_1849, type, produc1126150082675451753t_unit: produc7812382424243267045t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1850, type, produc8185483580310833921_ref_a: produc5288414631154139675_ref_a > ref_a).
% 28.44/7.23 thf(func_def_1851, type, product_snd_int_o: product_prod_int_o > $o).
% 28.44/7.23 thf(func_def_1852, type, produc2153544567185597776nteger: produc2963269191615333738nteger > code_integer).
% 28.44/7.23 thf(func_def_1853, type, product_snd_int_int: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_1854, type, product_snd_int_nat: product_prod_int_nat > nat).
% 28.44/7.23 thf(func_def_1855, type, product_snd_nat_o: product_prod_nat_o > $o).
% 28.44/7.23 thf(func_def_1856, type, product_snd_nat_int: product_prod_nat_int > int).
% 28.44/7.23 thf(func_def_1857, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_1858, type, product_snd_nat_num: product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_1859, type, produc8850949007409916470t_unit: produc526117512892780850t_unit > product_unit).
% 28.44/7.23 thf(func_def_1860, type, product_snd_num_nat: product_prod_num_nat > nat).
% 28.44/7.23 thf(func_def_1861, type, product_snd_num_num: product_prod_num_num > num).
% 28.44/7.23 thf(func_def_1862, type, produc668916169454083228_nat_o: produc652263959640188542_nat_o > $o).
% 28.44/7.23 thf(func_def_1863, type, produc3064508320661873192at_int: produc4196048018000912732at_int > int).
% 28.44/7.23 thf(func_def_1864, type, produc6408287024330202629at_nat: produc859450856879609959at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1865, type, produc7461459235754980752unit_o: produc7485711547916492274unit_o > $o).
% 28.44/7.23 thf(func_def_1866, type, produc996414825743149016it_nat: produc600557818389255820it_nat > nat).
% 28.44/7.23 thf(func_def_1867, type, produc6786084904866402309t_unit: produc8459935480633519975t_unit > product_unit).
% 28.44/7.23 thf(func_def_1868, type, produc2937545259423399429at_nat: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1869, type, produc826222791318859909at_nat: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1870, type, produc6214465446503547763_ref_a: produc1799199577659733785_ref_a > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1871, type, produc970745769005243767t_unit: produc7812382424243267045t_unit > produc1799199577659733785_ref_a).
% 28.44/7.23 thf(func_def_1872, type, product_swap_int_int: product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1873, type, product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_1874, type, product_swap_nat_num: product_prod_nat_num > product_prod_num_nat).
% 28.44/7.23 thf(func_def_1875, type, product_swap_num_nat: product_prod_num_nat > product_prod_nat_num).
% 28.44/7.23 thf(func_def_1876, type, produc3946833401584108663at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_1877, type, produc5396952528824381687at_nat: produc1319942482725812455at_nat > produc1319942482725812455at_nat).
% 28.44/7.23 thf(func_def_1878, type, produc929334515565554804at_nat: set_nat > set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1879, type, produc3241716407206042770at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1880, type, product_Abs_unit: $o > product_unit).
% 28.44/7.23 thf(func_def_1881, type, product_Rep_unit: product_unit > $o).
% 28.44/7.23 thf(func_def_1882, type, random6974930770145893639ompred: (produc7822875418678951345atural > produc4675096598859438275atural) > produc7822875418678951345atural > produc4675096598859438275atural).
% 28.44/7.23 thf(func_def_1883, type, fract: int > int > rat).
% 28.44/7.23 thf(func_def_1884, type, field_6020823756834552118ts_rat: set_rat).
% 28.44/7.23 thf(func_def_1885, type, normalize: product_prod_int_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_1886, type, quotient_of: rat > product_prod_int_int).
% 28.44/7.23 thf(func_def_1887, type, alloc_a: a > heap_e7401611519738050253t_unit > produc7812382424243267045t_unit).
% 28.44/7.23 thf(func_def_1888, type, change_ref_a: (ref_a > ref_a) > ref_ref_a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1889, type, change_a: (a > a) > ref_a > heap_Heap_a).
% 28.44/7.23 thf(func_def_1890, type, get_ref_a: heap_e7401611519738050253t_unit > ref_ref_a > ref_a).
% 28.44/7.23 thf(func_def_1891, type, get_a: heap_e7401611519738050253t_unit > ref_a > a).
% 28.44/7.23 thf(func_def_1892, type, lookup_ref_a: ref_ref_a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1893, type, lookup_a: ref_a > heap_Heap_a).
% 28.44/7.23 thf(func_def_1894, type, noteq_a_a: ref_a > ref_a > $o).
% 28.44/7.23 thf(func_def_1895, type, present_a: heap_e7401611519738050253t_unit > ref_a > $o).
% 28.44/7.23 thf(func_def_1896, type, ref_a2: a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1897, type, ref_a3: a > heap_Heap_ref_a).
% 28.44/7.23 thf(func_def_1898, type, set_ref_a2: ref_ref_a > ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1899, type, set_a: ref_a > a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_1900, type, update_a: ref_a > a > heap_H6156071679106078628t_unit).
% 28.44/7.23 thf(func_def_1901, type, field_o: set_Product_prod_o_o > set_o).
% 28.44/7.23 thf(func_def_1902, type, field_int: set_Pr958786334691620121nt_int > set_int).
% 28.44/7.23 thf(func_def_1903, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 28.44/7.23 thf(func_def_1904, type, field_4706345496283612622at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1905, type, field_3044959742847878580at_nat: set_Pr553994874890374343at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1906, type, field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1907, type, field_Product_unit: set_Pr5094982260447487303t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_1908, type, field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_1909, type, field_1428494348145443988at_nat: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_1910, type, id_o2: set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1911, type, id_int2: set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1912, type, id_nat2: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1913, type, id_Pro2258643101195443293at_nat: set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1914, type, id_Pro5428700290092274115at_nat: set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_1915, type, id_set1796276052702428605at_nat: set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1916, type, id_set4888139568991089827at_nat: set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1917, type, id_on_o: set_o > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_1918, type, id_on_int: set_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1919, type, id_on_nat: set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1920, type, id_on_num: set_num > set_Pr8218934625190621173um_num).
% 28.44/7.23 thf(func_def_1921, type, id_on_8598933527810153430nt_int: set_Pr958786334691620121nt_int > set_Pr2560585780119916871nt_int).
% 28.44/7.23 thf(func_def_1922, type, id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_1923, type, id_on_7869290023980668164at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_1924, type, id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1925, type, id_on_3275838214495744996at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1926, type, conver1062113817206378758nt_int: ((int > product_prod_int_int) > (int > int) > $o) > (int > int) > (int > product_prod_int_int) > $o).
% 28.44/7.23 thf(func_def_1927, type, conver1572571282669976050nt_nat: ((int > product_prod_nat_nat) > (int > nat) > $o) > (int > nat) > (int > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_1928, type, conver5699786650113435344nt_num: ((int > product_prod_num_num) > (int > num) > $o) > (int > num) > (int > product_prod_num_num) > $o).
% 28.44/7.23 thf(func_def_1929, type, conver6066198818478722162at_nat: ((list_nat > product_prod_nat_nat) > (list_nat > nat) > $o) > (list_nat > nat) > (list_nat > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_1930, type, conver2987682522074450438at_int: ((nat > product_prod_int_int) > (nat > int) > $o) > (nat > int) > (nat > product_prod_int_int) > $o).
% 28.44/7.23 thf(func_def_1931, type, conver3498139987538047730at_nat: ((nat > product_prod_nat_nat) > (nat > nat) > $o) > (nat > nat) > (nat > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_1932, type, conver3229387634306789365nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o) > (code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_1933, type, conver6967689361887734790at_int: ((rat > product_prod_int_int) > (rat > int) > $o) > (rat > int) > (rat > product_prod_int_int) > $o).
% 28.44/7.23 thf(func_def_1934, type, conver7478146827351332082at_nat: ((rat > product_prod_nat_nat) > (rat > nat) > $o) > (rat > nat) > (rat > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_1935, type, conver1155128050257070662ar_int: ((char > product_prod_int_int) > (char > int) > $o) > (char > int) > (char > product_prod_int_int) > $o).
% 28.44/7.23 thf(func_def_1936, type, conver5210974729819302706ar_nat: ((char > product_prod_nat_nat) > (char > nat) > $o) > (char > nat) > (char > product_prod_nat_nat) > $o).
% 28.44/7.23 thf(func_def_1937, type, conversep_o_o: ($o > $o > $o) > $o > $o > $o).
% 28.44/7.23 thf(func_def_1938, type, conver1462408618118490240er_int: (code_integer > int > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_1939, type, conver2101108097643427968nteger: (int > code_integer > $o) > code_integer > int > $o).
% 28.44/7.23 thf(func_def_1940, type, conversep_int_int: (int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_1941, type, conversep_int_nat: (int > nat > $o) > nat > int > $o).
% 28.44/7.23 thf(func_def_1942, type, conver1866313717161370910at_nat: (int > product_prod_nat_nat > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_1943, type, conver909888920752868663st_nat: (list_nat > list_nat > $o) > list_nat > list_nat > $o).
% 28.44/7.23 thf(func_def_1944, type, conversep_nat_o: (nat > $o > $o) > $o > nat > $o).
% 28.44/7.23 thf(func_def_1945, type, conversep_nat_int: (nat > int > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_1946, type, conversep_nat_nat: (nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_1947, type, conversep_nat_num: (nat > num > $o) > num > nat > $o).
% 28.44/7.23 thf(func_def_1948, type, conversep_nat_rat: (nat > rat > $o) > rat > nat > $o).
% 28.44/7.23 thf(func_def_1949, type, conversep_nat_char: (nat > char > $o) > char > nat > $o).
% 28.44/7.23 thf(func_def_1950, type, conversep_num_nat: (num > nat > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_1951, type, conversep_num_num: (num > num > $o) > num > num > $o).
% 28.44/7.23 thf(func_def_1952, type, conver4368408235330554745_ref_a: (produc7812382424243267045t_unit > ref_a > $o) > ref_a > produc7812382424243267045t_unit > $o).
% 28.44/7.23 thf(func_def_1953, type, conver7247880940930113968nt_int: (product_prod_int_int > int > $o) > int > product_prod_int_int > $o).
% 28.44/7.23 thf(func_def_1954, type, conver4689305806000247544at_int: (product_prod_nat_nat > int > $o) > int > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1955, type, conver4691796276509297820at_nat: (product_prod_nat_nat > nat > $o) > nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1956, type, conver6965824823119931701at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_1957, type, conversep_rat_int: (rat > int > $o) > int > rat > $o).
% 28.44/7.23 thf(func_def_1958, type, conversep_rat_nat: (rat > nat > $o) > nat > rat > $o).
% 28.44/7.23 thf(func_def_1959, type, conversep_rat_rat: (rat > rat > $o) > rat > rat > $o).
% 28.44/7.23 thf(func_def_1960, type, conversep_rat_char: (rat > char > $o) > char > rat > $o).
% 28.44/7.23 thf(func_def_1961, type, conver5243090411617913141at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1962, type, conver9095369822871743413at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1963, type, conversep_char_int: (char > int > $o) > int > char > $o).
% 28.44/7.23 thf(func_def_1964, type, conversep_char_nat: (char > nat > $o) > nat > char > $o).
% 28.44/7.23 thf(func_def_1965, type, conversep_char_rat: (char > rat > $o) > rat > char > $o).
% 28.44/7.23 thf(func_def_1966, type, conversep_char_char: (char > char > $o) > char > char > $o).
% 28.44/7.23 thf(func_def_1967, type, inv_image_int_int: set_Pr958786334691620121nt_int > (int > int) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1968, type, inv_image_int_nat: set_Pr958786334691620121nt_int > (nat > int) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1969, type, inv_im8510909985083594081at_nat: set_Pr958786334691620121nt_int > (set_Pr1261947904930325089at_nat > int) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1970, type, inv_image_nat_int: set_Pr1261947904930325089at_nat > (int > nat) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1971, type, inv_image_nat_nat: set_Pr1261947904930325089at_nat > (nat > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1972, type, inv_im6750873321330482877at_nat: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > nat) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1973, type, inv_im2354225701593503139at_nat: set_Pr1261947904930325089at_nat > (set_Pr4329608150637261639at_nat > nat) > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_1974, type, inv_im4434751243573137211at_int: set_Pr4329608150637261639at_nat > (int > set_Pr1261947904930325089at_nat) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1975, type, inv_im4437241714082187487at_nat: set_Pr4329608150637261639at_nat > (nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1976, type, inv_im7023619800666061458at_nat: set_Pr4329608150637261639at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_1977, type, inv_im2900519150384625825at_int: set_Pr7459493094073627847at_nat > (int > set_Pr4329608150637261639at_nat) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_1978, type, inv_im2903009620893676101at_nat: set_Pr7459493094073627847at_nat > (nat > set_Pr4329608150637261639at_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_1979, type, refl_on_o: set_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_1980, type, refl_on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_1981, type, refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_1982, type, refl_o7122697186039111552at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_1983, type, refl_o7446464703481863270at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_1984, type, refl_on_Product_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_1985, type, refl_o6955724340487615712at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_1986, type, refl_o6272981002401706822at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_1987, type, relcom1820845089908643850nteger: ((code_integer > code_integer) > (code_integer > code_integer) > $o) > ((code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_1988, type, relcom7212586982944386682nteger: ((int > int) > (int > int) > $o) > ((int > int) > (code_integer > code_integer) > $o) > (int > int) > (code_integer > code_integer) > $o).
% 28.44/7.23 thf(func_def_1989, type, relcom6733878598652036755nt_int: ((int > int) > (int > product_prod_int_int) > $o) > ((int > product_prod_int_int) > (int > int) > $o) > (int > int) > (int > int) > $o).
% 28.44/7.23 thf(func_def_1990, type, relcom2406850561174050523nt_nat: ((int > nat) > (int > product_prod_nat_nat) > $o) > ((int > product_prod_nat_nat) > (int > nat) > $o) > (int > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_1991, type, relcom1848932251921554756er_num: ((int > num) > (code_integer > num) > $o) > ((code_integer > num) > (code_integer > num) > $o) > (int > num) > (code_integer > num) > $o).
% 28.44/7.23 thf(func_def_1992, type, relcom7779292856395800339nt_num: ((int > num) > (code_integer > num) > $o) > ((code_integer > num) > (int > num) > $o) > (int > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_1993, type, relcom1533066287727470739er_num: ((int > num) > (int > num) > $o) > ((int > num) > (code_integer > num) > $o) > (int > num) > (code_integer > num) > $o).
% 28.44/7.23 thf(func_def_1994, type, relcom9025577121137075810nt_num: ((int > num) > (int > num) > $o) > ((int > num) > (int > num) > $o) > (int > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_1995, type, relcom1697847500783689711nt_num: ((int > num) > (int > product_prod_num_num) > $o) > ((int > product_prod_num_num) > (int > num) > $o) > (int > num) > (int > num) > $o).
% 28.44/7.23 thf(func_def_1996, type, relcom2127790875031262553er_int: ((int > product_prod_nat_nat) > (int > product_prod_nat_nat) > $o) > ((int > product_prod_nat_nat) > (code_integer > int) > $o) > (int > product_prod_nat_nat) > (code_integer > int) > $o).
% 28.44/7.23 thf(func_def_1997, type, relcom5920149085449455271at_nat: ((list_nat > nat) > (list_nat > product_prod_nat_nat) > $o) > ((list_nat > product_prod_nat_nat) > (list_nat > nat) > $o) > (list_nat > nat) > (list_nat > nat) > $o).
% 28.44/7.23 thf(func_def_1998, type, relcom3290293904592725231at_int: ((nat > int) > (nat > product_prod_int_int) > $o) > ((nat > product_prod_int_int) > (nat > int) > $o) > (nat > int) > (nat > int) > $o).
% 28.44/7.23 thf(func_def_1999, type, relcom8186637903969514807at_nat: ((nat > nat) > (nat > product_prod_nat_nat) > $o) > ((nat > product_prod_nat_nat) > (nat > nat) > $o) > (nat > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_2000, type, relcom458776940982682326nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o) > ((code_integer > code_integer) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > $o).
% 28.44/7.23 thf(func_def_2001, type, relcom4829277440228594702nteger: ((produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > $o) > ((code_integer > code_integer) > code_integer > $o) > (produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > $o).
% 28.44/7.23 thf(func_def_2002, type, relcom4574826104943343961nteger: ((product_prod_nat_nat > int) > (product_prod_nat_nat > int) > $o) > ((product_prod_nat_nat > int) > (int > code_integer) > $o) > (product_prod_nat_nat > int) > (int > code_integer) > $o).
% 28.44/7.23 thf(func_def_2003, type, relcom4272412204205018633nt_nat: ((product_prod_nat_nat > nat) > (int > nat) > $o) > ((int > nat) > (int > nat) > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_2004, type, relcom531901107642208332nt_nat: ((product_prod_nat_nat > nat) > (product_prod_nat_nat > nat) > $o) > ((product_prod_nat_nat > nat) > (int > nat) > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 28.44/7.23 thf(func_def_2005, type, relcom4982215633375716084nt_int: ((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) > (int > int) > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 28.44/7.23 thf(func_def_2006, type, relcom2810802720173317863at_int: ((rat > int) > (rat > product_prod_int_int) > $o) > ((rat > product_prod_int_int) > (rat > int) > $o) > (rat > int) > (rat > int) > $o).
% 28.44/7.23 thf(func_def_2007, type, relcom7707146719550107439at_nat: ((rat > nat) > (rat > product_prod_nat_nat) > $o) > ((rat > product_prod_nat_nat) > (rat > nat) > $o) > (rat > nat) > (rat > nat) > $o).
% 28.44/7.23 thf(func_def_2008, type, relcom4417706183330134766ar_int: ((char > int) > (char > product_prod_int_int) > $o) > ((char > product_prod_int_int) > (char > int) > $o) > (char > int) > (char > int) > $o).
% 28.44/7.23 thf(func_def_2009, type, relcom8141925468094106422ar_nat: ((char > nat) > (char > product_prod_nat_nat) > $o) > ((char > product_prod_nat_nat) > (char > nat) > $o) > (char > nat) > (char > nat) > $o).
% 28.44/7.23 thf(func_def_2010, type, relcompp_o_o_o: ($o > $o > $o) > ($o > $o > $o) > $o > $o > $o).
% 28.44/7.23 thf(func_def_2011, type, relcompp_o_o_nat: ($o > $o > $o) > ($o > nat > $o) > $o > nat > $o).
% 28.44/7.23 thf(func_def_2012, type, relcom692387321444912665nteger: (code_integer > int > $o) > (int > code_integer > $o) > code_integer > code_integer > $o).
% 28.44/7.23 thf(func_def_2013, type, relcom3789353511612409832nt_int: (code_integer > int > $o) > (int > int > $o) > code_integer > int > $o).
% 28.44/7.23 thf(func_def_2014, type, relcom3136146828236442456t_unit: (ref_a > produc7812382424243267045t_unit > $o) > (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > $o) > ref_a > heap_e7401611519738050253t_unit > $o).
% 28.44/7.23 thf(func_def_2015, type, relcom8320293257703906841nteger: (int > code_integer > $o) > (code_integer > code_integer > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_2016, type, relcom328798225758222312er_int: (int > code_integer > $o) > (code_integer > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_2017, type, relcom967497705283160040nteger: (int > int > $o) > (int > code_integer > $o) > int > code_integer > $o).
% 28.44/7.23 thf(func_def_2018, type, relcompp_int_int_int: (int > int > $o) > (int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_2019, type, relcompp_int_int_nat: (int > int > $o) > (int > nat > $o) > int > nat > $o).
% 28.44/7.23 thf(func_def_2020, type, relcompp_int_nat_int: (int > nat > $o) > (nat > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_2021, type, relcompp_int_nat_num: (int > nat > $o) > (nat > num > $o) > int > num > $o).
% 28.44/7.23 thf(func_def_2022, type, relcom3664783465810776136nt_int: (int > product_prod_int_int > $o) > (product_prod_int_int > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_2023, type, relcom1106208330880909712at_int: (int > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > int > int > $o).
% 28.44/7.23 thf(func_def_2024, type, relcom716700242784427165at_nat: (int > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_2025, type, relcom7887202796854296604nteger: (list_nat > int > $o) > (int > code_integer > $o) > list_nat > code_integer > $o).
% 28.44/7.23 thf(func_def_2026, type, relcom8030397737370142931st_nat: (list_nat > list_nat > $o) > (list_nat > list_nat > $o) > list_nat > list_nat > $o).
% 28.44/7.23 thf(func_def_2027, type, relcom170568170053003356at_int: (list_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > list_nat > int > $o).
% 28.44/7.23 thf(func_def_2028, type, relcompp_nat_o_o: (nat > $o > $o) > ($o > $o > $o) > nat > $o > $o).
% 28.44/7.23 thf(func_def_2029, type, relcompp_nat_o_nat: (nat > $o > $o) > ($o > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2030, type, relcom3277315637376110988nteger: (nat > int > $o) > (int > code_integer > $o) > nat > code_integer > $o).
% 28.44/7.23 thf(func_def_2031, type, relcompp_nat_int_int: (nat > int > $o) > (int > int > $o) > nat > int > $o).
% 28.44/7.23 thf(func_def_2032, type, relcompp_nat_int_nat: (nat > int > $o) > (int > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2033, type, relcompp_nat_nat_int: (nat > nat > $o) > (nat > int > $o) > nat > int > $o).
% 28.44/7.23 thf(func_def_2034, type, relcompp_nat_nat_nat: (nat > nat > $o) > (nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2035, type, relcompp_nat_nat_num: (nat > nat > $o) > (nat > num > $o) > nat > num > $o).
% 28.44/7.23 thf(func_def_2036, type, relcom8569543703982574316at_int: (nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > nat > int > $o).
% 28.44/7.23 thf(func_def_2037, type, relcom8572034174491624592at_nat: (nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2038, type, relcompp_nat_rat_nat: (nat > rat > $o) > (rat > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2039, type, relcom8112501251453913252ar_nat: (nat > char > $o) > (char > nat > $o) > nat > nat > $o).
% 28.44/7.23 thf(func_def_2040, type, relcompp_num_nat_int: (num > nat > $o) > (nat > int > $o) > num > int > $o).
% 28.44/7.23 thf(func_def_2041, type, relcompp_num_nat_num: (num > nat > $o) > (nat > num > $o) > num > num > $o).
% 28.44/7.23 thf(func_def_2042, type, relcompp_num_num_num: (num > num > $o) > (num > num > $o) > num > num > $o).
% 28.44/7.23 thf(func_def_2043, type, relcom2949942408940504938nt_int: (product_prod_nat_nat > int > $o) > (int > int > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_2044, type, relcom8911704206367525917at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > int > $o).
% 28.44/7.23 thf(func_def_2045, type, relcom282571730187242960at_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 > $o).
% 28.44/7.23 thf(func_def_2046, type, relcom3409376902655092628nteger: (rat > int > $o) > (int > code_integer > $o) > rat > code_integer > $o).
% 28.44/7.23 thf(func_def_2047, type, relcompp_rat_int_rat: (rat > int > $o) > (int > rat > $o) > rat > rat > $o).
% 28.44/7.23 thf(func_def_2048, type, relcompp_rat_nat_rat: (rat > nat > $o) > (nat > rat > $o) > rat > rat > $o).
% 28.44/7.23 thf(func_def_2049, type, relcom1211213461163567844at_int: (rat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > rat > int > $o).
% 28.44/7.23 thf(func_def_2050, type, relcompp_rat_rat_rat: (rat > rat > $o) > (rat > rat > $o) > rat > rat > $o).
% 28.44/7.23 thf(func_def_2051, type, relcom1505247221262953652ar_rat: (rat > char > $o) > (char > rat > $o) > rat > rat > $o).
% 28.44/7.23 thf(func_def_2052, type, relcom8363394528208558896at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2053, type, relcom5819909836510906509nteger: (char > int > $o) > (int > code_integer > $o) > char > code_integer > $o).
% 28.44/7.23 thf(func_def_2054, type, relcom750623199913152513t_char: (char > int > $o) > (int > char > $o) > char > char > $o).
% 28.44/7.23 thf(func_def_2055, type, relcom6755291642603558309t_char: (char > nat > $o) > (nat > char > $o) > char > char > $o).
% 28.44/7.23 thf(func_def_2056, type, relcom7879471502873553579at_int: (char > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > char > int > $o).
% 28.44/7.23 thf(func_def_2057, type, relcom3428143170894750637t_char: (char > rat > $o) > (rat > char > $o) > char > char > $o).
% 28.44/7.23 thf(func_def_2058, type, relcom5872928454965100966r_char: (char > char > $o) > (char > char > $o) > char > char > $o).
% 28.44/7.23 thf(func_def_2059, type, total_on_o: set_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_2060, type, total_on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_2061, type, total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2062, type, total_3592101749530773125at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_2063, type, total_1513685709984341995at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_2064, type, total_5665700600833547665t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_2065, type, total_7212417256332265445at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_2066, type, total_5117575981256876747at_nat: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_2067, type, trans_4347625901269045472at_nat: set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_2068, type, divide_divide_int: int > int > int).
% 28.44/7.23 thf(func_def_2069, type, divide_divide_rat: rat > rat > rat).
% 28.44/7.23 thf(func_def_2070, type, dvd_dvd_nat: nat > nat > $o).
% 28.44/7.23 thf(func_def_2071, type, modulo_modulo_nat: nat > nat > nat).
% 28.44/7.23 thf(func_def_2072, type, zero_n2684676970156552555ol_int: $o > int).
% 28.44/7.23 thf(func_def_2073, type, collec5651646645946169514nteger: ((code_integer > code_integer > code_integer) > $o) > set_Co4375521073081744395nteger).
% 28.44/7.23 thf(func_def_2074, type, collect_int_int: ((int > int) > $o) > set_int_int).
% 28.44/7.23 thf(func_def_2075, type, collect_int_nat: ((int > nat) > $o) > set_int_nat).
% 28.44/7.23 thf(func_def_2076, type, collect_int_num: ((int > num) > $o) > set_int_num).
% 28.44/7.23 thf(func_def_2077, type, collec2229320974926845999nt_int: ((int > product_prod_int_int) > $o) > set_in6154042108061588260nt_int).
% 28.44/7.23 thf(func_def_2078, type, collec2532482545165550967at_nat: ((int > product_prod_nat_nat) > $o) > set_in7748886932685137004at_nat).
% 28.44/7.23 thf(func_def_2079, type, collec266097228571071243um_num: ((int > product_prod_num_num) > $o) > set_in3169746454734514176um_num).
% 28.44/7.23 thf(func_def_2080, type, collec3092956710985254339at_nat: ((list_nat > product_prod_nat_nat) > $o) > set_li2168235667650531768at_nat).
% 28.44/7.23 thf(func_def_2081, type, collect_nat_o: ((nat > $o) > $o) > set_nat_o).
% 28.44/7.23 thf(func_def_2082, type, collect_nat_nat: ((nat > nat) > $o) > set_nat_nat).
% 28.44/7.23 thf(func_def_2083, type, collec8414850927317488011nt_int: ((nat > product_prod_int_int) > $o) > set_na7251125088705586816nt_int).
% 28.44/7.23 thf(func_def_2084, type, collec8718012497556192979at_nat: ((nat > product_prod_nat_nat) > $o) > set_na8845969913329135560at_nat).
% 28.44/7.23 thf(func_def_2085, type, collec2521308361159233923nt_int: ((rat > product_prod_int_int) > $o) > set_ra518564293221149304nt_int).
% 28.44/7.23 thf(func_def_2086, type, collec2824469931397938891at_nat: ((rat > product_prod_nat_nat) > $o) > set_ra2113409117844698048at_nat).
% 28.44/7.23 thf(func_def_2087, type, collec1380656525566158922nt_int: ((char > product_prod_int_int) > $o) > set_ch6383161263842509759nt_int).
% 28.44/7.23 thf(func_def_2088, type, collec1683818095804863890at_nat: ((char > product_prod_nat_nat) > $o) > set_ch7978006088466058503at_nat).
% 28.44/7.23 thf(func_def_2089, type, collect_o: ($o > $o) > set_o).
% 28.44/7.23 thf(func_def_2090, type, collect_ref_a: (ref_a > $o) > set_ref_a).
% 28.44/7.23 thf(func_def_2091, type, collect_int: (int > $o) > set_int).
% 28.44/7.23 thf(func_def_2092, type, collect_nat: (nat > $o) > set_nat).
% 28.44/7.23 thf(func_def_2093, type, collec3252306575900995386t_unit: (produc7812382424243267045t_unit > $o) > set_Pr1133966238863718811t_unit).
% 28.44/7.23 thf(func_def_2094, type, collec7215431352809750357nteger: (produc2963269191615333738nteger > $o) > set_Pr8415741480598773322nteger).
% 28.44/7.23 thf(func_def_2095, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2096, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2097, type, collec4100598399430923318at_num: (product_prod_nat_num > $o) > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2098, type, collec5600542410287506995nt_int: (produc6945250483304103390nt_int > $o) > set_Pr6123067485828015636nt_int).
% 28.44/7.23 thf(func_def_2099, type, collec5903703980526211963at_nat: (produc7248412053542808358at_nat > $o) > set_Pr7717912310451564380at_nat).
% 28.44/7.23 thf(func_def_2100, type, collec1522684865789554998um_nat: (product_prod_num_nat > $o) > set_Pr3280342998896498603um_nat).
% 28.44/7.23 thf(func_def_2101, type, collec2230928802738392704um_num: (product_prod_num_num > $o) > set_Pr8218934625190621173um_num).
% 28.44/7.23 thf(func_def_2102, type, collec364394062568603661nt_nat: (produc1709102135585200056nt_nat > $o) > set_Pr2543308735921124078nt_nat).
% 28.44/7.23 thf(func_def_2103, type, collec7447955092554649554nt_int: (produc1219242969750017639nt_int > $o) > set_Pr2560585780119916871nt_int).
% 28.44/7.23 thf(func_def_2104, type, collec7751116662793354522at_nat: (produc1522404539988722607at_nat > $o) > set_Pr4155430604743465615at_nat).
% 28.44/7.23 thf(func_def_2105, type, collec2851339944984316337at_int: (produc4196048018000912732at_int > $o) > set_Pr49084382684228242at_int).
% 28.44/7.23 thf(func_def_2106, type, collec7029190964493513045at_nat: (produc8373899037510109440at_nat > $o) > set_Pr2539167527615954998at_nat).
% 28.44/7.23 thf(func_def_2107, type, collec6785001409445536906nt_int: (produc556289286640904991nt_int > $o) > set_Pr7098892610798258687nt_int).
% 28.44/7.23 thf(func_def_2108, type, collec7088162979684241874at_nat: (produc859450856879609959at_nat > $o) > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2109, type, collec6321179662152712658at_nat: (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2110, type, collec7872792499061297490at_nat: (produc1319942482725812455at_nat > $o) > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_2111, type, collect_rat: (rat > $o) > set_rat).
% 28.44/7.23 thf(func_def_2112, type, collec5514110066124741708at_nat: (set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2113, type, collec4573900263915890866at_nat: (set_Pr4329608150637261639at_nat > $o) > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2114, type, pow_o: set_o > set_set_o).
% 28.44/7.23 thf(func_def_2115, type, pow_int: set_int > set_set_int).
% 28.44/7.23 thf(func_def_2116, type, pow_nat: set_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2117, type, pow_Pr3466873192417945886at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2118, type, pow_Pr1023649790151954692at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2119, type, pow_Product_unit: set_Product_unit > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2120, type, pow_rat: set_rat > set_set_rat).
% 28.44/7.23 thf(func_def_2121, type, image_o_o_set_o: (($o > $o) > set_o) > set_o_o > set_set_o).
% 28.44/7.23 thf(func_def_2122, type, image_1365644804893650413_int_o: ((int > int > $o) > product_prod_int_int > $o) > set_int_int_o > set_Pr8049984349381595834_int_o).
% 28.44/7.23 thf(func_def_2123, type, image_int_o_set_int: ((int > $o) > set_int) > set_int_o > set_set_int).
% 28.44/7.23 thf(func_def_2124, type, image_6646056845087809525nt_int: ((int > int) > int > int) > set_int_int > set_int_int).
% 28.44/7.23 thf(func_def_2125, type, image_1600535827742230425nt_nat: ((int > int) > int > nat) > set_int_int > set_int_nat).
% 28.44/7.23 thf(func_def_2126, type, image_1234974663384347033nt_int: ((int > nat) > int > int) > set_int_nat > set_int_int).
% 28.44/7.23 thf(func_def_2127, type, image_5412825682893543741nt_nat: ((int > nat) > int > nat) > set_int_nat > set_int_nat).
% 28.44/7.23 thf(func_def_2128, type, image_1904597124500147013nt_rat: ((int > nat) > int > rat) > set_int_nat > set_int_rat).
% 28.44/7.23 thf(func_def_2129, type, image_4174709274675160035t_unit: ((int > rat) > product_unit) > set_int_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2130, type, image_4409302170498516394t_unit: ((int > char) > product_unit) > set_int_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2131, type, image_7429393840292777309_nat_o: ((nat > nat > $o) > product_prod_nat_nat > $o) > set_nat_nat_o > set_Pr5582243495563764594_nat_o).
% 28.44/7.23 thf(func_def_2132, type, image_8484515203959327177_num_o: ((nat > num > $o) > product_prod_nat_num > $o) > set_nat_num_o > set_Pr5908833319024110760_num_o).
% 28.44/7.23 thf(func_def_2133, type, image_nat_o_set_nat: ((nat > $o) > set_nat) > set_nat_o > set_set_nat).
% 28.44/7.23 thf(func_def_2134, type, image_5437939712159429529nt_int: ((nat > int) > int > int) > set_nat_int > set_int_int).
% 28.44/7.23 thf(func_def_2135, type, image_392418694813850429nt_nat: ((nat > int) > int > nat) > set_nat_int > set_int_nat).
% 28.44/7.23 thf(func_def_2136, type, image_26857530455967037nt_int: ((nat > nat) > int > int) > set_nat_nat > set_int_int).
% 28.44/7.23 thf(func_def_2137, type, image_4204708549965163745nt_nat: ((nat > nat) > int > nat) > set_nat_nat > set_int_nat).
% 28.44/7.23 thf(func_def_2138, type, image_696479991571767017nt_rat: ((nat > nat) > int > rat) > set_nat_nat > set_int_rat).
% 28.44/7.23 thf(func_def_2139, type, image_340470173791133503t_unit: ((nat > rat) > product_unit) > set_nat_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2140, type, image_4600008085730780422t_unit: ((nat > char) > product_unit) > set_nat_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2141, type, image_4447441447610994254nt_int: ((product_prod_int_int > $o) > set_Pr958786334691620121nt_int) > set_Pr8049984349381595834_int_o > set_se6260736226359567993nt_int).
% 28.44/7.23 thf(func_def_2142, type, image_7124889717316225246at_nat: ((product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat) > set_Pr5582243495563764594_nat_o > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2143, type, image_6580737572886966642at_num: ((product_prod_nat_num > $o) > set_Pr6200539531224447659at_num) > set_Pr5908833319024110760_num_o > set_se4826145725398303499at_num).
% 28.44/7.23 thf(func_def_2144, type, image_4902389024228248874at_nat: ((produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat) > set_Pr7010166363911110284_nat_o > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2145, type, image_5694205205332509994at_nat: ((produc1319942482725812455at_nat > $o) > set_Pr7459493094073627847at_nat) > set_Pr7669914128964046860_nat_o > set_se7592288975875140775at_nat).
% 28.44/7.23 thf(func_def_2146, type, image_2910438736038083391t_unit: ((rat > nat) > product_unit) > set_rat_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2147, type, image_1193274288206594871t_unit: ((rat > rat) > product_unit) > set_rat_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2148, type, image_6940606515012899070t_unit: ((rat > char) > product_unit) > set_rat_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2149, type, image_6226802281960588479_nat_o: ((set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > produc3843707927480180839at_nat > $o) > set_se9180647916752606350_nat_o > set_Pr7010166363911110284_nat_o).
% 28.44/7.23 thf(func_def_2150, type, image_5235725667318448191_nat_o: ((set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > produc1319942482725812455at_nat > $o) > set_se7255092946006855566_nat_o > set_Pr7669914128964046860_nat_o).
% 28.44/7.23 thf(func_def_2151, type, image_108929247839792006t_unit: ((char > nat) > product_unit) > set_char_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2152, type, image_7615136836863079294t_unit: ((char > rat) > product_unit) > set_char_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2153, type, image_8077363282794994245t_unit: ((char > char) > product_unit) > set_char_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2154, type, image_o_o: ($o > $o) > set_o > set_o).
% 28.44/7.23 thf(func_def_2155, type, image_o_Code_integer: ($o > code_integer) > set_o > set_Code_integer).
% 28.44/7.23 thf(func_def_2156, type, image_o_int: ($o > int) > set_o > set_int).
% 28.44/7.23 thf(func_def_2157, type, image_o_nat: ($o > nat) > set_o > set_nat).
% 28.44/7.23 thf(func_def_2158, type, image_3855930084881510382at_nat: ($o > product_prod_nat_nat) > set_o > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2159, type, image_o_Product_unit: ($o > product_unit) > set_o > set_Product_unit).
% 28.44/7.23 thf(func_def_2160, type, image_o_rat: ($o > rat) > set_o > set_rat).
% 28.44/7.23 thf(func_def_2161, type, image_o_set_o: ($o > set_o) > set_o > set_set_o).
% 28.44/7.23 thf(func_def_2162, type, image_o_set_int: ($o > set_int) > set_o > set_set_int).
% 28.44/7.23 thf(func_def_2163, type, image_o_set_nat: ($o > set_nat) > set_o > set_set_nat).
% 28.44/7.23 thf(func_def_2164, type, image_7077428525161401678at_nat: ($o > set_Pr1261947904930325089at_nat) > set_o > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2165, type, image_8493167801588156084at_nat: ($o > set_Pr8693737435421807431at_nat) > set_o > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2166, type, image_2496312346330513076at_nat: ($o > set_Pr4329608150637261639at_nat) > set_o > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2167, type, image_663195431845683034t_unit: ($o > set_Product_unit) > set_o > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2168, type, image_o_set_rat: ($o > set_rat) > set_o > set_set_rat).
% 28.44/7.23 thf(func_def_2169, type, image_o_set_char: ($o > set_char) > set_o > set_set_char).
% 28.44/7.23 thf(func_def_2170, type, image_o_char: ($o > char) > set_o > set_char).
% 28.44/7.23 thf(func_def_2171, type, image_2177946750938214461nteger: (code_integer > code_integer > code_integer) > set_Code_integer > set_Co726186806682698383nteger).
% 28.44/7.23 thf(func_def_2172, type, image_4470545334726330049nteger: (code_integer > code_integer) > set_Code_integer > set_Code_integer).
% 28.44/7.23 thf(func_def_2173, type, image_5570573867351727369t_unit: (ref_a > set_he8644174446132254637t_unit) > set_ref_a > set_se4612898379794543757t_unit).
% 28.44/7.23 thf(func_def_2174, type, image_int_o: (int > $o) > set_int > set_o).
% 28.44/7.23 thf(func_def_2175, type, image_int_int: (int > int) > set_int > set_int).
% 28.44/7.23 thf(func_def_2176, type, image_int_nat: (int > nat) > set_int > set_nat).
% 28.44/7.23 thf(func_def_2177, type, image_int_num: (int > num) > set_int > set_num).
% 28.44/7.23 thf(func_def_2178, type, image_5705468584675977158nt_int: (int > product_prod_int_int) > set_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2179, type, image_659947567330398058nt_nat: (int > product_prod_int_nat) > set_int > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_2180, type, image_8883965892284119310at_nat: (int > product_prod_nat_nat) > set_int > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2181, type, image_7722540232540426402um_num: (int > product_prod_num_num) > set_int > set_Pr8218934625190621173um_num).
% 28.44/7.23 thf(func_def_2182, type, image_5846526143423701914t_unit: (int > product_unit) > set_int > set_Product_unit).
% 28.44/7.23 thf(func_def_2183, type, image_int_rat: (int > rat) > set_int > set_rat).
% 28.44/7.23 thf(func_def_2184, type, image_int_set_o: (int > set_o) > set_int > set_set_o).
% 28.44/7.23 thf(func_def_2185, type, image_int_set_int: (int > set_int) > set_int > set_set_int).
% 28.44/7.23 thf(func_def_2186, type, image_int_set_nat: (int > set_nat) > set_int > set_set_nat).
% 28.44/7.23 thf(func_def_2187, type, image_8635204845542730022nt_int: (int > set_Pr958786334691620121nt_int) > set_int > set_se6260736226359567993nt_int).
% 28.44/7.23 thf(func_def_2188, type, image_8938366415781434990at_nat: (int > set_Pr1261947904930325089at_nat) > set_int > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2189, type, image_525487068563185620at_nat: (int > set_Pr8693737435421807431at_nat) > set_int > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2190, type, image_8658272795163236474t_unit: (int > set_Product_unit) > set_int > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2191, type, image_7976474329151083847st_nat: (list_nat > list_nat) > set_list_nat > set_list_nat).
% 28.44/7.23 thf(func_def_2192, type, image_list_nat_nat: (list_nat > nat) > set_list_nat > set_nat).
% 28.44/7.23 thf(func_def_2193, type, image_2795870212791037530at_nat: (list_nat > product_prod_nat_nat) > set_list_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2194, type, image_nat_o: (nat > $o) > set_nat > set_o).
% 28.44/7.23 thf(func_def_2195, type, image_nat_int: (nat > int) > set_nat > set_int).
% 28.44/7.23 thf(func_def_2196, type, image_nat_list_nat: (nat > list_nat) > set_nat > set_list_nat).
% 28.44/7.23 thf(func_def_2197, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2198, type, image_nat_num: (nat > num) > set_nat > set_num).
% 28.44/7.23 thf(func_def_2199, type, image_2667626500211843362nt_int: (nat > product_prod_int_int) > set_nat > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2200, type, image_6845477519721040070nt_nat: (nat > product_prod_int_nat) > set_nat > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_2201, type, image_3337248961327643342nt_rat: (nat > product_prod_int_rat) > set_nat > set_Pr6292255179000445125nt_rat).
% 28.44/7.23 thf(func_def_2202, type, image_5846123807819985514at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2203, type, image_3276603626957510736at_nat: (nat > produc859450856879609959at_nat) > set_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2204, type, image_3978134465758882403it_nat: (nat > produc600557818389255820it_nat) > set_nat > set_Pr1763845938948868674it_nat).
% 28.44/7.23 thf(func_def_2205, type, image_469905907365485675it_rat: (nat > produc6315701296850634900it_rat) > set_nat > set_Pr4607231638325966922it_rat).
% 28.44/7.23 thf(func_def_2206, type, image_1351718144375922894at_int: (nat > product_prod_rat_int) > set_nat > set_Pr3594552606344371909at_int).
% 28.44/7.23 thf(func_def_2207, type, image_5529569163885119602at_nat: (nat > product_prod_rat_nat) > set_nat > set_Pr6084635751276098665at_nat).
% 28.44/7.23 thf(func_def_2208, type, image_2021340605491722874at_rat: (nat > product_prod_rat_rat) > set_nat > set_Pr8928021450653196913at_rat).
% 28.44/7.23 thf(func_def_2209, type, image_2499013659892586576at_nat: (nat > produc3843707927480180839at_nat) > set_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2210, type, image_8730104196221521654t_unit: (nat > product_unit) > set_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2211, type, image_nat_rat: (nat > rat) > set_nat > set_rat).
% 28.44/7.23 thf(func_def_2212, type, image_nat_set_o: (nat > set_o) > set_nat > set_set_o).
% 28.44/7.23 thf(func_def_2213, type, image_nat_set_int: (nat > set_int) > set_nat > set_set_int).
% 28.44/7.23 thf(func_def_2214, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2215, type, image_7178329752028323786at_nat: (nat > set_Pr1261947904930325089at_nat) > set_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2216, type, image_2893549341467670548at_num: (nat > set_Pr6200539531224447659at_num) > set_nat > set_se4826145725398303499at_num).
% 28.44/7.23 thf(func_def_2217, type, image_4592875511192039216at_nat: (nat > set_Pr8693737435421807431at_nat) > set_nat > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2218, type, image_1087905878993176368at_nat: (nat > set_Pr4329608150637261639at_nat) > set_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2219, type, image_4824033694279209942t_unit: (nat > set_Product_unit) > set_nat > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2220, type, image_nat_set_rat: (nat > set_rat) > set_nat > set_set_rat).
% 28.44/7.23 thf(func_def_2221, type, image_nat_set_char: (nat > set_char) > set_nat > set_set_char).
% 28.44/7.23 thf(func_def_2222, type, image_nat_char: (nat > char) > set_nat > set_char).
% 28.44/7.23 thf(func_def_2223, type, image_678696785212003926at_nat: (nat > sum_sum_nat_nat) > set_nat > set_Sum_sum_nat_nat).
% 28.44/7.23 thf(func_def_2224, type, image_num_o: (num > $o) > set_num > set_o).
% 28.44/7.23 thf(func_def_2225, type, image_num_int: (num > int) > set_num > set_int).
% 28.44/7.23 thf(func_def_2226, type, image_num_nat: (num > nat) > set_num > set_nat).
% 28.44/7.23 thf(func_def_2227, type, image_num_num: (num > num) > set_num > set_num).
% 28.44/7.23 thf(func_def_2228, type, image_4778453735051108682at_num: (num > set_Pr6200539531224447659at_num) > set_num > set_se4826145725398303499at_num).
% 28.44/7.23 thf(func_def_2229, type, image_7896445794123959606_o_o_o: (product_prod_o_o > $o) > set_Product_prod_o_o > set_o).
% 28.44/7.23 thf(func_def_2230, type, image_8105710389281276538_nat_o: (product_prod_o_nat > $o) > set_Pr2101469702781467981_o_nat > set_o).
% 28.44/7.23 thf(func_def_2231, type, image_4888532181312399726at_nat: (product_prod_o_nat > nat) > set_Pr2101469702781467981_o_nat > set_nat).
% 28.44/7.23 thf(func_def_2232, type, image_8742399529945250561unit_o: (produc3788275437394581276t_unit > $o) > set_Pr6671815714118170108t_unit > set_o).
% 28.44/7.23 thf(func_def_2233, type, image_4419268941131634678t_unit: (produc3788275437394581276t_unit > product_unit) > set_Pr6671815714118170108t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2234, type, image_17660834435998945t_unit: (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > set_Pr1133966238863718811t_unit > set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_2235, type, image_7136766188234240905_ref_a: (produc7812382424243267045t_unit > ref_a) > set_Pr1133966238863718811t_unit > set_ref_a).
% 28.44/7.23 thf(func_def_2236, type, image_1531683682067511245nt_int: (produc7812382424243267045t_unit > product_prod_int_int) > set_Pr1133966238863718811t_unit > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2237, type, image_4710180989675653397at_nat: (produc7812382424243267045t_unit > product_prod_nat_nat) > set_Pr1133966238863718811t_unit > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2238, type, image_90517134139374612_o_int: (product_prod_int_o > int) > set_Pr903927857289325719_int_o > set_int).
% 28.44/7.23 thf(func_def_2239, type, image_2135063354759101220_int_o: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int > set_o).
% 28.44/7.23 thf(func_def_2240, type, image_5042161079198086560nt_int: (product_prod_int_int > int) > set_Pr958786334691620121nt_int > set_int).
% 28.44/7.23 thf(func_def_2241, type, image_5044651549707136836nt_nat: (product_prod_int_int > nat) > set_Pr958786334691620121nt_int > set_nat).
% 28.44/7.23 thf(func_def_2242, type, image_2653370878348428101nt_int: (product_prod_int_int > product_prod_int_int) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2243, type, image_6831221897857624809nt_nat: (product_prod_int_int > product_prod_int_nat) > set_Pr958786334691620121nt_int > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_2244, type, image_1654017166447373545at_int: (product_prod_int_int > product_prod_nat_int) > set_Pr958786334691620121nt_int > set_Pr7995236796853374141at_int).
% 28.44/7.23 thf(func_def_2245, type, image_5831868185956570253at_nat: (product_prod_int_int > product_prod_nat_nat) > set_Pr958786334691620121nt_int > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2246, type, image_6540112122905407959at_num: (product_prod_int_int > product_prod_nat_num) > set_Pr958786334691620121nt_int > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2247, type, image_8858061497167895027at_nat: (product_prod_int_int > produc859450856879609959at_nat) > set_Pr958786334691620121nt_int > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2248, type, image_6029125644611338739at_nat: (product_prod_int_int > produc3843707927480180839at_nat) > set_Pr958786334691620121nt_int > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2249, type, image_2855239504505064772at_int: (product_prod_int_nat > int) > set_Pr3448869479623346877nt_nat > set_int).
% 28.44/7.23 thf(func_def_2250, type, image_7928304878501623365nt_nat: (product_prod_int_nat > product_prod_int_nat) > set_Pr3448869479623346877nt_nat > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_2251, type, image_4420076320108226637nt_rat: (product_prod_int_nat > product_prod_int_rat) > set_Pr3448869479623346877nt_nat > set_Pr6292255179000445125nt_rat).
% 28.44/7.23 thf(func_def_2252, type, image_2751100147091372101at_int: (product_prod_int_nat > product_prod_nat_int) > set_Pr3448869479623346877nt_nat > set_Pr7995236796853374141at_int).
% 28.44/7.23 thf(func_def_2253, type, image_3420722608207172081at_rat: (product_prod_int_nat > product_prod_nat_rat) > set_Pr3448869479623346877nt_nat > set_Pr4105333604307423337at_rat).
% 28.44/7.23 thf(func_def_2254, type, image_7716461468295075337it_int: (produc6865911496949736918t_unit > int) > set_Pr5889264611543340172t_unit > set_int).
% 28.44/7.23 thf(func_def_2255, type, image_7478392465989118804at_o_o: (product_prod_nat_o > $o) > set_Pr3149072824959771635_nat_o > set_o).
% 28.44/7.23 thf(func_def_2256, type, image_8629803608462650132_o_nat: (product_prod_nat_o > nat) > set_Pr3149072824959771635_nat_o > set_nat).
% 28.44/7.23 thf(func_def_2257, type, image_893334214595316897nt_int: (product_prod_nat_int > product_prod_int_int) > set_Pr7995236796853374141at_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2258, type, image_5071185234104513605nt_nat: (product_prod_nat_int > product_prod_int_nat) > set_Pr7995236796853374141at_int > set_Pr3448869479623346877nt_nat).
% 28.44/7.23 thf(func_def_2259, type, image_9117352539549038149at_int: (product_prod_nat_int > product_prod_nat_int) > set_Pr7995236796853374141at_int > set_Pr7995236796853374141at_int).
% 28.44/7.23 thf(func_def_2260, type, image_8800797895614172237at_int: (product_prod_nat_int > product_prod_rat_int) > set_Pr7995236796853374141at_int > set_Pr3594552606344371909at_int).
% 28.44/7.23 thf(func_def_2261, type, image_3755276878268593137at_nat: (product_prod_nat_int > product_prod_rat_nat) > set_Pr7995236796853374141at_int > set_Pr6084635751276098665at_nat).
% 28.44/7.23 thf(func_def_2262, type, image_3693632289388996572_nat_o: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > set_o).
% 28.44/7.23 thf(func_def_2263, type, image_2483585944268220136at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > set_int).
% 28.44/7.23 thf(func_def_2264, type, image_2486076414777270412at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat).
% 28.44/7.23 thf(func_def_2265, type, image_1990417195239315453nt_int: (product_prod_nat_nat > product_prod_int_int) > set_Pr1261947904930325089at_nat > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2266, type, image_5168914502847457605at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2267, type, image_5877158439796295311at_num: (product_prod_nat_nat > product_prod_nat_num) > set_Pr1261947904930325089at_nat > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2268, type, image_1119892238107900587at_nat: (product_prod_nat_nat > produc859450856879609959at_nat) > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2269, type, image_6169909464789311569t_unit: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2270, type, image_501298686397505212_set_o: (product_prod_nat_nat > set_o) > set_Pr1261947904930325089at_nat > set_set_o).
% 28.44/7.23 thf(func_def_2271, type, image_15824709712370754et_nat: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2272, type, image_5423882813909314213at_nat: (product_prod_nat_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2273, type, image_5803077947706746251at_nat: (product_prod_nat_nat > set_Pr8693737435421807431at_nat) > set_Pr1261947904930325089at_nat > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2274, type, image_121980125215734065t_unit: (product_prod_nat_nat > set_Product_unit) > set_Pr1261947904930325089at_nat > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2275, type, image_4451812852358507538_num_o: (product_prod_nat_num > $o) > set_Pr6200539531224447659at_num > set_o).
% 28.44/7.23 thf(func_def_2276, type, image_4501981038234393650um_int: (product_prod_nat_num > int) > set_Pr6200539531224447659at_num > set_int).
% 28.44/7.23 thf(func_def_2277, type, image_4504471508743443926um_nat: (product_prod_nat_num > nat) > set_Pr6200539531224447659at_num > set_nat).
% 28.44/7.23 thf(func_def_2278, type, image_1039142661021589043nt_int: (product_prod_nat_num > product_prod_int_int) > set_Pr6200539531224447659at_num > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2279, type, image_4217639968629731195at_nat: (product_prod_nat_num > product_prod_nat_nat) > set_Pr6200539531224447659at_num > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2280, type, image_4925883905578568901at_num: (product_prod_nat_num > product_prod_nat_num) > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2281, type, image_2347970371937200581um_nat: (product_prod_nat_num > product_prod_num_nat) > set_Pr6200539531224447659at_num > set_Pr3280342998896498603um_nat).
% 28.44/7.23 thf(func_def_2282, type, image_2708129733610033121at_nat: (product_prod_nat_num > produc3843707927480180839at_nat) > set_Pr6200539531224447659at_num > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2283, type, image_3884712837920099081it_nat: (produc526117512892780850t_unit > nat) > set_Pr4334478416066269672t_unit > set_nat).
% 28.44/7.23 thf(func_def_2284, type, image_5511522805742971924t_unit: (produc526117512892780850t_unit > product_unit) > set_Pr4334478416066269672t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2285, type, image_7762062833379733445at_num: (product_prod_num_nat > product_prod_nat_num) > set_Pr3280342998896498603um_nat > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2286, type, image_3275415580317762038_nat_o: (produc859450856879609959at_nat > $o) > set_Pr8693737435421807431at_nat > set_o).
% 28.44/7.23 thf(func_def_2287, type, image_6160980552072806642at_nat: (produc859450856879609959at_nat > nat) > set_Pr8693737435421807431at_nat > set_nat).
% 28.44/7.23 thf(func_def_2288, type, image_6706873702294942047at_nat: (produc859450856879609959at_nat > product_prod_nat_nat) > set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2289, type, image_6321802852832981957at_nat: (produc859450856879609959at_nat > produc859450856879609959at_nat) > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2290, type, image_7637461350386011077at_nat: (produc859450856879609959at_nat > produc3843707927480180839at_nat) > set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2291, type, image_8487516615895632747t_unit: (produc859450856879609959at_nat > product_unit) > set_Pr8693737435421807431at_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2292, type, image_2819269535336293544et_nat: (produc859450856879609959at_nat > set_nat) > set_Pr8693737435421807431at_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2293, type, image_1384942819424619199at_nat: (produc859450856879609959at_nat > set_Pr1261947904930325089at_nat) > set_Pr8693737435421807431at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2294, type, image_6654316230217496229at_nat: (produc859450856879609959at_nat > set_Pr8693737435421807431at_nat) > set_Pr8693737435421807431at_nat > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2295, type, image_3876558564303283877at_nat: (produc859450856879609959at_nat > set_Pr4329608150637261639at_nat) > set_Pr8693737435421807431at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2296, type, image_1801747192096393899it_o_o: (produc7485711547916492274unit_o > $o) > set_Pr5464989305201766866unit_o > set_o).
% 28.44/7.23 thf(func_def_2297, type, image_4246157487713968288t_unit: (produc7485711547916492274unit_o > product_unit) > set_Pr5464989305201766866unit_o > set_Product_unit).
% 28.44/7.23 thf(func_def_2298, type, image_6725568594985674851at_nat: (produc600557818389255820it_nat > nat) > set_Pr1763845938948868674it_nat > set_nat).
% 28.44/7.23 thf(func_def_2299, type, image_7474191388529947450t_unit: (produc600557818389255820it_nat > product_unit) > set_Pr1763845938948868674it_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2300, type, image_262127665112854123t_unit: (produc8459935480633519975t_unit > product_unit) > set_Pr5094982260447487303t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2301, type, image_8033574621161215657at_num: (produc3843707927480180839at_nat > product_prod_nat_num) > set_Pr4329608150637261639at_nat > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2302, type, image_5653576389946358725at_nat: (produc3843707927480180839at_nat > produc859450856879609959at_nat) > set_Pr4329608150637261639at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2303, type, image_960689587819713477at_nat: (produc3843707927480180839at_nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2304, type, image_7082456443403096939t_unit: (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2305, type, image_3160451284896210088et_nat: (produc3843707927480180839at_nat > set_nat) > set_Pr4329608150637261639at_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2306, type, image_7979982168039674559at_nat: (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2307, type, image_7260680879217540773at_nat: (produc3843707927480180839at_nat > set_Pr8693737435421807431at_nat) > set_Pr4329608150637261639at_nat > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2308, type, image_7364710425340685989at_nat: (produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2309, type, image_3313167189156628421at_nat: (produc1319942482725812455at_nat > produc1319942482725812455at_nat) > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_2310, type, image_2699825501378146573ar_rat: (produc3922234789054302210ar_nat > produc414006230660905482ar_rat) > set_Pr1413074515586503650ar_nat > set_Pr4256460214963601898ar_rat).
% 28.44/7.23 thf(func_def_2311, type, image_5973708714899544198r_char: (produc3922234789054302210ar_nat > produc143505574896075907r_char) > set_Pr1413074515586503650ar_nat > set_Pr3309569728657787619r_char).
% 28.44/7.23 thf(func_def_2312, type, image_4975014655635759961ar_int: (produc414006230660905482ar_rat > produc8967755806399881310ar_int) > set_Pr4256460214963601898ar_rat > set_Pr8146363407509552702ar_int).
% 28.44/7.23 thf(func_def_2313, type, image_9152865675144956669ar_nat: (produc414006230660905482ar_rat > produc3922234789054302210ar_nat) > set_Pr4256460214963601898ar_rat > set_Pr1413074515586503650ar_nat).
% 28.44/7.23 thf(func_def_2314, type, image_5644637116751559941ar_rat: (produc414006230660905482ar_rat > produc414006230660905482ar_rat) > set_Pr4256460214963601898ar_rat > set_Pr4256460214963601898ar_rat).
% 28.44/7.23 thf(func_def_2315, type, image_8036680598759533694r_char: (produc414006230660905482ar_rat > produc143505574896075907r_char) > set_Pr4256460214963601898ar_rat > set_Pr3309569728657787619r_char).
% 28.44/7.23 thf(func_def_2316, type, image_6605449789044937888ar_int: (produc143505574896075907r_char > produc8967755806399881310ar_int) > set_Pr3309569728657787619r_char > set_Pr8146363407509552702ar_int).
% 28.44/7.23 thf(func_def_2317, type, image_1559928771699358788ar_nat: (produc143505574896075907r_char > produc3922234789054302210ar_nat) > set_Pr3309569728657787619r_char > set_Pr1413074515586503650ar_nat).
% 28.44/7.23 thf(func_def_2318, type, image_7275072250160737868ar_rat: (produc143505574896075907r_char > produc414006230660905482ar_rat) > set_Pr3309569728657787619r_char > set_Pr4256460214963601898ar_rat).
% 28.44/7.23 thf(func_def_2319, type, image_7676512070627423941r_char: (produc143505574896075907r_char > produc143505574896075907r_char) > set_Pr3309569728657787619r_char > set_Pr3309569728657787619r_char).
% 28.44/7.23 thf(func_def_2320, type, image_Product_unit_o: (product_unit > $o) > set_Product_unit > set_o).
% 28.44/7.23 thf(func_def_2321, type, image_873079544045703924it_int: (product_unit > int) > set_Product_unit > set_int).
% 28.44/7.23 thf(func_def_2322, type, image_875570014554754200it_nat: (product_unit > nat) > set_Product_unit > set_nat).
% 28.44/7.23 thf(func_def_2323, type, image_405062704495631173t_unit: (product_unit > product_unit) > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2324, type, image_240439954468258464it_rat: (product_unit > rat) > set_Product_unit > set_rat).
% 28.44/7.23 thf(func_def_2325, type, image_6930536745178679216_set_o: (product_unit > set_o) > set_Product_unit > set_set_o).
% 28.44/7.23 thf(func_def_2326, type, image_3995998972318789802et_int: (product_unit > set_int) > set_Product_unit > set_set_int).
% 28.44/7.23 thf(func_def_2327, type, image_8173849991827986510et_nat: (product_unit > set_nat) > set_Product_unit > set_set_nat).
% 28.44/7.23 thf(func_def_2328, type, image_3617315916088684441at_nat: (product_unit > set_Pr1261947904930325089at_nat) > set_Product_unit > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2329, type, image_7288820656315755647at_nat: (product_unit > set_Pr8693737435421807431at_nat) > set_Product_unit > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2330, type, image_5172358348707908735at_nat: (product_unit > set_Pr4329608150637261639at_nat) > set_Product_unit > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2331, type, image_7778121751606633509t_unit: (product_unit > set_Product_unit) > set_Product_unit > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2332, type, image_4665621433434589782et_rat: (product_unit > set_rat) > set_Product_unit > set_set_rat).
% 28.44/7.23 thf(func_def_2333, type, image_5325685772115642575t_char: (product_unit > set_char) > set_Product_unit > set_set_char).
% 28.44/7.23 thf(func_def_2334, type, image_7248553556944771225t_char: (product_unit > char) > set_Product_unit > set_char).
% 28.44/7.23 thf(func_def_2335, type, image_rat_o: (rat > $o) > set_rat > set_o).
% 28.44/7.23 thf(func_def_2336, type, image_rat_int: (rat > int) > set_rat > set_int).
% 28.44/7.23 thf(func_def_2337, type, image_rat_nat: (rat > nat) > set_rat > set_nat).
% 28.44/7.23 thf(func_def_2338, type, image_5997455970908365082nt_int: (rat > product_prod_int_int) > set_rat > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2339, type, image_9175953278516507234at_nat: (rat > product_prod_nat_nat) > set_rat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2340, type, image_2327579789247107822t_unit: (rat > product_unit) > set_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2341, type, image_rat_rat: (rat > rat) > set_rat > set_rat).
% 28.44/7.23 thf(func_def_2342, type, image_rat_set_nat: (rat > set_nat) > set_rat > set_set_nat).
% 28.44/7.23 thf(func_def_2343, type, image_rat_char: (rat > char) > set_rat > set_char).
% 28.44/7.23 thf(func_def_2344, type, image_set_o_o_o: (set_o > $o > $o) > set_set_o > set_o_o).
% 28.44/7.23 thf(func_def_2345, type, image_set_o_o: (set_o > $o) > set_set_o > set_o).
% 28.44/7.23 thf(func_def_2346, type, image_set_o_set_o: (set_o > set_o) > set_set_o > set_set_o).
% 28.44/7.23 thf(func_def_2347, type, image_set_int_int_o: (set_int > int > $o) > set_set_int > set_int_o).
% 28.44/7.23 thf(func_def_2348, type, image_set_int_o: (set_int > $o) > set_set_int > set_o).
% 28.44/7.23 thf(func_def_2349, type, image_524474410958335435et_int: (set_int > set_int) > set_set_int > set_set_int).
% 28.44/7.23 thf(func_def_2350, type, image_4702325430467532143et_nat: (set_int > set_nat) > set_set_int > set_set_nat).
% 28.44/7.23 thf(func_def_2351, type, image_set_nat_nat_o: (set_nat > nat > $o) > set_set_nat > set_nat_o).
% 28.44/7.23 thf(func_def_2352, type, image_set_nat_o: (set_nat > $o) > set_set_nat > set_o).
% 28.44/7.23 thf(func_def_2353, type, image_6369283972875870912t_unit: (set_nat > product_unit) > set_set_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2354, type, image_3739036796817536367et_int: (set_nat > set_int) > set_set_nat > set_set_int).
% 28.44/7.23 thf(func_def_2355, type, image_7916887816326733075et_nat: (set_nat > set_nat) > set_set_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2356, type, image_6521575952113991828at_nat: (set_nat > set_Pr1261947904930325089at_nat) > set_set_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2357, type, image_4408659257933336347et_rat: (set_nat > set_rat) > set_set_nat > set_set_rat).
% 28.44/7.23 thf(func_def_2358, type, image_4446226961036766042_int_o: (set_Pr958786334691620121nt_int > int > int > $o) > set_se6260736226359567993nt_int > set_int_int_o).
% 28.44/7.23 thf(func_def_2359, type, image_701744273176368580_int_o: (set_Pr958786334691620121nt_int > $o) > set_se6260736226359567993nt_int > set_o).
% 28.44/7.23 thf(func_def_2360, type, image_6923511907955291850_nat_o: (set_Pr1261947904930325089at_nat > nat > nat > $o) > set_se7855581050983116737at_nat > set_nat_nat_o).
% 28.44/7.23 thf(func_def_2361, type, image_5253903537071781336_nat_o: (set_Pr1261947904930325089at_nat > product_prod_nat_nat > $o) > set_se7855581050983116737at_nat > set_Pr5582243495563764594_nat_o).
% 28.44/7.23 thf(func_def_2362, type, image_7457375456213313148_nat_o: (set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat > set_o).
% 28.44/7.23 thf(func_def_2363, type, image_5853224409075402146et_nat: (set_Pr1261947904930325089at_nat > set_nat) > set_se7855581050983116737at_nat > set_set_nat).
% 28.44/7.23 thf(func_def_2364, type, image_3684629450409544005at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2365, type, image_6898982319499645995at_nat: (set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat) > set_se7855581050983116737at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2366, type, image_2055017250723459638_num_o: (set_Pr6200539531224447659at_num > nat > num > $o) > set_se4826145725398303499at_num > set_nat_num_o).
% 28.44/7.23 thf(func_def_2367, type, image_1013614488123988933at_nat: (set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat) > set_se6425085446898223655at_nat > set_se6425085446898223655at_nat).
% 28.44/7.23 thf(func_def_2368, type, image_4859512832475012440_nat_o: (set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat > $o) > set_se5479201105039950375at_nat > set_Pr7010166363911110284_nat_o).
% 28.44/7.23 thf(func_def_2369, type, image_6595146019508340652_nat_o: (set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_se5479201105039950375at_nat > set_se9180647916752606350_nat_o).
% 28.44/7.23 thf(func_def_2370, type, image_3568060456209098518_nat_o: (set_Pr4329608150637261639at_nat > $o) > set_se5479201105039950375at_nat > set_o).
% 28.44/7.23 thf(func_def_2371, type, image_4303274092540115909at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2372, type, image_1124969593608450885at_nat: (set_Pr4329608150637261639at_nat > set_Pr7459493094073627847at_nat) > set_se5479201105039950375at_nat > set_se7592288975875140775at_nat).
% 28.44/7.23 thf(func_def_2373, type, image_5337237954834410540_nat_o: (set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_se7592288975875140775at_nat > set_se7255092946006855566_nat_o).
% 28.44/7.23 thf(func_def_2374, type, image_4019945301284682565t_unit: (set_Product_unit > set_Product_unit) > set_set_Product_unit > set_set_Product_unit).
% 28.44/7.23 thf(func_def_2375, type, image_char_o: (char > $o) > set_char > set_o).
% 28.44/7.23 thf(func_def_2376, type, image_char_int: (char > int) > set_char > set_int).
% 28.44/7.23 thf(func_def_2377, type, image_char_nat: (char > nat) > set_char > set_nat).
% 28.44/7.23 thf(func_def_2378, type, image_5204326662208377313nt_int: (char > product_prod_int_int) > set_char > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2379, type, image_8382823969816519465at_nat: (char > product_prod_nat_nat) > set_char > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2380, type, image_4337914935673063477t_unit: (char > product_unit) > set_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2381, type, image_char_rat: (char > rat) > set_char > set_rat).
% 28.44/7.23 thf(func_def_2382, type, image_char_char: (char > char) > set_char > set_char).
% 28.44/7.23 thf(func_def_2383, type, image_1320371278474632150at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > set_nat).
% 28.44/7.23 thf(func_def_2384, type, insert_o: $o > set_o > set_o).
% 28.44/7.23 thf(func_def_2385, type, insert8563697753282147485t_unit: heap_e7401611519738050253t_unit > set_he8644174446132254637t_unit > set_he8644174446132254637t_unit).
% 28.44/7.23 thf(func_def_2386, type, insert_ref_a: ref_a > set_ref_a > set_ref_a).
% 28.44/7.23 thf(func_def_2387, type, insert_int: int > set_int > set_int).
% 28.44/7.23 thf(func_def_2388, type, insert_nat: nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2389, type, insert_num: num > set_num > set_num).
% 28.44/7.23 thf(func_def_2390, type, insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 28.44/7.23 thf(func_def_2391, type, insert7948214739558299847_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > set_Pr2101469702781467981_o_nat).
% 28.44/7.23 thf(func_def_2392, type, insert9112848208840649964t_unit: produc3788275437394581276t_unit > set_Pr6671815714118170108t_unit > set_Pr6671815714118170108t_unit).
% 28.44/7.23 thf(func_def_2393, type, insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 28.44/7.23 thf(func_def_2394, type, insert2233377226759017069_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > set_Pr3149072824959771635_nat_o).
% 28.44/7.23 thf(func_def_2395, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2396, type, insert8920054152555992091at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num).
% 28.44/7.23 thf(func_def_2397, type, insert6804906068341198690t_unit: produc526117512892780850t_unit > set_Pr4334478416066269672t_unit > set_Pr4334478416066269672t_unit).
% 28.44/7.23 thf(func_def_2398, type, insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2399, type, insert5475735164933346999at_nat: produc349518998152878311at_nat > set_Pr553994874890374343at_nat > set_Pr553994874890374343at_nat).
% 28.44/7.23 thf(func_def_2400, type, insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat).
% 28.44/7.23 thf(func_def_2401, type, insert3586912282507785154unit_o: produc7485711547916492274unit_o > set_Pr5464989305201766866unit_o > set_Pr5464989305201766866unit_o).
% 28.44/7.23 thf(func_def_2402, type, insert6879346373837673660it_nat: produc600557818389255820it_nat > set_Pr1763845938948868674it_nat > set_Pr1763845938948868674it_nat).
% 28.44/7.23 thf(func_def_2403, type, insert4616891024742550839t_unit: produc8459935480633519975t_unit > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit).
% 28.44/7.23 thf(func_def_2404, type, insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2405, type, insert291458823148189367at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat).
% 28.44/7.23 thf(func_def_2406, type, insert_Product_unit: product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2407, type, insert_rat: rat > set_rat > set_rat).
% 28.44/7.23 thf(func_def_2408, type, insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2409, type, insert2290795007606087959at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_2410, type, the_elem_int: set_int > int).
% 28.44/7.23 thf(func_def_2411, type, the_elem_nat: set_nat > nat).
% 28.44/7.23 thf(func_def_2412, type, the_elem_rat: set_rat > rat).
% 28.44/7.23 thf(func_def_2413, type, vimage4289680085338140859nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Pr4111642102156807771nteger > set_Co726186806682698383nteger).
% 28.44/7.23 thf(func_def_2414, type, vimage_o_o: ($o > $o) > set_o > set_o).
% 28.44/7.23 thf(func_def_2415, type, vimage_o_nat: ($o > nat) > set_nat > set_o).
% 28.44/7.23 thf(func_def_2416, type, vimage8945963521958007626od_o_o: ($o > product_prod_o_o) > set_Product_prod_o_o > set_o).
% 28.44/7.23 thf(func_def_2417, type, vimage4304346610107161470_int_o: ($o > product_prod_int_o) > set_Pr903927857289325719_int_o > set_o).
% 28.44/7.23 thf(func_def_2418, type, vimage6125388955539849434_nat_o: ($o > product_prod_nat_o) > set_Pr3149072824959771635_nat_o > set_o).
% 28.44/7.23 thf(func_def_2419, type, vimage4222377557387472176t_unit: ($o > product_unit) > set_Product_unit > set_o).
% 28.44/7.23 thf(func_def_2420, type, vimage_o_rat: ($o > rat) > set_rat > set_o).
% 28.44/7.23 thf(func_def_2421, type, vimage_o_char: ($o > char) > set_char > set_o).
% 28.44/7.23 thf(func_def_2422, type, vimage6029918387083761651nteger: (code_integer > code_integer > code_integer) > set_Co726186806682698383nteger > set_Code_integer).
% 28.44/7.23 thf(func_def_2423, type, vimage6839621282666897215nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Pr4111642102156807771nteger > set_Code_integer).
% 28.44/7.23 thf(func_def_2424, type, vimage_int_int: (int > int) > set_int > set_int).
% 28.44/7.23 thf(func_def_2425, type, vimage_int_nat: (int > nat) > set_nat > set_int).
% 28.44/7.23 thf(func_def_2426, type, vimage_int_num: (int > num) > set_num > set_int).
% 28.44/7.23 thf(func_def_2427, type, vimage7872673496510460816nt_int: (int > product_prod_int_int) > set_Pr958786334691620121nt_int > set_int).
% 28.44/7.23 thf(func_def_2428, type, vimage1827798767263827160at_nat: (int > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_int).
% 28.44/7.23 thf(func_def_2429, type, vimage8527374361057053988at_nat: (list_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_list_nat).
% 28.44/7.23 thf(func_def_2430, type, vimage_nat_o: (nat > $o) > set_o > set_nat).
% 28.44/7.23 thf(func_def_2431, type, vimage_nat_int: (nat > int) > set_int > set_nat).
% 28.44/7.23 thf(func_def_2432, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2433, type, vimage_nat_num: (nat > num) > set_num > set_nat).
% 28.44/7.23 thf(func_def_2434, type, vimage5656379182745576100_o_nat: (nat > product_prod_o_nat) > set_Pr2101469702781467981_o_nat > set_nat).
% 28.44/7.23 thf(func_def_2435, type, vimage9012682431555523728nt_nat: (nat > product_prod_int_nat) > set_Pr3448869479623346877nt_nat > set_nat).
% 28.44/7.23 thf(func_def_2436, type, vimage8013328719654469172at_nat: (nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_nat).
% 28.44/7.23 thf(func_def_2437, type, vimage6435164912253009178at_nat: (nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > set_nat).
% 28.44/7.23 thf(func_def_2438, type, vimage4884490618288580032t_unit: (nat > product_unit) > set_Product_unit > set_nat).
% 28.44/7.23 thf(func_def_2439, type, vimage_nat_rat: (nat > rat) > set_rat > set_nat).
% 28.44/7.23 thf(func_def_2440, type, vimage_nat_char: (nat > char) > set_char > set_nat).
% 28.44/7.23 thf(func_def_2441, type, vimage5436458796434496692at_num: (num > product_prod_nat_num) > set_Pr6200539531224447659at_num > set_num).
% 28.44/7.23 thf(func_def_2442, type, vimage6116673589273818795t_unit: (produc7812382424243267045t_unit > heap_e7401611519738050253t_unit) > set_he8644174446132254637t_unit > set_Pr1133966238863718811t_unit).
% 28.44/7.23 thf(func_def_2443, type, vimage2910454108108208703_ref_a: (produc7812382424243267045t_unit > ref_a) > set_ref_a > set_Pr1133966238863718811t_unit).
% 28.44/7.23 thf(func_def_2444, type, vimage2444243245536687506_nat_o: (product_prod_nat_nat > $o) > set_o > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2445, type, vimage1024995831485383111t_unit: (product_prod_nat_nat > heap_e7401611519738050253t_unit) > set_he8644174446132254637t_unit > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2446, type, vimage7322659125625010723_ref_a: (product_prod_nat_nat > ref_a) > set_ref_a > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2447, type, vimage4650790856102703794at_int: (product_prod_nat_nat > int) > set_int > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2448, type, vimage4653281326611754070at_nat: (product_prod_nat_nat > nat) > set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2449, type, vimage4308919176130087787t_unit: (product_prod_nat_nat > produc7812382424243267045t_unit) > set_Pr1133966238863718811t_unit > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2450, type, vimage2449269961533847803at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2451, type, vimage3104651464403166471t_unit: (product_prod_nat_nat > product_unit) > set_Product_unit > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2452, type, vimage8808348054653608838unit_o: (product_unit > $o) > set_o > set_Product_unit).
% 28.44/7.23 thf(func_def_2453, type, vimage6253328473476588386it_nat: (product_unit > nat) > set_nat > set_Product_unit).
% 28.44/7.23 thf(func_def_2454, type, vimage508909887551888138t_unit: (product_unit > produc3788275437394581276t_unit) > set_Pr6671815714118170108t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2455, type, vimage4422279681566046568t_unit: (product_unit > produc6865911496949736918t_unit) > set_Pr5889264611543340172t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2456, type, vimage7305857734363866308t_unit: (product_unit > produc526117512892780850t_unit) > set_Pr4334478416066269672t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2457, type, vimage7995052115951654139t_unit: (product_unit > product_unit) > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_2458, type, vimage5618198413390092650it_rat: (product_unit > rat) > set_rat > set_Product_unit).
% 28.44/7.23 thf(func_def_2459, type, vimage2648087219933717859t_char: (product_unit > char) > set_char > set_Product_unit).
% 28.44/7.23 thf(func_def_2460, type, vimage_rat_int: (rat > int) > set_int > set_rat).
% 28.44/7.23 thf(func_def_2461, type, vimage_rat_nat: (rat > nat) > set_nat > set_rat).
% 28.44/7.23 thf(func_def_2462, type, vimage2119786153496215084at_nat: (rat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_rat).
% 28.44/7.23 thf(func_def_2463, type, vimage_rat_rat: (rat > rat) > set_rat > set_rat).
% 28.44/7.23 thf(func_def_2464, type, vimage_rat_char: (rat > char) > set_char > set_rat).
% 28.44/7.23 thf(func_def_2465, type, vimage_char_int: (char > int) > set_int > set_char).
% 28.44/7.23 thf(func_def_2466, type, vimage_char_nat: (char > nat) > set_nat > set_char).
% 28.44/7.23 thf(func_def_2467, type, vimage8942442433166402803at_nat: (char > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_char).
% 28.44/7.23 thf(func_def_2468, type, vimage_char_rat: (char > rat) > set_rat > set_char).
% 28.44/7.23 thf(func_def_2469, type, vimage_char_char: (char > char) > set_char > set_char).
% 28.44/7.23 thf(func_def_2470, type, set_or1266510415728281911st_int: int > int > set_int).
% 28.44/7.23 thf(func_def_2471, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 28.44/7.23 thf(func_def_2472, type, set_or4662586982721622107an_int: int > int > set_int).
% 28.44/7.23 thf(func_def_2473, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 28.44/7.23 thf(func_def_2474, type, set_ord_atLeast_nat: nat > set_nat).
% 28.44/7.23 thf(func_def_2475, type, set_ord_atMost_nat: nat > set_nat).
% 28.44/7.23 thf(func_def_2476, type, set_or1210151606488870762an_nat: nat > set_nat).
% 28.44/7.23 thf(func_def_2477, type, set_ord_lessThan_nat: nat > set_nat).
% 28.44/7.23 thf(func_def_2478, type, comm_s629917340098488124ar_nat: char > nat).
% 28.44/7.23 thf(func_def_2479, type, unique3096191561947761185of_nat: nat > char).
% 28.44/7.23 thf(func_def_2480, type, left_t2884206969071330nteger: (code_integer > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2481, type, left_t1735413524555719857er_int: (code_integer > int > $o) > $o).
% 28.44/7.23 thf(func_def_2482, type, left_t2374113004080657585nteger: (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2483, type, left_total_int_int: (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_2484, type, left_t8261381459436684205at_nat: (int > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2485, type, left_t1861001511420785031at_int: (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_2486, type, left_t5646938096895998950at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2487, type, left_u6156896403773009178er_int: (code_integer > int > $o) > $o).
% 28.44/7.23 thf(func_def_2488, type, left_u6795595883297946906nteger: (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2489, type, left_unique_int_int: (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_2490, type, left_u1182257597767569412at_nat: (int > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2491, type, left_unique_nat_nat: (nat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_2492, type, left_unique_num_num: (num > num > $o) > $o).
% 28.44/7.23 thf(func_def_2493, type, left_u4005249686606446046at_int: (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_2494, type, left_u7296345956935681743at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2495, type, right_7281159819619925802nteger: (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2496, type, right_total_int_int: (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_2497, type, right_total_nat_nat: (nat > nat > $o) > $o).
% 28.44/7.23 thf(func_def_2498, type, right_total_num_num: (num > num > $o) > $o).
% 28.44/7.23 thf(func_def_2499, type, right_1157779049177982926at_int: (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_2500, type, right_4094035864313884895at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2501, type, right_5866438497372881682nteger: (code_integer > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2502, type, right_7836862732553076961er_int: (code_integer > int > $o) > $o).
% 28.44/7.23 thf(func_def_2503, type, right_8475562212078014689nteger: (int > code_integer > $o) > $o).
% 28.44/7.23 thf(func_def_2504, type, right_unique_int_int: (int > int > $o) > $o).
% 28.44/7.23 thf(func_def_2505, type, right_8621877368619751767at_int: (product_prod_nat_nat > int > $o) > $o).
% 28.44/7.23 thf(func_def_2506, type, right_1383565826979811350at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 28.44/7.23 thf(func_def_2507, type, type_definition_o_o: ($o > $o) > ($o > $o) > set_o > $o).
% 28.44/7.23 thf(func_def_2508, type, type_d7121381646445849148_o_nat: ($o > nat) > (nat > $o) > set_nat > $o).
% 28.44/7.23 thf(func_def_2509, type, type_d3678713432601627782_o_num: ($o > num) > (num > $o) > set_num > $o).
% 28.44/7.23 thf(func_def_2510, type, type_d6486251586359353412_o_rat: ($o > rat) > (rat > $o) > set_rat > $o).
% 28.44/7.23 thf(func_def_2511, type, type_d9076672964931703357o_char: ($o > char) > (char > $o) > set_char > $o).
% 28.44/7.23 thf(func_def_2512, type, type_d8403010662121346494_int_o: (int > $o) > ($o > int) > set_o > $o).
% 28.44/7.23 thf(func_def_2513, type, type_d7247357190169752966nt_int: (int > int) > (int > int) > set_int > $o).
% 28.44/7.23 thf(func_def_2514, type, type_d7249847660678803242nt_nat: (int > nat) > (nat > int) > set_nat > $o).
% 28.44/7.23 thf(func_def_2515, type, type_d7732240953928457511at_nat: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2516, type, type_d1000680970699258650_nat_o: (nat > $o) > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_2517, type, type_d6248003478268698410at_int: (nat > int) > (int > nat) > set_int > $o).
% 28.44/7.23 thf(func_def_2518, type, type_d6250493948777748686at_nat: (nat > nat) > (nat > nat) > set_nat > $o).
% 28.44/7.23 thf(func_def_2519, type, type_d2807825734933527320at_num: (nat > num) > (num > nat) > set_num > $o).
% 28.44/7.23 thf(func_def_2520, type, type_d5615363888691252950at_rat: (nat > rat) > (rat > nat) > set_rat > $o).
% 28.44/7.23 thf(func_def_2521, type, type_d5945782884131516111t_char: (nat > char) > (char > nat) > set_char > $o).
% 28.44/7.23 thf(func_def_2522, type, type_d9070036042389994064_num_o: (num > $o) > ($o > num) > set_o > $o).
% 28.44/7.23 thf(func_def_2523, type, type_d4380824352085218072um_nat: (num > nat) > (nat > num) > set_nat > $o).
% 28.44/7.23 thf(func_def_2524, type, type_d938156138240996706um_num: (num > num) > (num > num) > set_num > $o).
% 28.44/7.23 thf(func_def_2525, type, type_d3745694291998722336um_rat: (num > rat) > (rat > num) > set_rat > $o).
% 28.44/7.23 thf(func_def_2526, type, type_d4396077731765706521m_char: (num > char) > (char > num) > set_char > $o).
% 28.44/7.23 thf(func_def_2527, type, type_d1331861005912558337at_int: (product_prod_nat_nat > int) > (int > product_prod_nat_nat) > set_int > $o).
% 28.44/7.23 thf(func_def_2528, type, type_d281131942595027436at_nat: (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2529, type, type_d6188575255521822967unit_o: (product_unit > $o) > ($o > product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_2530, type, type_d5933939304842882774at_nat: (rat > nat) > (nat > rat) > set_nat > $o).
% 28.44/7.23 thf(func_def_2531, type, accp_nat: (nat > nat > $o) > nat > $o).
% 28.44/7.23 thf(func_def_2532, type, less_than: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2533, type, lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 28.44/7.23 thf(func_def_2534, type, max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2535, type, min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2536, type, pred_nat: set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2537, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2538, type, wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_2539, type, member_o_o: ($o > $o) > set_o_o > $o).
% 28.44/7.23 thf(func_def_2540, type, member_o_nat: ($o > nat) > set_o_nat > $o).
% 28.44/7.23 thf(func_def_2541, type, member2370919827131729009t_unit: ($o > product_unit) > set_o_Product_unit > $o).
% 28.44/7.23 thf(func_def_2542, type, member2790140394383616496nteger: (code_integer > code_integer) > set_Co726186806682698383nteger > $o).
% 28.44/7.23 thf(func_def_2543, type, member254662033361028077nt_int: (int > product_prod_int_int) > set_in6154042108061588260nt_int > $o).
% 28.44/7.23 thf(func_def_2544, type, member557823603599733045at_nat: (int > product_prod_nat_nat) > set_in7748886932685137004at_nat > $o).
% 28.44/7.23 thf(func_def_2545, type, member7514810323860029129um_num: (int > product_prod_num_num) > set_in3169746454734514176um_num > $o).
% 28.44/7.23 thf(func_def_2546, type, member3963856813518191233at_nat: (list_nat > product_prod_nat_nat) > set_li2168235667650531768at_nat > $o).
% 28.44/7.23 thf(func_def_2547, type, member_nat_int: (nat > int) > set_nat_int > $o).
% 28.44/7.23 thf(func_def_2548, type, member6440191985751670089nt_int: (nat > product_prod_int_int) > set_na7251125088705586816nt_int > $o).
% 28.44/7.23 thf(func_def_2549, type, member6743353555990375057at_nat: (nat > product_prod_nat_nat) > set_na8845969913329135560at_nat > $o).
% 28.44/7.23 thf(func_def_2550, type, member_rat_o: (rat > $o) > set_rat_o > $o).
% 28.44/7.23 thf(func_def_2551, type, member_rat_nat: (rat > nat) > set_rat_nat > $o).
% 28.44/7.23 thf(func_def_2552, type, member546649419593416001nt_int: (rat > product_prod_int_int) > set_ra518564293221149304nt_int > $o).
% 28.44/7.23 thf(func_def_2553, type, member849810989832120969at_nat: (rat > product_prod_nat_nat) > set_ra2113409117844698048at_nat > $o).
% 28.44/7.23 thf(func_def_2554, type, member7011034171605722901t_unit: (rat > product_unit) > set_rat_Product_unit > $o).
% 28.44/7.23 thf(func_def_2555, type, member_char_o: (char > $o) > set_char_o > $o).
% 28.44/7.23 thf(func_def_2556, type, member_char_nat: (char > nat) > set_char_nat > $o).
% 28.44/7.23 thf(func_def_2557, type, member2992454361780672008nt_int: (char > product_prod_int_int) > set_ch6383161263842509759nt_int > $o).
% 28.44/7.23 thf(func_def_2558, type, member3295615932019376976at_nat: (char > product_prod_nat_nat) > set_ch7978006088466058503at_nat > $o).
% 28.44/7.23 thf(func_def_2559, type, member379592906918970460t_unit: (char > product_unit) > set_ch7814610555394875923t_unit > $o).
% 28.44/7.23 thf(func_def_2560, type, member_o: $o > set_o > $o).
% 28.44/7.23 thf(func_def_2561, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 28.44/7.23 thf(func_def_2562, type, member242389114213480694t_unit: heap_e7401611519738050253t_unit > set_he8644174446132254637t_unit > $o).
% 28.44/7.23 thf(func_def_2563, type, member_ref_a: ref_a > set_ref_a > $o).
% 28.44/7.23 thf(func_def_2564, type, member_int: int > set_int > $o).
% 28.44/7.23 thf(func_def_2565, type, member_nat: nat > set_nat > $o).
% 28.44/7.23 thf(func_def_2566, type, member_num: num > set_num > $o).
% 28.44/7.23 thf(func_def_2567, type, member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_2568, type, member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o).
% 28.44/7.23 thf(func_def_2569, type, member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o).
% 28.44/7.23 thf(func_def_2570, type, member7849944260330398460t_unit: produc7812382424243267045t_unit > set_Pr1133966238863718811t_unit > $o).
% 28.44/7.23 thf(func_def_2571, type, member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o).
% 28.44/7.23 thf(func_def_2572, type, member4345257455949424659nteger: produc2963269191615333738nteger > set_Pr8415741480598773322nteger > $o).
% 28.44/7.23 thf(func_def_2573, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 28.44/7.23 thf(func_def_2574, type, member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o).
% 28.44/7.23 thf(func_def_2575, type, member6310962623043647828_nat_o: product_prod_nat_o > set_Pr3149072824959771635_nat_o > $o).
% 28.44/7.23 thf(func_def_2576, type, member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o).
% 28.44/7.23 thf(func_def_2577, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2578, type, member9148766508732265716at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > $o).
% 28.44/7.23 thf(func_def_2579, type, member6570852975090897396um_nat: product_prod_num_nat > set_Pr3280342998896498603um_nat > $o).
% 28.44/7.23 thf(func_def_2580, type, member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o).
% 28.44/7.23 thf(func_def_2581, type, member2200362271989506215_nat_o: produc652263959640188542_nat_o > set_Pr6558897299634722526_nat_o > $o).
% 28.44/7.23 thf(func_def_2582, type, member8394280151737582451at_int: produc4196048018000912732at_int > set_Pr49084382684228242at_int > $o).
% 28.44/7.23 thf(func_def_2583, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 28.44/7.23 thf(func_def_2584, type, member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o).
% 28.44/7.23 thf(func_def_2585, type, member7821138191923116944t_unit: produc8459935480633519975t_unit > set_Pr5094982260447487303t_unit > $o).
% 28.44/7.23 thf(func_def_2586, type, member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o).
% 28.44/7.23 thf(func_def_2587, type, member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o).
% 28.44/7.23 thf(func_def_2588, type, member_Product_unit: product_unit > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_2589, type, member_rat: rat > set_rat > $o).
% 28.44/7.23 thf(func_def_2590, type, member_set_o: set_o > set_set_o > $o).
% 28.44/7.23 thf(func_def_2591, type, member_set_int: set_int > set_set_int > $o).
% 28.44/7.23 thf(func_def_2592, type, member_set_nat: set_nat > set_set_nat > $o).
% 28.44/7.23 thf(func_def_2593, type, member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o).
% 28.44/7.23 thf(func_def_2594, type, member6273874620674182256at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat > $o).
% 28.44/7.23 thf(func_def_2595, type, member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o).
% 28.44/7.23 thf(func_def_2596, type, member_char: char > set_char > $o).
% 28.44/7.23 thf(func_def_2597, type, h: heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_2598, type, h2: heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_2599, type, r: ref_a).
% 28.44/7.23 thf(func_def_2601, type, x: a).
% 28.44/7.23 thf(func_def_2620, type, sP0: set_Product_unit > set_Product_unit > set_nat > set_nat > $o).
% 28.44/7.23 thf(func_def_2621, type, sP1: nat > list_nat > $o).
% 28.44/7.23 thf(func_def_2622, type, sP2: set_o > set_nat > set_o > set_nat > $o).
% 28.44/7.23 thf(func_def_2623, type, sP3: set_Product_unit > set_Product_unit > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2624, type, sP4: set_o > set_Product_unit > set_Product_unit > set_o > $o).
% 28.44/7.23 thf(func_def_2625, type, sP5: set_Product_unit > set_Product_unit > set_Product_unit > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_2626, type, sP6: set_o > set_Product_unit > set_o > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_2627, type, sP7: set_o > set_o > set_o > set_o > $o).
% 28.44/7.23 thf(func_def_2628, type, sP8: set_Product_unit > set_Product_unit > set_nat > set_nat > $o).
% 28.44/7.23 thf(func_def_2629, type, sP9: set_nat > set_nat > set_nat > set_nat > $o).
% 28.44/7.23 thf(func_def_2630, type, sP10: set_o > set_nat > set_o > set_nat > $o).
% 28.44/7.23 thf(func_def_2631, type, sK11: set_int > (nat > int) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2632, type, sK12: (nat > product_unit) > ($o > product_unit) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_2633, type, sK13: (nat > product_unit) > ($o > product_unit) > set_nat > set_o > nat).
% 28.44/7.23 thf(func_def_2634, type, sK14: int > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_2635, type, sK15: set_nat > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2636, type, sK16: product_prod_nat_num > (nat > nat) > (nat > num) > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_2637, type, sK17: product_prod_nat_num > (nat > nat) > (nat > num) > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_2638, type, sK18: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > int) > int).
% 28.44/7.23 thf(func_def_2639, type, sK19: (rat > int) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_2640, type, sK20: int > set_o > ($o > set_int) > $o).
% 28.44/7.23 thf(func_def_2641, type, sK21: produc3843707927480180839at_nat > produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2642, type, sK22: produc3843707927480180839at_nat > produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2643, type, sK23: product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_2644, type, sK24: product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_2645, type, sK25: set_int > int).
% 28.44/7.23 thf(func_def_2646, type, sK26: (nat > int) > set_int > set_nat > nat).
% 28.44/7.23 thf(func_def_2647, type, sK27: (nat > int) > set_int > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_2648, type, sK28: (int > code_integer > $o) > (int > code_integer > $o) > int).
% 28.44/7.23 thf(func_def_2649, type, sK29: (int > code_integer > $o) > (int > code_integer > $o) > code_integer).
% 28.44/7.23 thf(func_def_2650, type, sK30: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_2651, type, sK31: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_2652, type, sK32: produc1319942482725812455at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2653, type, sK33: produc1319942482725812455at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2654, type, sK34: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int > (product_prod_int_int > $o) > product_prod_int_int).
% 28.44/7.23 thf(func_def_2655, type, sK35: (nat > nat) > set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2656, type, sK36: int > (nat > set_int) > set_nat > nat).
% 28.44/7.23 thf(func_def_2657, type, sK37: ($o > $o > $o) > (char > $o) > (char > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_2658, type, sK38: ($o > $o > $o) > (char > $o) > (char > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_2659, type, sK39: (num > set_Pr1261947904930325089at_nat) > (nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat > set_Pr6200539531224447659at_num > nat).
% 28.44/7.23 thf(func_def_2660, type, sK40: (num > set_Pr1261947904930325089at_nat) > (nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat > set_Pr6200539531224447659at_num > num).
% 28.44/7.23 thf(func_def_2661, type, sK41: set_nat > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2662, type, sK42: set_nat > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2663, type, sK43: product_prod_nat_nat > (num > nat) > set_Pr6200539531224447659at_num > (nat > nat) > num).
% 28.44/7.23 thf(func_def_2664, type, sK44: product_prod_nat_nat > (num > nat) > set_Pr6200539531224447659at_num > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2665, type, sK45: product_unit > (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2666, type, sK46: product_unit > (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > product_unit).
% 28.44/7.23 thf(func_def_2667, type, sK47: (int > nat) > set_nat > set_int > (nat > nat) > int).
% 28.44/7.23 thf(func_def_2668, type, sK48: set_int > nat > (int > nat) > int).
% 28.44/7.23 thf(func_def_2669, type, sK49: set_o > ($o > set_int) > $o).
% 28.44/7.23 thf(func_def_2670, type, sK50: (char > nat) > ($o > nat > $o) > (char > $o) > ($o > nat > $o) > $o).
% 28.44/7.23 thf(func_def_2671, type, sK51: (char > nat) > ($o > nat > $o) > (char > $o) > ($o > nat > $o) > nat).
% 28.44/7.23 thf(func_def_2672, type, sK52: int > (nat > int) > nat).
% 28.44/7.23 thf(func_def_2673, type, sK53: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2674, type, sK54: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2675, type, sK55: (nat > product_unit) > set_nat > product_unit).
% 28.44/7.23 thf(func_def_2676, type, sK56: ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > int > int).
% 28.44/7.23 thf(func_def_2677, type, sK57: ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2678, type, sK58: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_2679, type, sK59: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2680, type, sK60: (nat > $o) > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_2681, type, sK61: (rat > rat) > rat).
% 28.44/7.23 thf(func_def_2682, type, sK62: rat > (rat > rat) > rat).
% 28.44/7.23 thf(func_def_2683, type, sK63: (nat > set_nat) > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2684, type, sK64: (nat > nat) > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2685, type, sK65: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2686, type, sK66: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2687, type, sK67: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat) > (set_nat > $o) > set_nat).
% 28.44/7.23 thf(func_def_2688, type, sK68: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat) > (set_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2689, type, sK69: ($o > product_unit) > set_o > product_unit > $o).
% 28.44/7.23 thf(func_def_2690, type, sK70: (rat > char) > char > rat).
% 28.44/7.23 thf(func_def_2691, type, sK71: product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_2692, type, sK72: product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_2693, type, sK73: (product_prod_nat_nat > int) > (product_prod_nat_nat > $o) > set_int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2694, type, sK74: set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2695, type, sK75: int > product_prod_int_int > (int > int > set_int) > int).
% 28.44/7.23 thf(func_def_2696, type, sK76: int > product_prod_int_int > (int > int > set_int) > int).
% 28.44/7.23 thf(func_def_2697, type, sK77: set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2698, type, sK78: set_Pr4329608150637261639at_nat > produc1906917888121415911at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2699, type, sK79: (nat > nat > $o) > (nat > nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > $o) > nat).
% 28.44/7.23 thf(func_def_2700, type, sK80: (nat > nat > $o) > (nat > nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > $o) > nat).
% 28.44/7.23 thf(func_def_2701, type, sK81: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2702, type, sK82: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2703, type, sK83: set_int > set_nat > (int > nat) > set_int).
% 28.44/7.23 thf(func_def_2704, type, sK84: (int > int > $o) > (int > int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_2705, type, sK85: (int > int > $o) > (int > int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_2706, type, sK86: (int > product_unit) > (int > product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_2707, type, sK87: (nat > num) > (int > nat) > (nat > num) > (int > nat) > nat).
% 28.44/7.23 thf(func_def_2708, type, sK88: (nat > num) > (int > nat) > (nat > num) > (int > nat) > nat).
% 28.44/7.23 thf(func_def_2709, type, sK89: set_nat > (nat > int) > (nat > int) > nat).
% 28.44/7.23 thf(func_def_2710, type, sK90: set_int > (int > nat) > (int > nat) > int).
% 28.44/7.23 thf(func_def_2711, type, sK91: (nat > nat) > (product_unit > nat) > set_Product_unit > set_nat > product_unit).
% 28.44/7.23 thf(func_def_2712, type, sK92: produc859450856879609959at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2713, type, sK93: set_Product_unit > (product_unit > int) > (product_unit > int) > product_unit).
% 28.44/7.23 thf(func_def_2714, type, sK94: (produc3843707927480180839at_nat > product_unit) > (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2715, type, sK95: product_prod_nat_nat > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2716, type, sK96: set_Pr1261947904930325089at_nat > product_unit > (product_prod_nat_nat > product_unit) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2717, type, sK97: set_Pr1261947904930325089at_nat > product_unit > (product_prod_nat_nat > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_2718, type, sK98: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2719, type, sK99: set_Product_unit > (product_unit > nat) > nat > product_unit).
% 28.44/7.23 thf(func_def_2720, type, sK100: set_nat > nat > nat).
% 28.44/7.23 thf(func_def_2721, type, sK101: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > (product_prod_nat_nat > product_unit) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2722, type, sK102: (set_rat > $o) > set_nat > (nat > rat) > set_rat).
% 28.44/7.23 thf(func_def_2723, type, sK103: (set_rat > $o) > set_nat > (nat > rat) > set_nat).
% 28.44/7.23 thf(func_def_2724, type, sK104: ($o > set_nat) > set_o > set_nat > $o).
% 28.44/7.23 thf(func_def_2725, type, sK105: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2726, type, sK106: (nat > int) > set_nat > (set_int > $o) > set_nat).
% 28.44/7.23 thf(func_def_2727, type, sK107: (nat > int) > set_nat > (set_int > $o) > set_int).
% 28.44/7.23 thf(func_def_2728, type, sK108: set_o > set_nat > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_2729, type, sK109: (rat > int) > int > rat).
% 28.44/7.23 thf(func_def_2730, type, sK110: ($o > int) > set_o > ($o > int) > $o).
% 28.44/7.23 thf(func_def_2731, type, sK111: set_o > set_nat > ($o > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_2732, type, sK112: set_o > ($o > int) > int > $o).
% 28.44/7.23 thf(func_def_2733, type, sK113: (int > int) > set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_2734, type, sK114: nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_2735, type, sK115: set_o > ($o > nat) > $o).
% 28.44/7.23 thf(func_def_2736, type, sK116: (nat > int) > int > set_nat > nat).
% 28.44/7.23 thf(func_def_2737, type, sK117: ($o > int) > set_o > set_int > $o).
% 28.44/7.23 thf(func_def_2738, type, sK118: set_nat > $o > (nat > $o) > set_o > set_nat).
% 28.44/7.23 thf(func_def_2739, type, sK119: set_nat > $o > (nat > $o) > set_o > nat).
% 28.44/7.23 thf(func_def_2740, type, sK120: (nat > nat) > (int > nat) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_2741, type, sK121: (produc1319942482725812455at_nat > $o) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2742, type, sK122: (produc1319942482725812455at_nat > $o) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2743, type, sK123: (int > int) > set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_2744, type, sK124: set_rat > nat > rat).
% 28.44/7.23 thf(func_def_2745, type, sK125: set_int > (int > int) > (int > int) > int).
% 28.44/7.23 thf(func_def_2746, type, sK126: set_int > (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_2747, type, sK127: set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_2748, type, sK128: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2749, type, sK129: (int > int) > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_2750, type, sK130: (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_2751, type, sK131: (int > set_nat) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_2752, type, sK132: set_int > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_2753, type, sK133: set_nat > (nat > product_unit) > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_2754, type, sK134: set_int > (int > nat) > set_nat > set_int).
% 28.44/7.23 thf(func_def_2755, type, sK135: (int > nat) > nat > set_int > int).
% 28.44/7.23 thf(func_def_2756, type, sK136: (int > nat) > (set_nat > $o) > set_int > set_int).
% 28.44/7.23 thf(func_def_2757, type, sK137: (int > nat) > (set_nat > $o) > set_int > set_nat).
% 28.44/7.23 thf(func_def_2758, type, sK138: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2759, type, sK139: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat).
% 28.44/7.23 thf(func_def_2760, type, sK140: set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2761, type, sK141: (product_unit > set_nat) > set_Product_unit > set_nat > product_unit).
% 28.44/7.23 thf(func_def_2762, type, sK142: (product_unit > set_nat) > set_Product_unit > set_nat > product_unit).
% 28.44/7.23 thf(func_def_2763, type, sK143: set_Pr1261947904930325089at_nat > set_nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2764, type, sK144: (nat > rat) > set_nat > (rat > $o) > nat).
% 28.44/7.23 thf(func_def_2765, type, sK145: (product_prod_nat_nat > $o) > (product_prod_nat_nat > nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2766, type, sK146: set_rat > set_nat > (nat > rat) > set_nat).
% 28.44/7.23 thf(func_def_2767, type, sK147: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2768, type, sK148: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2769, type, sK149: (int > $o) > set_int > (int > $o) > int).
% 28.44/7.23 thf(func_def_2770, type, sK150: set_o > set_o > ($o > set_nat) > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_2771, type, sK151: set_o > set_o > ($o > set_nat) > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_2772, type, sK152: set_nat > (nat > set_nat) > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_2773, type, sK153: set_nat > int > (nat > int) > nat).
% 28.44/7.23 thf(func_def_2774, type, sK154: set_o > product_unit > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_2775, type, sK155: set_o > product_unit > ($o > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_2776, type, sK156: (int > rat) > set_int > rat > int).
% 28.44/7.23 thf(func_def_2777, type, sK157: (nat > rat) > (nat > rat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2778, type, sK158: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2779, type, sK159: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2780, type, sK160: (char > int) > (int > $o > $o) > (char > $o) > (int > $o > $o) > $o).
% 28.44/7.23 thf(func_def_2781, type, sK161: (char > int) > (int > $o > $o) > (char > $o) > (int > $o > $o) > int).
% 28.44/7.23 thf(func_def_2782, type, sK162: (rat > nat) > (rat > nat) > (nat > nat > $o) > rat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2783, type, sK163: (int > int > product_prod_int_int) > product_prod_int_int > (int > int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2784, type, sK164: (int > int > product_prod_int_int) > product_prod_int_int > (int > int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2785, type, sK165: product_unit > (nat > product_unit) > set_nat > nat).
% 28.44/7.23 thf(func_def_2786, type, sK166: product_unit > (nat > product_unit) > set_nat > product_unit).
% 28.44/7.23 thf(func_def_2787, type, sK167: ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2788, type, sK168: ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > int > int).
% 28.44/7.23 thf(func_def_2789, type, sK169: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_2790, type, sK170: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2791, type, sK171: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2792, type, sK172: (nat > product_unit) > set_nat > product_unit > product_unit).
% 28.44/7.23 thf(func_def_2793, type, sK173: set_int > (int > nat) > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_2794, type, sK174: (nat > nat) > nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2795, type, sK175: product_prod_nat_num > int > (nat > num > set_int) > nat).
% 28.44/7.23 thf(func_def_2796, type, sK176: product_prod_nat_num > int > (nat > num > set_int) > num).
% 28.44/7.23 thf(func_def_2797, type, sK177: heap_Heap_ref_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_2798, type, sK178: heap_Heap_ref_a > heap_e7401611519738050253t_unit > ref_a).
% 28.44/7.23 thf(func_def_2799, type, sK179: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_2800, type, sK180: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_2801, type, sK181: (product_prod_int_int > $o) > (int > int > product_prod_int_int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_2802, type, sK182: (product_prod_int_int > $o) > (int > int > product_prod_int_int) > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_2803, type, sK183: (nat > nat) > set_nat > (set_nat > $o) > set_nat).
% 28.44/7.23 thf(func_def_2804, type, sK184: (nat > nat) > set_nat > (set_nat > $o) > set_nat).
% 28.44/7.23 thf(func_def_2805, type, sK185: (int > nat) > set_int > set_nat > set_int).
% 28.44/7.23 thf(func_def_2806, type, sK186: ($o > int) > ($o > int) > set_o > $o).
% 28.44/7.23 thf(func_def_2807, type, sK187: (int > $o) > set_nat > (nat > int) > int).
% 28.44/7.23 thf(func_def_2808, type, sK188: set_int > int > (int > int) > int).
% 28.44/7.23 thf(func_def_2809, type, sK189: set_nat > set_rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_2810, type, sK190: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2811, type, sK191: set_Product_unit > set_o > $o > (product_unit > $o) > product_unit).
% 28.44/7.23 thf(func_def_2812, type, sK192: set_Product_unit > set_o > $o > (product_unit > $o) > set_Product_unit).
% 28.44/7.23 thf(func_def_2813, type, sK193: (int > product_unit) > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_2814, type, sK194: ($o > product_prod_nat_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_2815, type, sK195: (nat > $o) > $o > nat).
% 28.44/7.23 thf(func_def_2816, type, sK196: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2817, type, sK197: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2818, type, sK198: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2819, type, sK199: product_prod_nat_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2820, type, sK200: product_unit > $o).
% 28.44/7.23 thf(func_def_2821, type, sK201: $o > product_unit).
% 28.44/7.23 thf(func_def_2822, type, sK202: product_prod_nat_num > (int > nat) > (int > num) > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_2823, type, sK203: product_prod_nat_num > (int > nat) > (int > num) > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_2824, type, sK204: set_nat > (nat > rat) > rat).
% 28.44/7.23 thf(func_def_2825, type, sK205: (rat > nat) > (nat > rat) > rat).
% 28.44/7.23 thf(func_def_2826, type, sK206: (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_2827, type, sK207: set_nat > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_2828, type, sK208: int > ($o > int) > set_o > $o).
% 28.44/7.23 thf(func_def_2829, type, sK209: int > set_int > (int > set_int) > int).
% 28.44/7.23 thf(func_def_2830, type, sK210: (int > int) > int > set_int > int).
% 28.44/7.23 thf(func_def_2831, type, sK211: (nat > nat > $o) > (nat > nat > $o) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2832, type, sK212: (nat > nat > $o) > (nat > nat > $o) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2833, type, sK213: set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_2834, type, sK214: set_nat > (nat > product_unit) > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_2835, type, sK215: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2836, type, sK216: set_Pr1261947904930325089at_nat > set_nat > (product_prod_nat_nat > set_nat) > set_nat).
% 28.44/7.23 thf(func_def_2837, type, sK217: set_Pr1261947904930325089at_nat > set_nat > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2838, type, sK218: (product_unit > int) > set_Product_unit > int > product_unit).
% 28.44/7.23 thf(func_def_2839, type, sK219: set_int > (int > int) > (int > int) > int).
% 28.44/7.23 thf(func_def_2840, type, sK220: int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_2841, type, sK221: (int > int > $o) > (char > int) > (char > int) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_2842, type, sK222: (int > int > $o) > (char > int) > (char > int) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_2843, type, sK223: product_unit > (product_unit > product_unit) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_2844, type, sK224: ($o > int) > int > set_o > $o).
% 28.44/7.23 thf(func_def_2845, type, sK225: (rat > rat) > (rat > rat) > rat).
% 28.44/7.23 thf(func_def_2846, type, sK226: (int > int > $o) > (nat > int) > (nat > int) > nat > product_prod_int_int).
% 28.44/7.23 thf(func_def_2847, type, sK227: set_o > $o).
% 28.44/7.23 thf(func_def_2848, type, sK228: (nat > int) > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_2849, type, sK229: (nat > nat > set_nat) > nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2850, type, sK230: (nat > nat > set_nat) > nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2851, type, sK231: (int > int) > set_int > (set_int > $o) > set_int).
% 28.44/7.23 thf(func_def_2852, type, sK232: (int > int) > set_int > (set_int > $o) > set_int).
% 28.44/7.23 thf(func_def_2853, type, sK233: set_Product_unit > (int > product_unit) > set_int > product_unit > int).
% 28.44/7.23 thf(func_def_2854, type, sK234: set_Product_unit > (int > product_unit) > set_int > product_unit > set_int).
% 28.44/7.23 thf(func_def_2855, type, sK235: ($o > code_integer) > set_o > code_integer > $o).
% 28.44/7.23 thf(func_def_2856, type, sK236: product_prod_nat_nat > (nat > nat) > set_Pr1261947904930325089at_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2857, type, sK237: product_prod_nat_nat > (nat > nat) > set_Pr1261947904930325089at_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2858, type, sK238: set_o > set_int > (int > product_unit) > ($o > product_unit) > int).
% 28.44/7.23 thf(func_def_2859, type, sK239: set_o > set_int > (int > product_unit) > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_2860, type, sK240: $o > (product_prod_nat_nat > set_o) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2861, type, sK241: (int > char) > (char > int) > int).
% 28.44/7.23 thf(func_def_2862, type, sK242: (nat > set_o) > $o > set_nat > nat).
% 28.44/7.23 thf(func_def_2863, type, sK243: (nat > nat) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2864, type, sK244: (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_2865, type, sK245: (nat > rat) > rat > nat).
% 28.44/7.23 thf(func_def_2866, type, sK246: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat > $o).
% 28.44/7.23 thf(func_def_2867, type, sK247: product_prod_nat_num > nat > (nat > num > set_nat) > num).
% 28.44/7.23 thf(func_def_2868, type, sK248: product_prod_nat_num > nat > (nat > num > set_nat) > nat).
% 28.44/7.23 thf(func_def_2869, type, sK249: product_unit > (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit).
% 28.44/7.23 thf(func_def_2870, type, sK250: product_unit > (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2871, type, sK251: nat > (rat > nat) > rat).
% 28.44/7.23 thf(func_def_2872, type, sK252: rat > nat > (rat > nat) > rat).
% 28.44/7.23 thf(func_def_2873, type, sK253: set_nat > set_rat > nat > rat).
% 28.44/7.23 thf(func_def_2874, type, sK254: set_nat > set_rat > rat > nat).
% 28.44/7.23 thf(func_def_2875, type, sK255: ((product_prod_nat_nat > $o) > $o) > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_2876, type, sK256: ((product_prod_nat_nat > $o) > $o) > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_2877, type, sK257: product_prod_nat_nat > $o > (nat > nat > set_o) > nat).
% 28.44/7.23 thf(func_def_2878, type, sK258: product_prod_nat_nat > $o > (nat > nat > set_o) > nat).
% 28.44/7.23 thf(func_def_2879, type, sK259: produc1319942482725812455at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2880, type, sK260: produc1319942482725812455at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2881, type, sK261: set_nat > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_2882, type, sK262: ($o > set_nat) > set_o > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_2883, type, sK263: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > $o) > (produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2884, type, sK264: set_o > ($o > set_Pr1261947904930325089at_nat) > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_2885, type, sK265: set_rat > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_2886, type, sK266: $o > (rat > $o) > rat).
% 28.44/7.23 thf(func_def_2887, type, sK267: rat > $o > (rat > $o) > rat).
% 28.44/7.23 thf(func_def_2888, type, sK268: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2889, type, sK269: (int > product_unit) > set_int > product_unit > product_unit).
% 28.44/7.23 thf(func_def_2890, type, sK270: (int > product_unit) > set_int > product_unit > int).
% 28.44/7.23 thf(func_def_2891, type, sK271: set_nat > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_2892, type, sK272: (int > num) > (num > num > $o) > (code_integer > num) > (int > code_integer > $o) > code_integer).
% 28.44/7.23 thf(func_def_2893, type, sK273: (int > num) > (num > num > $o) > (code_integer > num) > (int > code_integer > $o) > int).
% 28.44/7.23 thf(func_def_2894, type, sK274: (char > int) > ($o > int > $o) > (char > $o) > ($o > int > $o) > $o).
% 28.44/7.23 thf(func_def_2895, type, sK275: (char > int) > ($o > int > $o) > (char > $o) > ($o > int > $o) > int).
% 28.44/7.23 thf(func_def_2896, type, sK276: set_int > set_nat > (nat > int) > set_nat).
% 28.44/7.23 thf(func_def_2897, type, sK277: nat > (rat > nat) > rat).
% 28.44/7.23 thf(func_def_2898, type, sK278: (rat > nat) > nat).
% 28.44/7.23 thf(func_def_2899, type, sK279: set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2900, type, sK280: set_o > ($o > set_nat) > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_2901, type, sK281: set_o > ($o > product_unit) > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_2902, type, sK282: nat > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2903, type, sK283: ($o > product_unit) > (nat > product_unit) > set_nat > set_o > nat).
% 28.44/7.23 thf(func_def_2904, type, sK284: ($o > product_unit) > (nat > product_unit) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_2905, type, sK285: int > set_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_2906, type, sK286: set_nat > (nat > set_nat) > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_2907, type, sK287: (nat > rat) > rat > nat).
% 28.44/7.23 thf(func_def_2908, type, sK288: (product_prod_int_int > $o) > (int > int > $o) > (int > int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2909, type, sK289: (product_prod_int_int > $o) > (int > int > $o) > (int > int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2910, type, sK290: set_o > set_nat > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_2911, type, sK291: ($o > $o > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_2912, type, sK292: set_int > (int > set_Pr1261947904930325089at_nat) > int).
% 28.44/7.23 thf(func_def_2913, type, sK293: set_Product_unit > set_nat > (nat > nat) > (product_unit > nat) > product_unit).
% 28.44/7.23 thf(func_def_2914, type, sK294: (ref_a > heap_e7401611519738050253t_unit > $o) > set_ref_a > (ref_a > heap_e7401611519738050253t_unit > $o) > set_he8644174446132254637t_unit > ref_a).
% 28.44/7.23 thf(func_def_2915, type, sK295: (ref_a > heap_e7401611519738050253t_unit > $o) > set_ref_a > (ref_a > heap_e7401611519738050253t_unit > $o) > set_he8644174446132254637t_unit > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_2916, type, sK296: (nat > int) > set_nat > set_int > nat).
% 28.44/7.23 thf(func_def_2917, type, sK297: set_o > rat > ($o > rat) > $o).
% 28.44/7.23 thf(func_def_2918, type, sK298: nat > list_nat > nat).
% 28.44/7.23 thf(func_def_2919, type, sK299: set_int > set_o > ($o > product_unit) > (int > product_unit) > $o).
% 28.44/7.23 thf(func_def_2920, type, sK300: set_int > set_o > ($o > product_unit) > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_2921, type, sK301: set_nat > (nat > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_2922, type, sK302: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_2923, type, sK303: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_2924, type, sK304: set_int > (nat > int) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2925, type, sK305: set_o > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2926, type, sK306: nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2927, type, sK307: (product_unit > product_unit) > set_Product_unit > (product_unit > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_2928, type, sK308: (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_2929, type, sK309: (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_2930, type, sK310: (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_2931, type, sK311: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2932, type, sK312: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_2933, type, sK313: product_prod_nat_nat > ((product_prod_nat_nat > product_prod_nat_nat) > $o) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_2934, type, sK314: product_prod_nat_nat > ((product_prod_nat_nat > product_prod_nat_nat) > $o) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_2935, type, sK315: ($o > $o) > ($o > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_2936, type, sK316: (int > int) > int > set_int > int).
% 28.44/7.23 thf(func_def_2937, type, sK317: set_int > set_nat > (nat > set_int) > nat).
% 28.44/7.23 thf(func_def_2938, type, sK318: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_2939, type, sK319: (product_unit > nat) > (product_unit > nat) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_2940, type, sK320: int > set_Product_unit > (product_unit > int) > product_unit).
% 28.44/7.23 thf(func_def_2941, type, sK321: (rat > $o) > set_nat > (nat > rat) > rat).
% 28.44/7.23 thf(func_def_2942, type, sK322: (char > int) > int > char).
% 28.44/7.23 thf(func_def_2943, type, sK323: (int > int) > set_Pr958786334691620121nt_int > product_prod_int_int > (int > int) > int).
% 28.44/7.23 thf(func_def_2944, type, sK324: (int > int) > set_Pr958786334691620121nt_int > product_prod_int_int > (int > int) > int).
% 28.44/7.23 thf(func_def_2945, type, sK325: (nat > set_nat) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2946, type, sK326: ($o > product_unit) > ($o > product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_2947, type, sK327: set_Product_unit > product_unit > (product_unit > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_2948, type, sK328: (produc3843707927480180839at_nat > set_nat) > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2949, type, sK329: (nat > num > set_nat) > product_prod_nat_num > nat > nat).
% 28.44/7.23 thf(func_def_2950, type, sK330: (nat > num > set_nat) > product_prod_nat_num > nat > num).
% 28.44/7.23 thf(func_def_2951, type, sK331: set_int > (int > set_nat) > nat > int).
% 28.44/7.23 thf(func_def_2952, type, sK332: (nat > rat) > set_nat > (set_rat > $o) > set_rat).
% 28.44/7.23 thf(func_def_2953, type, sK333: (nat > rat) > set_nat > (set_rat > $o) > set_nat).
% 28.44/7.23 thf(func_def_2954, type, sK334: set_o > ($o > rat) > rat > $o).
% 28.44/7.23 thf(func_def_2955, type, sK335: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > nat).
% 28.44/7.23 thf(func_def_2956, type, sK336: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > num).
% 28.44/7.23 thf(func_def_2957, type, sK337: set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2958, type, sK338: nat > (nat > nat) > nat > nat).
% 28.44/7.23 thf(func_def_2959, type, sK339: (nat > nat) > nat > nat).
% 28.44/7.23 thf(func_def_2960, type, sK340: ($o > set_o) > set_o > $o).
% 28.44/7.23 thf(func_def_2961, type, sK341: set_int > (int > set_nat) > set_nat > int).
% 28.44/7.23 thf(func_def_2962, type, sK342: set_int > (int > set_nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_2963, type, sK343: set_nat > nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_2964, type, sK344: set_o > set_o > $o > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_2965, type, sK345: set_o > set_o > $o > ($o > $o) > set_o).
% 28.44/7.23 thf(func_def_2966, type, sK346: (nat > nat > set_nat) > nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2967, type, sK347: (nat > nat > set_nat) > nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_2968, type, sK348: set_int > (int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_2969, type, sK349: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2970, type, sK350: set_Product_unit > nat > (product_unit > nat) > product_unit).
% 28.44/7.23 thf(func_def_2971, type, sK351: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2972, type, sK352: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2973, type, sK353: (nat > rat) > set_nat > nat).
% 28.44/7.23 thf(func_def_2974, type, sK354: set_nat > nat).
% 28.44/7.23 thf(func_def_2975, type, sK355: (nat > product_unit) > set_nat > product_unit > nat).
% 28.44/7.23 thf(func_def_2976, type, sK356: (int > int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2977, type, sK357: (int > int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > int).
% 28.44/7.23 thf(func_def_2978, type, sK358: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_2979, type, sK359: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_Pr1261947904930325089at_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2980, type, sK360: set_int > (int > set_o) > $o > int).
% 28.44/7.23 thf(func_def_2981, type, sK361: (nat > produc3843707927480180839at_nat) > set_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_2982, type, sK362: (rat > int) > int > rat).
% 28.44/7.23 thf(func_def_2983, type, sK363: rat > (rat > int) > int > rat).
% 28.44/7.23 thf(func_def_2984, type, sK364: (product_prod_nat_nat > nat) > set_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_2985, type, sK365: set_int > nat > (int > nat) > int).
% 28.44/7.23 thf(func_def_2986, type, sK366: set_o > product_unit > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_2987, type, sK367: (nat > set_nat) > product_prod_nat_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2988, type, sK368: (nat > set_nat) > product_prod_nat_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_2989, type, sK369: ($o > set_nat) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_2990, type, sK370: set_Product_unit > (product_unit > set_o) > product_unit).
% 28.44/7.23 thf(func_def_2991, type, sK371: (nat > int) > set_nat > int).
% 28.44/7.23 thf(func_def_2992, type, sK372: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_2993, type, sK373: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_2994, type, sK374: (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_2995, type, sK375: (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_2996, type, sK376: (nat > nat) > set_nat > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_2997, type, sK377: set_nat > (nat > int) > (nat > int) > nat).
% 28.44/7.23 thf(func_def_2998, type, sK378: (nat > nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_2999, type, sK379: (nat > nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_3000, type, sK380: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3001, type, sK381: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3002, type, sK382: set_int > (int > set_nat) > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3003, type, sK383: set_Pr1261947904930325089at_nat > set_nat).
% 28.44/7.23 thf(func_def_3004, type, sK384: nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3005, type, sK385: set_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3006, type, sK386: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3007, type, sK387: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3008, type, sK388: (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3009, type, sK389: (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3010, type, sK390: product_unit > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3011, type, sK391: (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3012, type, sK392: nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3013, type, sK393: set_int > product_unit > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3014, type, sK394: (rat > rat) > rat > rat).
% 28.44/7.23 thf(func_def_3015, type, sK395: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3016, type, sK396: set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3017, type, sK397: (int > nat) > set_int > set_nat > set_int).
% 28.44/7.23 thf(func_def_3018, type, sK398: (product_unit > nat) > (product_unit > nat) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3019, type, sK399: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3020, type, sK400: (char > char) > (char > char) > char).
% 28.44/7.23 thf(func_def_3021, type, sK401: product_prod_nat_num > (nat > num > set_Pr1261947904930325089at_nat) > product_prod_nat_nat > num).
% 28.44/7.23 thf(func_def_3022, type, sK402: product_prod_nat_num > (nat > num > set_Pr1261947904930325089at_nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3023, type, sK403: int > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3024, type, sK404: set_nat > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3025, type, sK405: int > (rat > int) > rat).
% 28.44/7.23 thf(func_def_3026, type, sK406: (int > nat) > set_o > set_int > ($o > nat) > $o).
% 28.44/7.23 thf(func_def_3027, type, sK407: rat > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3028, type, sK408: (nat > nat) > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3029, type, sK409: (int > int) > set_int > (int > int) > int).
% 28.44/7.23 thf(func_def_3030, type, sK410: ($o > set_nat) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_3031, type, sK411: (nat > set_int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3032, type, sK412: (int > int) > (int > int) > int).
% 28.44/7.23 thf(func_def_3033, type, sK413: set_Product_unit > set_nat > (nat > product_unit) > product_unit > set_nat).
% 28.44/7.23 thf(func_def_3034, type, sK414: set_Product_unit > set_nat > (nat > product_unit) > product_unit > nat).
% 28.44/7.23 thf(func_def_3035, type, sK415: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (int > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3036, type, sK416: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3037, type, sK417: int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3038, type, sK418: (int > set_nat) > set_int > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3039, type, sK419: product_prod_nat_nat > (int > nat) > (int > nat) > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_3040, type, sK420: product_prod_nat_nat > (int > nat) > (int > nat) > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_3041, type, sK421: (int > nat) > set_int > (set_nat > $o) > set_nat).
% 28.44/7.23 thf(func_def_3042, type, sK422: (int > nat) > set_int > (set_nat > $o) > set_int).
% 28.44/7.23 thf(func_def_3043, type, sK423: (nat > nat) > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3044, type, sK424: set_Product_unit > (product_unit > product_unit) > product_unit > product_unit).
% 28.44/7.23 thf(func_def_3045, type, sK425: set_nat > (produc3843707927480180839at_nat > set_nat) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3046, type, sK426: rat > (int > rat) > set_int > int).
% 28.44/7.23 thf(func_def_3047, type, sK427: (rat > int) > int).
% 28.44/7.23 thf(func_def_3048, type, sK428: int > (rat > int) > rat).
% 28.44/7.23 thf(func_def_3049, type, sK429: set_rat > set_nat > (nat > rat) > set_nat).
% 28.44/7.23 thf(func_def_3050, type, sK430: (char > rat) > rat).
% 28.44/7.23 thf(func_def_3051, type, sK431: rat > (char > rat) > char).
% 28.44/7.23 thf(func_def_3052, type, sK432: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3053, type, sK433: (nat > nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3054, type, sK434: (nat > nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3055, type, sK435: nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3056, type, sK436: ($o > nat > $o) > (char > $o) > (char > nat) > ($o > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3057, type, sK437: ($o > nat > $o) > (char > $o) > (char > nat) > ($o > nat > $o) > $o).
% 28.44/7.23 thf(func_def_3058, type, sK438: (rat > rat) > (rat > rat) > rat).
% 28.44/7.23 thf(func_def_3059, type, sK439: product_prod_int_int > (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3060, type, sK440: product_prod_int_int > (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3061, type, sK441: (nat > product_unit) > (nat > product_unit) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3062, type, sK442: (nat > product_unit) > (nat > product_unit) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3063, type, sK443: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3064, type, sK444: product_prod_int_int > (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_3065, type, sK445: product_prod_int_int > (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_3066, type, sK446: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3067, type, sK447: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3068, type, sK448: int > set_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3069, type, sK449: (char > char) > char > char).
% 28.44/7.23 thf(func_def_3070, type, sK450: (int > int > set_int) > int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3071, type, sK451: (int > int > set_int) > int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3072, type, sK452: set_nat > (int > nat) > (int > $o) > int).
% 28.44/7.23 thf(func_def_3073, type, sK453: (nat > nat) > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3074, type, sK454: set_nat > ($o > $o) > (nat > $o) > ($o > $o) > nat).
% 28.44/7.23 thf(func_def_3075, type, sK455: set_Product_unit > (product_unit > int) > (product_unit > int) > product_unit).
% 28.44/7.23 thf(func_def_3076, type, sK456: set_int > set_nat > (int > nat) > int).
% 28.44/7.23 thf(func_def_3077, type, sK457: (char > nat) > nat > char).
% 28.44/7.23 thf(func_def_3078, type, sK458: nat > (rat > nat) > rat).
% 28.44/7.23 thf(func_def_3079, type, sK459: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat > nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3080, type, sK460: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > nat > nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3081, type, sK461: product_unit > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > product_unit) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3082, type, sK462: product_unit > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3083, type, sK463: (product_prod_int_int > $o) > int).
% 28.44/7.23 thf(func_def_3084, type, sK464: (product_prod_int_int > $o) > int).
% 28.44/7.23 thf(func_def_3085, type, sK465: (char > rat) > rat > char).
% 28.44/7.23 thf(func_def_3086, type, sK466: (int > int > $o) > (char > int) > (char > int) > char > product_prod_int_int).
% 28.44/7.23 thf(func_def_3087, type, sK467: (char > char) > char > char).
% 28.44/7.23 thf(func_def_3088, type, sK468: set_nat > (nat > set_int) > nat).
% 28.44/7.23 thf(func_def_3089, type, sK469: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3090, type, sK470: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3091, type, sK471: int > set_int > (int > int) > int).
% 28.44/7.23 thf(func_def_3092, type, sK472: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer).
% 28.44/7.23 thf(func_def_3093, type, sK473: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer).
% 28.44/7.23 thf(func_def_3094, type, sK474: set_o > product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_3095, type, sK475: (int > nat) > set_int > nat > int).
% 28.44/7.23 thf(func_def_3096, type, sK476: set_int > product_unit > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3097, type, sK477: set_int > product_unit > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3098, type, sK478: set_nat > (nat > set_nat) > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3099, type, sK479: rat > (rat > rat) > rat).
% 28.44/7.23 thf(func_def_3100, type, sK480: set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3101, type, sK481: ($o > set_o) > $o > set_o > $o).
% 28.44/7.23 thf(func_def_3102, type, sK482: (int > int) > (set_int > $o) > set_int > set_int).
% 28.44/7.23 thf(func_def_3103, type, sK483: (int > int) > (set_int > $o) > set_int > set_int).
% 28.44/7.23 thf(func_def_3104, type, sK484: set_nat > product_unit > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3105, type, sK485: (rat > int) > (int > rat) > int).
% 28.44/7.23 thf(func_def_3106, type, sK486: rat > (nat > rat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3107, type, sK487: int > code_integer > (int > int > $o) > (int > code_integer > $o) > int).
% 28.44/7.23 thf(func_def_3108, type, sK488: product_prod_int_int > (int > int > int) > (int > int > int) > int).
% 28.44/7.23 thf(func_def_3109, type, sK489: product_prod_int_int > (int > int > int) > (int > int > int) > int).
% 28.44/7.23 thf(func_def_3110, type, sK490: ($o > int > $o) > (char > $o) > ($o > int > $o) > (char > int) > int).
% 28.44/7.23 thf(func_def_3111, type, sK491: ($o > int > $o) > (char > $o) > ($o > int > $o) > (char > int) > $o).
% 28.44/7.23 thf(func_def_3112, type, sK492: set_int > set_int > int > int).
% 28.44/7.23 thf(func_def_3113, type, sK493: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3114, type, sK494: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_3115, type, sK495: ((product_prod_nat_nat > $o) > (int > $o) > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_3116, type, sK496: ((product_prod_nat_nat > $o) > (int > $o) > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > int > $o).
% 28.44/7.23 thf(func_def_3117, type, sK497: nat > rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3118, type, sK498: rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3119, type, sK499: set_Product_unit > (product_unit > product_unit) > product_unit > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3120, type, sK500: set_Product_unit > (product_unit > product_unit) > product_unit > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_3121, type, sK501: set_nat > (set_Pr1261947904930325089at_nat > $o) > (nat > product_prod_nat_nat) > set_nat).
% 28.44/7.23 thf(func_def_3122, type, sK502: set_nat > (set_Pr1261947904930325089at_nat > $o) > (nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3123, type, sK503: set_int > set_int > int > int).
% 28.44/7.23 thf(func_def_3124, type, sK504: set_int > set_int > int > int).
% 28.44/7.23 thf(func_def_3125, type, sK505: nat > rat).
% 28.44/7.23 thf(func_def_3126, type, sK506: set_o > ($o > $o) > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_3127, type, sK507: set_Product_unit > set_Pr5094982260447487303t_unit > product_unit).
% 28.44/7.23 thf(func_def_3128, type, sK508: set_Pr5094982260447487303t_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_3129, type, sK509: product_unit > set_Pr5094982260447487303t_unit > product_unit).
% 28.44/7.23 thf(func_def_3130, type, sK510: rat > (char > rat) > char).
% 28.44/7.23 thf(func_def_3131, type, sK511: set_rat > set_nat > rat > nat).
% 28.44/7.23 thf(func_def_3132, type, sK512: set_rat > set_nat > nat > rat).
% 28.44/7.23 thf(func_def_3133, type, sK513: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3134, type, sK514: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3135, type, sK515: produc3843707927480180839at_nat > set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3136, type, sK516: (nat > num > $o) > product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3137, type, sK517: (nat > num > $o) > product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_3138, type, sK518: set_nat > (nat > set_nat) > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3139, type, sK519: (nat > nat) > set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3140, type, sK520: set_int > (nat > set_int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3141, type, sK521: (rat > nat) > (nat > rat) > rat).
% 28.44/7.23 thf(func_def_3142, type, sK522: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3143, type, sK523: nat > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3144, type, sK524: (nat > char) > char > nat).
% 28.44/7.23 thf(func_def_3145, type, sK525: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3146, type, sK526: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3147, type, sK527: set_Pr1261947904930325089at_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3148, type, sK528: set_Pr1261947904930325089at_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3149, type, sK529: (int > product_unit) > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3150, type, sK530: set_Product_unit > (product_unit > int) > int > product_unit).
% 28.44/7.23 thf(func_def_3151, type, sK531: set_o > product_unit > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3152, type, sK532: nat > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_3153, type, sK533: (nat > $o) > ($o > $o) > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_3154, type, sK534: set_int > (int > int) > (int > int) > int).
% 28.44/7.23 thf(func_def_3155, type, sK535: set_Pr1261947904930325089at_nat > (nat > $o) > (nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_3156, type, sK536: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int > product_prod_int_int).
% 28.44/7.23 thf(func_def_3157, type, sK537: (produc3843707927480180839at_nat > nat > nat) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3158, type, sK538: (produc3843707927480180839at_nat > nat > nat) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3159, type, sK539: (char > rat) > (rat > char) > char).
% 28.44/7.23 thf(func_def_3160, type, sK540: int > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3161, type, sK541: (int > nat) > (int > int) > (int > nat) > int).
% 28.44/7.23 thf(func_def_3162, type, sK542: product_unit > set_o > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3163, type, sK543: product_unit > set_o > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3164, type, sK544: product_unit > ($o > product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_3165, type, sK545: product_unit > ($o > product_unit) > set_o > product_unit).
% 28.44/7.23 thf(func_def_3166, type, sK546: (rat > $o) > ($o > $o > $o) > (rat > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3167, type, sK547: (rat > $o) > ($o > $o > $o) > (rat > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3168, type, sK548: set_int > (int > product_prod_nat_nat) > int).
% 28.44/7.23 thf(func_def_3169, type, sK549: set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3170, type, sK550: set_int > nat > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3171, type, sK551: (int > product_unit) > set_int > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3172, type, sK552: (int > product_unit) > set_int > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3173, type, sK553: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit).
% 28.44/7.23 thf(func_def_3174, type, sK554: (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3175, type, sK555: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3176, type, sK556: (int > nat) > (int > int) > (int > nat) > (int > int) > int).
% 28.44/7.23 thf(func_def_3177, type, sK557: (int > nat) > (int > int) > (int > nat) > (int > int) > int).
% 28.44/7.23 thf(func_def_3178, type, sK558: set_nat > set_o > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3179, type, sK559: set_nat > set_o > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3180, type, sK560: (nat > nat) > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3181, type, sK561: product_unit > (product_unit > product_unit) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3182, type, sK562: product_unit > (product_unit > product_unit) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3183, type, sK563: (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3184, type, sK564: (char > int) > int).
% 28.44/7.23 thf(func_def_3185, type, sK565: int > (char > int) > char).
% 28.44/7.23 thf(func_def_3186, type, sK566: (product_prod_nat_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3187, type, sK567: (rat > nat) > nat > rat).
% 28.44/7.23 thf(func_def_3188, type, sK568: set_int > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_3189, type, sK569: set_Pr958786334691620121nt_int > set_int).
% 28.44/7.23 thf(func_def_3190, type, sK570: int > set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_3191, type, sK571: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3192, type, sK572: ($o > $o) > product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3193, type, sK573: ($o > $o) > product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3194, type, sK574: product_unit > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3195, type, sK575: product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3196, type, sK576: product_prod_int_int > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3197, type, sK577: list_nat > nat > nat).
% 28.44/7.23 thf(func_def_3198, type, sK578: ($o > set_int) > set_int > set_o > $o).
% 28.44/7.23 thf(func_def_3199, type, sK579: produc7812382424243267045t_unit > heap_e7401611519738050253t_unit > ref_a).
% 28.44/7.23 thf(func_def_3200, type, sK580: (nat > nat) > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3201, type, sK581: set_int > set_nat > nat > int).
% 28.44/7.23 thf(func_def_3202, type, sK582: set_int > set_nat > int > nat).
% 28.44/7.23 thf(func_def_3203, type, sK583: (nat > nat > $o) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3204, type, sK584: int > (char > int) > char).
% 28.44/7.23 thf(func_def_3205, type, sK585: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3206, type, sK586: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3207, type, sK587: set_rat > set_nat > (nat > rat) > set_nat).
% 28.44/7.23 thf(func_def_3208, type, sK588: set_nat > (nat > rat) > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3209, type, sK589: ($o > set_Pr1261947904930325089at_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3210, type, sK590: set_o > (nat > product_unit) > ($o > product_unit) > set_nat > $o).
% 28.44/7.23 thf(func_def_3211, type, sK591: set_o > (nat > product_unit) > ($o > product_unit) > set_nat > nat).
% 28.44/7.23 thf(func_def_3212, type, sK592: ($o > product_unit) > ($o > product_unit) > set_o > set_o > $o).
% 28.44/7.23 thf(func_def_3213, type, sK593: ($o > product_unit) > ($o > product_unit) > set_o > set_o > $o).
% 28.44/7.23 thf(func_def_3214, type, sK594: set_nat > nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3215, type, sK595: set_nat > ($o > set_nat) > set_o > set_nat).
% 28.44/7.23 thf(func_def_3216, type, sK596: set_nat > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3217, type, sK597: (int > set_o) > $o > set_int > int).
% 28.44/7.23 thf(func_def_3218, type, sK598: (nat > char) > (char > nat) > nat).
% 28.44/7.23 thf(func_def_3219, type, sK599: (nat > nat) > set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3220, type, sK600: set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3221, type, sK601: (int > num) > (num > num > $o) > (int > num) > int > product_prod_num_num).
% 28.44/7.23 thf(func_def_3222, type, sK602: (nat > int) > set_nat > int > nat).
% 28.44/7.23 thf(func_def_3223, type, sK603: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3224, type, sK604: ((product_prod_nat_nat > $o) > (int > $o) > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > product_prod_nat_nat > $o).
% 28.44/7.23 thf(func_def_3225, type, sK605: ((product_prod_nat_nat > $o) > (int > $o) > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > int > $o).
% 28.44/7.23 thf(func_def_3226, type, sK606: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > int).
% 28.44/7.23 thf(func_def_3227, type, sK607: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3228, type, sK608: ($o > nat) > set_o > (int > nat) > set_int > $o).
% 28.44/7.23 thf(func_def_3229, type, sK609: int > set_o > ($o > int) > $o).
% 28.44/7.23 thf(func_def_3230, type, sK610: (nat > int) > product_prod_int_int > set_Pr1261947904930325089at_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3231, type, sK611: (nat > int) > product_prod_int_int > set_Pr1261947904930325089at_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3232, type, sK612: (produc3843707927480180839at_nat > product_unit) > (produc3843707927480180839at_nat > product_unit) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3233, type, sK613: (nat > set_nat) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3234, type, sK614: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3235, type, sK615: set_o > ($o > set_nat) > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3236, type, sK616: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_3237, type, sK617: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_3238, type, sK618: set_o > ($o > nat) > nat > $o).
% 28.44/7.23 thf(func_def_3239, type, sK619: nat > set_Product_unit > (product_unit > nat) > product_unit).
% 28.44/7.23 thf(func_def_3240, type, sK620: ($o > set_nat) > set_o > product_prod_o_nat > $o).
% 28.44/7.23 thf(func_def_3241, type, sK621: ($o > set_nat) > set_o > product_prod_o_nat > nat).
% 28.44/7.23 thf(func_def_3242, type, sK622: set_nat > (nat > product_unit) > set_nat > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3243, type, sK623: set_nat > (nat > product_unit) > set_nat > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3244, type, sK624: set_o > ($o > nat) > ($o > nat) > $o).
% 28.44/7.23 thf(func_def_3245, type, sK625: (int > product_unit) > set_int > (nat > product_unit) > set_nat > nat).
% 28.44/7.23 thf(func_def_3246, type, sK626: (int > product_unit) > set_int > (nat > product_unit) > set_nat > int).
% 28.44/7.23 thf(func_def_3247, type, sK627: (nat > nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3248, type, sK628: (nat > nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3249, type, sK629: int > set_Product_unit > (product_unit > int) > product_unit).
% 28.44/7.23 thf(func_def_3250, type, sK630: set_int > (int > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3251, type, sK631: nat > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3252, type, sK632: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3253, type, sK633: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3254, type, sK634: (product_prod_nat_nat > nat) > set_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3255, type, sK635: nat > (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3256, type, sK636: (nat > nat) > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3257, type, sK637: (int > code_integer > $o) > code_integer > (int > int > $o) > int > int).
% 28.44/7.23 thf(func_def_3258, type, sK638: code_integer > set_o > ($o > code_integer) > $o).
% 28.44/7.23 thf(func_def_3259, type, sK639: set_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3260, type, sK640: (nat > int) > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3261, type, sK641: set_se7855581050983116737at_nat > produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3262, type, sK642: (nat > char) > char > nat).
% 28.44/7.23 thf(func_def_3263, type, sK643: set_int > product_unit > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3264, type, sK644: (int > product_unit) > set_int > set_o > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3265, type, sK645: (int > product_unit) > set_int > set_o > ($o > product_unit) > int).
% 28.44/7.23 thf(func_def_3266, type, sK646: (product_prod_int_int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3267, type, sK647: (product_prod_int_int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3268, type, sK648: product_prod_nat_o > (nat > set_o) > set_nat > nat).
% 28.44/7.23 thf(func_def_3269, type, sK649: product_prod_nat_o > (nat > set_o) > set_nat > $o).
% 28.44/7.23 thf(func_def_3270, type, sK650: ((product_prod_nat_nat > product_prod_nat_nat) > $o) > (nat > nat > $o) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_3271, type, sK651: ((product_prod_nat_nat > product_prod_nat_nat) > $o) > (nat > nat > $o) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 28.44/7.23 thf(func_def_3272, type, sK652: set_o > product_unit > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3273, type, sK653: (int > int) > set_int > set_int > set_int).
% 28.44/7.23 thf(func_def_3274, type, sK654: set_Pr958786334691620121nt_int > int).
% 28.44/7.23 thf(func_def_3275, type, sK655: (nat > rat) > set_rat > rat > set_nat > nat).
% 28.44/7.23 thf(func_def_3276, type, sK656: (nat > rat) > set_rat > rat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3277, type, sK657: (product_unit > $o) > $o).
% 28.44/7.23 thf(func_def_3278, type, sK658: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3279, type, sK659: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3280, type, sK660: set_o > set_o > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_3281, type, sK661: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3282, type, sK662: set_o > ($o > set_nat) > set_o > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3283, type, sK663: set_o > ($o > set_nat) > set_o > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3284, type, sK664: set_Product_unit > (product_unit > product_unit) > (product_unit > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3285, type, sK665: nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3286, type, sK666: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3287, type, sK667: set_Pr7459493094073627847at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3288, type, sK668: (int > nat) > (int > nat) > (nat > nat > $o) > int > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3289, type, sK669: (int > $o) > set_int > set_o > int).
% 28.44/7.23 thf(func_def_3290, type, sK670: (nat > int) > (set_int > $o) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3291, type, sK671: (nat > int) > (set_int > $o) > set_nat > set_int).
% 28.44/7.23 thf(func_def_3292, type, sK672: $o > ($o > $o) > set_o > $o).
% 28.44/7.23 thf(func_def_3293, type, sK673: product_prod_int_nat > (int > set_nat) > set_int > int).
% 28.44/7.23 thf(func_def_3294, type, sK674: product_prod_int_nat > (int > set_nat) > set_int > nat).
% 28.44/7.23 thf(func_def_3295, type, sK675: set_int > set_int > (int > int) > int).
% 28.44/7.23 thf(func_def_3296, type, sK676: set_nat > (nat > product_unit) > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3297, type, sK677: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3298, type, sK678: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3299, type, sK679: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > heap_Heap_ref_a > (ref_a > heap_Heap_ref_a) > ref_a).
% 28.44/7.23 thf(func_def_3300, type, sK680: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > ref_a > heap_Heap_ref_a > (ref_a > heap_Heap_ref_a) > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_3301, type, sK681: (int > product_unit) > product_unit > set_int > int).
% 28.44/7.23 thf(func_def_3302, type, sK682: (nat > set_num) > set_nat > product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_3303, type, sK683: (nat > set_num) > set_nat > product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3304, type, sK684: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3305, type, sK685: set_nat > $o > (nat > set_o) > nat).
% 28.44/7.23 thf(func_def_3306, type, sK686: set_int > (set_int > $o) > (int > int) > set_int).
% 28.44/7.23 thf(func_def_3307, type, sK687: set_int > (set_int > $o) > (int > int) > set_int).
% 28.44/7.23 thf(func_def_3308, type, sK688: char > (char > int) > int > char).
% 28.44/7.23 thf(func_def_3309, type, sK689: (char > int) > int > char).
% 28.44/7.23 thf(func_def_3310, type, sK690: (char > $o) > (nat > $o > $o) > (char > nat) > (nat > $o > $o) > nat).
% 28.44/7.23 thf(func_def_3311, type, sK691: (char > $o) > (nat > $o > $o) > (char > nat) > (nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3312, type, sK692: (int > int) > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3313, type, sK693: (nat > set_nat) > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3314, type, sK694: set_o > ($o > nat) > nat > $o).
% 28.44/7.23 thf(func_def_3315, type, sK695: (product_unit > set_int) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3316, type, sK696: nat > product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3317, type, sK697: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3318, type, sK698: nat > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3319, type, sK699: int > (char > int) > char).
% 28.44/7.23 thf(func_def_3320, type, sK700: set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3321, type, sK701: (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_3322, type, sK702: set_int > nat > int).
% 28.44/7.23 thf(func_def_3323, type, sK703: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3324, type, sK704: set_nat > set_int > (int > set_nat) > set_nat).
% 28.44/7.23 thf(func_def_3325, type, sK705: set_nat > set_int > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3326, type, sK706: set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3327, type, sK707: produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3328, type, sK708: produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3329, type, sK709: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > set_Code_integer > code_integer).
% 28.44/7.23 thf(func_def_3330, type, sK710: (nat > nat) > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3331, type, sK711: (rat > char) > char > rat).
% 28.44/7.23 thf(func_def_3332, type, sK712: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit).
% 28.44/7.23 thf(func_def_3333, type, sK713: product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3334, type, sK714: (nat > int) > (int > nat) > int).
% 28.44/7.23 thf(func_def_3335, type, sK715: (char > rat) > (rat > char) > rat).
% 28.44/7.23 thf(func_def_3336, type, sK716: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3337, type, sK717: set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3338, type, sK718: (int > $o) > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3339, type, sK719: ($o > $o > $o) > (char > $o) > ($o > $o > $o) > (char > $o) > $o).
% 28.44/7.23 thf(func_def_3340, type, sK720: ($o > $o > $o) > (char > $o) > ($o > $o > $o) > (char > $o) > $o).
% 28.44/7.23 thf(func_def_3341, type, sK721: set_int > set_int > int > int).
% 28.44/7.23 thf(func_def_3342, type, sK722: product_prod_int_o > (int > set_o) > set_int > int).
% 28.44/7.23 thf(func_def_3343, type, sK723: product_prod_int_o > (int > set_o) > set_int > $o).
% 28.44/7.23 thf(func_def_3344, type, sK724: set_se7855581050983116737at_nat > product_prod_nat_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3345, type, sK725: set_nat > set_o > ($o > nat) > (nat > nat) > $o).
% 28.44/7.23 thf(func_def_3346, type, sK726: set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3347, type, sK727: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3348, type, sK728: product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3349, type, sK729: (int > nat) > nat > set_int > int).
% 28.44/7.23 thf(func_def_3350, type, sK730: (nat > rat) > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3351, type, sK731: int > ($o > int) > set_o > $o).
% 28.44/7.23 thf(func_def_3352, type, sK732: (nat > int) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3353, type, sK733: int > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3354, type, sK734: set_Product_unit > set_nat > (product_unit > set_nat) > product_unit).
% 28.44/7.23 thf(func_def_3355, type, sK735: (product_unit > nat) > set_Product_unit > set_int > (int > nat) > product_unit).
% 28.44/7.23 thf(func_def_3356, type, sK736: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3357, type, sK737: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3358, type, sK738: set_o > ($o > set_nat) > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3359, type, sK739: set_nat > (nat > rat) > (set_rat > $o) > set_rat).
% 28.44/7.23 thf(func_def_3360, type, sK740: set_nat > (nat > rat) > (set_rat > $o) > set_nat).
% 28.44/7.23 thf(func_def_3361, type, sK741: (nat > nat > $o) > (list_nat > nat) > (list_nat > nat) > list_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3362, type, sK742: (nat > nat > $o) > (rat > nat) > nat).
% 28.44/7.23 thf(func_def_3363, type, sK743: set_nat > set_int > nat > int).
% 28.44/7.23 thf(func_def_3364, type, sK744: set_nat > set_int > int > nat).
% 28.44/7.23 thf(func_def_3365, type, sK745: set_int > (int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_3366, type, sK746: set_o > product_unit > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3367, type, sK747: (int > int) > product_prod_int_int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3368, type, sK748: (int > int) > product_prod_int_int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3369, type, sK749: (nat > nat) > (nat > nat > $o) > (nat > nat) > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3370, type, sK750: set_nat > set_rat > nat > rat).
% 28.44/7.23 thf(func_def_3371, type, sK751: (char > nat) > nat).
% 28.44/7.23 thf(func_def_3372, type, sK752: nat > (char > nat) > char).
% 28.44/7.23 thf(func_def_3373, type, sK753: set_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3374, type, sK754: set_int > set_nat > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3375, type, sK755: set_int > set_nat > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3376, type, sK756: nat > set_o > ($o > nat) > $o).
% 28.44/7.23 thf(func_def_3377, type, sK757: (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3378, type, sK758: set_int > set_int > (int > set_int) > int).
% 28.44/7.23 thf(func_def_3379, type, sK759: (heap_e7401611519738050253t_unit > ref_a > $o) > ref_a).
% 28.44/7.23 thf(func_def_3380, type, sK760: (heap_e7401611519738050253t_unit > ref_a > $o) > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_3381, type, sK761: (nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3382, type, sK762: set_int > set_nat > int > nat).
% 28.44/7.23 thf(func_def_3383, type, sK763: produc3843707927480180839at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3384, type, sK764: product_prod_nat_num > product_prod_nat_num > (nat > nat) > num).
% 28.44/7.23 thf(func_def_3385, type, sK765: product_prod_nat_num > product_prod_nat_num > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3386, type, sK766: set_nat > (nat > product_unit) > product_unit > nat).
% 28.44/7.23 thf(func_def_3387, type, sK767: (product_unit > set_nat) > set_Product_unit > set_nat > product_unit).
% 28.44/7.23 thf(func_def_3388, type, sK768: (rat > nat) > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3389, type, sK769: ($o > int) > set_o > ($o > int) > $o).
% 28.44/7.23 thf(func_def_3390, type, sK770: (nat > $o) > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3391, type, sK771: (char > char) > char).
% 28.44/7.23 thf(func_def_3392, type, sK772: char > (char > char) > char).
% 28.44/7.23 thf(func_def_3393, type, sK773: (int > nat > $o) > (int > nat > $o) > (char > nat) > (char > int) > nat).
% 28.44/7.23 thf(func_def_3394, type, sK774: (int > nat > $o) > (int > nat > $o) > (char > nat) > (char > int) > int).
% 28.44/7.23 thf(func_def_3395, type, sK775: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3396, type, sK776: (set_nat > $o) > set_int > (int > nat) > set_nat).
% 28.44/7.23 thf(func_def_3397, type, sK777: (set_nat > $o) > set_int > (int > nat) > set_int).
% 28.44/7.23 thf(func_def_3398, type, sK778: set_Product_prod_o_o > set_o > $o).
% 28.44/7.23 thf(func_def_3399, type, sK779: set_Product_prod_o_o > set_o > $o).
% 28.44/7.23 thf(func_def_3400, type, sK780: set_o > ($o > int) > int > $o).
% 28.44/7.23 thf(func_def_3401, type, sK781: (int > int) > set_int > int > int).
% 28.44/7.23 thf(func_def_3402, type, sK782: set_nat > (nat > int) > int > nat).
% 28.44/7.23 thf(func_def_3403, type, sK783: (nat > $o) > (nat > rat) > set_rat > nat).
% 28.44/7.23 thf(func_def_3404, type, sK784: (int > int > int) > (product_prod_int_int > int) > int).
% 28.44/7.23 thf(func_def_3405, type, sK785: (int > int > int) > (product_prod_int_int > int) > int).
% 28.44/7.23 thf(func_def_3406, type, sK786: (nat > nat) > (set_nat > $o) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3407, type, sK787: (nat > nat) > (set_nat > $o) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3408, type, sK788: set_nat > (nat > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3409, type, sK789: set_Product_unit > (product_unit > nat) > nat > product_unit).
% 28.44/7.23 thf(func_def_3410, type, sK790: set_nat > nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3411, type, sK791: (int > int > $o) > (int > int > $o) > ($o > $o) > int).
% 28.44/7.23 thf(func_def_3412, type, sK792: (int > int > $o) > (int > int > $o) > ($o > $o) > int).
% 28.44/7.23 thf(func_def_3413, type, sK793: (int > product_unit) > set_nat > set_int > (nat > product_unit) > int).
% 28.44/7.23 thf(func_def_3414, type, sK794: (int > product_unit) > set_nat > set_int > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3415, type, sK795: $o > set_set_o > set_o).
% 28.44/7.23 thf(func_def_3416, type, sK796: (int > int) > set_int > set_int > int).
% 28.44/7.23 thf(func_def_3417, type, sK797: (char > $o) > $o > char).
% 28.44/7.23 thf(func_def_3418, type, sK798: char > (char > $o) > $o > char).
% 28.44/7.23 thf(func_def_3419, type, sK799: rat > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3420, type, sK800: (nat > rat) > (rat > rat > $o) > rat).
% 28.44/7.23 thf(func_def_3421, type, sK801: nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3422, type, sK802: set_nat > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3423, type, sK803: set_o > set_nat > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3424, type, sK804: set_Product_unit > (product_unit > set_Product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3425, type, sK805: (int > int > set_o) > $o > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3426, type, sK806: (int > int > set_o) > $o > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3427, type, sK807: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > set_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3428, type, sK808: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > set_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3429, type, sK809: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3430, type, sK810: set_nat > set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3431, type, sK811: set_Product_unit > (product_unit > set_o) > product_unit).
% 28.44/7.23 thf(func_def_3432, type, sK812: set_nat > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3433, type, sK813: set_o > ($o > $o) > $o).
% 28.44/7.23 thf(func_def_3434, type, sK814: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3435, type, sK815: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3436, type, sK816: (nat > int) > set_Pr6200539531224447659at_num > product_prod_int_int > (num > int) > nat).
% 28.44/7.23 thf(func_def_3437, type, sK817: (nat > int) > set_Pr6200539531224447659at_num > product_prod_int_int > (num > int) > num).
% 28.44/7.23 thf(func_def_3438, type, sK818: product_prod_int_int > (int > int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_3439, type, sK819: product_prod_int_int > (int > int > int) > (int > $o) > int).
% 28.44/7.23 thf(func_def_3440, type, sK820: (product_unit > product_unit) > product_unit > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3441, type, sK821: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3442, type, sK822: (int > int > set_o) > $o > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3443, type, sK823: (int > int > set_o) > $o > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3444, type, sK824: set_int > (int > set_Product_unit) > int).
% 28.44/7.23 thf(func_def_3445, type, sK825: (nat > nat > $o) > (char > nat) > (char > nat) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3446, type, sK826: (nat > nat > $o) > (char > nat) > (char > nat) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3447, type, sK827: product_prod_nat_num > num > nat).
% 28.44/7.23 thf(func_def_3448, type, sK828: set_nat > (nat > product_prod_nat_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3449, type, sK829: set_nat > (nat > nat) > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3450, type, sK830: ($o > set_nat) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_3451, type, sK831: ($o > set_nat) > set_nat > set_o > $o).
% 28.44/7.23 thf(func_def_3452, type, sK832: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3453, type, sK833: (product_prod_nat_nat > set_nat) > set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3454, type, sK834: (product_prod_nat_nat > set_nat) > set_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3455, type, sK835: (nat > set_nat) > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3456, type, sK836: set_int > (int > set_nat) > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3457, type, sK837: set_Product_unit > (product_unit > product_unit) > product_unit > product_unit).
% 28.44/7.23 thf(func_def_3458, type, sK838: set_Product_unit > (product_unit > product_unit) > product_unit > product_unit).
% 28.44/7.23 thf(func_def_3459, type, sK839: (nat > product_unit) > set_nat > (nat > product_unit) > nat).
% 28.44/7.23 thf(func_def_3460, type, sK840: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3461, type, sK841: set_nat > (int > set_nat) > set_int > int).
% 28.44/7.23 thf(func_def_3462, type, sK842: (product_prod_nat_nat > product_prod_nat_nat > $o) > int > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3463, type, sK843: set_int > (int > product_unit) > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3464, type, sK844: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat).
% 28.44/7.23 thf(func_def_3465, type, sK845: set_Pr4329608150637261639at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3466, type, sK846: set_se5479201105039950375at_nat > set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3467, type, sK847: set_int > (int > product_unit) > (int > product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_3468, type, sK848: set_int > (int > product_unit) > (int > product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_3469, type, sK849: (produc3843707927480180839at_nat > product_unit) > product_unit > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3470, type, sK850: set_nat > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3471, type, sK851: set_nat > (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3472, type, sK852: (int > nat) > (nat > num) > (nat > num) > nat).
% 28.44/7.23 thf(func_def_3473, type, sK853: (nat > nat) > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3474, type, sK854: (nat > $o) > set_nat > nat).
% 28.44/7.23 thf(func_def_3475, type, sK855: ($o > set_int) > product_prod_o_int > set_o > $o).
% 28.44/7.23 thf(func_def_3476, type, sK856: ($o > set_int) > product_prod_o_int > set_o > int).
% 28.44/7.23 thf(func_def_3477, type, sK857: set_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3478, type, sK858: set_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_nat).
% 28.44/7.23 thf(func_def_3479, type, sK859: set_nat > (nat > nat > nat) > nat).
% 28.44/7.23 thf(func_def_3480, type, sK860: set_nat > (nat > nat > nat) > nat).
% 28.44/7.23 thf(func_def_3481, type, sK861: set_int > set_nat > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3482, type, sK862: nat > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3483, type, sK863: (int > int) > (nat > int) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_3484, type, sK864: (char > nat) > nat > char).
% 28.44/7.23 thf(func_def_3485, type, sK865: char > (char > nat) > nat > char).
% 28.44/7.23 thf(func_def_3486, type, sK866: nat > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_3487, type, sK867: nat > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_3488, type, sK868: set_Product_prod_o_o > set_o > $o).
% 28.44/7.23 thf(func_def_3489, type, sK869: product_unit > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3490, type, sK870: product_unit > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3491, type, sK871: (int > nat) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_3492, type, sK872: set_o > set_nat > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3493, type, sK873: set_o > set_nat > ($o > set_nat) > set_nat).
% 28.44/7.23 thf(func_def_3494, type, sK874: set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3495, type, sK875: set_int > $o > (int > $o) > int).
% 28.44/7.23 thf(func_def_3496, type, sK876: set_int > set_int > (int > int) > (int > int) > int).
% 28.44/7.23 thf(func_def_3497, type, sK877: (int > int > $o) > set_int > (int > int > $o) > set_int > int).
% 28.44/7.23 thf(func_def_3498, type, sK878: (int > int > $o) > set_int > (int > int > $o) > set_int > int).
% 28.44/7.23 thf(func_def_3499, type, sK879: (int > int) > set_int > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3500, type, sK880: set_nat > (nat > int) > int).
% 28.44/7.23 thf(func_def_3501, type, sK881: (nat > set_Pr1261947904930325089at_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3502, type, sK882: (nat > set_nat) > set_nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3503, type, sK883: (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3504, type, sK884: (char > int) > (int > $o > $o) > (char > $o) > (int > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3505, type, sK885: (char > int) > (int > $o > $o) > (char > $o) > (int > $o > $o) > int).
% 28.44/7.23 thf(func_def_3506, type, sK886: (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3507, type, sK887: set_nat > (nat > int) > (set_int > $o) > set_int).
% 28.44/7.23 thf(func_def_3508, type, sK888: set_nat > (nat > int) > (set_int > $o) > set_nat).
% 28.44/7.23 thf(func_def_3509, type, sK889: ($o > product_unit) > set_o > (nat > product_unit) > set_nat > $o).
% 28.44/7.23 thf(func_def_3510, type, sK890: ($o > product_unit) > set_o > (nat > product_unit) > set_nat > nat).
% 28.44/7.23 thf(func_def_3511, type, sK891: (int > int) > (int > nat) > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3512, type, sK892: (nat > nat) > set_nat > (int > nat) > set_int > nat).
% 28.44/7.23 thf(func_def_3513, type, sK893: (char > nat) > nat > char).
% 28.44/7.23 thf(func_def_3514, type, sK894: produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3515, type, sK895: (int > set_nat) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_3516, type, sK896: (int > set_nat) > set_int > set_nat > int).
% 28.44/7.23 thf(func_def_3517, type, sK897: set_int > (int > set_o) > int).
% 28.44/7.23 thf(func_def_3518, type, sK898: nat > (rat > nat) > rat).
% 28.44/7.23 thf(func_def_3519, type, sK899: product_prod_o_o > ($o > set_o) > set_o > $o).
% 28.44/7.23 thf(func_def_3520, type, sK900: product_prod_o_o > ($o > set_o) > set_o > $o).
% 28.44/7.23 thf(func_def_3521, type, sK901: set_nat > rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3522, type, sK902: (nat > product_prod_nat_nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3523, type, sK903: (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3524, type, sK904: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3525, type, sK905: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3526, type, sK906: (int > code_integer > $o) > (int > code_integer > $o) > code_integer).
% 28.44/7.23 thf(func_def_3527, type, sK907: (int > code_integer > $o) > (int > code_integer > $o) > int).
% 28.44/7.23 thf(func_def_3528, type, sK908: (nat > set_Pr1261947904930325089at_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3529, type, sK909: int > (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_3530, type, sK910: product_prod_nat_num > (nat > num > set_o) > $o > nat).
% 28.44/7.23 thf(func_def_3531, type, sK911: product_prod_nat_num > (nat > num > set_o) > $o > num).
% 28.44/7.23 thf(func_def_3532, type, sK912: product_prod_nat_nat > (nat > nat > set_int) > int > nat).
% 28.44/7.23 thf(func_def_3533, type, sK913: product_prod_nat_nat > (nat > nat > set_int) > int > nat).
% 28.44/7.23 thf(func_def_3534, type, sK914: set_int > (int > set_o) > int).
% 28.44/7.23 thf(func_def_3535, type, sK915: set_int > (int > product_unit) > product_unit > int).
% 28.44/7.23 thf(func_def_3536, type, sK916: ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3537, type, sK917: nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3538, type, sK918: char > (rat > char) > rat).
% 28.44/7.23 thf(func_def_3539, type, sK919: (rat > char) > char).
% 28.44/7.23 thf(func_def_3540, type, sK920: $o > (nat > num > set_o) > product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_3541, type, sK921: $o > (nat > num > set_o) > product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3542, type, sK922: (product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_3543, type, sK923: (product_prod_nat_nat > $o) > nat).
% 28.44/7.23 thf(func_def_3544, type, sK924: (nat > num) > (int > nat) > (nat > num) > set_int > int).
% 28.44/7.23 thf(func_def_3545, type, sK925: (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer).
% 28.44/7.23 thf(func_def_3546, type, sK926: (produc3843707927480180839at_nat > set_nat) > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3547, type, sK927: (nat > num) > (nat > num) > (int > nat) > nat).
% 28.44/7.23 thf(func_def_3548, type, sK928: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3549, type, sK929: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3550, type, sK930: int > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3551, type, sK931: set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3552, type, sK932: set_o > nat > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3553, type, sK933: set_o > ($o > set_int) > set_int > $o).
% 28.44/7.23 thf(func_def_3554, type, sK934: (nat > $o) > $o > set_nat > nat).
% 28.44/7.23 thf(func_def_3555, type, sK935: (nat > nat) > (nat > nat) > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3556, type, sK936: (nat > nat) > (nat > nat) > (nat > nat) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3557, type, sK937: set_nat > (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3558, type, sK938: set_nat > (nat > $o) > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_3559, type, sK939: ($o > nat) > set_o > ($o > nat) > $o).
% 28.44/7.23 thf(func_def_3560, type, sK940: set_int > int > (int > int) > int).
% 28.44/7.23 thf(func_def_3561, type, sK941: set_nat > (set_nat > $o) > (nat > nat) > set_nat).
% 28.44/7.23 thf(func_def_3562, type, sK942: set_nat > (set_nat > $o) > (nat > nat) > set_nat).
% 28.44/7.23 thf(func_def_3563, type, sK943: (int > int) > set_int > int > int).
% 28.44/7.23 thf(func_def_3564, type, sK944: (product_prod_nat_num > $o) > nat).
% 28.44/7.23 thf(func_def_3565, type, sK945: (product_prod_nat_num > $o) > num).
% 28.44/7.23 thf(func_def_3566, type, sK946: (int > int > $o) > (char > int) > int).
% 28.44/7.23 thf(func_def_3567, type, sK947: set_se7855581050983116737at_nat > (set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3568, type, sK948: set_set_nat > nat > set_nat).
% 28.44/7.23 thf(func_def_3569, type, sK949: set_nat > (int > product_unit) > (nat > product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_3570, type, sK950: set_nat > (int > product_unit) > (nat > product_unit) > set_int > nat).
% 28.44/7.23 thf(func_def_3571, type, sK951: (char > nat) > (char > int) > (nat > int > $o) > (nat > int > $o) > nat).
% 28.44/7.23 thf(func_def_3572, type, sK952: (char > nat) > (char > int) > (nat > int > $o) > (nat > int > $o) > int).
% 28.44/7.23 thf(func_def_3573, type, sK953: produc7812382424243267045t_unit > ref_a > heap_e7401611519738050253t_unit).
% 28.44/7.23 thf(func_def_3574, type, sK954: set_Pr958786334691620121nt_int > (product_prod_int_int > nat) > product_prod_int_int).
% 28.44/7.23 thf(func_def_3575, type, sK955: set_int > product_prod_int_int > int).
% 28.44/7.23 thf(func_def_3576, type, sK956: set_nat > ($o > nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3577, type, sK957: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int).
% 28.44/7.23 thf(func_def_3578, type, sK958: (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3579, type, sK959: (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) > int).
% 28.44/7.23 thf(func_def_3580, type, sK960: (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) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3581, type, sK961: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3582, type, sK962: set_Pr7459493094073627847at_nat > set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3583, type, sK963: product_prod_nat_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3584, type, sK964: int > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_3585, type, sK965: (nat > nat) > set_nat > set_int > (int > nat) > nat).
% 28.44/7.23 thf(func_def_3586, type, sK966: set_Pr1261947904930325089at_nat > (set_nat > $o) > (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3587, type, sK967: set_Pr1261947904930325089at_nat > (set_nat > $o) > (product_prod_nat_nat > nat) > set_nat).
% 28.44/7.23 thf(func_def_3588, type, sK968: rat > (int > rat) > set_int > int).
% 28.44/7.23 thf(func_def_3589, type, sK969: (int > product_unit) > (int > product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_3590, type, sK970: set_rat > nat > rat).
% 28.44/7.23 thf(func_def_3591, type, sK971: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3592, type, sK972: set_nat > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3593, type, sK973: set_nat > set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > set_nat).
% 28.44/7.23 thf(func_def_3594, type, sK974: (nat > rat) > (rat > nat) > nat).
% 28.44/7.23 thf(func_def_3595, type, sK975: (nat > set_nat) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3596, type, sK976: (nat > set_nat) > set_nat > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3597, type, sK977: nat > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3598, type, sK978: set_Product_unit > (int > nat) > (product_unit > nat) > set_int > product_unit).
% 28.44/7.23 thf(func_def_3599, type, sK979: set_Pr958786334691620121nt_int > set_int > int).
% 28.44/7.23 thf(func_def_3600, type, sK980: set_Pr958786334691620121nt_int > set_int > int).
% 28.44/7.23 thf(func_def_3601, type, sK981: set_Product_unit > set_nat > (product_unit > set_nat) > product_unit).
% 28.44/7.23 thf(func_def_3602, type, sK982: set_Product_unit > set_nat > (product_unit > set_nat) > product_unit).
% 28.44/7.23 thf(func_def_3603, type, sK983: (int > nat) > (int > nat) > set_int > set_int > int).
% 28.44/7.23 thf(func_def_3604, type, sK984: ($o > product_unit) > product_unit > set_o > $o).
% 28.44/7.23 thf(func_def_3605, type, sK985: product_prod_nat_num > product_prod_nat_nat > (nat > num > set_Pr1261947904930325089at_nat) > num).
% 28.44/7.23 thf(func_def_3606, type, sK986: product_prod_nat_num > product_prod_nat_nat > (nat > num > set_Pr1261947904930325089at_nat) > nat).
% 28.44/7.23 thf(func_def_3607, type, sK987: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3608, type, sK988: (int > set_Product_unit) > set_int > int).
% 28.44/7.23 thf(func_def_3609, type, sK989: (rat > int) > (int > rat) > int).
% 28.44/7.23 thf(func_def_3610, type, sK990: (char > nat) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3611, type, sK991: set_o > ($o > set_int) > $o).
% 28.44/7.23 thf(func_def_3612, type, sK992: (char > nat) > (char > nat) > (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3613, type, sK993: (char > nat) > (char > nat) > (nat > nat > $o) > (nat > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3614, type, sK994: set_nat > product_prod_nat_int > (nat > set_int) > nat).
% 28.44/7.23 thf(func_def_3615, type, sK995: set_nat > product_prod_nat_int > (nat > set_int) > int).
% 28.44/7.23 thf(func_def_3616, type, sK996: (nat > nat) > (nat > $o) > set_nat > nat).
% 28.44/7.23 thf(func_def_3617, type, sK997: produc859450856879609959at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3618, type, sK998: set_set_int > int > set_int).
% 28.44/7.23 thf(func_def_3619, type, sK999: (int > int > set_nat) > product_prod_int_int > nat > int).
% 28.44/7.23 thf(func_def_3620, type, sK1000: (int > int > set_nat) > product_prod_int_int > nat > int).
% 28.44/7.23 thf(func_def_3621, type, sK1001: set_o > set_nat > ($o > set_nat) > $o).
% 28.44/7.23 thf(func_def_3622, type, sK1002: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3623, type, sK1003: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3624, type, sK1004: set_nat > (int > set_nat) > set_int > int).
% 28.44/7.23 thf(func_def_3625, type, sK1005: ($o > product_unit) > product_unit > set_o > $o).
% 28.44/7.23 thf(func_def_3626, type, sK1006: ($o > product_unit) > product_unit > set_o > $o).
% 28.44/7.23 thf(func_def_3627, type, sK1007: (nat > $o) > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_3628, type, sK1008: (nat > int) > set_nat > (int > $o) > nat).
% 28.44/7.23 thf(func_def_3629, type, sK1009: ($o > product_unit) > set_o > ($o > product_unit) > $o).
% 28.44/7.23 thf(func_def_3630, type, sK1010: nat > set_int > (int > nat) > int).
% 28.44/7.23 thf(func_def_3631, type, sK1011: set_nat > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3632, type, sK1012: (char > nat) > (nat > int > $o) > (nat > int > $o) > (char > int) > nat).
% 28.44/7.23 thf(func_def_3633, type, sK1013: (char > nat) > (nat > int > $o) > (nat > int > $o) > (char > int) > int).
% 28.44/7.23 thf(func_def_3634, type, sK1014: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3635, type, sK1015: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3636, type, sK1016: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3637, type, sK1017: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3638, type, sK1018: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3639, type, sK1019: (char > nat) > (nat > char) > char).
% 28.44/7.23 thf(func_def_3640, type, sK1020: (nat > nat > $o) > (product_prod_nat_nat > nat) > (product_prod_nat_nat > int > $o) > (int > nat) > int).
% 28.44/7.23 thf(func_def_3641, type, sK1021: (nat > nat > $o) > (product_prod_nat_nat > nat) > (product_prod_nat_nat > int > $o) > (int > nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3642, type, sK1022: set_nat > set_int > nat > int).
% 28.44/7.23 thf(func_def_3643, type, sK1023: (int > set_nat) > (int > set_nat) > set_int > int).
% 28.44/7.23 thf(func_def_3644, type, sK1024: set_Pr1261947904930325089at_nat > nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3645, type, sK1025: set_nat > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3646, type, sK1026: (nat > set_nat) > set_nat > set_nat > nat).
% 28.44/7.23 thf(func_def_3647, type, sK1027: set_int > nat > int).
% 28.44/7.23 thf(func_def_3648, type, sK1028: set_nat > (int > set_nat) > set_int > int).
% 28.44/7.23 thf(func_def_3649, type, sK1029: (int > nat) > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3650, type, sK1030: (nat > set_nat) > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3651, type, sK1031: set_o > ($o > int) > ($o > int) > $o).
% 28.44/7.23 thf(func_def_3652, type, sK1032: ($o > $o) > product_unit).
% 28.44/7.23 thf(func_def_3653, type, sK1033: set_nat > (nat > nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3654, type, sK1034: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > product_unit) > product_unit > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3655, type, sK1035: (int > int > $o) > (int > int) > (int > int) > int > product_prod_int_int).
% 28.44/7.23 thf(func_def_3656, type, sK1036: (char > nat) > (nat > nat > $o) > (char > nat) > char > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3657, type, sK1037: (nat > nat) > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3658, type, sK1038: (int > rat) > (rat > int) > rat).
% 28.44/7.23 thf(func_def_3659, type, sK1039: (rat > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3660, type, sK1040: (nat > char) > char).
% 28.44/7.23 thf(func_def_3661, type, sK1041: char > (nat > char) > nat).
% 28.44/7.23 thf(func_def_3662, type, sK1042: nat > (nat > $o) > $o > nat).
% 28.44/7.23 thf(func_def_3663, type, sK1043: (nat > $o) > $o > nat).
% 28.44/7.23 thf(func_def_3664, type, sK1044: (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3665, type, sK1045: product_unit > set_int > (int > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3666, type, sK1046: product_unit > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3667, type, sK1047: set_o > ($o > nat > nat) > $o).
% 28.44/7.23 thf(func_def_3668, type, sK1048: set_o > ($o > nat > nat) > $o).
% 28.44/7.23 thf(func_def_3669, type, sK1049: ($o > $o) > ($o > $o) > (nat > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_3670, type, sK1050: ($o > $o) > ($o > $o) > (nat > $o) > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_3671, type, sK1051: set_nat > set_int > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3672, type, sK1052: set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3673, type, sK1053: (int > product_unit) > set_int > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3674, type, sK1054: $o > (char > $o) > char).
% 28.44/7.23 thf(func_def_3675, type, sK1055: (char > int) > (int > nat > $o) > (char > nat) > (int > nat > $o) > int).
% 28.44/7.23 thf(func_def_3676, type, sK1056: (char > int) > (int > nat > $o) > (char > nat) > (int > nat > $o) > nat).
% 28.44/7.23 thf(func_def_3677, type, sK1057: (num > num > $o) > (int > num) > (int > num) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3678, type, sK1058: (num > num > $o) > (int > num) > (int > num) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3679, type, sK1059: set_Pr4329608150637261639at_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3680, type, sK1060: (nat > $o > $o) > (char > $o) > (char > nat) > (nat > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3681, type, sK1061: (nat > $o > $o) > (char > $o) > (char > nat) > (nat > $o > $o) > nat).
% 28.44/7.23 thf(func_def_3682, type, sK1062: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3683, type, sK1063: nat > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3684, type, sK1064: ($o > set_o) > set_o > $o).
% 28.44/7.23 thf(func_def_3685, type, sK1065: (int > nat) > set_int > nat).
% 28.44/7.23 thf(func_def_3686, type, sK1066: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(func_def_3687, type, sK1067: set_int > nat > (int > nat) > int).
% 28.44/7.23 thf(func_def_3688, type, sK1068: (int > nat) > set_int > nat).
% 28.44/7.23 thf(func_def_3689, type, sK1069: produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3690, type, sK1070: produc3843707927480180839at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3691, type, sK1071: (produc3843707927480180839at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3692, type, sK1072: (produc3843707927480180839at_nat > $o) > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3693, type, sK1073: int > set_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3694, type, sK1074: product_unit > set_set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_3695, type, sK1075: set_o > (int > $o) > $o > set_int > set_int).
% 28.44/7.23 thf(func_def_3696, type, sK1076: set_o > (int > $o) > $o > set_int > int).
% 28.44/7.23 thf(func_def_3697, type, sK1077: product_unit > (product_unit > product_unit) > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3698, type, sK1078: set_se5479201105039950375at_nat > produc1319942482725812455at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3699, type, sK1079: (char > $o) > ($o > $o > $o) > $o).
% 28.44/7.23 thf(func_def_3700, type, sK1080: set_o > (nat > $o) > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_3701, type, sK1081: ($o > set_nat) > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3702, type, sK1082: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3703, type, sK1083: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3704, type, sK1084: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3705, type, sK1085: (int > set_int) > set_int > int).
% 28.44/7.23 thf(func_def_3706, type, sK1086: set_nat > (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3707, type, sK1087: nat > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3708, type, sK1088: $o > set_o > ($o > set_o) > $o).
% 28.44/7.23 thf(func_def_3709, type, sK1089: product_prod_nat_num > set_Pr6200539531224447659at_num > (num > num) > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3710, type, sK1090: product_prod_nat_num > set_Pr6200539531224447659at_num > (num > num) > (nat > nat) > num).
% 28.44/7.23 thf(func_def_3711, type, sK1091: set_Product_unit > product_unit > (product_unit > product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3712, type, sK1092: set_Product_unit > (product_unit > set_Product_unit) > product_unit).
% 28.44/7.23 thf(func_def_3713, type, sK1093: set_nat > (nat > $o) > $o).
% 28.44/7.23 thf(func_def_3714, type, sK1094: rat > set_nat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3715, type, sK1095: set_nat > (nat > rat) > set_rat > rat).
% 28.44/7.23 thf(func_def_3716, type, sK1096: set_int > (int > int) > set_int > set_int).
% 28.44/7.23 thf(func_def_3717, type, sK1097: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3718, type, sK1098: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_unit) > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3719, type, sK1099: (nat > nat > product_prod_nat_nat > $o) > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3720, type, sK1100: (nat > nat > product_prod_nat_nat > $o) > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3721, type, sK1101: (int > nat) > (int > nat) > (int > int) > int).
% 28.44/7.23 thf(func_def_3722, type, sK1102: product_prod_nat_num > (nat > num > $o) > nat).
% 28.44/7.23 thf(func_def_3723, type, sK1103: product_prod_nat_num > (nat > num > $o) > num).
% 28.44/7.23 thf(func_def_3724, type, sK1104: set_o > ($o > set_Product_unit) > $o).
% 28.44/7.23 thf(func_def_3725, type, sK1105: (code_integer > code_integer > code_integer) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > code_integer > code_integer).
% 28.44/7.23 thf(func_def_3726, type, sK1106: (nat > $o) > set_nat > $o).
% 28.44/7.23 thf(func_def_3727, type, sK1107: set_int > (nat > int) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3728, type, sK1108: ($o > set_int) > set_o > int > $o).
% 28.44/7.23 thf(func_def_3729, type, sK1109: (nat > product_prod_nat_nat) > (set_Pr1261947904930325089at_nat > $o) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3730, type, sK1110: (nat > product_prod_nat_nat) > (set_Pr1261947904930325089at_nat > $o) > set_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3731, type, sK1111: product_prod_nat_nat > (nat > nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3732, type, sK1112: product_prod_nat_nat > (nat > nat) > product_prod_nat_nat > nat).
% 28.44/7.23 thf(func_def_3733, type, sK1113: set_Product_unit > (product_unit > set_int) > product_unit).
% 28.44/7.23 thf(func_def_3734, type, sK1114: set_nat > (nat > set_nat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3735, type, sK1115: set_nat > (nat > set_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3736, type, sK1116: ($o > rat) > rat > set_o > $o).
% 28.44/7.23 thf(func_def_3737, type, sK1117: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 28.44/7.23 thf(func_def_3738, type, sK1118: product_unit > (nat > product_unit) > set_nat > nat).
% 28.44/7.23 thf(func_def_3739, type, sK1119: set_nat > set_int > nat > int).
% 28.44/7.23 thf(func_def_3740, type, sK1120: set_int > (int > set_nat) > int).
% 28.44/7.23 thf(func_def_3741, type, sK1121: set_Pr4329608150637261639at_nat > set_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3742, type, sK1122: (nat > nat) > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3743, type, sK1123: (nat > rat) > rat).
% 28.44/7.23 thf(func_def_3744, type, sK1124: rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3745, type, sK1125: product_unit > ($o > product_unit) > set_o > set_Product_unit > $o).
% 28.44/7.23 thf(func_def_3746, type, sK1126: product_unit > ($o > product_unit) > set_o > set_Product_unit > set_o).
% 28.44/7.23 thf(func_def_3747, type, sK1127: (nat > int) > set_nat > set_int > int).
% 28.44/7.23 thf(func_def_3748, type, sK1128: int > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3749, type, sK1129: product_prod_nat_nat > int > (nat > nat > set_int) > nat).
% 28.44/7.23 thf(func_def_3750, type, sK1130: product_prod_nat_nat > int > (nat > nat > set_int) > nat).
% 28.44/7.23 thf(func_def_3751, type, sK1131: set_int > (int > nat > nat) > int).
% 28.44/7.23 thf(func_def_3752, type, sK1132: set_int > (int > nat > nat) > int).
% 28.44/7.23 thf(func_def_3753, type, sK1133: set_o > ($o > int) > int > $o).
% 28.44/7.23 thf(func_def_3754, type, sK1134: (char > int) > (char > int) > (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3755, type, sK1135: (char > int) > (char > int) > (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3756, type, sK1136: (nat > int) > set_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3757, type, sK1137: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3758, type, sK1138: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3759, type, sK1139: (char > nat) > nat > char).
% 28.44/7.23 thf(func_def_3760, type, sK1140: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3761, type, sK1141: set_nat > set_nat > (nat > set_nat) > nat).
% 28.44/7.23 thf(func_def_3762, type, sK1142: ($o > set_nat) > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3763, type, sK1143: product_prod_nat_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3764, type, sK1144: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3765, type, sK1145: (int > int) > set_int > (int > int) > int).
% 28.44/7.23 thf(func_def_3766, type, sK1146: (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3767, type, sK1147: (int > int > $o) > (int > int > $o) > int).
% 28.44/7.23 thf(func_def_3768, type, sK1148: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3769, type, sK1149: (num > num > $o) > (num > num > $o) > num).
% 28.44/7.23 thf(func_def_3770, type, sK1150: int > (nat > num > set_int) > product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3771, type, sK1151: int > (nat > num > set_int) > product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_3772, type, sK1152: (rat > $o) > $o > rat).
% 28.44/7.23 thf(func_def_3773, type, sK1153: nat > ($o > set_nat) > set_o > $o).
% 28.44/7.23 thf(func_def_3774, type, sK1154: (rat > int) > int > rat).
% 28.44/7.23 thf(func_def_3775, type, sK1155: (nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3776, type, sK1156: product_prod_nat_nat > (nat > product_prod_nat_nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3777, type, sK1157: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3778, type, sK1158: (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_unit > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3779, type, sK1159: int > (int > int) > set_int > int).
% 28.44/7.23 thf(func_def_3780, type, sK1160: (int > int) > set_int > set_int > int).
% 28.44/7.23 thf(func_def_3781, type, sK1161: nat > (nat > int) > int > nat).
% 28.44/7.23 thf(func_def_3782, type, sK1162: (nat > int) > int > nat).
% 28.44/7.23 thf(func_def_3783, type, sK1163: ($o > $o > $o) > (rat > $o) > ($o > $o > $o) > (rat > $o) > $o).
% 28.44/7.23 thf(func_def_3784, type, sK1164: ($o > $o > $o) > (rat > $o) > ($o > $o > $o) > (rat > $o) > $o).
% 28.44/7.23 thf(func_def_3785, type, sK1165: set_Product_prod_o_o > set_o).
% 28.44/7.23 thf(func_def_3786, type, sK1166: $o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_3787, type, sK1167: set_o > set_Product_prod_o_o > $o).
% 28.44/7.23 thf(func_def_3788, type, sK1168: set_int > set_o > ($o > product_unit) > (int > product_unit) > $o).
% 28.44/7.23 thf(func_def_3789, type, sK1169: set_int > set_o > ($o > product_unit) > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3790, type, sK1170: set_int > (int > nat) > nat).
% 28.44/7.23 thf(func_def_3791, type, sK1171: ($o > set_Product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_3792, type, sK1172: set_int > set_nat > int > nat).
% 28.44/7.23 thf(func_def_3793, type, sK1173: set_int > (int > int) > set_nat > (nat > int) > int).
% 28.44/7.23 thf(func_def_3794, type, sK1174: product_prod_nat_nat > (nat > nat > set_o) > $o > nat).
% 28.44/7.23 thf(func_def_3795, type, sK1175: product_prod_nat_nat > (nat > nat > set_o) > $o > nat).
% 28.44/7.23 thf(func_def_3796, type, sK1176: (nat > nat) > set_nat > (nat > nat) > nat).
% 28.44/7.23 thf(func_def_3797, type, sK1177: rat > (nat > rat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3798, type, sK1178: set_int > (nat > product_unit) > set_nat > (int > product_unit) > nat).
% 28.44/7.23 thf(func_def_3799, type, sK1179: set_int > (nat > product_unit) > set_nat > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3800, type, sK1180: set_int > (int > $o) > int).
% 28.44/7.23 thf(func_def_3801, type, sK1181: nat > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_3802, type, sK1182: set_nat > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3803, type, sK1183: set_nat > set_nat > nat > nat).
% 28.44/7.23 thf(func_def_3804, type, sK1184: (int > int > set_nat) > product_prod_int_int > nat > int).
% 28.44/7.23 thf(func_def_3805, type, sK1185: (int > int > set_nat) > product_prod_int_int > nat > int).
% 28.44/7.23 thf(func_def_3806, type, sK1186: set_o > ($o > int) > int > $o).
% 28.44/7.23 thf(func_def_3807, type, sK1187: product_unit > (product_prod_nat_nat > product_unit) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3808, type, sK1188: ($o > product_unit) > ($o > product_unit) > set_o > set_o > $o).
% 28.44/7.23 thf(func_def_3809, type, sK1189: ($o > product_unit) > ($o > product_unit) > set_o > set_o > $o).
% 28.44/7.23 thf(func_def_3810, type, sK1190: (nat > $o) > set_int > (int > nat) > nat).
% 28.44/7.23 thf(func_def_3811, type, sK1191: (nat > int) > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3812, type, sK1192: code_integer > ($o > code_integer) > set_o > $o).
% 28.44/7.23 thf(func_def_3813, type, sK1193: (nat > set_int) > set_nat > int > nat).
% 28.44/7.23 thf(func_def_3814, type, sK1194: set_rat > (nat > rat) > set_nat > set_nat).
% 28.44/7.23 thf(func_def_3815, type, sK1195: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > set_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3816, type, sK1196: (nat > rat) > set_nat > rat).
% 28.44/7.23 thf(func_def_3817, type, sK1197: set_nat > (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3818, type, sK1198: set_nat > set_rat > nat > rat).
% 28.44/7.23 thf(func_def_3819, type, sK1199: (rat > int) > (rat > int) > (int > int > $o) > rat > product_prod_int_int).
% 28.44/7.23 thf(func_def_3820, type, sK1200: (nat > int) > (nat > int) > set_nat > nat).
% 28.44/7.23 thf(func_def_3821, type, sK1201: set_nat > (nat > product_prod_nat_nat) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3822, type, sK1202: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3823, type, sK1203: rat > (nat > rat) > nat).
% 28.44/7.23 thf(func_def_3824, type, sK1204: (product_prod_nat_nat > set_nat) > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3825, type, sK1205: set_int > (int > set_nat) > set_nat > int).
% 28.44/7.23 thf(func_def_3826, type, sK1206: (nat > nat) > set_nat > nat).
% 28.44/7.23 thf(func_def_3827, type, sK1207: product_prod_nat_num > nat).
% 28.44/7.23 thf(func_def_3828, type, sK1208: product_prod_nat_num > num).
% 28.44/7.23 thf(func_def_3829, type, sK1209: set_nat > (product_unit > nat) > nat > set_Product_unit > product_unit).
% 28.44/7.23 thf(func_def_3830, type, sK1210: set_nat > (product_unit > nat) > nat > set_Product_unit > set_Product_unit).
% 28.44/7.23 thf(func_def_3831, type, sK1211: set_Pr4329608150637261639at_nat > set_nat > (produc3843707927480180839at_nat > set_nat) > produc3843707927480180839at_nat).
% 28.44/7.23 thf(func_def_3832, type, sK1212: (int > nat) > (int > nat) > set_int > int).
% 28.44/7.23 thf(func_def_3833, type, sK1213: ($o > set_nat) > set_o > set_nat > $o).
% 28.44/7.23 thf(func_def_3834, type, sK1214: set_Pr1261947904930325089at_nat > (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 28.44/7.23 thf(func_def_3835, type, sK1215: set_int > product_unit > (int > product_unit) > int).
% 28.44/7.23 thf(func_def_3836, type, sK1216: set_Pr7459493094073627847at_nat > set_Pr4329608150637261639at_nat).
% 28.44/7.23 thf(func_def_3837, type, sK1217: ($o > product_unit) > ($o > product_unit) > set_o > $o).
% 28.44/7.23 thf(func_def_3838, type, sK1218: set_nat > (nat > nat) > (nat > $o) > nat).
% 28.44/7.23 thf(func_def_3839, type, sK1219: (nat > int) > set_nat > (nat > int) > nat).
% 28.44/7.23 thf(func_def_3841, type, ph1221: !>[X0: $tType]:(X0)).
% 28.44/7.23 thf(func_def_3842, type, sK1222: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > nat).
% 28.44/7.23 thf(f31075,plain,(
% 28.44/7.23 $false),
% 28.44/7.23 inference(avatar_sat_refutation,[status(thm)],[f26897,f26902,f30799,f31074])).
% 28.44/7.23 thf(f31074,plain,(
% 28.44/7.23 spl1220_26 | ~spl1220_28),
% 28.44/7.23 inference(avatar_contradiction_clause,[status(thm)],[f31073])).
% 28.44/7.23 thf(f31073,plain,(
% 28.44/7.23 $false | (spl1220_26 | ~spl1220_28)),
% 28.44/7.23 inference(subsumption_resolution,[status(thm)],[f31059,f26888])).
% 28.44/7.23 thf(f26888,plain,(
% 28.44/7.23 (h2 != (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) | spl1220_26),
% 28.44/7.23 inference(avatar_component_clause,[status(thm)],[f26886])).
% 28.44/7.23 thf(f26886,definition,(
% 28.44/7.23 spl1220_26 <=> (h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 introduced(definition,[new_symbols(naming,[spl1220_26])],[avatar_definition])).
% 28.44/7.23 thf(f31059,plain,(
% 28.44/7.23 (h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) | ~spl1220_28),
% 28.44/7.23 inference(trivial_inequality_removal,[status(thm)],[f31044])).
% 28.44/7.23 thf(f31044,plain,(
% 28.44/7.23 ($true != $true) | (h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) | ~spl1220_28),
% 28.44/7.23 inference(superposition,[status(thm)],[f27028,f30834])).
% 28.44/7.23 thf(f30834,plain,(
% 28.44/7.23 ((heap_effect_ref_a @ (ref_a2 @ x) @ h @ (produc1126150082675451753t_unit @ (alloc_a @ x @ h)) @ r) = $true) | ~spl1220_28),
% 28.44/7.23 inference(forward_demodulation,[status(thm)],[f30833,f26947])).
% 28.44/7.23 thf(f26947,plain,(
% 28.44/7.23 ( ! [X1 : a] : (((ref_a2 @ X1) = (heap_heap_ref_a @ (alloc_a @ X1)))) )),
% 28.44/7.23 inference(beta_eta_normalization,[status(thm)],[f26946])).
% 28.44/7.23 thf(f26946,plain,(
% 28.44/7.23 ( ! [X1 : a] : (((ref_a2 @ X1) = ((^[Y0 : a]: (heap_heap_ref_a @ (alloc_a @ Y0))) @ X1))) )),
% 28.44/7.23 inference(argument_congruence,[status(thm)],[f19965])).
% 28.44/7.23 thf(f19965,plain,(
% 28.44/7.23 (ref_a2 = (^[Y0 : a]: (heap_heap_ref_a @ (alloc_a @ Y0))))),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f10389])).
% 28.44/7.23 thf(f10389,plain,(
% 28.44/7.23 (ref_a2 = (^[Y0 : a]: (heap_heap_ref_a @ (alloc_a @ Y0))))),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f10388])).
% 28.44/7.23 thf(f10388,plain,(
% 28.44/7.23 ((^[X0 : a] : (heap_heap_ref_a @ (alloc_a @ X0))) = ref_a2)),
% 28.44/7.23 inference(rectify,[status(thm)],[f24])).
% 28.44/7.23 thf(f24,axiom,(
% 28.44/7.23 ((^[X22 : a] : (heap_heap_ref_a @ (alloc_a @ X22))) = ref_a2)),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_23_ref__def)).
% 28.44/7.23 thf(f30833,plain,(
% 28.44/7.23 ($true = (heap_effect_ref_a @ (heap_heap_ref_a @ (alloc_a @ x)) @ h @ (produc1126150082675451753t_unit @ (alloc_a @ x @ h)) @ r)) | ~spl1220_28),
% 28.44/7.23 inference(superposition,[status(thm)],[f25914,f26895])).
% 28.44/7.23 thf(f26895,plain,(
% 28.44/7.23 (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h))) | ~spl1220_28),
% 28.44/7.23 inference(avatar_component_clause,[status(thm)],[f26894])).
% 28.44/7.23 thf(f26894,definition,(
% 28.44/7.23 spl1220_28 <=> (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 introduced(definition,[new_symbols(naming,[spl1220_28])],[avatar_definition])).
% 28.44/7.23 thf(f25914,plain,(
% 28.44/7.23 ( ! [X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X1 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ (produc1126150082675451753t_unit @ (X3 @ X1)) @ (produc473321116828791851t_unit @ (X3 @ X1))) = $true)) )),
% 28.44/7.23 inference(equality_resolution,[status(thm)],[f25913])).
% 28.44/7.23 thf(f25913,plain,(
% 28.44/7.23 ( ! [X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X1 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ (produc473321116828791851t_unit @ (X3 @ X1))) = $true) | ((produc1126150082675451753t_unit @ (X3 @ X1)) != X2)) )),
% 28.44/7.23 inference(equality_resolution,[status(thm)],[f23922])).
% 28.44/7.23 thf(f23922,plain,(
% 28.44/7.23 ( ! [X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X0 : ref_a,X1 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ X0) = $true) | ((produc473321116828791851t_unit @ (X3 @ X1)) != X0) | ((produc1126150082675451753t_unit @ (X3 @ X1)) != X2)) )),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f13403])).
% 28.44/7.23 thf(f13403,plain,(
% 28.44/7.23 ! [X0 : ref_a,X1 : heap_e7401611519738050253t_unit,X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : (((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ X0) = $true) | ((produc473321116828791851t_unit @ (X3 @ X1)) != X0) | ((produc1126150082675451753t_unit @ (X3 @ X1)) != X2))),
% 28.44/7.23 inference(flattening,[status(thm)],[f13402])).
% 28.44/7.23 thf(f13402,plain,(
% 28.44/7.23 ! [X0 : ref_a,X1 : heap_e7401611519738050253t_unit,X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : ((((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ X0) = $true) | ((produc473321116828791851t_unit @ (X3 @ X1)) != X0)) | ((produc1126150082675451753t_unit @ (X3 @ X1)) != X2))),
% 28.44/7.23 inference(ennf_transformation,[status(thm)],[f5338])).
% 28.44/7.23 thf(f5338,plain,(
% 28.44/7.23 ! [X0 : ref_a,X1 : heap_e7401611519738050253t_unit,X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : (((produc1126150082675451753t_unit @ (X3 @ X1)) = X2) => (((produc473321116828791851t_unit @ (X3 @ X1)) = X0) => ((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ X0) = $true)))),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f5337])).
% 28.44/7.23 thf(f5337,plain,(
% 28.44/7.23 ! [X0 : ref_a,X1 : heap_e7401611519738050253t_unit,X2 : heap_e7401611519738050253t_unit,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : (((produc1126150082675451753t_unit @ (X3 @ X1)) = X2) => (((produc473321116828791851t_unit @ (X3 @ X1)) = X0) => (heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X1 @ X2 @ X0)))),
% 28.44/7.23 inference(rectify,[status(thm)],[f150])).
% 28.44/7.23 thf(f150,axiom,(
% 28.44/7.23 ! [X16 : ref_a,X12 : heap_e7401611519738050253t_unit,X18 : heap_e7401611519738050253t_unit,X19 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : (((produc1126150082675451753t_unit @ (X19 @ X12)) = X18) => (((produc473321116828791851t_unit @ (X19 @ X12)) = X16) => (heap_effect_ref_a @ (heap_heap_ref_a @ X19) @ X12 @ X18 @ X16)))),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_149_effect__heapI)).
% 28.44/7.23 thf(f27028,plain,(
% 28.44/7.23 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : ref_a] : (($true != (heap_effect_ref_a @ (ref_a2 @ x) @ h @ X0 @ X1)) | (h2 = X0)) )),
% 28.44/7.23 inference(trivial_inequality_removal,[status(thm)],[f27027])).
% 28.44/7.23 thf(f27027,plain,(
% 28.44/7.23 ( ! [X0 : heap_e7401611519738050253t_unit,X1 : ref_a] : ((h2 = X0) | ($true != $true) | ($true != (heap_effect_ref_a @ (ref_a2 @ x) @ h @ X0 @ X1))) )),
% 28.44/7.23 inference(superposition,[status(thm)],[f21964,f24381])).
% 28.44/7.23 thf(f24381,plain,(
% 28.44/7.23 ((heap_effect_ref_a @ (ref_a2 @ x) @ h @ h2 @ r) = $true)),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f6686])).
% 28.44/7.23 thf(f6686,plain,(
% 28.44/7.23 ((heap_effect_ref_a @ (ref_a2 @ x) @ h @ h2 @ r) = $true)),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f6685])).
% 28.44/7.23 thf(f6685,plain,(
% 28.44/7.23 (heap_effect_ref_a @ (ref_a2 @ x) @ h @ h2 @ r)),
% 28.44/7.23 inference(rectify,[status(thm)],[f2])).
% 28.44/7.23 thf(f2,axiom,(
% 28.44/7.23 (heap_effect_ref_a @ (ref_a2 @ x) @ h @ h2 @ r)),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_1_assms)).
% 28.44/7.23 thf(f21964,plain,(
% 28.44/7.23 ( ! [X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X0 : heap_e7401611519738050253t_unit,X1 : heap_Heap_ref_a,X4 : ref_a,X5 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ X1 @ X2 @ X5 @ X4) != $true) | ((heap_effect_ref_a @ X1 @ X2 @ X0 @ X3) != $true) | (X0 = X5)) )),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f14332])).
% 28.44/7.23 thf(f14332,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_Heap_ref_a,X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X4 : ref_a,X5 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ X1 @ X2 @ X5 @ X4) != $true) | (X0 = X5) | ((heap_effect_ref_a @ X1 @ X2 @ X0 @ X3) != $true))),
% 28.44/7.23 inference(flattening,[status(thm)],[f14331])).
% 28.44/7.23 thf(f14331,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_Heap_ref_a,X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X4 : ref_a,X5 : heap_e7401611519738050253t_unit] : (((X0 = X5) | ((heap_effect_ref_a @ X1 @ X2 @ X0 @ X3) != $true)) | ((heap_effect_ref_a @ X1 @ X2 @ X5 @ X4) != $true))),
% 28.44/7.23 inference(ennf_transformation,[status(thm)],[f11037])).
% 28.44/7.23 thf(f11037,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_Heap_ref_a,X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X4 : ref_a,X5 : heap_e7401611519738050253t_unit] : (((heap_effect_ref_a @ X1 @ X2 @ X5 @ X4) = $true) => (((heap_effect_ref_a @ X1 @ X2 @ X0 @ X3) = $true) => (X0 = X5)))),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f11036])).
% 28.44/7.23 thf(f11036,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_Heap_ref_a,X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X4 : ref_a,X5 : heap_e7401611519738050253t_unit] : ((heap_effect_ref_a @ X1 @ X2 @ X5 @ X4) => ((heap_effect_ref_a @ X1 @ X2 @ X0 @ X3) => (X0 = X5)))),
% 28.44/7.23 inference(rectify,[status(thm)],[f184])).
% 28.44/7.23 thf(f184,axiom,(
% 28.44/7.23 ! [X43 : heap_e7401611519738050253t_unit,X19 : heap_Heap_ref_a,X12 : heap_e7401611519738050253t_unit,X28 : ref_a,X27 : ref_a,X18 : heap_e7401611519738050253t_unit] : ((heap_effect_ref_a @ X19 @ X12 @ X18 @ X27) => ((heap_effect_ref_a @ X19 @ X12 @ X43 @ X28) => (X18 = X43)))),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_183_effect__deterministic_I2_J)).
% 28.44/7.23 thf(f30799,plain,(
% 28.44/7.23 spl1220_28),
% 28.44/7.23 inference(avatar_split_clause,[status(thm)],[f30797,f26894])).
% 28.44/7.23 thf(f30797,plain,(
% 28.44/7.23 (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 inference(trivial_inequality_removal,[status(thm)],[f30783])).
% 28.44/7.23 thf(f30783,plain,(
% 28.44/7.23 ($true != $true) | (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 inference(superposition,[status(thm)],[f27921,f24381])).
% 28.44/7.23 thf(f27921,plain,(
% 28.44/7.23 ( ! [X2 : heap_e7401611519738050253t_unit,X3 : ref_a,X0 : a,X1 : heap_e7401611519738050253t_unit] : (($true != (heap_effect_ref_a @ (ref_a2 @ X0) @ X1 @ X2 @ X3)) | ((produc473321116828791851t_unit @ (alloc_a @ X0 @ X1)) = X3)) )),
% 28.44/7.23 inference(superposition,[status(thm)],[f21547,f26947])).
% 28.44/7.23 thf(f21547,plain,(
% 28.44/7.23 ( ! [X2 : ref_a,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit,X0 : heap_e7401611519738050253t_unit,X1 : heap_e7401611519738050253t_unit] : (($true != (heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X0 @ X1 @ X2)) | ((produc473321116828791851t_unit @ (X3 @ X0)) = X2)) )),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f14497])).
% 28.44/7.23 thf(f14497,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_e7401611519738050253t_unit,X2 : ref_a,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : ((((produc1126150082675451753t_unit @ (X3 @ X0)) = X1) & ((produc473321116828791851t_unit @ (X3 @ X0)) = X2)) | ($true != (heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X0 @ X1 @ X2)))),
% 28.44/7.23 inference(ennf_transformation,[status(thm)],[f6334])).
% 28.44/7.23 thf(f6334,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_e7401611519738050253t_unit,X2 : ref_a,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : (($true = (heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X0 @ X1 @ X2)) => ~(((produc1126150082675451753t_unit @ (X3 @ X0)) = X1) => ((produc473321116828791851t_unit @ (X3 @ X0)) != X2)))),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f6333])).
% 28.44/7.23 thf(f6333,plain,(
% 28.44/7.23 ! [X0 : heap_e7401611519738050253t_unit,X1 : heap_e7401611519738050253t_unit,X2 : ref_a,X3 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : ((heap_effect_ref_a @ (heap_heap_ref_a @ X3) @ X0 @ X1 @ X2) => ~(((produc1126150082675451753t_unit @ (X3 @ X0)) = X1) => ((produc473321116828791851t_unit @ (X3 @ X0)) != X2)))),
% 28.44/7.23 inference(rectify,[status(thm)],[f149])).
% 28.44/7.23 thf(f149,axiom,(
% 28.44/7.23 ! [X12 : heap_e7401611519738050253t_unit,X18 : heap_e7401611519738050253t_unit,X16 : ref_a,X19 : heap_e7401611519738050253t_unit > produc7812382424243267045t_unit] : ((heap_effect_ref_a @ (heap_heap_ref_a @ X19) @ X12 @ X18 @ X16) => ~(((produc1126150082675451753t_unit @ (X19 @ X12)) = X18) => ((produc473321116828791851t_unit @ (X19 @ X12)) != X16)))),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_148_effect__heapE)).
% 28.44/7.23 thf(f26902,plain,(
% 28.44/7.23 ~spl1220_27),
% 28.44/7.23 inference(avatar_split_clause,[status(thm)],[f21552,f26890])).
% 28.44/7.23 thf(f26890,definition,(
% 28.44/7.23 spl1220_27 <=> (thesis = $true)),
% 28.44/7.23 introduced(definition,[new_symbols(naming,[spl1220_27])],[avatar_definition])).
% 28.44/7.23 thf(f21552,plain,(
% 28.44/7.23 (thesis != $true)),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f11980])).
% 28.44/7.23 thf(f11980,plain,(
% 28.44/7.23 (thesis != $true)),
% 28.44/7.23 inference(flattening,[status(thm)],[f9695])).
% 28.44/7.23 thf(f9695,plain,(
% 28.44/7.23 ~(thesis = $true)),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f9694])).
% 28.44/7.23 thf(f9694,plain,(
% 28.44/7.23 ~thesis),
% 28.44/7.23 inference(rectify,[status(thm)],[f4331])).
% 28.44/7.23 thf(f4331,negated_conjecture,(
% 28.44/7.23 ~thesis),
% 28.44/7.23 inference(negated_conjecture,[status(cth)],[f4330])).
% 28.44/7.23 thf(f4330,conjecture,(
% 28.44/7.23 thesis),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',conj_1)).
% 28.44/7.23 thf(f26897,plain,(
% 28.44/7.23 ~spl1220_26 | spl1220_27 | ~spl1220_28),
% 28.44/7.23 inference(avatar_split_clause,[status(thm)],[f24204,f26894,f26890,f26886])).
% 28.44/7.23 thf(f24204,plain,(
% 28.44/7.23 (r != (produc473321116828791851t_unit @ (alloc_a @ x @ h))) | (h2 != (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) | (thesis = $true)),
% 28.44/7.23 inference(cnf_transformation,[status(thm)],[f14477])).
% 28.44/7.23 thf(f14477,plain,(
% 28.44/7.23 (r != (produc473321116828791851t_unit @ (alloc_a @ x @ h))) | (thesis = $true) | (h2 != (produc1126150082675451753t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 inference(flattening,[status(thm)],[f14476])).
% 28.44/7.23 thf(f14476,plain,(
% 28.44/7.23 ((thesis = $true) | (h2 != (produc1126150082675451753t_unit @ (alloc_a @ x @ h)))) | (r != (produc473321116828791851t_unit @ (alloc_a @ x @ h)))),
% 28.44/7.23 inference(ennf_transformation,[status(thm)],[f6624])).
% 28.44/7.23 thf(f6624,plain,(
% 28.44/7.23 (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h))) => ((h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) => (thesis = $true))),
% 28.44/7.23 inference(fool_elimination,[status(thm)],[f6623])).
% 28.44/7.23 thf(f6623,plain,(
% 28.44/7.23 (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h))) => ((h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) => thesis)),
% 28.44/7.23 inference(rectify,[status(thm)],[f1])).
% 28.44/7.23 thf(f1,axiom,(
% 28.44/7.23 (r = (produc473321116828791851t_unit @ (alloc_a @ x @ h))) => ((h2 = (produc1126150082675451753t_unit @ (alloc_a @ x @ h))) => thesis)),
% 28.44/7.23 file('/export/starexec/sandbox2/tmp/tmp.MANeLcuenr/DTF2THF_14919.p',fact_0_that)).
% 28.44/7.23 % SZS output end Proof for DTF2THF_14919
% 28.44/7.23 % (15554)------------------------------
% 28.44/7.23 % (15554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.44/7.23 % (15554)Termination reason: Refutation
% 28.44/7.23
% 28.44/7.23 % (15554)Memory used [KB]: 35180
% 28.44/7.23 % (15554)Time elapsed: 1.260 s
% 28.44/7.23 % (15554)Instructions burned: 3950 (million)
% 28.44/7.23 % (15554)------------------------------
% 28.44/7.23 % (15554)------------------------------
% 28.44/7.23 % (15193)Success in time 3.224 s
%------------------------------------------------------------------------------