%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP036^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 08:55:02 AM UTC 2026
% Result : Theorem 3.14s 1.73s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 238 ( 11 ~; 3 |; 4 &; 220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 22 ( 21 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 196 ( 193 usr; 15 con; 0-4 aty)
% Number of variables : 6 ( 0 ^; 2 !; 4 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1389752855real_c: $tType ).
thf(type_def_6,type,
finite1398487019real_c: $tType ).
thf(type_def_7,type,
set_Su1783761653um_b_c: $tType ).
thf(type_def_9,type,
set_Sum_sum_c_c: $tType ).
thf(type_def_10,type,
set_Pr754230471real_c: $tType ).
thf(type_def_11,type,
produc190496183real_c: $tType ).
thf(type_def_12,type,
hp_a_b_c: $tType ).
thf(type_def_13,type,
denota231621370t_unit: $tType ).
thf(type_def_14,type,
produc640052711real_c: $tType ).
thf(type_def_15,type,
produc1360640805um_b_c: $tType ).
thf(type_def_16,type,
produc793920321um_c_c: $tType ).
thf(type_def_17,type,
produc1415638375um_b_c: $tType ).
thf(type_def_18,type,
produc1573491071um_c_c: $tType ).
thf(type_def_19,type,
produc1470506001real_c: $tType ).
thf(type_def_20,type,
produc777402865um_c_c: $tType ).
thf(type_def_21,type,
produc263671631um_b_c: $tType ).
thf(type_def_22,type,
produc214722967um_c_c: $tType ).
thf(type_def_23,type,
set_Pr242060487real_c: $tType ).
thf(type_def_24,type,
produc1037099239real_c: $tType ).
thf(type_def_25,type,
sum_su737395349um_b_c: $tType ).
thf(type_def_26,type,
sum_sum_c_c: $tType ).
thf(func_def_0,type,
set_Pr242060487real_c: $tType ).
thf(func_def_1,type,
produc1037099239real_c: $tType ).
thf(func_def_2,type,
set_Pr754230471real_c: $tType ).
thf(func_def_3,type,
produc640052711real_c: $tType ).
thf(func_def_4,type,
produc1360640805um_b_c: $tType ).
thf(func_def_5,type,
produc1470506001real_c: $tType ).
thf(func_def_6,type,
produc793920321um_c_c: $tType ).
thf(func_def_7,type,
produc777402865um_c_c: $tType ).
thf(func_def_8,type,
produc1415638375um_b_c: $tType ).
thf(func_def_9,type,
set_Pr1389752855real_c: $tType ).
thf(func_def_10,type,
produc263671631um_b_c: $tType ).
thf(func_def_11,type,
produc1573491071um_c_c: $tType ).
thf(func_def_12,type,
produc190496183real_c: $tType ).
thf(func_def_13,type,
produc214722967um_c_c: $tType ).
thf(func_def_14,type,
denota231621370t_unit: $tType ).
thf(func_def_15,type,
set_Su1783761653um_b_c: $tType ).
thf(func_def_16,type,
sum_su737395349um_b_c: $tType ).
thf(func_def_17,type,
finite1398487019real_c: $tType ).
thf(func_def_18,type,
set_Sum_sum_c_c: $tType ).
thf(func_def_19,type,
hp_a_b_c: $tType ).
thf(func_def_20,type,
sum_sum_c_c: $tType ).
thf(func_def_21,type,
bNF_Ca318582436um_b_c: set_Pr1389752855real_c > ( finite1398487019real_c > set_Su1783761653um_b_c ) > $o ).
thf(func_def_22,type,
bNF_Ca1693016812um_c_c: set_Pr1389752855real_c > ( finite1398487019real_c > set_Sum_sum_c_c ) > $o ).
thf(func_def_23,type,
bNF_Ca419199138um_b_c: set_Pr754230471real_c > ( produc190496183real_c > set_Su1783761653um_b_c ) > $o ).
thf(func_def_24,type,
bNF_Ca1667803246um_c_c: set_Pr754230471real_c > ( produc190496183real_c > set_Sum_sum_c_c ) > $o ).
thf(func_def_25,type,
coinci354700372_a_b_c: hp_a_b_c > denota231621370t_unit > denota231621370t_unit > $o ).
thf(func_def_26,type,
coinci1852866155_a_b_c: hp_a_b_c > $o ).
thf(func_def_27,type,
coinci772602909_a_b_c: hp_a_b_c > denota231621370t_unit > $o ).
thf(func_def_28,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(func_def_29,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(func_def_30,type,
denota904684656_a_b_c: denota231621370t_unit > hp_a_b_c > set_Pr754230471real_c ).
thf(func_def_31,type,
sup_su2141622551real_c: finite1398487019real_c > finite1398487019real_c > finite1398487019real_c ).
thf(func_def_32,type,
sup_su1639086475real_c: produc190496183real_c > produc190496183real_c > produc190496183real_c ).
thf(func_def_33,type,
sup_su1399591867real_c: produc640052711real_c > produc640052711real_c > produc640052711real_c ).
thf(func_def_34,type,
sup_su1009753337um_b_c: produc1360640805um_b_c > produc1360640805um_b_c > produc1360640805um_b_c ).
thf(func_def_35,type,
sup_su1347303021um_c_c: produc793920321um_c_c > produc793920321um_c_c > produc793920321um_c_c ).
thf(func_def_36,type,
sup_su1580927803um_b_c: produc1415638375um_b_c > produc1415638375um_b_c > produc1415638375um_b_c ).
thf(func_def_37,type,
sup_su1731217579um_c_c: produc1573491071um_c_c > produc1573491071um_c_c > produc1573491071um_c_c ).
thf(func_def_38,type,
sup_su2023888701real_c: produc1470506001real_c > produc1470506001real_c > produc1470506001real_c ).
thf(func_def_39,type,
sup_su505296157um_c_c: produc777402865um_c_c > produc777402865um_c_c > produc777402865um_c_c ).
thf(func_def_40,type,
sup_su421398139um_b_c: produc263671631um_b_c > produc263671631um_b_c > produc263671631um_b_c ).
thf(func_def_41,type,
sup_su1672617323um_c_c: produc214722967um_c_c > produc214722967um_c_c > produc214722967um_c_c ).
thf(func_def_42,type,
sup_su1857314283real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > set_Pr1389752855real_c ).
thf(func_def_43,type,
sup_su588839579real_c: set_Pr754230471real_c > set_Pr754230471real_c > set_Pr754230471real_c ).
thf(func_def_44,type,
sup_su880588443real_c: set_Pr242060487real_c > set_Pr242060487real_c > set_Pr242060487real_c ).
thf(func_def_45,type,
sup_su1968964297um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ).
thf(func_def_46,type,
sup_su1349021703um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_47,type,
ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o ).
thf(func_def_48,type,
ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o ).
thf(func_def_49,type,
ord_le652477831real_c: produc640052711real_c > produc640052711real_c > $o ).
thf(func_def_50,type,
ord_le907560199um_b_c: produc1415638375um_b_c > produc1415638375um_b_c > $o ).
thf(func_def_51,type,
ord_le1852514783um_c_c: produc1573491071um_c_c > produc1573491071um_c_c > $o ).
thf(func_def_52,type,
ord_le542695343um_b_c: produc263671631um_b_c > produc263671631um_b_c > $o ).
thf(func_def_53,type,
ord_le684454199um_c_c: produc214722967um_c_c > produc214722967um_c_c > $o ).
thf(func_def_54,type,
ord_le977353143real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > $o ).
thf(func_def_55,type,
ord_le1988344935real_c: set_Pr754230471real_c > set_Pr754230471real_c > $o ).
thf(func_def_56,type,
ord_le100418663real_c: set_Pr242060487real_c > set_Pr242060487real_c > $o ).
thf(func_def_57,type,
ord_le929608341um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > $o ).
thf(func_def_58,type,
ord_le1772180283um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > $o ).
thf(func_def_59,type,
order_365181262um_b_c: ( set_Su1783761653um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_60,type,
order_1776530114um_c_c: ( set_Sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
thf(func_def_61,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_62,type,
produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
thf(func_def_63,type,
produc2010919061um_b_c: produc190496183real_c > set_Su1783761653um_b_c > produc1360640805um_b_c ).
thf(func_def_64,type,
produc639456571um_c_c: produc190496183real_c > set_Sum_sum_c_c > produc793920321um_c_c ).
thf(func_def_65,type,
produc544496471real_c: produc640052711real_c > produc640052711real_c > produc1037099239real_c ).
thf(func_def_66,type,
produc754249687um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > produc1415638375um_b_c ).
thf(func_def_67,type,
produc616453753um_c_c: set_Su1783761653um_b_c > set_Sum_sum_c_c > produc1573491071um_c_c ).
thf(func_def_68,type,
produc439851843real_c: set_Sum_sum_c_c > produc190496183real_c > produc1470506001real_c ).
thf(func_def_69,type,
produc1333497635um_c_c: set_Sum_sum_c_c > produc214722967um_c_c > produc777402865um_c_c ).
thf(func_def_70,type,
produc919784577um_b_c: set_Sum_sum_c_c > set_Su1783761653um_b_c > produc263671631um_b_c ).
thf(func_def_71,type,
produc1439061071um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > produc214722967um_c_c ).
thf(func_def_72,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_73,type,
produc876006723real_c: produc640052711real_c > produc190496183real_c ).
thf(func_def_74,type,
produc1961869763um_b_c: produc1415638375um_b_c > set_Su1783761653um_b_c ).
thf(func_def_75,type,
produc1455464333um_c_c: produc1573491071um_c_c > set_Su1783761653um_b_c ).
thf(func_def_76,type,
produc1758795157um_b_c: produc263671631um_b_c > set_Sum_sum_c_c ).
thf(func_def_77,type,
produc1983230011um_c_c: produc214722967um_c_c > set_Sum_sum_c_c ).
thf(func_def_78,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_79,type,
produc415593093real_c: produc640052711real_c > produc190496183real_c ).
thf(func_def_80,type,
produc932426501um_b_c: produc1415638375um_b_c > set_Su1783761653um_b_c ).
thf(func_def_81,type,
produc890433227um_c_c: produc1573491071um_c_c > set_Sum_sum_c_c ).
thf(func_def_82,type,
produc1193764051um_b_c: produc263671631um_b_c > set_Su1783761653um_b_c ).
thf(func_def_83,type,
produc1132019837um_c_c: produc214722967um_c_c > set_Sum_sum_c_c ).
thf(func_def_84,type,
produc704157711real_c: produc190496183real_c > produc190496183real_c ).
thf(func_def_85,type,
produc350724343real_c: produc640052711real_c > produc640052711real_c ).
thf(func_def_86,type,
collec1126017874real_c: ( produc640052711real_c > $o ) > set_Pr754230471real_c ).
thf(func_def_87,type,
collec2086029184um_b_c: ( sum_su737395349um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_88,type,
collect_Sum_sum_c_c: ( sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
thf(func_def_89,type,
static_FVP_a_b_c: hp_a_b_c > set_Sum_sum_c_c ).
thf(func_def_90,type,
static_MBV_a_b_c: hp_a_b_c > set_Sum_sum_c_c ).
thf(func_def_91,type,
static_SIGP_a_b_c: hp_a_b_c > set_Su1783761653um_b_c ).
thf(func_def_92,type,
choice_a_b_c: hp_a_b_c > hp_a_b_c > hp_a_b_c ).
thf(func_def_93,type,
hpsafe_a_b_c: hp_a_b_c > $o ).
thf(func_def_94,type,
same_f1974156740real_c: ( finite1398487019real_c > $o ) > ( finite1398487019real_c > set_Pr1389752855real_c ) > set_Pr754230471real_c ).
thf(func_def_95,type,
same_f598810924real_c: ( produc190496183real_c > $o ) > ( produc190496183real_c > set_Pr754230471real_c ) > set_Pr242060487real_c ).
thf(func_def_96,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(func_def_97,type,
member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
thf(func_def_98,type,
member616151824real_c: produc1037099239real_c > set_Pr242060487real_c > $o ).
thf(func_def_99,type,
member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
thf(func_def_100,type,
member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
thf(func_def_101,type,
i: denota231621370t_unit ).
thf(func_def_102,type,
j: denota231621370t_unit ).
thf(func_def_103,type,
v: set_Sum_sum_c_c ).
thf(func_def_104,type,
mu: produc190496183real_c ).
thf(func_def_105,type,
mu2: finite1398487019real_c ).
thf(func_def_106,type,
mu3: finite1398487019real_c ).
thf(func_def_107,type,
nu_1: finite1398487019real_c ).
thf(func_def_108,type,
nu_12: finite1398487019real_c ).
thf(func_def_109,type,
nu_2: finite1398487019real_c ).
thf(func_def_110,type,
nu_22: finite1398487019real_c ).
thf(func_def_111,type,
a: hp_a_b_c ).
thf(func_def_112,type,
b: hp_a_b_c ).
thf(func_def_130,type,
sK0: ( set_Su1783761653um_b_c > $o ) > ( set_Su1783761653um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_131,type,
sK1: set_Su1783761653um_b_c > ( set_Su1783761653um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_132,type,
sK2: set_Su1783761653um_b_c > set_Su1783761653um_b_c > sum_su737395349um_b_c ).
thf(func_def_133,type,
sK3: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_134,type,
sK4: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_135,type,
sK5: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_136,type,
sK6: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_137,type,
sK7: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_138,type,
sK8: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_139,type,
sK9: produc640052711real_c > produc190496183real_c ).
thf(func_def_140,type,
sK10: produc640052711real_c > produc190496183real_c ).
thf(func_def_141,type,
sK11: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_142,type,
sK12: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_143,type,
sK13: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_144,type,
sK14: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_145,type,
sK15: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_146,type,
sK16: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_147,type,
sK17: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_148,type,
sK18: produc640052711real_c > produc190496183real_c ).
thf(func_def_149,type,
sK19: produc640052711real_c > produc190496183real_c ).
thf(func_def_150,type,
sK20: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_151,type,
sK21: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_152,type,
sK22: set_Su1783761653um_b_c > ( set_Su1783761653um_b_c > $o ) > set_Su1783761653um_b_c ).
thf(func_def_153,type,
sK23: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_154,type,
sK24: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_155,type,
sK25: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_156,type,
sK26: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_157,type,
sK27: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_158,type,
sK28: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_159,type,
sK29: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_160,type,
sK30: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_161,type,
sK31: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_162,type,
sK32: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_163,type,
sK33: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_164,type,
sK34: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_165,type,
sK35: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_166,type,
sK36: ( set_Su1783761653um_b_c > set_Sum_sum_c_c ) > set_Su1783761653um_b_c ).
thf(func_def_167,type,
sK37: set_Pr242060487real_c > set_Pr242060487real_c > produc1037099239real_c ).
thf(func_def_168,type,
sK38: produc190496183real_c > set_Sum_sum_c_c > produc190496183real_c > denota231621370t_unit > produc190496183real_c ).
thf(func_def_169,type,
sK39: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_170,type,
sK40: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_171,type,
sK41: produc190496183real_c > set_Sum_sum_c_c > produc190496183real_c > denota231621370t_unit > produc190496183real_c ).
thf(func_def_172,type,
sK42: set_Sum_sum_c_c > ( set_Sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
thf(func_def_173,type,
sK43: ( set_Sum_sum_c_c > $o ) > ( set_Sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
thf(func_def_174,type,
sK44: ( sum_sum_c_c > $o ) > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_175,type,
sK45: produc190496183real_c > finite1398487019real_c ).
thf(func_def_176,type,
sK46: produc190496183real_c > finite1398487019real_c ).
thf(func_def_177,type,
sK47: produc190496183real_c > finite1398487019real_c ).
thf(func_def_178,type,
sK48: produc190496183real_c > finite1398487019real_c ).
thf(func_def_179,type,
sK49: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_180,type,
sK50: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_181,type,
sK51: ( sum_su737395349um_b_c > $o ) > ( sum_su737395349um_b_c > $o ) > sum_su737395349um_b_c ).
thf(func_def_182,type,
sK52: set_Sum_sum_c_c > set_Sum_sum_c_c > sum_sum_c_c ).
thf(func_def_183,type,
sK53: ( set_Sum_sum_c_c > $o ) > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_184,type,
sK54: produc190496183real_c > produc640052711real_c > produc190496183real_c ).
thf(func_def_185,type,
sK55: produc640052711real_c > produc190496183real_c > produc190496183real_c ).
thf(func_def_186,type,
sK56: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_187,type,
sK57: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_188,type,
sK58: set_Sum_sum_c_c > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_189,type,
sK59: set_Sum_sum_c_c > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_190,type,
sK60: set_Sum_sum_c_c > set_Sum_sum_c_c > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_191,type,
sK61: ( sum_sum_c_c > $o ) > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_192,type,
sK62: set_Sum_sum_c_c > ( sum_sum_c_c > $o ) > sum_sum_c_c ).
thf(func_def_193,type,
sK63: ( sum_sum_c_c > $o ) > set_Sum_sum_c_c > sum_sum_c_c ).
thf(func_def_194,type,
sK64: set_Sum_sum_c_c > ( sum_sum_c_c > $o ) > set_Sum_sum_c_c > sum_sum_c_c ).
thf(func_def_195,type,
sK65: set_Pr1389752855real_c > set_Pr1389752855real_c > produc190496183real_c ).
thf(func_def_196,type,
sK66: ( produc640052711real_c > $o ) > produc190496183real_c ).
thf(func_def_197,type,
sK67: ( produc640052711real_c > $o ) > produc190496183real_c ).
thf(func_def_198,type,
sK68: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ).
thf(func_def_199,type,
sK69: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c ).
thf(func_def_200,type,
sK70: produc190496183real_c > finite1398487019real_c > finite1398487019real_c ).
thf(func_def_201,type,
sK71: produc190496183real_c ).
thf(func_def_202,type,
sK72: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_203,type,
sK73: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_204,type,
sK74: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_205,type,
sK75: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_206,type,
sK76: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_207,type,
sK77: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_208,type,
sK78: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_209,type,
sK79: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_210,type,
sK80: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_211,type,
sK81: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_212,type,
sK82: ( set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_213,type,
sK83: ( produc640052711real_c > $o ) > produc190496183real_c ).
thf(func_def_214,type,
sK84: ( produc640052711real_c > $o ) > produc190496183real_c ).
thf(func_def_215,type,
sK85: produc640052711real_c > finite1398487019real_c ).
thf(func_def_216,type,
sK86: produc640052711real_c > finite1398487019real_c ).
thf(func_def_217,type,
sK87: produc640052711real_c > produc190496183real_c ).
thf(func_def_218,type,
sK88: produc190496183real_c > finite1398487019real_c > finite1398487019real_c ).
thf(func_def_219,type,
sK89: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_220,type,
sK90: ( set_Sum_sum_c_c > set_Su1783761653um_b_c ) > set_Sum_sum_c_c ).
thf(func_def_221,type,
sK91: ( sum_su737395349um_b_c > $o ) > ( sum_su737395349um_b_c > $o ) > sum_su737395349um_b_c ).
thf(func_def_222,type,
sK92: ( produc640052711real_c > $o ) > finite1398487019real_c ).
thf(func_def_223,type,
sK93: ( produc640052711real_c > $o ) > produc190496183real_c ).
thf(func_def_224,type,
sK94: ( produc640052711real_c > $o ) > finite1398487019real_c ).
thf(func_def_225,type,
sK95: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_226,type,
sK96: ( set_Sum_sum_c_c > set_Sum_sum_c_c ) > set_Sum_sum_c_c ).
thf(func_def_227,type,
sK97: set_Pr754230471real_c > set_Pr754230471real_c > produc640052711real_c ).
thf(func_def_228,type,
sK98: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_229,type,
sK99: ( set_Su1783761653um_b_c > set_Su1783761653um_b_c ) > set_Su1783761653um_b_c ).
thf(func_def_231,type,
ph101:
!>[X0: $tType] : X0 ).
thf(f2060,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2055]) ).
thf(f2055,plain,
$true != $true,
inference(superposition,[status(thm)],[f2010,f1871]) ).
thf(f1871,plain,
( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f531]) ).
thf(f531,plain,
( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f530]) ).
thf(f530,plain,
member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',fact_2_prog__sem_H) ).
thf(f2010,plain,
( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2003]) ).
thf(f2003,plain,
( ( $true != $true )
| ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1557,f1708]) ).
thf(f1708,plain,
( ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f479]) ).
thf(f479,plain,
( ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) )
= $true ),
inference(fool_elimination,[status(thm)],[f478]) ).
thf(f478,plain,
denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ),
file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',fact_3_agree_H) ).
thf(f1557,plain,
! [X0: produc190496183real_c] :
( ( $true
!= ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) )
| ( $true
!= ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X0 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1183]) ).
thf(f1183,plain,
! [X0: produc190496183real_c] :
( ( $true
!= ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) )
| ( $true
!= ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X0 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f717]) ).
thf(f717,plain,
~ ? [X0: produc190496183real_c] :
( ( $true
= ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X0 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) )
& ( $true
= ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ) ),
inference(fool_elimination,[status(thm)],[f716]) ).
thf(f716,plain,
~ ? [X0: produc190496183real_c] :
( ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) )
& ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X0 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
~ ? [X79: produc190496183real_c] :
( ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X79 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) )
& ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X79 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
? [X79: produc190496183real_c] :
( ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X79 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) )
& ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X79 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP036^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:24:25 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP036^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer Coincidence problem prob_1096__7244526_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : Coincidence/prob_1096__7244526_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 468 ( 195 unt; 113 typ; 0 def)
% 0.20/0.46 % Number of atoms : 826 ( 271 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.20/0.46 % Number of connectives : 2724 ( 36 ~; 7 |; 43 &;2295 @)
% 0.20/0.46 % ( 0 <=>; 343 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 18 ( 6 avg)
% 0.20/0.46 % Number of types : 22 ( 21 usr)
% 0.20/0.46 % Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 93 ( 92 usr; 12 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 997 ( 101 ^; 881 !; 15 ?; 997 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:47:10.370
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (21)
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J_J,type,
% 0.20/0.46 set_Pr242060487real_c: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
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% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.20/0.46 member616151824real_c: produc1037099239real_c > set_Pr242060487real_c > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 0.20/0.46 member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 0.20/0.46 member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_I____,type,
% 0.20/0.46 i: denota231621370t_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_J____,type,
% 0.20/0.46 j: denota231621370t_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_V____,type,
% 0.20/0.46 v: set_Sum_sum_c_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060mu_062_H_H____,type,
% 0.20/0.46 mu: produc190496183real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060mu_062_H____,type,
% 0.20/0.46 mu2: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060mu_062____,type,
% 0.20/0.46 mu3: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_0621_H____,type,
% 0.20/0.46 nu_1: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_0621____,type,
% 0.20/0.46 nu_12: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_0622_H____,type,
% 0.20/0.46 nu_2: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060nu_0622____,type,
% 0.20/0.46 nu_22: finite1398487019real_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_a____,type,
% 0.20/0.46 a: hp_a_b_c ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_b____,type,
% 0.20/0.46 b: hp_a_b_c ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (354)
% 0.20/0.46 thf(fact_0_hpsafe__Choice_OIH_I2_J,axiom,
% 0.20/0.46 coinci1852866155_a_b_c @ b ).
% 0.20/0.46
% 0.20/0.46 % hpsafe_Choice.IH(2)
% 0.20/0.46 thf(fact_1_hpsafe__Choice_OIH_I1_J,axiom,
% 0.20/0.46 coinci1852866155_a_b_c @ a ).
% 0.20/0.46
% 0.20/0.46 % hpsafe_Choice.IH(1)
% 0.20/0.46 thf(fact_2_prog__sem_H,axiom,
% 0.20/0.46 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ).
% 0.20/0.46
% 0.20/0.46 % prog_sem'
% 0.20/0.46 thf(fact_3_agree_H,axiom,
% 0.20/0.46 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ).
% 0.20/0.46
% 0.20/0.46 % agree'
% 0.20/0.46 thf(fact_4_prog__sem,axiom,
% 0.20/0.46 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ b ) ).
% 0.20/0.46
% 0.20/0.46 % prog_sem
% 0.20/0.46 thf(fact_5_safe_I2_J,axiom,
% 0.20/0.46 hpsafe_a_b_c @ b ).
% 0.20/0.46
% 0.20/0.46 % safe(2)
% 0.20/0.46 thf(fact_6_safe_I1_J,axiom,
% 0.20/0.46 hpsafe_a_b_c @ a ).
% 0.20/0.46
% 0.20/0.46 % safe(1)
% 0.20/0.46 thf(fact_7_agree,axiom,
% 0.20/0.46 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ).
% 0.20/0.46
% 0.20/0.46 % agree
% 0.20/0.46 thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [Mu: produc190496183real_c] :
% 0.20/0.46 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu ) @ ( denota904684656_a_b_c @ j @ b ) )
% 0.20/0.46 => ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>\<mu>''. \<lbrakk>((\<nu>2, \<nu>2'), \<mu>'') \<in> prog_sem J b; Vagree (\<mu>, \<mu>') \<mu>'' (MBV b \<union> V)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_9_VA,axiom,
% 0.20/0.46 denota1997846518gree_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ v ).
% 0.20/0.46
% 0.20/0.46 % VA
% 0.20/0.46 thf(fact_10_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 0.20/0.46 = ( produc394644079real_c @ ( sup_su2141622551real_c @ A @ C ) @ ( sup_su2141622551real_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_11_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 0.20/0.46 = ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_12_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 0.20/0.46 = ( produc1687028567real_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_13_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su421398139um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 0.20/0.46 = ( produc919784577um_b_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_14_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1731217579um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 0.20/0.46 = ( produc616453753um_c_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_15_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: produc190496183real_c,C: set_Sum_sum_c_c,D: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su2023888701real_c @ ( produc439851843real_c @ A @ B ) @ ( produc439851843real_c @ C @ D ) )
% 0.20/0.46 = ( produc439851843real_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_16_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: set_Sum_sum_c_c,C: produc190496183real_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1347303021um_c_c @ ( produc639456571um_c_c @ A @ B ) @ ( produc639456571um_c_c @ C @ D ) )
% 0.20/0.46 = ( produc639456571um_c_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_17_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1580927803um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 0.20/0.46 = ( produc754249687um_b_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_18_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: produc214722967um_c_c,C: set_Sum_sum_c_c,D: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su505296157um_c_c @ ( produc1333497635um_c_c @ A @ B ) @ ( produc1333497635um_c_c @ C @ D ) )
% 0.20/0.46 = ( produc1333497635um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1672617323um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_19_sup__Pair__Pair,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: set_Su1783761653um_b_c,C: produc190496183real_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1009753337um_b_c @ ( produc2010919061um_b_c @ A @ B ) @ ( produc2010919061um_b_c @ C @ D ) )
% 0.20/0.46 = ( produc2010919061um_b_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_Pair_Pair
% 0.20/0.46 thf(fact_20_sem,axiom,
% 0.20/0.46 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ ( choice_a_b_c @ a @ b ) ) ).
% 0.20/0.46
% 0.20/0.46 % sem
% 0.20/0.46 thf(fact_21_sub,axiom,
% 0.20/0.46 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ).
% 0.20/0.46
% 0.20/0.46 % sub
% 0.20/0.46 thf(fact_22_False,axiom,
% 0.20/0.46 ~ ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) ) ).
% 0.20/0.46
% 0.20/0.46 % False
% 0.20/0.46 thf(fact_23_hp_Oinject_I6_J,axiom,
% 0.20/0.46 ! [X61: hp_a_b_c,X62: hp_a_b_c,Y61: hp_a_b_c,Y62: hp_a_b_c] :
% 0.20/0.46 ( ( ( choice_a_b_c @ X61 @ X62 )
% 0.20/0.46 = ( choice_a_b_c @ Y61 @ Y62 ) )
% 0.20/0.46 = ( ( X61 = Y61 )
% 0.20/0.46 & ( X62 = Y62 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hp.inject(6)
% 0.20/0.46 thf(fact_24_UnCI,axiom,
% 0.20/0.46 ! [C: produc190496183real_c,B2: set_Pr1389752855real_c,A2: set_Pr1389752855real_c] :
% 0.20/0.46 ( ( ~ ( member1895684704real_c @ C @ B2 )
% 0.20/0.46 => ( member1895684704real_c @ C @ A2 ) )
% 0.20/0.46 => ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_25_UnCI,axiom,
% 0.20/0.46 ! [C: produc1037099239real_c,B2: set_Pr242060487real_c,A2: set_Pr242060487real_c] :
% 0.20/0.46 ( ( ~ ( member616151824real_c @ C @ B2 )
% 0.20/0.46 => ( member616151824real_c @ C @ A2 ) )
% 0.20/0.46 => ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_26_UnCI,axiom,
% 0.20/0.46 ! [C: sum_su737395349um_b_c,B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ~ ( member1893232190um_b_c @ C @ B2 )
% 0.20/0.46 => ( member1893232190um_b_c @ C @ A2 ) )
% 0.20/0.46 => ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_27_UnCI,axiom,
% 0.20/0.46 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( ~ ( member346808080real_c @ C @ B2 )
% 0.20/0.46 => ( member346808080real_c @ C @ A2 ) )
% 0.20/0.46 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_28_UnCI,axiom,
% 0.20/0.46 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ~ ( member_Sum_sum_c_c @ C @ B2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ A2 ) )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_29_Un__iff,axiom,
% 0.20/0.46 ! [C: produc190496183real_c,A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 0.20/0.46 ( ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) )
% 0.20/0.46 = ( ( member1895684704real_c @ C @ A2 )
% 0.20/0.46 | ( member1895684704real_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_30_Un__iff,axiom,
% 0.20/0.46 ! [C: produc1037099239real_c,A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 0.20/0.46 ( ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) )
% 0.20/0.46 = ( ( member616151824real_c @ C @ A2 )
% 0.20/0.46 | ( member616151824real_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_31_Un__iff,axiom,
% 0.20/0.46 ! [C: sum_su737395349um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 0.20/0.46 = ( ( member1893232190um_b_c @ C @ A2 )
% 0.20/0.46 | ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_32_Un__iff,axiom,
% 0.20/0.46 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 0.20/0.46 = ( ( member346808080real_c @ C @ A2 )
% 0.20/0.46 | ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_33_Un__iff,axiom,
% 0.20/0.46 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 = ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.20/0.46 | ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_34_sup_Oidem,axiom,
% 0.20/0.46 ! [A: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_35_sup_Oidem,axiom,
% 0.20/0.46 ! [A: produc640052711real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_36_sup_Oidem,axiom,
% 0.20/0.46 ! [A: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_37_sup_Oidem,axiom,
% 0.20/0.46 ! [A: set_Pr754230471real_c] :
% 0.20/0.46 ( ( sup_su588839579real_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_38_sup_Oidem,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_39_sup_Oidem,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup.idem
% 0.20/0.46 thf(fact_40_sup__idem,axiom,
% 0.20/0.46 ! [X: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_41_sup__idem,axiom,
% 0.20/0.46 ! [X: produc640052711real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_42_sup__idem,axiom,
% 0.20/0.46 ! [X: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_43_sup__idem,axiom,
% 0.20/0.46 ! [X: set_Pr754230471real_c] :
% 0.20/0.46 ( ( sup_su588839579real_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_44_sup__idem,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_45_sup__idem,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_idem
% 0.20/0.46 thf(fact_46_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ A @ ( sup_su1639086475real_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_47_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ A @ ( sup_su1399591867real_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_48_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ A @ ( sup_su1672617323um_c_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_49_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 0.20/0.46 ( ( sup_su588839579real_c @ A @ ( sup_su588839579real_c @ A @ B ) )
% 0.20/0.46 = ( sup_su588839579real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_50_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_51_sup_Oleft__idem,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_idem
% 0.20/0.46 thf(fact_52_subsetI,axiom,
% 0.20/0.46 ! [A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 0.20/0.46 ( ! [X2: produc190496183real_c] :
% 0.20/0.46 ( ( member1895684704real_c @ X2 @ A2 )
% 0.20/0.46 => ( member1895684704real_c @ X2 @ B2 ) )
% 0.20/0.46 => ( ord_le977353143real_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_53_subsetI,axiom,
% 0.20/0.46 ! [A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 0.20/0.46 ( ! [X2: produc1037099239real_c] :
% 0.20/0.46 ( ( member616151824real_c @ X2 @ A2 )
% 0.20/0.46 => ( member616151824real_c @ X2 @ B2 ) )
% 0.20/0.46 => ( ord_le100418663real_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_54_subsetI,axiom,
% 0.20/0.46 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.20/0.46 ( ! [X2: produc640052711real_c] :
% 0.20/0.46 ( ( member346808080real_c @ X2 @ A2 )
% 0.20/0.46 => ( member346808080real_c @ X2 @ B2 ) )
% 0.20/0.46 => ( ord_le1988344935real_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_55_subsetI,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ! [X2: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X2 @ A2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ X2 @ B2 ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_56_subsetI,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ! [X2: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( member1893232190um_b_c @ X2 @ A2 )
% 0.20/0.46 => ( member1893232190um_b_c @ X2 @ B2 ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_57_subset__antisym,axiom,
% 0.20/0.46 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1988344935real_c @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_antisym
% 0.20/0.46 thf(fact_58_subset__antisym,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_antisym
% 0.20/0.46 thf(fact_59_subset__antisym,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_antisym
% 0.20/0.46 thf(fact_60_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ ( sup_su1639086475real_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_61_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ ( sup_su1399591867real_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_62_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ ( sup_su1672617323um_c_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_63_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 0.20/0.46 ( ( sup_su588839579real_c @ ( sup_su588839579real_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su588839579real_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_64_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_65_sup_Oright__idem,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ B )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.right_idem
% 0.20/0.46 thf(fact_66_sup__left__idem,axiom,
% 0.20/0.46 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.20/0.46 ( ( sup_su1639086475real_c @ X @ ( sup_su1639086475real_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1639086475real_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_67_sup__left__idem,axiom,
% 0.20/0.46 ! [X: produc640052711real_c,Y: produc640052711real_c] :
% 0.20/0.46 ( ( sup_su1399591867real_c @ X @ ( sup_su1399591867real_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1399591867real_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_68_sup__left__idem,axiom,
% 0.20/0.46 ! [X: produc214722967um_c_c,Y: produc214722967um_c_c] :
% 0.20/0.46 ( ( sup_su1672617323um_c_c @ X @ ( sup_su1672617323um_c_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1672617323um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_69_sup__left__idem,axiom,
% 0.20/0.46 ! [X: set_Pr754230471real_c,Y: set_Pr754230471real_c] :
% 0.20/0.46 ( ( sup_su588839579real_c @ X @ ( sup_su588839579real_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su588839579real_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_70_sup__left__idem,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_71_sup__left__idem,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_idem
% 0.20/0.46 thf(fact_72_sub2,axiom,
% 0.20/0.46 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ v ).
% 0.20/0.46
% 0.20/0.46 % sub2
% 0.20/0.46 thf(fact_73_sub1,axiom,
% 0.20/0.46 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ v ).
% 0.20/0.46
% 0.20/0.46 % sub1
% 0.20/0.46 thf(fact_74_Pair__le,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 0.20/0.46 ( ( ord_le652477831real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le850691415real_c @ A @ C )
% 0.20/0.46 & ( ord_le850691415real_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_75_Pair__le,axiom,
% 0.20/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 0.20/0.46 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le775706699real_c @ A @ C )
% 0.20/0.46 & ( ord_le775706699real_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_76_Pair__le,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le1772180283um_c_c @ A @ C )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_77_Pair__le,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le1772180283um_c_c @ A @ C )
% 0.20/0.46 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_78_Pair__le,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le929608341um_b_c @ A @ C )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_79_Pair__le,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 0.20/0.46 = ( ( ord_le929608341um_b_c @ A @ C )
% 0.20/0.46 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_le
% 0.20/0.46 thf(fact_80_sup_Obounded__iff,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 0.20/0.46 = ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.bounded_iff
% 0.20/0.46 thf(fact_81_sup_Obounded__iff,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 0.20/0.46 = ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 & ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.bounded_iff
% 0.20/0.46 thf(fact_82_le__sup__iff,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.20/0.46 = ( ( ord_le1772180283um_c_c @ X @ Z )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ Y @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_sup_iff
% 0.20/0.46 thf(fact_83_le__sup__iff,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ X @ Y ) @ Z )
% 0.20/0.46 = ( ( ord_le929608341um_b_c @ X @ Z )
% 0.20/0.46 & ( ord_le929608341um_b_c @ Y @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_sup_iff
% 0.20/0.46 thf(fact_84_Un__subset__iff,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 0.20/0.46 = ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ B2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_subset_iff
% 0.20/0.46 thf(fact_85_Un__subset__iff,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 )
% 0.20/0.46 = ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.20/0.46 & ( ord_le929608341um_b_c @ B2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_subset_iff
% 0.20/0.46 thf(fact_86_hpsafe__Choice__simps,axiom,
% 0.20/0.46 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.20/0.46 ( ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 0.20/0.46 = ( ( hpsafe_a_b_c @ A )
% 0.20/0.46 & ( hpsafe_a_b_c @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hpsafe_Choice_simps
% 0.20/0.46 thf(fact_87_sem2,axiom,
% 0.20/0.46 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ).
% 0.20/0.46
% 0.20/0.46 % sem2
% 0.20/0.46 thf(fact_88_eitherSem,axiom,
% 0.20/0.46 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) )
% 0.20/0.46 | ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eitherSem
% 0.20/0.46 thf(fact_89_in__mono,axiom,
% 0.20/0.46 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,X: produc640052711real_c] :
% 0.20/0.46 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member346808080real_c @ X @ A2 )
% 0.20/0.46 => ( member346808080real_c @ X @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_mono
% 0.20/0.46 thf(fact_90_in__mono,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,X: sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member_Sum_sum_c_c @ X @ A2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ X @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_mono
% 0.20/0.46 thf(fact_91_in__mono,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,X: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member1893232190um_b_c @ X @ A2 )
% 0.20/0.46 => ( member1893232190um_b_c @ X @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_mono
% 0.20/0.46 thf(fact_92_subsetD,axiom,
% 0.20/0.46 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,C: produc640052711real_c] :
% 0.20/0.46 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member346808080real_c @ C @ A2 )
% 0.20/0.46 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetD
% 0.20/0.46 thf(fact_93_subsetD,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C: sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetD
% 0.20/0.46 thf(fact_94_subsetD,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( member1893232190um_b_c @ C @ A2 )
% 0.20/0.46 => ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetD
% 0.20/0.46 thf(fact_95_equalityE,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ~ ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityE
% 0.20/0.46 thf(fact_96_equalityE,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ~ ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_le929608341um_b_c @ B2 @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityE
% 0.20/0.46 thf(fact_97_subset__eq,axiom,
% 0.20/0.46 ( ord_le1988344935real_c
% 0.20/0.46 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 0.20/0.46 ! [X3: produc640052711real_c] :
% 0.20/0.46 ( ( member346808080real_c @ X3 @ A3 )
% 0.20/0.46 => ( member346808080real_c @ X3 @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_eq
% 0.20/0.46 thf(fact_98_subset__eq,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.20/0.46 ! [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ A3 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ X3 @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_eq
% 0.20/0.46 thf(fact_99_subset__eq,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.20/0.46 ! [X3: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( member1893232190um_b_c @ X3 @ A3 )
% 0.20/0.46 => ( member1893232190um_b_c @ X3 @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_eq
% 0.20/0.46 thf(fact_100_equalityD1,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD1
% 0.20/0.46 thf(fact_101_equalityD1,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD1
% 0.20/0.46 thf(fact_102_equalityD2,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD2
% 0.20/0.46 thf(fact_103_equalityD2,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD2
% 0.20/0.46 thf(fact_104_subset__iff,axiom,
% 0.20/0.46 ( ord_le1988344935real_c
% 0.20/0.46 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 0.20/0.46 ! [T: produc640052711real_c] :
% 0.20/0.46 ( ( member346808080real_c @ T @ A3 )
% 0.20/0.46 => ( member346808080real_c @ T @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff
% 0.20/0.46 thf(fact_105_subset__iff,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.20/0.46 ! [T: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ T @ A3 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ T @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff
% 0.20/0.46 thf(fact_106_subset__iff,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.20/0.46 ! [T: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( member1893232190um_b_c @ T @ A3 )
% 0.20/0.46 => ( member1893232190um_b_c @ T @ B3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff
% 0.20/0.46 thf(fact_107_subset__refl,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % subset_refl
% 0.20/0.46 thf(fact_108_subset__refl,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % subset_refl
% 0.20/0.46 thf(fact_109_Collect__mono,axiom,
% 0.20/0.46 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 0.20/0.46 ( ! [X2: sum_sum_c_c] :
% 0.20/0.46 ( ( P @ X2 )
% 0.20/0.46 => ( Q @ X2 ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono
% 0.20/0.46 thf(fact_110_Collect__mono,axiom,
% 0.20/0.46 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.20/0.46 ( ! [X2: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( P @ X2 )
% 0.20/0.46 => ( Q @ X2 ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono
% 0.20/0.46 thf(fact_111_subset__trans,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_trans
% 0.20/0.46 thf(fact_112_subset__trans,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_trans
% 0.20/0.46 thf(fact_113_set__eq__subset,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A3 @ B3 )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ B3 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_eq_subset
% 0.20/0.46 thf(fact_114_set__eq__subset,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A3 @ B3 )
% 0.20/0.46 & ( ord_le929608341um_b_c @ B3 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_eq_subset
% 0.20/0.46 thf(fact_115_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: produc640052711real_c,P: produc640052711real_c > $o] :
% 0.20/0.46 ( ( member346808080real_c @ A @ ( collec1126017874real_c @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_116_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( collec1126017874real_c
% 0.20/0.46 @ ^ [X3: produc640052711real_c] : ( member346808080real_c @ X3 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_117_Collect__mono__iff,axiom,
% 0.20/0.46 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) )
% 0.20/0.46 = ( ! [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( Q @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono_iff
% 0.20/0.46 thf(fact_118_Collect__mono__iff,axiom,
% 0.20/0.46 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 0.20/0.46 = ( ! [X3: sum_su737395349um_b_c] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( Q @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono_iff
% 0.20/0.46 thf(fact_119_Pair__mono,axiom,
% 0.20/0.46 ! [X: produc190496183real_c,X4: produc190496183real_c,Y: produc190496183real_c,Y3: produc190496183real_c] :
% 0.20/0.46 ( ( ord_le850691415real_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le850691415real_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le652477831real_c @ ( produc1687028567real_c @ X @ Y ) @ ( produc1687028567real_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_120_Pair__mono,axiom,
% 0.20/0.46 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.20/0.46 ( ( ord_le775706699real_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le775706699real_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_121_Pair__mono,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ X @ Y ) @ ( produc1439061071um_c_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_122_Pair__mono,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ X @ Y ) @ ( produc919784577um_b_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_123_Pair__mono,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ X @ Y ) @ ( produc616453753um_c_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_124_Pair__mono,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ X4 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 0.20/0.46 => ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ X @ Y ) @ ( produc754249687um_b_c @ X4 @ Y3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_mono
% 0.20/0.46 thf(fact_125_sup_OcoboundedI2,axiom,
% 0.20/0.46 ! [C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ C @ B )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.coboundedI2
% 0.20/0.46 thf(fact_126_sup_OcoboundedI2,axiom,
% 0.20/0.46 ! [C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ C @ B )
% 0.20/0.46 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.coboundedI2
% 0.20/0.46 thf(fact_127_sup_OcoboundedI1,axiom,
% 0.20/0.46 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ C @ A )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.coboundedI1
% 0.20/0.46 thf(fact_128_sup_OcoboundedI1,axiom,
% 0.20/0.46 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ C @ A )
% 0.20/0.46 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.coboundedI1
% 0.20/0.46 thf(fact_129_sup_Oabsorb__iff2,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 0.20/0.46 = B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb_iff2
% 0.20/0.46 thf(fact_130_sup_Oabsorb__iff2,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 0.20/0.46 = B4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb_iff2
% 0.20/0.46 thf(fact_131_sup_Oabsorb__iff1,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 0.20/0.46 = A4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb_iff1
% 0.20/0.46 thf(fact_132_sup_Oabsorb__iff1,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 0.20/0.46 = A4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb_iff1
% 0.20/0.46 thf(fact_133_sup_Ocobounded2,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.cobounded2
% 0.20/0.46 thf(fact_134_sup_Ocobounded2,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.cobounded2
% 0.20/0.46 thf(fact_135_sup_Ocobounded1,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.cobounded1
% 0.20/0.46 thf(fact_136_sup_Ocobounded1,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.cobounded1
% 0.20/0.46 thf(fact_137_sup_Oorder__iff,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.20/0.46 ( A4
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A4 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.order_iff
% 0.20/0.46 thf(fact_138_sup_Oorder__iff,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( A4
% 0.20/0.46 = ( sup_su1968964297um_b_c @ A4 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.order_iff
% 0.20/0.46 thf(fact_139_sup_OboundedI,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ C @ A )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.boundedI
% 0.20/0.46 thf(fact_140_sup_OboundedI,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ C @ A )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.boundedI
% 0.20/0.46 thf(fact_141_sup_OboundedE,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 0.20/0.46 => ~ ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ~ ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.boundedE
% 0.20/0.46 thf(fact_142_sup_OboundedE,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 0.20/0.46 => ~ ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ~ ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.boundedE
% 0.20/0.46 thf(fact_143_sup__absorb2,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.20/0.46 = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_absorb2
% 0.20/0.46 thf(fact_144_sup__absorb2,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.20/0.46 = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_absorb2
% 0.20/0.46 thf(fact_145_sup__absorb1,axiom,
% 0.20/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.20/0.46 = X ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_absorb1
% 0.20/0.46 thf(fact_146_sup__absorb1,axiom,
% 0.20/0.46 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.20/0.46 = X ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_absorb1
% 0.20/0.46 thf(fact_147_sup_Oabsorb2,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A @ B )
% 0.20/0.46 = B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb2
% 0.20/0.46 thf(fact_148_sup_Oabsorb2,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ A @ B )
% 0.20/0.46 = B ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb2
% 0.20/0.46 thf(fact_149_sup_Oabsorb1,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A @ B )
% 0.20/0.46 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb1
% 0.20/0.46 thf(fact_150_sup_Oabsorb1,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ A @ B )
% 0.20/0.46 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.absorb1
% 0.20/0.46 thf(fact_151_sup__unique,axiom,
% 0.20/0.46 ! [F: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c,X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X2 @ ( F @ X2 @ Y4 ) )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c,Z3: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ Y4 @ X2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Z3 @ X2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.20/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_unique
% 0.20/0.46 thf(fact_152_sup__unique,axiom,
% 0.20/0.46 ! [F: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X2 @ ( F @ X2 @ Y4 ) )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c,Z3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ Y4 @ X2 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Z3 @ X2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.20/0.46 = ( F @ X @ Y ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_unique
% 0.20/0.46 thf(fact_153_sup_OorderI,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ B ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ B @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.orderI
% 0.20/0.46 thf(fact_154_sup_OorderI,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( sup_su1968964297um_b_c @ A @ B ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ B @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.orderI
% 0.20/0.46 thf(fact_155_sup_OorderE,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( A
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.orderE
% 0.20/0.46 thf(fact_156_sup_OorderE,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( A
% 0.20/0.46 = ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.orderE
% 0.20/0.46 thf(fact_157_le__iff__sup,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X3 @ Y5 )
% 0.20/0.46 = Y5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_iff_sup
% 0.20/0.46 thf(fact_158_le__iff__sup,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ X3 @ Y5 )
% 0.20/0.46 = Y5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_iff_sup
% 0.20/0.46 thf(fact_159_sup__least,axiom,
% 0.20/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Z @ X )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ Y @ Z ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_least
% 0.20/0.46 thf(fact_160_sup__least,axiom,
% 0.20/0.46 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Z @ X )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ Y @ Z ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_least
% 0.20/0.46 thf(fact_161_sup__mono,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ C )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ D )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ ( sup_su1349021703um_c_c @ C @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_mono
% 0.20/0.46 thf(fact_162_sup__mono,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ C )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ D )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ ( sup_su1968964297um_b_c @ C @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_mono
% 0.20/0.46 thf(fact_163_sup_Omono,axiom,
% 0.20/0.46 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,D: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ C @ A )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ D @ B )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ C @ D ) @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.mono
% 0.20/0.46 thf(fact_164_sup_Omono,axiom,
% 0.20/0.46 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ C @ A )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ D @ B )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ C @ D ) @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.mono
% 0.20/0.46 thf(fact_165_le__supI2,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ B )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI2
% 0.20/0.46 thf(fact_166_le__supI2,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ B )
% 0.20/0.46 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI2
% 0.20/0.46 thf(fact_167_le__supI1,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ A )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI1
% 0.20/0.46 thf(fact_168_le__supI1,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ A )
% 0.20/0.46 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI1
% 0.20/0.46 thf(fact_169_sup__ge2,axiom,
% 0.20/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_ge2
% 0.20/0.46 thf(fact_170_sup__ge2,axiom,
% 0.20/0.46 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_ge2
% 0.20/0.46 thf(fact_171_sup__ge1,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_ge1
% 0.20/0.46 thf(fact_172_sup__ge1,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_ge1
% 0.20/0.46 thf(fact_173_le__supI,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,X: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ X )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ X )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI
% 0.20/0.46 thf(fact_174_le__supI,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ X )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ X )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supI
% 0.20/0.46 thf(fact_175_le__supE,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X )
% 0.20/0.46 => ~ ( ( ord_le1772180283um_c_c @ A @ X )
% 0.20/0.46 => ~ ( ord_le1772180283um_c_c @ B @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supE
% 0.20/0.46 thf(fact_176_le__supE,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X )
% 0.20/0.46 => ~ ( ( ord_le929608341um_b_c @ A @ X )
% 0.20/0.46 => ~ ( ord_le929608341um_b_c @ B @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_supE
% 0.20/0.46 thf(fact_177_inf__sup__ord_I3_J,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(3)
% 0.20/0.46 thf(fact_178_inf__sup__ord_I3_J,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(3)
% 0.20/0.46 thf(fact_179_inf__sup__ord_I4_J,axiom,
% 0.20/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(4)
% 0.20/0.46 thf(fact_180_inf__sup__ord_I4_J,axiom,
% 0.20/0.46 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(4)
% 0.20/0.46 thf(fact_181_subset__Un__eq,axiom,
% 0.20/0.46 ( ord_le1772180283um_c_c
% 0.20/0.46 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A3 @ B3 )
% 0.20/0.46 = B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_Un_eq
% 0.20/0.46 thf(fact_182_subset__Un__eq,axiom,
% 0.20/0.46 ( ord_le929608341um_b_c
% 0.20/0.46 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( sup_su1968964297um_b_c @ A3 @ B3 )
% 0.20/0.46 = B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_Un_eq
% 0.20/0.46 thf(fact_183_subset__UnE,axiom,
% 0.20/0.46 ! [C2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ C2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 => ~ ! [A5: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A5 @ A2 )
% 0.20/0.46 => ! [B5: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B5 @ B2 )
% 0.20/0.46 => ( C2
% 0.20/0.46 != ( sup_su1349021703um_c_c @ A5 @ B5 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_UnE
% 0.20/0.46 thf(fact_184_subset__UnE,axiom,
% 0.20/0.46 ! [C2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ C2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 0.20/0.46 => ~ ! [A5: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A5 @ A2 )
% 0.20/0.46 => ! [B5: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B5 @ B2 )
% 0.20/0.46 => ( C2
% 0.20/0.46 != ( sup_su1968964297um_b_c @ A5 @ B5 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_UnE
% 0.20/0.46 thf(fact_185_Un__absorb2,axiom,
% 0.20/0.46 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb2
% 0.20/0.46 thf(fact_186_Un__absorb2,axiom,
% 0.20/0.46 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb2
% 0.20/0.46 thf(fact_187_Un__absorb1,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 0.20/0.46 = B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb1
% 0.20/0.46 thf(fact_188_Un__absorb1,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 0.20/0.46 = B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb1
% 0.20/0.46 thf(fact_189_Un__upper2,axiom,
% 0.20/0.46 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_upper2
% 0.20/0.46 thf(fact_190_Un__upper2,axiom,
% 0.20/0.46 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_upper2
% 0.20/0.46 thf(fact_191_Un__upper1,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_upper1
% 0.20/0.46 thf(fact_192_Un__upper1,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_upper1
% 0.20/0.46 thf(fact_193_Un__least,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_least
% 0.20/0.46 thf(fact_194_Un__least,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_least
% 0.20/0.46 thf(fact_195_Un__mono,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,D2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B2 @ D2 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ ( sup_su1349021703um_c_c @ C2 @ D2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_mono
% 0.20/0.46 thf(fact_196_Un__mono,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,D2: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B2 @ D2 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ ( sup_su1968964297um_b_c @ C2 @ D2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_mono
% 0.20/0.46 thf(fact_197_hpsafe__fsafe_Ohpsafe__Choice,axiom,
% 0.20/0.46 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.20/0.46 ( ( hpsafe_a_b_c @ A )
% 0.20/0.46 => ( ( hpsafe_a_b_c @ B )
% 0.20/0.46 => ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hpsafe_fsafe.hpsafe_Choice
% 0.20/0.46 thf(fact_198_sup__left__commute,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_left_commute
% 0.20/0.46 thf(fact_199_sup_Oleft__commute,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ C ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.left_commute
% 0.20/0.46 thf(fact_200_sup__commute,axiom,
% 0.20/0.46 ( sup_su1349021703um_c_c
% 0.20/0.46 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_commute
% 0.20/0.46 thf(fact_201_sup_Ocommute,axiom,
% 0.20/0.46 ( sup_su1349021703um_c_c
% 0.20/0.46 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B4 @ A4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.commute
% 0.20/0.46 thf(fact_202_sup__assoc,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_assoc
% 0.20/0.46 thf(fact_203_sup_Oassoc,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ C )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup.assoc
% 0.20/0.46 thf(fact_204_boolean__algebra__cancel_Osup2,axiom,
% 0.20/0.46 ! [B2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( B2
% 0.20/0.46 = ( sup_su1349021703um_c_c @ K @ B ) )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A @ B2 )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % boolean_algebra_cancel.sup2
% 0.20/0.46 thf(fact_205_boolean__algebra__cancel_Osup1,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( sup_su1349021703um_c_c @ K @ A ) )
% 0.20/0.46 => ( ( sup_su1349021703um_c_c @ A2 @ B )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % boolean_algebra_cancel.sup1
% 0.20/0.46 thf(fact_206_inf__sup__aci_I5_J,axiom,
% 0.20/0.46 ( sup_su1349021703um_c_c
% 0.20/0.46 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(5)
% 0.20/0.46 thf(fact_207_inf__sup__aci_I6_J,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(6)
% 0.20/0.46 thf(fact_208_inf__sup__aci_I7_J,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(7)
% 0.20/0.46 thf(fact_209_inf__sup__aci_I8_J,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(8)
% 0.20/0.46 thf(fact_210_Un__left__commute,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_commute
% 0.20/0.46 thf(fact_211_Un__left__absorb,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_absorb
% 0.20/0.46 thf(fact_212_Un__commute,axiom,
% 0.20/0.46 ( sup_su1349021703um_c_c
% 0.20/0.46 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B3 @ A3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_commute
% 0.20/0.46 thf(fact_213_Un__absorb,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ A2 @ A2 )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb
% 0.20/0.46 thf(fact_214_Un__assoc,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_assoc
% 0.20/0.46 thf(fact_215_ball__Un,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.20/0.46 ( ( ! [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 => ( P @ X3 ) ) )
% 0.20/0.46 = ( ! [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 0.20/0.46 => ( P @ X3 ) )
% 0.20/0.46 & ! [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 0.20/0.46 => ( P @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ball_Un
% 0.20/0.46 thf(fact_216_bex__Un,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.20/0.46 ( ( ? [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 & ( P @ X3 ) ) )
% 0.20/0.46 = ( ? [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 0.20/0.46 & ( P @ X3 ) )
% 0.20/0.46 | ? [X3: sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 0.20/0.46 & ( P @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bex_Un
% 0.20/0.46 thf(fact_217_UnI2,axiom,
% 0.20/0.46 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( member346808080real_c @ C @ B2 )
% 0.20/0.46 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_218_UnI2,axiom,
% 0.20/0.46 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ C @ B2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_219_UnI1,axiom,
% 0.20/0.46 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( member346808080real_c @ C @ A2 )
% 0.20/0.46 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_220_UnI1,axiom,
% 0.20/0.46 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_221_UnE,axiom,
% 0.20/0.46 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.20/0.46 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 0.20/0.46 => ( ~ ( member346808080real_c @ C @ A2 )
% 0.20/0.46 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_222_UnE,axiom,
% 0.20/0.46 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.20/0.46 => ( ~ ( member_Sum_sum_c_c @ C @ A2 )
% 0.20/0.46 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_223_IA,axiom,
% 0.20/0.46 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.20/0.46
% 0.20/0.46 % IA
% 0.20/0.46 thf(fact_224_IH1,axiom,
% 0.20/0.46 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.20/0.46 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ a ) )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ V )
% 0.20/0.46 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ a ) )
% 0.20/0.46 => ? [Mu3: produc190496183real_c] :
% 0.20/0.46 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ a ) )
% 0.20/0.46 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ a ) @ V ) ) ) ) ) ) )
% 0.20/0.46 & ( coinci772602909_a_b_c @ a @ I ) ) ).
% 0.20/0.46
% 0.20/0.46 % IH1
% 0.20/0.46 thf(fact_225_IH2,axiom,
% 0.20/0.46 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.20/0.46 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ b ) )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ V )
% 0.20/0.46 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ b ) )
% 0.20/0.46 => ? [Mu3: produc190496183real_c] :
% 0.20/0.46 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ b ) )
% 0.20/0.46 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ V ) ) ) ) ) ) )
% 0.20/0.46 & ( coinci772602909_a_b_c @ b @ I ) ) ).
% 0.20/0.46
% 0.20/0.46 % IH2
% 0.20/0.46 thf(fact_226_coincide__hp_H__def,axiom,
% 0.20/0.46 ( coinci1852866155_a_b_c
% 0.20/0.46 = ( ^ [Alpha: hp_a_b_c] :
% 0.20/0.46 ! [I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 0.20/0.46 ( ( coinci354700372_a_b_c @ Alpha @ I2 @ J2 )
% 0.20/0.46 & ( coinci772602909_a_b_c @ Alpha @ I2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % coincide_hp'_def
% 0.20/0.46 thf(fact_227_FVP_Osimps_I6_J,axiom,
% 0.20/0.46 ! [Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 0.20/0.46 ( ( static_FVP_a_b_c @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 0.20/0.46 = ( sup_su1349021703um_c_c @ ( static_FVP_a_b_c @ Alpha2 ) @ ( static_FVP_a_b_c @ Beta ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % FVP.simps(6)
% 0.20/0.46 thf(fact_228_agree__supset,axiom,
% 0.20/0.46 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ A2 )
% 0.20/0.46 => ( denota1997846518gree_c @ Nu3 @ Nu4 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_supset
% 0.20/0.46 thf(fact_229_agree__sub,axiom,
% 0.20/0.46 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 0.20/0.46 => ( denota1997846518gree_c @ Nu3 @ Omega @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % agree_sub
% 0.20/0.46 thf(fact_230_old_Oprod_Oinject,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 0.20/0.46 ( ( ( produc1687028567real_c @ A @ B )
% 0.20/0.46 = ( produc1687028567real_c @ A6 @ B6 ) )
% 0.20/0.46 = ( ( A = A6 )
% 0.20/0.46 & ( B = B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.inject
% 0.20/0.46 thf(fact_231_old_Oprod_Oinject,axiom,
% 0.20/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 0.20/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.20/0.46 = ( produc394644079real_c @ A6 @ B6 ) )
% 0.20/0.46 = ( ( A = A6 )
% 0.20/0.46 & ( B = B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.inject
% 0.20/0.46 thf(fact_232_prod_Oinject,axiom,
% 0.20/0.46 ! [X1: produc190496183real_c,X22: produc190496183real_c,Y1: produc190496183real_c,Y22: produc190496183real_c] :
% 0.20/0.46 ( ( ( produc1687028567real_c @ X1 @ X22 )
% 0.20/0.46 = ( produc1687028567real_c @ Y1 @ Y22 ) )
% 0.20/0.46 = ( ( X1 = Y1 )
% 0.20/0.46 & ( X22 = Y22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod.inject
% 0.20/0.46 thf(fact_233_prod_Oinject,axiom,
% 0.20/0.46 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 0.20/0.46 ( ( ( produc394644079real_c @ X1 @ X22 )
% 0.20/0.46 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 0.20/0.46 = ( ( X1 = Y1 )
% 0.20/0.46 & ( X22 = Y22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod.inject
% 0.20/0.46 thf(fact_234_order__refl,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_235_order__refl,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_236_Ssub_I2_J,axiom,
% 0.20/0.46 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ b ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.20/0.46
% 0.20/0.46 % Ssub(2)
% 0.20/0.46 thf(fact_237_Ssub_I1_J,axiom,
% 0.20/0.46 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ a ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.20/0.46
% 0.20/0.46 % Ssub(1)
% 0.20/0.46 thf(fact_238_IA2,axiom,
% 0.20/0.46 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ b ) ).
% 0.20/0.46
% 0.20/0.46 % IA2
% 0.20/0.46 thf(fact_239_IA1,axiom,
% 0.20/0.46 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ a ) ).
% 0.20/0.46
% 0.20/0.46 % IA1
% 0.20/0.46 thf(fact_240_coincide__hp__def,axiom,
% 0.20/0.46 ( coinci354700372_a_b_c
% 0.20/0.46 = ( ^ [Alpha: hp_a_b_c,I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 0.20/0.46 ! [Nu5: produc190496183real_c,Nu6: produc190496183real_c,Mu4: produc190496183real_c,V2: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( denota69106024_a_b_c @ I2 @ J2 @ ( static_SIGP_a_b_c @ Alpha ) )
% 0.20/0.46 => ( ( denota1997846518gree_c @ Nu5 @ Nu6 @ V2 )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ Alpha ) @ V2 )
% 0.20/0.46 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu5 @ Mu4 ) @ ( denota904684656_a_b_c @ I2 @ Alpha ) )
% 0.20/0.46 => ? [Mu5: produc190496183real_c] :
% 0.20/0.46 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu6 @ Mu5 ) @ ( denota904684656_a_b_c @ J2 @ Alpha ) )
% 0.20/0.46 & ( denota1997846518gree_c @ Mu4 @ Mu5 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ Alpha ) @ V2 ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % coincide_hp_def
% 0.20/0.46 thf(fact_241_Iagree__sub,axiom,
% 0.20/0.46 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,I3: denota231621370t_unit,J3: denota231621370t_unit] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.20/0.46 => ( ( denota69106024_a_b_c @ I3 @ J3 @ B2 )
% 0.20/0.46 => ( denota69106024_a_b_c @ I3 @ J3 @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Iagree_sub
% 0.20/0.46 thf(fact_242_Iagree__refl,axiom,
% 0.20/0.46 ! [I3: denota231621370t_unit,A2: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Iagree_refl
% 0.20/0.46 thf(fact_243_Iagree__comm,axiom,
% 0.20/0.46 ! [A2: denota231621370t_unit,B2: denota231621370t_unit,V3: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( denota69106024_a_b_c @ A2 @ B2 @ V3 )
% 0.20/0.46 => ( denota69106024_a_b_c @ B2 @ A2 @ V3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Iagree_comm
% 0.20/0.46 thf(fact_244_SIGP_Osimps_I6_J,axiom,
% 0.20/0.46 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.20/0.46 ( ( static_SIGP_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 0.20/0.46 = ( sup_su1968964297um_b_c @ ( static_SIGP_a_b_c @ A ) @ ( static_SIGP_a_b_c @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SIGP.simps(6)
% 0.20/0.46 thf(fact_245_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_246_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_247_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B4 @ A4 )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ A4 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_248_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B4 @ A4 )
% 0.20/0.46 & ( ord_le929608341um_b_c @ A4 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_249_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ C @ B )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_250_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ C @ B )
% 0.20/0.46 => ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_251_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ A ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_252_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ A ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_253_order__trans,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Y @ Z )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ X @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_254_order__trans,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Y @ Z )
% 0.20/0.46 => ( ord_le929608341um_b_c @ X @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_255_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_256_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_257_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( B = C )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_258_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( B = C )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_259_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_260_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_261_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ B4 @ A4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_262_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A4 @ B4 )
% 0.20/0.46 & ( ord_le929608341um_b_c @ B4 @ A4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_263_antisym__conv,axiom,
% 0.20/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_264_antisym__conv,axiom,
% 0.20/0.46 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ X @ Y )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_265_order_Otrans,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_266_order_Otrans,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_267_eq__refl,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_268_eq__refl,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 => ( ord_le929608341um_b_c @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_269_antisym,axiom,
% 0.20/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_270_antisym,axiom,
% 0.20/0.46 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ Y @ X )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_271_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X3 @ Y5 )
% 0.20/0.46 & ( ord_le1772180283um_c_c @ Y5 @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_272_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.20/0.46 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X3 @ Y5 )
% 0.20/0.46 & ( ord_le929608341um_b_c @ Y5 @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_273_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_274_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_275_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_276_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ( F @ B )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_277_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_278_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_279_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_280_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( A
% 0.20/0.46 = ( F @ B ) )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_281_order__subst2,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_282_order__subst2,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_283_order__subst2,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_284_order__subst2,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ B )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_285_order__subst1,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_286_order__subst1,axiom,
% 0.20/0.46 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_287_order__subst1,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.20/0.46 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_288_order__subst1,axiom,
% 0.20/0.46 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 0.20/0.46 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.20/0.46 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.20/0.46 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.20/0.46 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.20/0.46 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_289_surj__pair,axiom,
% 0.20/0.46 ! [P2: produc640052711real_c] :
% 0.20/0.46 ? [X2: produc190496183real_c,Y4: produc190496183real_c] :
% 0.20/0.46 ( P2
% 0.20/0.46 = ( produc1687028567real_c @ X2 @ Y4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % surj_pair
% 0.20/0.46 thf(fact_290_surj__pair,axiom,
% 0.20/0.46 ! [P2: produc190496183real_c] :
% 0.20/0.46 ? [X2: finite1398487019real_c,Y4: finite1398487019real_c] :
% 0.20/0.46 ( P2
% 0.20/0.46 = ( produc394644079real_c @ X2 @ Y4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % surj_pair
% 0.20/0.46 thf(fact_291_prod__cases,axiom,
% 0.20/0.46 ! [P: produc640052711real_c > $o,P2: produc640052711real_c] :
% 0.20/0.46 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 0.20/0.46 => ( P @ P2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod_cases
% 0.20/0.46 thf(fact_292_prod__cases,axiom,
% 0.20/0.46 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.20/0.46 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 0.20/0.46 => ( P @ P2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod_cases
% 0.20/0.46 thf(fact_293_Pair__inject,axiom,
% 0.20/0.46 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 0.20/0.46 ( ( ( produc1687028567real_c @ A @ B )
% 0.20/0.46 = ( produc1687028567real_c @ A6 @ B6 ) )
% 0.20/0.46 => ~ ( ( A = A6 )
% 0.20/0.46 => ( B != B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_inject
% 0.20/0.46 thf(fact_294_Pair__inject,axiom,
% 0.20/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 0.20/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.20/0.46 = ( produc394644079real_c @ A6 @ B6 ) )
% 0.20/0.46 => ~ ( ( A = A6 )
% 0.20/0.46 => ( B != B6 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_inject
% 0.20/0.46 thf(fact_295_old_Oprod_Oexhaust,axiom,
% 0.20/0.46 ! [Y: produc640052711real_c] :
% 0.20/0.46 ~ ! [A7: produc190496183real_c,B7: produc190496183real_c] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( produc1687028567real_c @ A7 @ B7 ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.exhaust
% 0.20/0.46 thf(fact_296_old_Oprod_Oexhaust,axiom,
% 0.20/0.46 ! [Y: produc190496183real_c] :
% 0.20/0.46 ~ ! [A7: finite1398487019real_c,B7: finite1398487019real_c] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( produc394644079real_c @ A7 @ B7 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.exhaust
% 0.20/0.47 thf(fact_297_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc640052711real_c > $o,Prod: produc640052711real_c] :
% 0.20/0.47 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_298_old_Oprod_Oinducts,axiom,
% 0.20/0.47 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.20/0.47 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 0.20/0.47 => ( P @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inducts
% 0.20/0.47 thf(fact_299_agree__comm,axiom,
% 0.20/0.47 ! [A2: produc190496183real_c,B2: produc190496183real_c,V3: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( denota1997846518gree_c @ A2 @ B2 @ V3 )
% 0.20/0.47 => ( denota1997846518gree_c @ B2 @ A2 @ V3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_comm
% 0.20/0.47 thf(fact_300_agree__refl,axiom,
% 0.20/0.47 ! [Nu3: produc190496183real_c,A2: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A2 ) ).
% 0.20/0.47
% 0.20/0.47 % agree_refl
% 0.20/0.47 thf(fact_301_prod__cases3,axiom,
% 0.20/0.47 ! [Y: produc640052711real_c] :
% 0.20/0.47 ~ ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_cases3
% 0.20/0.47 thf(fact_302_prod__induct3,axiom,
% 0.20/0.47 ! [P: produc640052711real_c > $o,X: produc640052711real_c] :
% 0.20/0.47 ( ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] : ( P @ ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) )
% 0.20/0.47 => ( P @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod_induct3
% 0.20/0.47 thf(fact_303_agree__union,axiom,
% 0.20/0.47 ! [Nu3: produc190496183real_c,Omega: produc190496183real_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( denota1997846518gree_c @ Nu3 @ Omega @ A2 )
% 0.20/0.47 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 0.20/0.47 => ( denota1997846518gree_c @ Nu3 @ Omega @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % agree_union
% 0.20/0.47 thf(fact_304_prog__sem_Osimps_I5_J,axiom,
% 0.20/0.47 ! [I3: denota231621370t_unit,Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 0.20/0.47 ( ( denota904684656_a_b_c @ I3 @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 0.20/0.47 = ( sup_su588839579real_c @ ( denota904684656_a_b_c @ I3 @ Alpha2 ) @ ( denota904684656_a_b_c @ I3 @ Beta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prog_sem.simps(5)
% 0.20/0.47 thf(fact_305_same__fstI,axiom,
% 0.20/0.47 ! [P: produc190496183real_c > $o,X: produc190496183real_c,Y3: produc190496183real_c,Y: produc190496183real_c,R: produc190496183real_c > set_Pr754230471real_c] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ( member346808080real_c @ ( produc1687028567real_c @ Y3 @ Y ) @ ( R @ X ) )
% 0.20/0.47 => ( member616151824real_c @ ( produc544496471real_c @ ( produc1687028567real_c @ X @ Y3 ) @ ( produc1687028567real_c @ X @ Y ) ) @ ( same_f598810924real_c @ P @ R ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % same_fstI
% 0.20/0.47 thf(fact_306_same__fstI,axiom,
% 0.20/0.47 ! [P: finite1398487019real_c > $o,X: finite1398487019real_c,Y3: finite1398487019real_c,Y: finite1398487019real_c,R: finite1398487019real_c > set_Pr1389752855real_c] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ( member1895684704real_c @ ( produc394644079real_c @ Y3 @ Y ) @ ( R @ X ) )
% 0.20/0.47 => ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ X @ Y3 ) @ ( produc394644079real_c @ X @ Y ) ) @ ( same_f1974156740real_c @ P @ R ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % same_fstI
% 0.20/0.47 thf(fact_307_relChain__def,axiom,
% 0.20/0.47 ( bNF_Ca1667803246um_c_c
% 0.20/0.47 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Sum_sum_c_c] :
% 0.20/0.47 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 0.20/0.47 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 0.20/0.47 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relChain_def
% 0.20/0.47 thf(fact_308_relChain__def,axiom,
% 0.20/0.47 ( bNF_Ca1693016812um_c_c
% 0.20/0.47 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Sum_sum_c_c] :
% 0.20/0.47 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 0.20/0.47 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 0.20/0.47 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relChain_def
% 0.20/0.47 thf(fact_309_relChain__def,axiom,
% 0.20/0.47 ( bNF_Ca419199138um_b_c
% 0.20/0.47 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Su1783761653um_b_c] :
% 0.20/0.47 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 0.20/0.47 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 0.20/0.47 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relChain_def
% 0.20/0.47 thf(fact_310_relChain__def,axiom,
% 0.20/0.47 ( bNF_Ca318582436um_b_c
% 0.20/0.47 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Su1783761653um_b_c] :
% 0.20/0.47 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 0.20/0.47 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 0.20/0.47 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % relChain_def
% 0.20/0.47 thf(fact_311_GreatestI2__order,axiom,
% 0.20/0.47 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c,Q: set_Sum_sum_c_c > $o] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ! [Y4: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( P @ Y4 )
% 0.20/0.47 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 0.20/0.47 => ( ! [X2: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( P @ X2 )
% 0.20/0.47 => ( ! [Y6: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( P @ Y6 )
% 0.20/0.47 => ( ord_le1772180283um_c_c @ Y6 @ X2 ) )
% 0.20/0.47 => ( Q @ X2 ) ) )
% 0.20/0.47 => ( Q @ ( order_1776530114um_c_c @ P ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % GreatestI2_order
% 0.20/0.47 thf(fact_312_GreatestI2__order,axiom,
% 0.20/0.47 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c,Q: set_Su1783761653um_b_c > $o] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ! [Y4: set_Su1783761653um_b_c] :
% 0.20/0.47 ( ( P @ Y4 )
% 0.20/0.47 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 0.20/0.47 => ( ! [X2: set_Su1783761653um_b_c] :
% 0.20/0.47 ( ( P @ X2 )
% 0.20/0.47 => ( ! [Y6: set_Su1783761653um_b_c] :
% 0.20/0.47 ( ( P @ Y6 )
% 0.20/0.47 => ( ord_le929608341um_b_c @ Y6 @ X2 ) )
% 0.20/0.47 => ( Q @ X2 ) ) )
% 0.20/0.47 => ( Q @ ( order_365181262um_b_c @ P ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % GreatestI2_order
% 0.20/0.47 thf(fact_313_Greatest__equality,axiom,
% 0.20/0.47 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( P @ X )
% 0.20/0.47 => ( ! [Y4: set_Sum_sum_c_c] :
% 0.20/0.47 ( ( P @ Y4 )
% 0.20/0.47 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 0.32/0.47 => ( ( order_1776530114um_c_c @ P )
% 0.32/0.47 = X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Greatest_equality
% 0.32/0.47 thf(fact_314_Greatest__equality,axiom,
% 0.32/0.47 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c] :
% 0.32/0.47 ( ( P @ X )
% 0.32/0.47 => ( ! [Y4: set_Su1783761653um_b_c] :
% 0.32/0.47 ( ( P @ Y4 )
% 0.32/0.47 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 0.32/0.47 => ( ( order_365181262um_b_c @ P )
% 0.32/0.47 = X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Greatest_equality
% 0.32/0.47 thf(fact_315_prod_Ocollapse,axiom,
% 0.32/0.47 ! [Prod: produc640052711real_c] :
% 0.32/0.47 ( ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) )
% 0.32/0.47 = Prod ) ).
% 0.32/0.47
% 0.32/0.47 % prod.collapse
% 0.32/0.47 thf(fact_316_prod_Ocollapse,axiom,
% 0.32/0.47 ! [Prod: produc190496183real_c] :
% 0.32/0.47 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.32/0.47 = Prod ) ).
% 0.32/0.47
% 0.32/0.47 % prod.collapse
% 0.32/0.47 thf(fact_317_less__eq__prod__def,axiom,
% 0.32/0.47 ( ord_le684454199um_c_c
% 0.32/0.47 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] :
% 0.32/0.47 ( ( ord_le1772180283um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) )
% 0.32/0.47 & ( ord_le1772180283um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_prod_def
% 0.32/0.47 thf(fact_318_less__eq__prod__def,axiom,
% 0.32/0.47 ( ord_le542695343um_b_c
% 0.32/0.47 = ( ^ [X3: produc263671631um_b_c,Y5: produc263671631um_b_c] :
% 0.32/0.47 ( ( ord_le1772180283um_c_c @ ( produc1758795157um_b_c @ X3 ) @ ( produc1758795157um_b_c @ Y5 ) )
% 0.32/0.47 & ( ord_le929608341um_b_c @ ( produc1193764051um_b_c @ X3 ) @ ( produc1193764051um_b_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_prod_def
% 0.32/0.47 thf(fact_319_less__eq__prod__def,axiom,
% 0.32/0.47 ( ord_le1852514783um_c_c
% 0.32/0.47 = ( ^ [X3: produc1573491071um_c_c,Y5: produc1573491071um_c_c] :
% 0.32/0.47 ( ( ord_le929608341um_b_c @ ( produc1455464333um_c_c @ X3 ) @ ( produc1455464333um_c_c @ Y5 ) )
% 0.32/0.47 & ( ord_le1772180283um_c_c @ ( produc890433227um_c_c @ X3 ) @ ( produc890433227um_c_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_prod_def
% 0.32/0.47 thf(fact_320_less__eq__prod__def,axiom,
% 0.32/0.47 ( ord_le907560199um_b_c
% 0.32/0.47 = ( ^ [X3: produc1415638375um_b_c,Y5: produc1415638375um_b_c] :
% 0.32/0.47 ( ( ord_le929608341um_b_c @ ( produc1961869763um_b_c @ X3 ) @ ( produc1961869763um_b_c @ Y5 ) )
% 0.32/0.47 & ( ord_le929608341um_b_c @ ( produc932426501um_b_c @ X3 ) @ ( produc932426501um_b_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_prod_def
% 0.32/0.47 thf(fact_321_sup__prod__def,axiom,
% 0.32/0.47 ( sup_su1399591867real_c
% 0.32/0.47 = ( ^ [X3: produc640052711real_c,Y5: produc640052711real_c] : ( produc1687028567real_c @ ( sup_su1639086475real_c @ ( produc876006723real_c @ X3 ) @ ( produc876006723real_c @ Y5 ) ) @ ( sup_su1639086475real_c @ ( produc415593093real_c @ X3 ) @ ( produc415593093real_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_prod_def
% 0.32/0.47 thf(fact_322_sup__prod__def,axiom,
% 0.32/0.47 ( sup_su1639086475real_c
% 0.32/0.47 = ( ^ [X3: produc190496183real_c,Y5: produc190496183real_c] : ( produc394644079real_c @ ( sup_su2141622551real_c @ ( produc2010422875real_c @ X3 ) @ ( produc2010422875real_c @ Y5 ) ) @ ( sup_su2141622551real_c @ ( produc314122909real_c @ X3 ) @ ( produc314122909real_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_prod_def
% 0.32/0.47 thf(fact_323_sup__prod__def,axiom,
% 0.32/0.47 ( sup_su1672617323um_c_c
% 0.32/0.47 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] : ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) ) @ ( sup_su1349021703um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_prod_def
% 0.32/0.47 thf(fact_324_fst__conv,axiom,
% 0.32/0.47 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 0.32/0.47 ( ( produc876006723real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 0.32/0.47 = X1 ) ).
% 0.32/0.47
% 0.32/0.47 % fst_conv
% 0.32/0.47 thf(fact_325_fst__conv,axiom,
% 0.32/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.32/0.47 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.32/0.47 = X1 ) ).
% 0.32/0.47
% 0.32/0.47 % fst_conv
% 0.32/0.47 thf(fact_326_fst__eqD,axiom,
% 0.32/0.47 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 0.32/0.47 ( ( ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.32/0.47 = A )
% 0.32/0.47 => ( X = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % fst_eqD
% 0.32/0.47 thf(fact_327_fst__eqD,axiom,
% 0.32/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.32/0.47 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.32/0.47 = A )
% 0.32/0.47 => ( X = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % fst_eqD
% 0.32/0.47 thf(fact_328_snd__conv,axiom,
% 0.32/0.47 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 0.32/0.47 ( ( produc415593093real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 0.32/0.47 = X22 ) ).
% 0.32/0.47
% 0.32/0.47 % snd_conv
% 0.32/0.47 thf(fact_329_snd__conv,axiom,
% 0.32/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.32/0.47 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.32/0.47 = X22 ) ).
% 0.32/0.47
% 0.32/0.47 % snd_conv
% 0.32/0.47 thf(fact_330_snd__eqD,axiom,
% 0.32/0.47 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 0.32/0.47 ( ( ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.32/0.47 = A )
% 0.32/0.47 => ( Y = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % snd_eqD
% 0.32/0.47 thf(fact_331_snd__eqD,axiom,
% 0.32/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.32/0.47 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.32/0.47 = A )
% 0.32/0.47 => ( Y = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % snd_eqD
% 0.32/0.47 thf(fact_332_surjective__pairing,axiom,
% 0.32/0.47 ! [T2: produc640052711real_c] :
% 0.32/0.47 ( T2
% 0.32/0.47 = ( produc1687028567real_c @ ( produc876006723real_c @ T2 ) @ ( produc415593093real_c @ T2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % surjective_pairing
% 0.32/0.47 thf(fact_333_surjective__pairing,axiom,
% 0.32/0.47 ! [T2: produc190496183real_c] :
% 0.32/0.47 ( T2
% 0.32/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ T2 ) @ ( produc314122909real_c @ T2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % surjective_pairing
% 0.32/0.47 thf(fact_334_prod_Oexhaust__sel,axiom,
% 0.32/0.47 ! [Prod: produc640052711real_c] :
% 0.32/0.47 ( Prod
% 0.32/0.47 = ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.exhaust_sel
% 0.32/0.47 thf(fact_335_prod_Oexhaust__sel,axiom,
% 0.32/0.47 ! [Prod: produc190496183real_c] :
% 0.32/0.47 ( Prod
% 0.32/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.exhaust_sel
% 0.32/0.47 thf(fact_336_exI__realizer,axiom,
% 0.32/0.47 ! [P: produc190496183real_c > produc190496183real_c > $o,Y: produc190496183real_c,X: produc190496183real_c] :
% 0.32/0.47 ( ( P @ Y @ X )
% 0.32/0.47 => ( P @ ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) ) @ ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % exI_realizer
% 0.32/0.47 thf(fact_337_exI__realizer,axiom,
% 0.32/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 0.32/0.47 ( ( P @ Y @ X )
% 0.32/0.47 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % exI_realizer
% 0.32/0.47 thf(fact_338_conjI__realizer,axiom,
% 0.32/0.47 ! [P: produc190496183real_c > $o,P2: produc190496183real_c,Q: produc190496183real_c > $o,Q2: produc190496183real_c] :
% 0.32/0.47 ( ( P @ P2 )
% 0.32/0.47 => ( ( Q @ Q2 )
% 0.32/0.47 => ( ( P @ ( produc876006723real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) )
% 0.32/0.47 & ( Q @ ( produc415593093real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % conjI_realizer
% 0.32/0.47 thf(fact_339_conjI__realizer,axiom,
% 0.32/0.47 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 0.32/0.47 ( ( P @ P2 )
% 0.32/0.47 => ( ( Q @ Q2 )
% 0.32/0.47 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 0.32/0.47 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % conjI_realizer
% 0.32/0.47 thf(fact_340_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.32/0.47 ! [P: produc190496183real_c > produc190496183real_c > $o,X: produc190496183real_c,Y: produc190496183real_c,A: produc640052711real_c] :
% 0.32/0.47 ( ( P @ X @ Y )
% 0.32/0.47 => ( ( A
% 0.32/0.47 = ( produc1687028567real_c @ X @ Y ) )
% 0.32/0.47 => ( P @ ( produc876006723real_c @ A ) @ ( produc415593093real_c @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.32/0.47 thf(fact_341_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.32/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A: produc190496183real_c] :
% 0.32/0.47 ( ( P @ X @ Y )
% 0.32/0.47 => ( ( A
% 0.32/0.47 = ( produc394644079real_c @ X @ Y ) )
% 0.32/0.47 => ( P @ ( produc2010422875real_c @ A ) @ ( produc314122909real_c @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.32/0.47 thf(fact_342_sndI,axiom,
% 0.32/0.47 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( produc1687028567real_c @ Y @ Z ) )
% 0.32/0.47 => ( ( produc415593093real_c @ X )
% 0.32/0.47 = Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % sndI
% 0.32/0.47 thf(fact_343_sndI,axiom,
% 0.32/0.47 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( produc394644079real_c @ Y @ Z ) )
% 0.32/0.47 => ( ( produc314122909real_c @ X )
% 0.32/0.47 = Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % sndI
% 0.32/0.47 thf(fact_344_fstI,axiom,
% 0.32/0.47 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( produc1687028567real_c @ Y @ Z ) )
% 0.32/0.47 => ( ( produc876006723real_c @ X )
% 0.32/0.47 = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % fstI
% 0.32/0.47 thf(fact_345_fstI,axiom,
% 0.32/0.47 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( produc394644079real_c @ Y @ Z ) )
% 0.32/0.47 => ( ( produc2010422875real_c @ X )
% 0.32/0.47 = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % fstI
% 0.32/0.47 thf(fact_346_eq__snd__iff,axiom,
% 0.32/0.47 ! [B: produc190496183real_c,P2: produc640052711real_c] :
% 0.32/0.47 ( ( B
% 0.32/0.47 = ( produc415593093real_c @ P2 ) )
% 0.32/0.47 = ( ? [A4: produc190496183real_c] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc1687028567real_c @ A4 @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_snd_iff
% 0.32/0.47 thf(fact_347_eq__snd__iff,axiom,
% 0.32/0.47 ! [B: finite1398487019real_c,P2: produc190496183real_c] :
% 0.32/0.47 ( ( B
% 0.32/0.47 = ( produc314122909real_c @ P2 ) )
% 0.32/0.47 = ( ? [A4: finite1398487019real_c] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc394644079real_c @ A4 @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_snd_iff
% 0.32/0.47 thf(fact_348_eq__fst__iff,axiom,
% 0.32/0.47 ! [A: produc190496183real_c,P2: produc640052711real_c] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( produc876006723real_c @ P2 ) )
% 0.32/0.47 = ( ? [B4: produc190496183real_c] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc1687028567real_c @ A @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_fst_iff
% 0.32/0.47 thf(fact_349_eq__fst__iff,axiom,
% 0.32/0.47 ! [A: finite1398487019real_c,P2: produc190496183real_c] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( produc2010422875real_c @ P2 ) )
% 0.32/0.47 = ( ? [B4: finite1398487019real_c] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc394644079real_c @ A @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_fst_iff
% 0.32/0.47 thf(fact_350_prod_Oswap__def,axiom,
% 0.32/0.47 ( produc350724343real_c
% 0.32/0.47 = ( ^ [P3: produc640052711real_c] : ( produc1687028567real_c @ ( produc415593093real_c @ P3 ) @ ( produc876006723real_c @ P3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.swap_def
% 0.32/0.47 thf(fact_351_prod_Oswap__def,axiom,
% 0.32/0.47 ( produc704157711real_c
% 0.32/0.47 = ( ^ [P3: produc190496183real_c] : ( produc394644079real_c @ ( produc314122909real_c @ P3 ) @ ( produc2010422875real_c @ P3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.swap_def
% 0.32/0.47 thf(fact_352_swap__simp,axiom,
% 0.32/0.47 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.32/0.47 ( ( produc350724343real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.32/0.47 = ( produc1687028567real_c @ Y @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % swap_simp
% 0.32/0.47 thf(fact_353_swap__simp,axiom,
% 0.32/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.32/0.47 ( ( produc704157711real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.32/0.47 = ( produc394644079real_c @ Y @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % swap_simp
% 0.32/0.47
% 0.32/0.47 % Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 ? [Mu6: produc190496183real_c] :
% 0.32/0.47 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu6 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
% 0.32/0.47 & ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu6 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 3.05/1.52 ---- Embedded in THF ---
% 3.05/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.05/1.52 %%% Generated on Tue Feb 24 08:24:26 EST 2026
% 3.05/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 3.05/1.52 %%% Logic specification used:
% 3.05/1.52 %%% thf(spec, logic, $$dhol).
% 3.05/1.52
% 3.05/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2DTF24065.p
% See solution above
% 3.05/1.52 ------------------------
% 3.05/1.58 ---- Cleaned THF ---
% 3.05/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J_J,type,
% 3.05/1.58 set_Pr242060487real_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.05/1.58 produc1037099239real_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.05/1.58 set_Pr754230471real_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.05/1.58 produc640052711real_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J_J_J,type,
% 3.05/1.58 produc1360640805um_b_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.05/1.58 produc1470506001real_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.05/1.58 produc793920321um_c_c: $tType ).
% 3.05/1.58
% 3.05/1.58 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J_J,type,
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% 3.05/1.58 coinci1852866155_a_b_c @ b ).
% 3.05/1.58
% 3.05/1.58 thf(fact_1_hpsafe__Choice_OIH_I1_J,axiom,
% 3.05/1.58 coinci1852866155_a_b_c @ a ).
% 3.05/1.58
% 3.05/1.58 thf(fact_2_prog__sem_H,axiom,
% 3.05/1.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_3_agree_H,axiom,
% 3.05/1.58 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_4_prog__sem,axiom,
% 3.05/1.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ b ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_5_safe_I2_J,axiom,
% 3.05/1.58 hpsafe_a_b_c @ b ).
% 3.05/1.58
% 3.05/1.58 thf(fact_6_safe_I1_J,axiom,
% 3.05/1.58 hpsafe_a_b_c @ a ).
% 3.05/1.58
% 3.05/1.58 thf(fact_7_agree,axiom,
% 3.05/1.58 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.05/1.58 ~ ! [Mu: produc190496183real_c] :
% 3.05/1.58 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu ) @ ( denota904684656_a_b_c @ j @ b ) )
% 3.05/1.58 => ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_9_VA,axiom,
% 3.05/1.58 denota1997846518gree_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ v ).
% 3.05/1.58
% 3.05/1.58 thf(fact_10_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 3.05/1.58 = ( produc394644079real_c @ ( sup_su2141622551real_c @ A @ C ) @ ( sup_su2141622551real_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_11_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 3.05/1.58 = ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_12_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 3.05/1.58 = ( produc1687028567real_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_13_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su421398139um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 3.05/1.58 = ( produc919784577um_b_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_14_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1731217579um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 3.05/1.58 = ( produc616453753um_c_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_15_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: produc190496183real_c,C: set_Sum_sum_c_c,D: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su2023888701real_c @ ( produc439851843real_c @ A @ B ) @ ( produc439851843real_c @ C @ D ) )
% 3.05/1.58 = ( produc439851843real_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_16_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: set_Sum_sum_c_c,C: produc190496183real_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1347303021um_c_c @ ( produc639456571um_c_c @ A @ B ) @ ( produc639456571um_c_c @ C @ D ) )
% 3.05/1.58 = ( produc639456571um_c_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_17_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1580927803um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 3.05/1.58 = ( produc754249687um_b_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_18_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: produc214722967um_c_c,C: set_Sum_sum_c_c,D: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su505296157um_c_c @ ( produc1333497635um_c_c @ A @ B ) @ ( produc1333497635um_c_c @ C @ D ) )
% 3.05/1.58 = ( produc1333497635um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1672617323um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_19_sup__Pair__Pair,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: set_Su1783761653um_b_c,C: produc190496183real_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1009753337um_b_c @ ( produc2010919061um_b_c @ A @ B ) @ ( produc2010919061um_b_c @ C @ D ) )
% 3.05/1.58 = ( produc2010919061um_b_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_20_sem,axiom,
% 3.05/1.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ ( choice_a_b_c @ a @ b ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_21_sub,axiom,
% 3.05/1.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ).
% 3.05/1.58
% 3.05/1.58 thf(fact_22_False,axiom,
% 3.05/1.58 ~ ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_23_hp_Oinject_I6_J,axiom,
% 3.05/1.58 ! [X61: hp_a_b_c,X62: hp_a_b_c,Y61: hp_a_b_c,Y62: hp_a_b_c] :
% 3.05/1.58 ( ( ( choice_a_b_c @ X61 @ X62 )
% 3.05/1.58 = ( choice_a_b_c @ Y61 @ Y62 ) )
% 3.05/1.58 = ( ( X61 = Y61 )
% 3.05/1.58 & ( X62 = Y62 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_24_UnCI,axiom,
% 3.05/1.58 ! [C: produc190496183real_c,B2: set_Pr1389752855real_c,A2: set_Pr1389752855real_c] :
% 3.05/1.58 ( ( ~ ( member1895684704real_c @ C @ B2 )
% 3.05/1.58 => ( member1895684704real_c @ C @ A2 ) )
% 3.05/1.58 => ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_25_UnCI,axiom,
% 3.05/1.58 ! [C: produc1037099239real_c,B2: set_Pr242060487real_c,A2: set_Pr242060487real_c] :
% 3.05/1.58 ( ( ~ ( member616151824real_c @ C @ B2 )
% 3.05/1.58 => ( member616151824real_c @ C @ A2 ) )
% 3.05/1.58 => ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_26_UnCI,axiom,
% 3.05/1.58 ! [C: sum_su737395349um_b_c,B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ~ ( member1893232190um_b_c @ C @ B2 )
% 3.05/1.58 => ( member1893232190um_b_c @ C @ A2 ) )
% 3.05/1.58 => ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_27_UnCI,axiom,
% 3.05/1.58 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( ~ ( member346808080real_c @ C @ B2 )
% 3.05/1.58 => ( member346808080real_c @ C @ A2 ) )
% 3.05/1.58 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_28_UnCI,axiom,
% 3.05/1.58 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ~ ( member_Sum_sum_c_c @ C @ B2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ A2 ) )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_29_Un__iff,axiom,
% 3.05/1.58 ! [C: produc190496183real_c,A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 3.05/1.58 ( ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) )
% 3.05/1.58 = ( ( member1895684704real_c @ C @ A2 )
% 3.05/1.58 | ( member1895684704real_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_30_Un__iff,axiom,
% 3.05/1.58 ! [C: produc1037099239real_c,A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 3.05/1.58 ( ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) )
% 3.05/1.58 = ( ( member616151824real_c @ C @ A2 )
% 3.05/1.58 | ( member616151824real_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_31_Un__iff,axiom,
% 3.05/1.58 ! [C: sum_su737395349um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 3.05/1.58 = ( ( member1893232190um_b_c @ C @ A2 )
% 3.05/1.58 | ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_32_Un__iff,axiom,
% 3.05/1.58 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 3.05/1.58 = ( ( member346808080real_c @ C @ A2 )
% 3.05/1.58 | ( member346808080real_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_33_Un__iff,axiom,
% 3.05/1.58 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 = ( ( member_Sum_sum_c_c @ C @ A2 )
% 3.05/1.58 | ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_34_sup_Oidem,axiom,
% 3.05/1.58 ! [A: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_35_sup_Oidem,axiom,
% 3.05/1.58 ! [A: produc640052711real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_36_sup_Oidem,axiom,
% 3.05/1.58 ! [A: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_37_sup_Oidem,axiom,
% 3.05/1.58 ! [A: set_Pr754230471real_c] :
% 3.05/1.58 ( ( sup_su588839579real_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_38_sup_Oidem,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_39_sup_Oidem,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A @ A )
% 3.05/1.58 = A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_40_sup__idem,axiom,
% 3.05/1.58 ! [X: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_41_sup__idem,axiom,
% 3.05/1.58 ! [X: produc640052711real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_42_sup__idem,axiom,
% 3.05/1.58 ! [X: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_43_sup__idem,axiom,
% 3.05/1.58 ! [X: set_Pr754230471real_c] :
% 3.05/1.58 ( ( sup_su588839579real_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_44_sup__idem,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_45_sup__idem,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X @ X )
% 3.05/1.58 = X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_46_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ A @ ( sup_su1639086475real_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_47_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ A @ ( sup_su1399591867real_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_48_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ A @ ( sup_su1672617323um_c_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_49_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 3.05/1.58 ( ( sup_su588839579real_c @ A @ ( sup_su588839579real_c @ A @ B ) )
% 3.05/1.58 = ( sup_su588839579real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_50_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_51_sup_Oleft__idem,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_52_subsetI,axiom,
% 3.05/1.58 ! [A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 3.05/1.58 ( ! [X2: produc190496183real_c] :
% 3.05/1.58 ( ( member1895684704real_c @ X2 @ A2 )
% 3.05/1.58 => ( member1895684704real_c @ X2 @ B2 ) )
% 3.05/1.58 => ( ord_le977353143real_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_53_subsetI,axiom,
% 3.05/1.58 ! [A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 3.05/1.58 ( ! [X2: produc1037099239real_c] :
% 3.05/1.58 ( ( member616151824real_c @ X2 @ A2 )
% 3.05/1.58 => ( member616151824real_c @ X2 @ B2 ) )
% 3.05/1.58 => ( ord_le100418663real_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_54_subsetI,axiom,
% 3.05/1.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 3.05/1.58 ( ! [X2: produc640052711real_c] :
% 3.05/1.58 ( ( member346808080real_c @ X2 @ A2 )
% 3.05/1.58 => ( member346808080real_c @ X2 @ B2 ) )
% 3.05/1.58 => ( ord_le1988344935real_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_55_subsetI,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ! [X2: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X2 @ A2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ X2 @ B2 ) )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_56_subsetI,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ! [X2: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( member1893232190um_b_c @ X2 @ A2 )
% 3.05/1.58 => ( member1893232190um_b_c @ X2 @ B2 ) )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_57_subset__antisym,axiom,
% 3.05/1.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 3.05/1.58 => ( ( ord_le1988344935real_c @ B2 @ A2 )
% 3.05/1.58 => ( A2 = B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_58_subset__antisym,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 3.05/1.58 => ( A2 = B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_59_subset__antisym,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 3.05/1.58 => ( A2 = B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_60_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ ( sup_su1639086475real_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_61_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ ( sup_su1399591867real_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_62_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ ( sup_su1672617323um_c_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_63_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 3.05/1.58 ( ( sup_su588839579real_c @ ( sup_su588839579real_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su588839579real_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_64_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_65_sup_Oright__idem,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ B )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_66_sup__left__idem,axiom,
% 3.05/1.58 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.05/1.58 ( ( sup_su1639086475real_c @ X @ ( sup_su1639086475real_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1639086475real_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_67_sup__left__idem,axiom,
% 3.05/1.58 ! [X: produc640052711real_c,Y: produc640052711real_c] :
% 3.05/1.58 ( ( sup_su1399591867real_c @ X @ ( sup_su1399591867real_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1399591867real_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_68_sup__left__idem,axiom,
% 3.05/1.58 ! [X: produc214722967um_c_c,Y: produc214722967um_c_c] :
% 3.05/1.58 ( ( sup_su1672617323um_c_c @ X @ ( sup_su1672617323um_c_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1672617323um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_69_sup__left__idem,axiom,
% 3.05/1.58 ! [X: set_Pr754230471real_c,Y: set_Pr754230471real_c] :
% 3.05/1.58 ( ( sup_su588839579real_c @ X @ ( sup_su588839579real_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su588839579real_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_70_sup__left__idem,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_71_sup__left__idem,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_72_sub2,axiom,
% 3.05/1.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ v ).
% 3.05/1.58
% 3.05/1.58 thf(fact_73_sub1,axiom,
% 3.05/1.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ v ).
% 3.05/1.58
% 3.05/1.58 thf(fact_74_Pair__le,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 3.05/1.58 ( ( ord_le652477831real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le850691415real_c @ A @ C )
% 3.05/1.58 & ( ord_le850691415real_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_75_Pair__le,axiom,
% 3.05/1.58 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 3.05/1.58 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le775706699real_c @ A @ C )
% 3.05/1.58 & ( ord_le775706699real_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_76_Pair__le,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le1772180283um_c_c @ A @ C )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_77_Pair__le,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le1772180283um_c_c @ A @ C )
% 3.05/1.58 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_78_Pair__le,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le929608341um_b_c @ A @ C )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_79_Pair__le,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 3.05/1.58 = ( ( ord_le929608341um_b_c @ A @ C )
% 3.05/1.58 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_80_sup_Obounded__iff,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 3.05/1.58 = ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_81_sup_Obounded__iff,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 3.05/1.58 = ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 & ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_82_le__sup__iff,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 3.05/1.58 = ( ( ord_le1772180283um_c_c @ X @ Z )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ Y @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_83_le__sup__iff,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ X @ Y ) @ Z )
% 3.05/1.58 = ( ( ord_le929608341um_b_c @ X @ Z )
% 3.05/1.58 & ( ord_le929608341um_b_c @ Y @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_84_Un__subset__iff,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 3.05/1.58 = ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ B2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_85_Un__subset__iff,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 )
% 3.05/1.58 = ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 3.05/1.58 & ( ord_le929608341um_b_c @ B2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_86_hpsafe__Choice__simps,axiom,
% 3.05/1.58 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 3.05/1.58 ( ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 3.05/1.58 = ( ( hpsafe_a_b_c @ A )
% 3.05/1.58 & ( hpsafe_a_b_c @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_87_sem2,axiom,
% 3.05/1.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_88_eitherSem,axiom,
% 3.05/1.58 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) )
% 3.05/1.58 | ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_89_in__mono,axiom,
% 3.05/1.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,X: produc640052711real_c] :
% 3.05/1.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member346808080real_c @ X @ A2 )
% 3.05/1.58 => ( member346808080real_c @ X @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_90_in__mono,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,X: sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member_Sum_sum_c_c @ X @ A2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ X @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_91_in__mono,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,X: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member1893232190um_b_c @ X @ A2 )
% 3.05/1.58 => ( member1893232190um_b_c @ X @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_92_subsetD,axiom,
% 3.05/1.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,C: produc640052711real_c] :
% 3.05/1.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member346808080real_c @ C @ A2 )
% 3.05/1.58 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_93_subsetD,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C: sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member_Sum_sum_c_c @ C @ A2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_94_subsetD,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( member1893232190um_b_c @ C @ A2 )
% 3.05/1.58 => ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_95_equalityE,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ~ ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ~ ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_96_equalityE,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ~ ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ~ ( ord_le929608341um_b_c @ B2 @ A2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_97_subset__eq,axiom,
% 3.05/1.58 ( ord_le1988344935real_c
% 3.05/1.58 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 3.05/1.58 ! [X3: produc640052711real_c] :
% 3.05/1.58 ( ( member346808080real_c @ X3 @ A3 )
% 3.05/1.58 => ( member346808080real_c @ X3 @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_98_subset__eq,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 3.05/1.58 ! [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ A3 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ X3 @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_99_subset__eq,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 3.05/1.58 ! [X3: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( member1893232190um_b_c @ X3 @ A3 )
% 3.05/1.58 => ( member1893232190um_b_c @ X3 @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_100_equalityD1,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_101_equalityD1,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_102_equalityD2,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_103_equalityD2,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( A2 = B2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ B2 @ A2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_104_subset__iff,axiom,
% 3.05/1.58 ( ord_le1988344935real_c
% 3.05/1.58 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 3.05/1.58 ! [T: produc640052711real_c] :
% 3.05/1.58 ( ( member346808080real_c @ T @ A3 )
% 3.05/1.58 => ( member346808080real_c @ T @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_105_subset__iff,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 3.05/1.58 ! [T: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ T @ A3 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ T @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_106_subset__iff,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 3.05/1.58 ! [T: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( member1893232190um_b_c @ T @ A3 )
% 3.05/1.58 => ( member1893232190um_b_c @ T @ B3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_107_subset__refl,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ A2 ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_108_subset__refl,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ A2 ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_109_Collect__mono,axiom,
% 3.05/1.58 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 3.05/1.58 ( ! [X2: sum_sum_c_c] :
% 3.05/1.58 ( ( P @ X2 )
% 3.05/1.58 => ( Q @ X2 ) )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_110_Collect__mono,axiom,
% 3.05/1.58 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 3.05/1.58 ( ! [X2: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( P @ X2 )
% 3.05/1.58 => ( Q @ X2 ) )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_111_subset__trans,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_112_subset__trans,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_113_set__eq__subset,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A3 @ B3 )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ B3 @ A3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_114_set__eq__subset,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A3 @ B3 )
% 3.05/1.58 & ( ord_le929608341um_b_c @ B3 @ A3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_115_mem__Collect__eq,axiom,
% 3.05/1.58 ! [A: produc640052711real_c,P: produc640052711real_c > $o] :
% 3.05/1.58 ( ( member346808080real_c @ A @ ( collec1126017874real_c @ P ) )
% 3.05/1.58 = ( P @ A ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_116_Collect__mem__eq,axiom,
% 3.05/1.58 ! [A2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( collec1126017874real_c
% 3.05/1.58 @ ^ [X3: produc640052711real_c] : ( member346808080real_c @ X3 @ A2 ) )
% 3.05/1.58 = A2 ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_117_Collect__mono__iff,axiom,
% 3.05/1.58 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) )
% 3.05/1.58 = ( ! [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( P @ X3 )
% 3.05/1.58 => ( Q @ X3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_118_Collect__mono__iff,axiom,
% 3.05/1.58 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 3.05/1.58 = ( ! [X3: sum_su737395349um_b_c] :
% 3.05/1.58 ( ( P @ X3 )
% 3.05/1.58 => ( Q @ X3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_119_Pair__mono,axiom,
% 3.05/1.58 ! [X: produc190496183real_c,X4: produc190496183real_c,Y: produc190496183real_c,Y3: produc190496183real_c] :
% 3.05/1.58 ( ( ord_le850691415real_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le850691415real_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le652477831real_c @ ( produc1687028567real_c @ X @ Y ) @ ( produc1687028567real_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_120_Pair__mono,axiom,
% 3.05/1.58 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.05/1.58 ( ( ord_le775706699real_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le775706699real_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_121_Pair__mono,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ X @ Y ) @ ( produc1439061071um_c_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_122_Pair__mono,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ X @ Y ) @ ( produc919784577um_b_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_123_Pair__mono,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ X @ Y ) @ ( produc616453753um_c_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_124_Pair__mono,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ X4 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 3.05/1.58 => ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ X @ Y ) @ ( produc754249687um_b_c @ X4 @ Y3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_125_sup_OcoboundedI2,axiom,
% 3.05/1.58 ! [C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ C @ B )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_126_sup_OcoboundedI2,axiom,
% 3.05/1.58 ! [C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ C @ B )
% 3.05/1.58 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_127_sup_OcoboundedI1,axiom,
% 3.05/1.58 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ C @ A )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_128_sup_OcoboundedI1,axiom,
% 3.05/1.58 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ C @ A )
% 3.05/1.58 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_129_sup_Oabsorb__iff2,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 3.05/1.58 = B4 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_130_sup_Oabsorb__iff2,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 3.05/1.58 = B4 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_131_sup_Oabsorb__iff1,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 3.05/1.58 = A4 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_132_sup_Oabsorb__iff1,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 3.05/1.58 = A4 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_133_sup_Ocobounded2,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_134_sup_Ocobounded2,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_135_sup_Ocobounded1,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_136_sup_Ocobounded1,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_137_sup_Oorder__iff,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.05/1.58 ( A4
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_138_sup_Oorder__iff,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 3.05/1.58 ( A4
% 3.05/1.58 = ( sup_su1968964297um_b_c @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_139_sup_OboundedI,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ C @ A )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_140_sup_OboundedI,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ C @ A )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_141_sup_OboundedE,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 3.05/1.58 => ~ ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ~ ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_142_sup_OboundedE,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 3.05/1.58 => ~ ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ~ ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_143_sup__absorb2,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ Y )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 3.05/1.58 = Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_144_sup__absorb2,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ Y )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 3.05/1.58 = Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_145_sup__absorb1,axiom,
% 3.05/1.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ Y @ X )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 3.05/1.58 = X ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_146_sup__absorb1,axiom,
% 3.05/1.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ Y @ X )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 3.05/1.58 = X ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_147_sup_Oabsorb2,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A @ B )
% 3.05/1.58 = B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_148_sup_Oabsorb2,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ A @ B )
% 3.05/1.58 = B ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_149_sup_Oabsorb1,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A @ B )
% 3.05/1.58 = A ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_150_sup_Oabsorb1,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ A @ B )
% 3.05/1.58 = A ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_151_sup__unique,axiom,
% 3.05/1.58 ! [F: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c,X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X2 @ ( F @ X2 @ Y4 ) )
% 3.05/1.58 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 3.05/1.58 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c,Z3: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ Y4 @ X2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Z3 @ X2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 3.05/1.58 = ( F @ X @ Y ) ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_152_sup__unique,axiom,
% 3.05/1.58 ! [F: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X2 @ ( F @ X2 @ Y4 ) )
% 3.05/1.58 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 3.05/1.58 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c,Z3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ Y4 @ X2 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ Z3 @ X2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 3.05/1.58 = ( F @ X @ Y ) ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_153_sup_OorderI,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ B ) )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ B @ A ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_154_sup_OorderI,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( A
% 3.05/1.58 = ( sup_su1968964297um_b_c @ A @ B ) )
% 3.05/1.58 => ( ord_le929608341um_b_c @ B @ A ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_155_sup_OorderE,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( A
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_156_sup_OorderE,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( A
% 3.05/1.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_157_le__iff__sup,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X3 @ Y5 )
% 3.05/1.58 = Y5 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_158_le__iff__sup,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ X3 @ Y5 )
% 3.05/1.58 = Y5 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_159_sup__least,axiom,
% 3.05/1.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ Y @ X )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Z @ X )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ Y @ Z ) @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_160_sup__least,axiom,
% 3.05/1.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ Y @ X )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ Z @ X )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ Y @ Z ) @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_161_sup__mono,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ C )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B @ D )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ ( sup_su1349021703um_c_c @ C @ D ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_162_sup__mono,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ C )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B @ D )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ ( sup_su1968964297um_b_c @ C @ D ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_163_sup_Omono,axiom,
% 3.05/1.58 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,D: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ C @ A )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ D @ B )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ C @ D ) @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_164_sup_Omono,axiom,
% 3.05/1.58 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ C @ A )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ D @ B )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ C @ D ) @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_165_le__supI2,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ B )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_166_le__supI2,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ B )
% 3.05/1.58 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_167_le__supI1,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ A )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_168_le__supI1,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ A )
% 3.05/1.58 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_169_sup__ge2,axiom,
% 3.05/1.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_170_sup__ge2,axiom,
% 3.05/1.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_171_sup__ge1,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_172_sup__ge1,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_173_le__supI,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,X: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ X )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B @ X )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_174_le__supI,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ X )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B @ X )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_175_le__supE,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X )
% 3.05/1.58 => ~ ( ( ord_le1772180283um_c_c @ A @ X )
% 3.05/1.58 => ~ ( ord_le1772180283um_c_c @ B @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_176_le__supE,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X )
% 3.05/1.58 => ~ ( ( ord_le929608341um_b_c @ A @ X )
% 3.05/1.58 => ~ ( ord_le929608341um_b_c @ B @ X ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_177_inf__sup__ord_I3_J,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_178_inf__sup__ord_I3_J,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_179_inf__sup__ord_I4_J,axiom,
% 3.05/1.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_180_inf__sup__ord_I4_J,axiom,
% 3.05/1.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_181_subset__Un__eq,axiom,
% 3.05/1.58 ( ord_le1772180283um_c_c
% 3.05/1.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A3 @ B3 )
% 3.05/1.58 = B3 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_182_subset__Un__eq,axiom,
% 3.05/1.58 ( ord_le929608341um_b_c
% 3.05/1.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( sup_su1968964297um_b_c @ A3 @ B3 )
% 3.05/1.58 = B3 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_183_subset__UnE,axiom,
% 3.05/1.58 ! [C2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ C2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 => ~ ! [A5: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A5 @ A2 )
% 3.05/1.58 => ! [B5: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B5 @ B2 )
% 3.05/1.58 => ( C2
% 3.05/1.58 != ( sup_su1349021703um_c_c @ A5 @ B5 ) ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_184_subset__UnE,axiom,
% 3.05/1.58 ! [C2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ C2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 3.05/1.58 => ~ ! [A5: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A5 @ A2 )
% 3.05/1.58 => ! [B5: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B5 @ B2 )
% 3.05/1.58 => ( C2
% 3.05/1.58 != ( sup_su1968964297um_b_c @ A5 @ B5 ) ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_185_Un__absorb2,axiom,
% 3.05/1.58 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 3.05/1.58 = A2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_186_Un__absorb2,axiom,
% 3.05/1.58 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 3.05/1.58 = A2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_187_Un__absorb1,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 3.05/1.58 = B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_188_Un__absorb1,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 3.05/1.58 = B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_189_Un__upper2,axiom,
% 3.05/1.58 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_190_Un__upper2,axiom,
% 3.05/1.58 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_191_Un__upper1,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_192_Un__upper1,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_193_Un__least,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_194_Un__least,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_195_Un__mono,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,D2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B2 @ D2 )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ ( sup_su1349021703um_c_c @ C2 @ D2 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_196_Un__mono,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,D2: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B2 @ D2 )
% 3.05/1.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ ( sup_su1968964297um_b_c @ C2 @ D2 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_197_hpsafe__fsafe_Ohpsafe__Choice,axiom,
% 3.05/1.58 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 3.05/1.58 ( ( hpsafe_a_b_c @ A )
% 3.05/1.58 => ( ( hpsafe_a_b_c @ B )
% 3.05/1.58 => ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_198_sup__left__commute,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_199_sup_Oleft__commute,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ C ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_200_sup__commute,axiom,
% 3.05/1.58 ( sup_su1349021703um_c_c
% 3.05/1.58 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_201_sup_Ocommute,axiom,
% 3.05/1.58 ( sup_su1349021703um_c_c
% 3.05/1.58 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B4 @ A4 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_202_sup__assoc,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_203_sup_Oassoc,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ C )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_204_boolean__algebra__cancel_Osup2,axiom,
% 3.05/1.58 ! [B2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( B2
% 3.05/1.58 = ( sup_su1349021703um_c_c @ K @ B ) )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A @ B2 )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_205_boolean__algebra__cancel_Osup1,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A2
% 3.05/1.58 = ( sup_su1349021703um_c_c @ K @ A ) )
% 3.05/1.58 => ( ( sup_su1349021703um_c_c @ A2 @ B )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_206_inf__sup__aci_I5_J,axiom,
% 3.05/1.58 ( sup_su1349021703um_c_c
% 3.05/1.58 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_207_inf__sup__aci_I6_J,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_208_inf__sup__aci_I7_J,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_209_inf__sup__aci_I8_J,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_210_Un__left__commute,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_211_Un__left__absorb,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_212_Un__commute,axiom,
% 3.05/1.58 ( sup_su1349021703um_c_c
% 3.05/1.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B3 @ A3 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_213_Un__absorb,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ A2 @ A2 )
% 3.05/1.58 = A2 ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_214_Un__assoc,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_215_ball__Un,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 3.05/1.58 ( ( ! [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 => ( P @ X3 ) ) )
% 3.05/1.58 = ( ! [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 3.05/1.58 => ( P @ X3 ) )
% 3.05/1.58 & ! [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 3.05/1.58 => ( P @ X3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_216_bex__Un,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 3.05/1.58 ( ( ? [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 & ( P @ X3 ) ) )
% 3.05/1.58 = ( ? [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 3.05/1.58 & ( P @ X3 ) )
% 3.05/1.58 | ? [X3: sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 3.05/1.58 & ( P @ X3 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_217_UnI2,axiom,
% 3.05/1.58 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( member346808080real_c @ C @ B2 )
% 3.05/1.58 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_218_UnI2,axiom,
% 3.05/1.58 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ C @ B2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_219_UnI1,axiom,
% 3.05/1.58 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( member346808080real_c @ C @ A2 )
% 3.05/1.58 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_220_UnI1,axiom,
% 3.05/1.58 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ C @ A2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_221_UnE,axiom,
% 3.05/1.58 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 3.05/1.58 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 3.05/1.58 => ( ~ ( member346808080real_c @ C @ A2 )
% 3.05/1.58 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_222_UnE,axiom,
% 3.05/1.58 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 3.05/1.58 => ( ~ ( member_Sum_sum_c_c @ C @ A2 )
% 3.05/1.58 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_223_IA,axiom,
% 3.05/1.58 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_224_IH1,axiom,
% 3.05/1.58 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.05/1.58 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ a ) )
% 3.05/1.58 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ V )
% 3.05/1.58 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ a ) )
% 3.05/1.58 => ? [Mu3: produc190496183real_c] :
% 3.05/1.58 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ a ) )
% 3.05/1.58 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ a ) @ V ) ) ) ) ) ) )
% 3.05/1.58 & ( coinci772602909_a_b_c @ a @ I ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_225_IH2,axiom,
% 3.05/1.58 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.05/1.58 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ b ) )
% 3.05/1.58 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ V )
% 3.05/1.58 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ b ) )
% 3.05/1.58 => ? [Mu3: produc190496183real_c] :
% 3.05/1.58 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ b ) )
% 3.05/1.58 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ V ) ) ) ) ) ) )
% 3.05/1.58 & ( coinci772602909_a_b_c @ b @ I ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_226_coincide__hp_H__def,axiom,
% 3.05/1.58 ( coinci1852866155_a_b_c
% 3.05/1.58 = ( ^ [Alpha: hp_a_b_c] :
% 3.05/1.58 ! [I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 3.05/1.58 ( ( coinci354700372_a_b_c @ Alpha @ I2 @ J2 )
% 3.05/1.58 & ( coinci772602909_a_b_c @ Alpha @ I2 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_227_FVP_Osimps_I6_J,axiom,
% 3.05/1.58 ! [Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 3.05/1.58 ( ( static_FVP_a_b_c @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 3.05/1.58 = ( sup_su1349021703um_c_c @ ( static_FVP_a_b_c @ Alpha2 ) @ ( static_FVP_a_b_c @ Beta ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_228_agree__supset,axiom,
% 3.05/1.58 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 3.05/1.58 => ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ A2 )
% 3.05/1.58 => ( denota1997846518gree_c @ Nu3 @ Nu4 @ B2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_229_agree__sub,axiom,
% 3.05/1.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 3.05/1.58 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 3.05/1.58 => ( denota1997846518gree_c @ Nu3 @ Omega @ A2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_230_old_Oprod_Oinject,axiom,
% 3.05/1.58 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 3.05/1.58 ( ( ( produc1687028567real_c @ A @ B )
% 3.05/1.58 = ( produc1687028567real_c @ A6 @ B6 ) )
% 3.05/1.58 = ( ( A = A6 )
% 3.05/1.58 & ( B = B6 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_231_old_Oprod_Oinject,axiom,
% 3.05/1.58 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 3.05/1.58 ( ( ( produc394644079real_c @ A @ B )
% 3.05/1.58 = ( produc394644079real_c @ A6 @ B6 ) )
% 3.05/1.58 = ( ( A = A6 )
% 3.05/1.58 & ( B = B6 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_232_prod_Oinject,axiom,
% 3.05/1.58 ! [X1: produc190496183real_c,X22: produc190496183real_c,Y1: produc190496183real_c,Y22: produc190496183real_c] :
% 3.05/1.58 ( ( ( produc1687028567real_c @ X1 @ X22 )
% 3.05/1.58 = ( produc1687028567real_c @ Y1 @ Y22 ) )
% 3.05/1.58 = ( ( X1 = Y1 )
% 3.05/1.58 & ( X22 = Y22 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_233_prod_Oinject,axiom,
% 3.05/1.58 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 3.05/1.58 ( ( ( produc394644079real_c @ X1 @ X22 )
% 3.05/1.58 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 3.05/1.58 = ( ( X1 = Y1 )
% 3.05/1.58 & ( X22 = Y22 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_234_order__refl,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_235_order__refl,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ X ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_236_Ssub_I2_J,axiom,
% 3.05/1.58 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ b ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_237_Ssub_I1_J,axiom,
% 3.05/1.58 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ a ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_238_IA2,axiom,
% 3.05/1.58 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ b ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_239_IA1,axiom,
% 3.05/1.58 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ a ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_240_coincide__hp__def,axiom,
% 3.05/1.58 ( coinci354700372_a_b_c
% 3.05/1.58 = ( ^ [Alpha: hp_a_b_c,I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 3.05/1.58 ! [Nu5: produc190496183real_c,Nu6: produc190496183real_c,Mu4: produc190496183real_c,V2: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( denota69106024_a_b_c @ I2 @ J2 @ ( static_SIGP_a_b_c @ Alpha ) )
% 3.05/1.58 => ( ( denota1997846518gree_c @ Nu5 @ Nu6 @ V2 )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ Alpha ) @ V2 )
% 3.05/1.58 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu5 @ Mu4 ) @ ( denota904684656_a_b_c @ I2 @ Alpha ) )
% 3.05/1.58 => ? [Mu5: produc190496183real_c] :
% 3.05/1.58 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu6 @ Mu5 ) @ ( denota904684656_a_b_c @ J2 @ Alpha ) )
% 3.05/1.58 & ( denota1997846518gree_c @ Mu4 @ Mu5 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ Alpha ) @ V2 ) ) ) ) ) ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_241_Iagree__sub,axiom,
% 3.05/1.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,I3: denota231621370t_unit,J3: denota231621370t_unit] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 3.05/1.58 => ( ( denota69106024_a_b_c @ I3 @ J3 @ B2 )
% 3.05/1.58 => ( denota69106024_a_b_c @ I3 @ J3 @ A2 ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_242_Iagree__refl,axiom,
% 3.05/1.58 ! [I3: denota231621370t_unit,A2: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A2 ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_243_Iagree__comm,axiom,
% 3.05/1.58 ! [A2: denota231621370t_unit,B2: denota231621370t_unit,V3: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( denota69106024_a_b_c @ A2 @ B2 @ V3 )
% 3.05/1.58 => ( denota69106024_a_b_c @ B2 @ A2 @ V3 ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_244_SIGP_Osimps_I6_J,axiom,
% 3.05/1.58 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 3.05/1.58 ( ( static_SIGP_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 3.05/1.58 = ( sup_su1968964297um_b_c @ ( static_SIGP_a_b_c @ A ) @ ( static_SIGP_a_b_c @ B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_245_dual__order_Oantisym,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.58 => ( A = B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_246_dual__order_Oantisym,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.58 => ( A = B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_247_dual__order_Oeq__iff,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B4 @ A4 )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_248_dual__order_Oeq__iff,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B4 @ A4 )
% 3.05/1.58 & ( ord_le929608341um_b_c @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_249_dual__order_Otrans,axiom,
% 3.05/1.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ C @ B )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_250_dual__order_Otrans,axiom,
% 3.05/1.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ C @ B )
% 3.05/1.58 => ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_251_dual__order_Orefl,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_252_dual__order_Orefl,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ A ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_253_order__trans,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ Y )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Y @ Z )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ X @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_254_order__trans,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ X @ Y )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ Y @ Z )
% 3.05/1.58 => ( ord_le929608341um_b_c @ X @ Z ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_255_order__class_Oorder_Oantisym,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B @ A )
% 3.05/1.58 => ( A = B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_256_order__class_Oorder_Oantisym,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B @ A )
% 3.05/1.58 => ( A = B ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_257_ord__le__eq__trans,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.58 => ( ( B = C )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_258_ord__le__eq__trans,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.58 => ( ( B = C )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_259_ord__eq__le__trans,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( A = B )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_260_ord__eq__le__trans,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( A = B )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_261_order__class_Oorder_Oeq__iff,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 3.05/1.58 & ( ord_le1772180283um_c_c @ B4 @ A4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_262_order__class_Oorder_Oeq__iff,axiom,
% 3.05/1.58 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 3.05/1.58 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A4 @ B4 )
% 3.05/1.58 & ( ord_le929608341um_b_c @ B4 @ A4 ) ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_263_antisym__conv,axiom,
% 3.05/1.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ Y @ X )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ X @ Y )
% 3.05/1.58 = ( X = Y ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_264_antisym__conv,axiom,
% 3.05/1.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ Y @ X )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ X @ Y )
% 3.05/1.58 = ( X = Y ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_265_order_Otrans,axiom,
% 3.05/1.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_266_order_Otrans,axiom,
% 3.05/1.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.58 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.58 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_267_eq__refl,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( X = Y )
% 3.05/1.58 => ( ord_le1772180283um_c_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_268_eq__refl,axiom,
% 3.05/1.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 3.05/1.58 ( ( X = Y )
% 3.05/1.58 => ( ord_le929608341um_b_c @ X @ Y ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_269_antisym,axiom,
% 3.05/1.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.05/1.58 ( ( ord_le1772180283um_c_c @ X @ Y )
% 3.05/1.58 => ( ( ord_le1772180283um_c_c @ Y @ X )
% 3.05/1.58 => ( X = Y ) ) ) ).
% 3.05/1.58
% 3.05/1.58 thf(fact_270_antisym,axiom,
% 3.05/1.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X @ Y )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ Y @ X )
% 3.05/1.59 => ( X = Y ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_271_eq__iff,axiom,
% 3.05/1.59 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 3.05/1.59 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X3 @ Y5 )
% 3.05/1.59 & ( ord_le1772180283um_c_c @ Y5 @ X3 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_272_eq__iff,axiom,
% 3.05/1.59 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 3.05/1.59 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X3 @ Y5 )
% 3.05/1.59 & ( ord_le929608341um_b_c @ Y5 @ X3 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_273_ord__le__eq__subst,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.59 => ( ( ( F @ B )
% 3.05/1.59 = C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_274_ord__le__eq__subst,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.59 => ( ( ( F @ B )
% 3.05/1.59 = C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_275_ord__le__eq__subst,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.59 => ( ( ( F @ B )
% 3.05/1.59 = C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_276_ord__le__eq__subst,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.59 => ( ( ( F @ B )
% 3.05/1.59 = C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_277_ord__eq__le__subst,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( F @ B ) )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_278_ord__eq__le__subst,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( F @ B ) )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_279_ord__eq__le__subst,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( F @ B ) )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_280_ord__eq__le__subst,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( F @ B ) )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_281_order__subst2,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_282_order__subst2,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_283_order__subst2,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_284_order__subst2,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ B )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_285_order__subst1,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_286_order__subst1,axiom,
% 3.05/1.59 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_287_order__subst1,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 3.05/1.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_288_order__subst1,axiom,
% 3.05/1.59 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 3.05/1.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 3.05/1.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_289_surj__pair,axiom,
% 3.05/1.59 ! [P2: produc640052711real_c] :
% 3.05/1.59 ? [X2: produc190496183real_c,Y4: produc190496183real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc1687028567real_c @ X2 @ Y4 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_290_surj__pair,axiom,
% 3.05/1.59 ! [P2: produc190496183real_c] :
% 3.05/1.59 ? [X2: finite1398487019real_c,Y4: finite1398487019real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc394644079real_c @ X2 @ Y4 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_291_prod__cases,axiom,
% 3.05/1.59 ! [P: produc640052711real_c > $o,P2: produc640052711real_c] :
% 3.05/1.59 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 3.05/1.59 => ( P @ P2 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_292_prod__cases,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 3.05/1.59 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 3.05/1.59 => ( P @ P2 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_293_Pair__inject,axiom,
% 3.05/1.59 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 3.05/1.59 ( ( ( produc1687028567real_c @ A @ B )
% 3.05/1.59 = ( produc1687028567real_c @ A6 @ B6 ) )
% 3.05/1.59 => ~ ( ( A = A6 )
% 3.05/1.59 => ( B != B6 ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_294_Pair__inject,axiom,
% 3.05/1.59 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 3.05/1.59 ( ( ( produc394644079real_c @ A @ B )
% 3.05/1.59 = ( produc394644079real_c @ A6 @ B6 ) )
% 3.05/1.59 => ~ ( ( A = A6 )
% 3.05/1.59 => ( B != B6 ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_295_old_Oprod_Oexhaust,axiom,
% 3.05/1.59 ! [Y: produc640052711real_c] :
% 3.05/1.59 ~ ! [A7: produc190496183real_c,B7: produc190496183real_c] :
% 3.05/1.59 ( Y
% 3.05/1.59 != ( produc1687028567real_c @ A7 @ B7 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_296_old_Oprod_Oexhaust,axiom,
% 3.05/1.59 ! [Y: produc190496183real_c] :
% 3.05/1.59 ~ ! [A7: finite1398487019real_c,B7: finite1398487019real_c] :
% 3.05/1.59 ( Y
% 3.05/1.59 != ( produc394644079real_c @ A7 @ B7 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_297_old_Oprod_Oinducts,axiom,
% 3.05/1.59 ! [P: produc640052711real_c > $o,Prod: produc640052711real_c] :
% 3.05/1.59 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 3.05/1.59 => ( P @ Prod ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_298_old_Oprod_Oinducts,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 3.05/1.59 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 3.05/1.59 => ( P @ Prod ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_299_agree__comm,axiom,
% 3.05/1.59 ! [A2: produc190496183real_c,B2: produc190496183real_c,V3: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( denota1997846518gree_c @ A2 @ B2 @ V3 )
% 3.05/1.59 => ( denota1997846518gree_c @ B2 @ A2 @ V3 ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_300_agree__refl,axiom,
% 3.05/1.59 ! [Nu3: produc190496183real_c,A2: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A2 ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_301_prod__cases3,axiom,
% 3.05/1.59 ! [Y: produc640052711real_c] :
% 3.05/1.59 ~ ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] :
% 3.05/1.59 ( Y
% 3.05/1.59 != ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_302_prod__induct3,axiom,
% 3.05/1.59 ! [P: produc640052711real_c > $o,X: produc640052711real_c] :
% 3.05/1.59 ( ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] : ( P @ ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) )
% 3.05/1.59 => ( P @ X ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_303_agree__union,axiom,
% 3.05/1.59 ! [Nu3: produc190496183real_c,Omega: produc190496183real_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( denota1997846518gree_c @ Nu3 @ Omega @ A2 )
% 3.05/1.59 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 3.05/1.59 => ( denota1997846518gree_c @ Nu3 @ Omega @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_304_prog__sem_Osimps_I5_J,axiom,
% 3.05/1.59 ! [I3: denota231621370t_unit,Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 3.05/1.59 ( ( denota904684656_a_b_c @ I3 @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 3.05/1.59 = ( sup_su588839579real_c @ ( denota904684656_a_b_c @ I3 @ Alpha2 ) @ ( denota904684656_a_b_c @ I3 @ Beta ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_305_same__fstI,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > $o,X: produc190496183real_c,Y3: produc190496183real_c,Y: produc190496183real_c,R: produc190496183real_c > set_Pr754230471real_c] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ( member346808080real_c @ ( produc1687028567real_c @ Y3 @ Y ) @ ( R @ X ) )
% 3.05/1.59 => ( member616151824real_c @ ( produc544496471real_c @ ( produc1687028567real_c @ X @ Y3 ) @ ( produc1687028567real_c @ X @ Y ) ) @ ( same_f598810924real_c @ P @ R ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_306_same__fstI,axiom,
% 3.05/1.59 ! [P: finite1398487019real_c > $o,X: finite1398487019real_c,Y3: finite1398487019real_c,Y: finite1398487019real_c,R: finite1398487019real_c > set_Pr1389752855real_c] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ( member1895684704real_c @ ( produc394644079real_c @ Y3 @ Y ) @ ( R @ X ) )
% 3.05/1.59 => ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ X @ Y3 ) @ ( produc394644079real_c @ X @ Y ) ) @ ( same_f1974156740real_c @ P @ R ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_307_relChain__def,axiom,
% 3.05/1.59 ( bNF_Ca1667803246um_c_c
% 3.05/1.59 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Sum_sum_c_c] :
% 3.05/1.59 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 3.05/1.59 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_308_relChain__def,axiom,
% 3.05/1.59 ( bNF_Ca1693016812um_c_c
% 3.05/1.59 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Sum_sum_c_c] :
% 3.05/1.59 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 3.05/1.59 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_309_relChain__def,axiom,
% 3.05/1.59 ( bNF_Ca419199138um_b_c
% 3.05/1.59 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Su1783761653um_b_c] :
% 3.05/1.59 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 3.05/1.59 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_310_relChain__def,axiom,
% 3.05/1.59 ( bNF_Ca318582436um_b_c
% 3.05/1.59 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Su1783761653um_b_c] :
% 3.05/1.59 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 3.05/1.59 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_311_GreatestI2__order,axiom,
% 3.05/1.59 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c,Q: set_Sum_sum_c_c > $o] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ! [Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( P @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 3.05/1.59 => ( ! [X2: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( P @ X2 )
% 3.05/1.59 => ( ! [Y6: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( P @ Y6 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ Y6 @ X2 ) )
% 3.05/1.59 => ( Q @ X2 ) ) )
% 3.05/1.59 => ( Q @ ( order_1776530114um_c_c @ P ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_312_GreatestI2__order,axiom,
% 3.05/1.59 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c,Q: set_Su1783761653um_b_c > $o] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ! [Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( P @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 3.05/1.59 => ( ! [X2: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( P @ X2 )
% 3.05/1.59 => ( ! [Y6: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( P @ Y6 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ Y6 @ X2 ) )
% 3.05/1.59 => ( Q @ X2 ) ) )
% 3.05/1.59 => ( Q @ ( order_365181262um_b_c @ P ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_313_Greatest__equality,axiom,
% 3.05/1.59 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ! [Y4: set_Sum_sum_c_c] :
% 3.05/1.59 ( ( P @ Y4 )
% 3.05/1.59 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 3.05/1.59 => ( ( order_1776530114um_c_c @ P )
% 3.05/1.59 = X ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_314_Greatest__equality,axiom,
% 3.05/1.59 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( P @ X )
% 3.05/1.59 => ( ! [Y4: set_Su1783761653um_b_c] :
% 3.05/1.59 ( ( P @ Y4 )
% 3.05/1.59 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 3.05/1.59 => ( ( order_365181262um_b_c @ P )
% 3.05/1.59 = X ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_315_prod_Ocollapse,axiom,
% 3.05/1.59 ! [Prod: produc640052711real_c] :
% 3.05/1.59 ( ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) )
% 3.05/1.59 = Prod ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_316_prod_Ocollapse,axiom,
% 3.05/1.59 ! [Prod: produc190496183real_c] :
% 3.05/1.59 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 3.05/1.59 = Prod ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_317_less__eq__prod__def,axiom,
% 3.05/1.59 ( ord_le684454199um_c_c
% 3.05/1.59 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) )
% 3.05/1.59 & ( ord_le1772180283um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_318_less__eq__prod__def,axiom,
% 3.05/1.59 ( ord_le542695343um_b_c
% 3.05/1.59 = ( ^ [X3: produc263671631um_b_c,Y5: produc263671631um_b_c] :
% 3.05/1.59 ( ( ord_le1772180283um_c_c @ ( produc1758795157um_b_c @ X3 ) @ ( produc1758795157um_b_c @ Y5 ) )
% 3.05/1.59 & ( ord_le929608341um_b_c @ ( produc1193764051um_b_c @ X3 ) @ ( produc1193764051um_b_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_319_less__eq__prod__def,axiom,
% 3.05/1.59 ( ord_le1852514783um_c_c
% 3.05/1.59 = ( ^ [X3: produc1573491071um_c_c,Y5: produc1573491071um_c_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ ( produc1455464333um_c_c @ X3 ) @ ( produc1455464333um_c_c @ Y5 ) )
% 3.05/1.59 & ( ord_le1772180283um_c_c @ ( produc890433227um_c_c @ X3 ) @ ( produc890433227um_c_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_320_less__eq__prod__def,axiom,
% 3.05/1.59 ( ord_le907560199um_b_c
% 3.05/1.59 = ( ^ [X3: produc1415638375um_b_c,Y5: produc1415638375um_b_c] :
% 3.05/1.59 ( ( ord_le929608341um_b_c @ ( produc1961869763um_b_c @ X3 ) @ ( produc1961869763um_b_c @ Y5 ) )
% 3.05/1.59 & ( ord_le929608341um_b_c @ ( produc932426501um_b_c @ X3 ) @ ( produc932426501um_b_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_321_sup__prod__def,axiom,
% 3.05/1.59 ( sup_su1399591867real_c
% 3.05/1.59 = ( ^ [X3: produc640052711real_c,Y5: produc640052711real_c] : ( produc1687028567real_c @ ( sup_su1639086475real_c @ ( produc876006723real_c @ X3 ) @ ( produc876006723real_c @ Y5 ) ) @ ( sup_su1639086475real_c @ ( produc415593093real_c @ X3 ) @ ( produc415593093real_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_322_sup__prod__def,axiom,
% 3.05/1.59 ( sup_su1639086475real_c
% 3.05/1.59 = ( ^ [X3: produc190496183real_c,Y5: produc190496183real_c] : ( produc394644079real_c @ ( sup_su2141622551real_c @ ( produc2010422875real_c @ X3 ) @ ( produc2010422875real_c @ Y5 ) ) @ ( sup_su2141622551real_c @ ( produc314122909real_c @ X3 ) @ ( produc314122909real_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_323_sup__prod__def,axiom,
% 3.05/1.59 ( sup_su1672617323um_c_c
% 3.05/1.59 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] : ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) ) @ ( sup_su1349021703um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_324_fst__conv,axiom,
% 3.05/1.59 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 3.05/1.59 ( ( produc876006723real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 3.05/1.59 = X1 ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_325_fst__conv,axiom,
% 3.05/1.59 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 3.05/1.59 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 3.05/1.59 = X1 ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_326_fst__eqD,axiom,
% 3.05/1.59 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 3.05/1.59 ( ( ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) )
% 3.05/1.59 = A )
% 3.05/1.59 => ( X = A ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_327_fst__eqD,axiom,
% 3.05/1.59 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 3.05/1.59 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.05/1.59 = A )
% 3.05/1.59 => ( X = A ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_328_snd__conv,axiom,
% 3.05/1.59 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 3.05/1.59 ( ( produc415593093real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 3.05/1.59 = X22 ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_329_snd__conv,axiom,
% 3.05/1.59 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 3.05/1.59 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 3.05/1.59 = X22 ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_330_snd__eqD,axiom,
% 3.05/1.59 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 3.05/1.59 ( ( ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) )
% 3.05/1.59 = A )
% 3.05/1.59 => ( Y = A ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_331_snd__eqD,axiom,
% 3.05/1.59 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 3.05/1.59 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.05/1.59 = A )
% 3.05/1.59 => ( Y = A ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_332_surjective__pairing,axiom,
% 3.05/1.59 ! [T2: produc640052711real_c] :
% 3.05/1.59 ( T2
% 3.05/1.59 = ( produc1687028567real_c @ ( produc876006723real_c @ T2 ) @ ( produc415593093real_c @ T2 ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_333_surjective__pairing,axiom,
% 3.05/1.59 ! [T2: produc190496183real_c] :
% 3.05/1.59 ( T2
% 3.05/1.59 = ( produc394644079real_c @ ( produc2010422875real_c @ T2 ) @ ( produc314122909real_c @ T2 ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_334_prod_Oexhaust__sel,axiom,
% 3.05/1.59 ! [Prod: produc640052711real_c] :
% 3.05/1.59 ( Prod
% 3.05/1.59 = ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_335_prod_Oexhaust__sel,axiom,
% 3.05/1.59 ! [Prod: produc190496183real_c] :
% 3.05/1.59 ( Prod
% 3.05/1.59 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_336_exI__realizer,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > produc190496183real_c > $o,Y: produc190496183real_c,X: produc190496183real_c] :
% 3.05/1.59 ( ( P @ Y @ X )
% 3.05/1.59 => ( P @ ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) ) @ ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_337_exI__realizer,axiom,
% 3.05/1.59 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 3.05/1.59 ( ( P @ Y @ X )
% 3.05/1.59 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_338_conjI__realizer,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > $o,P2: produc190496183real_c,Q: produc190496183real_c > $o,Q2: produc190496183real_c] :
% 3.05/1.59 ( ( P @ P2 )
% 3.05/1.59 => ( ( Q @ Q2 )
% 3.05/1.59 => ( ( P @ ( produc876006723real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) )
% 3.05/1.59 & ( Q @ ( produc415593093real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_339_conjI__realizer,axiom,
% 3.05/1.59 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 3.05/1.59 ( ( P @ P2 )
% 3.05/1.59 => ( ( Q @ Q2 )
% 3.05/1.59 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 3.05/1.59 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_340_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.05/1.59 ! [P: produc190496183real_c > produc190496183real_c > $o,X: produc190496183real_c,Y: produc190496183real_c,A: produc640052711real_c] :
% 3.05/1.59 ( ( P @ X @ Y )
% 3.05/1.59 => ( ( A
% 3.05/1.59 = ( produc1687028567real_c @ X @ Y ) )
% 3.05/1.59 => ( P @ ( produc876006723real_c @ A ) @ ( produc415593093real_c @ A ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_341_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.05/1.59 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A: produc190496183real_c] :
% 3.05/1.59 ( ( P @ X @ Y )
% 3.05/1.59 => ( ( A
% 3.05/1.59 = ( produc394644079real_c @ X @ Y ) )
% 3.05/1.59 => ( P @ ( produc2010422875real_c @ A ) @ ( produc314122909real_c @ A ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_342_sndI,axiom,
% 3.05/1.59 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 3.05/1.59 ( ( X
% 3.05/1.59 = ( produc1687028567real_c @ Y @ Z ) )
% 3.05/1.59 => ( ( produc415593093real_c @ X )
% 3.05/1.59 = Z ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_343_sndI,axiom,
% 3.05/1.59 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 3.05/1.59 ( ( X
% 3.05/1.59 = ( produc394644079real_c @ Y @ Z ) )
% 3.05/1.59 => ( ( produc314122909real_c @ X )
% 3.05/1.59 = Z ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_344_fstI,axiom,
% 3.05/1.59 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 3.05/1.59 ( ( X
% 3.05/1.59 = ( produc1687028567real_c @ Y @ Z ) )
% 3.05/1.59 => ( ( produc876006723real_c @ X )
% 3.05/1.59 = Y ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_345_fstI,axiom,
% 3.05/1.59 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 3.05/1.59 ( ( X
% 3.05/1.59 = ( produc394644079real_c @ Y @ Z ) )
% 3.05/1.59 => ( ( produc2010422875real_c @ X )
% 3.05/1.59 = Y ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_346_eq__snd__iff,axiom,
% 3.05/1.59 ! [B: produc190496183real_c,P2: produc640052711real_c] :
% 3.05/1.59 ( ( B
% 3.05/1.59 = ( produc415593093real_c @ P2 ) )
% 3.05/1.59 = ( ? [A4: produc190496183real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc1687028567real_c @ A4 @ B ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_347_eq__snd__iff,axiom,
% 3.05/1.59 ! [B: finite1398487019real_c,P2: produc190496183real_c] :
% 3.05/1.59 ( ( B
% 3.05/1.59 = ( produc314122909real_c @ P2 ) )
% 3.05/1.59 = ( ? [A4: finite1398487019real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc394644079real_c @ A4 @ B ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_348_eq__fst__iff,axiom,
% 3.05/1.59 ! [A: produc190496183real_c,P2: produc640052711real_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( produc876006723real_c @ P2 ) )
% 3.05/1.59 = ( ? [B4: produc190496183real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc1687028567real_c @ A @ B4 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_349_eq__fst__iff,axiom,
% 3.05/1.59 ! [A: finite1398487019real_c,P2: produc190496183real_c] :
% 3.05/1.59 ( ( A
% 3.05/1.59 = ( produc2010422875real_c @ P2 ) )
% 3.05/1.59 = ( ? [B4: finite1398487019real_c] :
% 3.05/1.59 ( P2
% 3.05/1.59 = ( produc394644079real_c @ A @ B4 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_350_prod_Oswap__def,axiom,
% 3.05/1.59 ( produc350724343real_c
% 3.05/1.59 = ( ^ [P3: produc640052711real_c] : ( produc1687028567real_c @ ( produc415593093real_c @ P3 ) @ ( produc876006723real_c @ P3 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_351_prod_Oswap__def,axiom,
% 3.05/1.59 ( produc704157711real_c
% 3.05/1.59 = ( ^ [P3: produc190496183real_c] : ( produc394644079real_c @ ( produc314122909real_c @ P3 ) @ ( produc2010422875real_c @ P3 ) ) ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_352_swap__simp,axiom,
% 3.05/1.59 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.05/1.59 ( ( produc350724343real_c @ ( produc1687028567real_c @ X @ Y ) )
% 3.05/1.59 = ( produc1687028567real_c @ Y @ X ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(fact_353_swap__simp,axiom,
% 3.05/1.59 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.05/1.59 ( ( produc704157711real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.05/1.59 = ( produc394644079real_c @ Y @ X ) ) ).
% 3.05/1.59
% 3.05/1.59 thf(conj_0,conjecture,
% 3.05/1.59 ? [Mu6: produc190496183real_c] :
% 3.05/1.59 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu6 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
% 3.05/1.59 & ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu6 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ) ).
% 3.05/1.59 ------------------------
% 3.14/1.62 % (24371)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_24065 for (2999ds/4Mi)
% 3.14/1.62 % (24371)Instruction limit reached!
% 3.14/1.62 % (24371)------------------------------
% 3.14/1.62 % (24371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.62 % (24371)Termination reason: Unknown
% 3.14/1.62 % (24371)Termination phase: shuffling
% 3.14/1.62
% 3.14/1.62 % (24371)Memory used [KB]: 1535
% 3.14/1.62 % (24371)Time elapsed: 0.003 s
% 3.14/1.62 % (24371)Instructions burned: 5 (million)
% 3.14/1.62 % (24371)------------------------------
% 3.14/1.62 % (24371)------------------------------
% 3.14/1.62 % (24372)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_24065 for (2999ds/27Mi)
% 3.14/1.63 % (24373)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/2Mi)
% 3.14/1.63 % (24373)Instruction limit reached!
% 3.14/1.63 % (24373)------------------------------
% 3.14/1.63 % (24373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.63 % (24373)Termination reason: Unknown
% 3.14/1.63 % (24373)Termination phase: shuffling
% 3.14/1.63
% 3.14/1.63 % (24373)Memory used [KB]: 1407
% 3.14/1.63 % (24373)Time elapsed: 0.003 s
% 3.14/1.63 % (24373)Instructions burned: 2 (million)
% 3.14/1.63 % (24373)------------------------------
% 3.14/1.63 % (24373)------------------------------
% 3.14/1.63 % (24370)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/183Mi)
% 3.14/1.63 % (24374)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_24065 for (2999ds/2Mi)
% 3.14/1.63 % (24375)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_24065 for (2999ds/275Mi)
% 3.14/1.63 % (24376)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/18Mi)
% 3.14/1.63 % (24374)Instruction limit reached!
% 3.14/1.63 % (24374)------------------------------
% 3.14/1.63 % (24374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.63 % (24374)Termination reason: Unknown
% 3.14/1.63 % (24374)Termination phase: shuffling
% 3.14/1.63
% 3.14/1.63 % (24374)Memory used [KB]: 1407
% 3.14/1.63 % (24374)Time elapsed: 0.004 s
% 3.14/1.63 % (24374)Instructions burned: 2 (million)
% 3.14/1.63 % (24374)------------------------------
% 3.14/1.63 % (24374)------------------------------
% 3.14/1.63 % (24378)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/3Mi)
% 3.14/1.63 % (24378)Instruction limit reached!
% 3.14/1.63 % (24378)------------------------------
% 3.14/1.63 % (24378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.63 % (24378)Termination reason: Unknown
% 3.14/1.63 % (24378)Termination phase: shuffling
% 3.14/1.63
% 3.14/1.63 % (24378)Memory used [KB]: 1407
% 3.14/1.63 % (24378)Time elapsed: 0.003 s
% 3.14/1.63 % (24378)Instructions burned: 5 (million)
% 3.14/1.63 % (24378)------------------------------
% 3.14/1.63 % (24378)------------------------------
% 3.14/1.64 % (24372)Instruction limit reached!
% 3.14/1.64 % (24372)------------------------------
% 3.14/1.64 % (24372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.64 % (24372)Termination reason: Unknown
% 3.14/1.64 % (24372)Termination phase: Property scanning
% 3.14/1.64
% 3.14/1.64 % (24372)Memory used [KB]: 1791
% 3.14/1.64 % (24372)Time elapsed: 0.015 s
% 3.14/1.64 % (24372)Instructions burned: 28 (million)
% 3.14/1.64 % (24372)------------------------------
% 3.14/1.64 % (24372)------------------------------
% 3.14/1.64 % (24376)Instruction limit reached!
% 3.14/1.64 % (24376)------------------------------
% 3.14/1.64 % (24376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.64 % (24376)Termination reason: Unknown
% 3.14/1.64 % (24376)Termination phase: shuffling
% 3.14/1.64
% 3.14/1.64 % (24376)Memory used [KB]: 1791
% 3.14/1.64 % (24376)Time elapsed: 0.014 s
% 3.14/1.64 % (24376)Instructions burned: 19 (million)
% 3.14/1.64 % (24376)------------------------------
% 3.14/1.64 % (24376)------------------------------
% 3.14/1.64 % (24382)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_24065 for (2999ds/37Mi)
% 3.14/1.64 % (24384)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_24065 for (2999ds/3Mi)
% 3.14/1.65 % (24384)Instruction limit reached!
% 3.14/1.65 % (24384)------------------------------
% 3.14/1.65 % (24384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.65 % (24384)Termination reason: Unknown
% 3.14/1.65 % (24384)Termination phase: shuffling
% 3.14/1.65
% 3.14/1.65 % (24384)Memory used [KB]: 1407
% 3.14/1.65 % (24384)Time elapsed: 0.003 s
% 3.14/1.65 % (24384)Instructions burned: 6 (million)
% 3.14/1.65 % (24384)------------------------------
% 3.14/1.65 % (24384)------------------------------
% 3.14/1.65 % (24385)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_24065 for (2999ds/1041Mi)
% 3.14/1.65 % (24383)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_24065 for (2999ds/15Mi)
% 3.14/1.65 % (24382)Instruction limit reached!
% 3.14/1.65 % (24382)------------------------------
% 3.14/1.65 % (24382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.65 % (24382)Termination reason: Unknown
% 3.14/1.65 % (24382)Termination phase: shuffling
% 3.14/1.65
% 3.14/1.65 % (24382)Memory used [KB]: 2174
% 3.14/1.65 % (24382)Time elapsed: 0.013 s
% 3.14/1.65 % (24382)Instructions burned: 37 (million)
% 3.14/1.65 % (24382)------------------------------
% 3.14/1.65 % (24382)------------------------------
% 3.14/1.66 % (24391)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/16Mi)
% 3.14/1.66 % (24383)Instruction limit reached!
% 3.14/1.66 % (24383)------------------------------
% 3.14/1.66 % (24383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.66 % (24383)Termination reason: Unknown
% 3.14/1.66 % (24383)Termination phase: shuffling
% 3.14/1.66
% 3.14/1.66 % (24383)Memory used [KB]: 1791
% 3.14/1.66 % (24383)Time elapsed: 0.012 s
% 3.14/1.66 % (24383)Instructions burned: 16 (million)
% 3.14/1.66 % (24383)------------------------------
% 3.14/1.66 % (24383)------------------------------
% 3.14/1.66 % (24387)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/7Mi)
% 3.14/1.66 % (24391)Instruction limit reached!
% 3.14/1.66 % (24391)------------------------------
% 3.14/1.66 % (24391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.66 % (24391)Termination reason: Unknown
% 3.14/1.66 % (24391)Termination phase: shuffling
% 3.14/1.66
% 3.14/1.66 % (24391)Memory used [KB]: 1791
% 3.14/1.66 % (24391)Time elapsed: 0.007 s
% 3.14/1.66 % (24391)Instructions burned: 17 (million)
% 3.14/1.66 % (24391)------------------------------
% 3.14/1.66 % (24391)------------------------------
% 3.14/1.66 % (24387)Instruction limit reached!
% 3.14/1.66 % (24387)------------------------------
% 3.14/1.66 % (24387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.66 % (24387)Termination reason: Unknown
% 3.14/1.66 % (24387)Termination phase: shuffling
% 3.14/1.66
% 3.14/1.66 % (24387)Memory used [KB]: 1535
% 3.14/1.66 % (24387)Time elapsed: 0.006 s
% 3.14/1.66 % (24387)Instructions burned: 7 (million)
% 3.14/1.66 % (24387)------------------------------
% 3.14/1.66 % (24387)------------------------------
% 3.14/1.66 % (24396)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_24065 for (2999ds/3Mi)
% 3.14/1.67 % (24396)Instruction limit reached!
% 3.14/1.67 % (24396)------------------------------
% 3.14/1.67 % (24396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.67 % (24396)Termination reason: Unknown
% 3.14/1.67 % (24396)Termination phase: shuffling
% 3.14/1.67
% 3.14/1.67 % (24396)Memory used [KB]: 1407
% 3.14/1.67 % (24396)Time elapsed: 0.002 s
% 3.14/1.67 % (24396)Instructions burned: 3 (million)
% 3.14/1.67 % (24396)------------------------------
% 3.14/1.67 % (24396)------------------------------
% 3.14/1.67 % (24402)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/7Mi)
% 3.14/1.67 % (24399)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_24065 for (2999ds/3Mi)
% 3.14/1.67 % (24399)Instruction limit reached!
% 3.14/1.67 % (24399)------------------------------
% 3.14/1.67 % (24399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.67 % (24399)Termination reason: Unknown
% 3.14/1.67 % (24399)Termination phase: shuffling
% 3.14/1.67
% 3.14/1.67 % (24399)Memory used [KB]: 1407
% 3.14/1.67 % (24399)Time elapsed: 0.003 s
% 3.14/1.67 % (24399)Instructions burned: 4 (million)
% 3.14/1.67 % (24399)------------------------------
% 3.14/1.67 % (24399)------------------------------
% 3.14/1.67 % (24402)Instruction limit reached!
% 3.14/1.67 % (24402)------------------------------
% 3.14/1.67 % (24402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.67 % (24402)Termination reason: Unknown
% 3.14/1.67 % (24402)Termination phase: shuffling
% 3.14/1.67
% 3.14/1.67 % (24402)Memory used [KB]: 1535
% 3.14/1.67 % (24402)Time elapsed: 0.004 s
% 3.14/1.67 % (24402)Instructions burned: 9 (million)
% 3.14/1.67 % (24402)------------------------------
% 3.14/1.67 % (24402)------------------------------
% 3.14/1.68 % (24403)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/3Mi)
% 3.14/1.68 % (24406)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/4Mi)
% 3.14/1.68 % (24403)Instruction limit reached!
% 3.14/1.68 % (24403)------------------------------
% 3.14/1.68 % (24403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.68 % (24403)Termination reason: Unknown
% 3.14/1.68 % (24403)Termination phase: shuffling
% 3.14/1.68
% 3.14/1.68 % (24403)Memory used [KB]: 1407
% 3.14/1.68 % (24403)Time elapsed: 0.003 s
% 3.14/1.68 % (24403)Instructions burned: 4 (million)
% 3.14/1.68 % (24403)------------------------------
% 3.14/1.68 % (24403)------------------------------
% 3.14/1.68 % (24406)Instruction limit reached!
% 3.14/1.68 % (24406)------------------------------
% 3.14/1.68 % (24406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.68 % (24406)Termination reason: Unknown
% 3.14/1.68 % (24406)Termination phase: shuffling
% 3.14/1.68
% 3.14/1.68 % (24406)Memory used [KB]: 1535
% 3.14/1.68 % (24406)Time elapsed: 0.004 s
% 3.14/1.68 % (24406)Instructions burned: 6 (million)
% 3.14/1.68 % (24406)------------------------------
% 3.14/1.68 % (24406)------------------------------
% 3.14/1.68 % (24411)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/18Mi)
% 3.14/1.68 % (24413)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/710Mi)
% 3.14/1.69 % (24416)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/6Mi)
% 3.14/1.69 % (24417)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_24065 for (2999ds/902Mi)
% 3.14/1.69 % (24411)Instruction limit reached!
% 3.14/1.69 % (24411)------------------------------
% 3.14/1.69 % (24411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.69 % (24411)Termination reason: Unknown
% 3.14/1.69 % (24411)Termination phase: shuffling
% 3.14/1.69
% 3.14/1.69 % (24411)Memory used [KB]: 1791
% 3.14/1.69 % (24411)Time elapsed: 0.008 s
% 3.14/1.69 % (24411)Instructions burned: 20 (million)
% 3.14/1.69 % (24411)------------------------------
% 3.14/1.69 % (24411)------------------------------
% 3.14/1.69 % (24416)Instruction limit reached!
% 3.14/1.69 % (24416)------------------------------
% 3.14/1.69 % (24416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.69 % (24416)Termination reason: Unknown
% 3.14/1.69 % (24416)Termination phase: shuffling
% 3.14/1.69
% 3.14/1.69 % (24416)Memory used [KB]: 1535
% 3.14/1.69 % (24416)Time elapsed: 0.004 s
% 3.14/1.69 % (24416)Instructions burned: 6 (million)
% 3.14/1.69 % (24416)------------------------------
% 3.14/1.69 % (24416)------------------------------
% 3.14/1.70 % (24370)Instruction limit reached!
% 3.14/1.70 % (24370)------------------------------
% 3.14/1.70 % (24370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (24370)Termination reason: Unknown
% 3.14/1.70 % (24370)Termination phase: Saturation
% 3.14/1.70
% 3.14/1.70 % (24370)Memory used [KB]: 7291
% 3.14/1.70 % (24370)Time elapsed: 0.071 s
% 3.14/1.70 % (24370)Instructions burned: 184 (million)
% 3.14/1.70 % (24370)------------------------------
% 3.14/1.70 % (24370)------------------------------
% 3.14/1.70 % (24424)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_24065 for (2999ds/21Mi)
% 3.14/1.70 % (24426)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24065 for (2999ds/5Mi)
% 3.14/1.70 % (24426)Instruction limit reached!
% 3.14/1.70 % (24426)------------------------------
% 3.14/1.70 % (24426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (24426)Termination reason: Unknown
% 3.14/1.70 % (24426)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (24426)Memory used [KB]: 1535
% 3.14/1.70 % (24426)Time elapsed: 0.004 s
% 3.14/1.70 % (24426)Instructions burned: 7 (million)
% 3.14/1.70 % (24426)------------------------------
% 3.14/1.70 % (24426)------------------------------
% 3.14/1.71 % (24424)Instruction limit reached!
% 3.14/1.71 % (24424)------------------------------
% 3.14/1.71 % (24424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (24424)Termination reason: Unknown
% 3.14/1.71 % (24424)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (24424)Memory used [KB]: 1791
% 3.14/1.71 % (24424)Time elapsed: 0.009 s
% 3.14/1.71 % (24424)Instructions burned: 23 (million)
% 3.14/1.71 % (24424)------------------------------
% 3.14/1.71 % (24424)------------------------------
% 3.14/1.71 % (24431)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_24065 for (2999ds/6Mi)
% 3.14/1.71 % (24431)Instruction limit reached!
% 3.14/1.71 % (24431)------------------------------
% 3.14/1.71 % (24431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (24431)Termination reason: Unknown
% 3.14/1.71 % (24431)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (24431)Memory used [KB]: 1535
% 3.14/1.71 % (24431)Time elapsed: 0.003 s
% 3.14/1.71 % (24431)Instructions burned: 7 (million)
% 3.14/1.71 % (24431)------------------------------
% 3.14/1.71 % (24431)------------------------------
% 3.14/1.71 % (24433)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24065 for (2998ds/377Mi)
% 3.14/1.72 % (24436)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_24065 for (2998ds/779Mi)
% 3.14/1.72 % (24437)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_24065 for (2998ds/19Mi)
% 3.14/1.73 % (24437)Instruction limit reached!
% 3.14/1.73 % (24437)------------------------------
% 3.14/1.73 % (24437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (24437)Termination reason: Unknown
% 3.14/1.73 % (24437)Termination phase: shuffling
% 3.14/1.73
% 3.14/1.73 % (24437)Memory used [KB]: 1791
% 3.14/1.73 % (24437)Time elapsed: 0.008 s
% 3.14/1.73 % (24437)Instructions burned: 21 (million)
% 3.14/1.73 % (24437)------------------------------
% 3.14/1.73 % (24437)------------------------------
% 3.14/1.73 % (24417)First to succeed.
% 3.14/1.73 % (24417)Refutation found. Thanks to Tanya!
% 3.14/1.73 % SZS status Theorem for DTF2THF_24065
% 3.14/1.73 % SZS output start Proof for DTF2THF_24065
% 3.14/1.73 thf(type_def_5, type, set_Pr1389752855real_c: $tType).
% 3.14/1.73 thf(type_def_6, type, finite1398487019real_c: $tType).
% 3.14/1.73 thf(type_def_7, type, set_Su1783761653um_b_c: $tType).
% 3.14/1.73 thf(type_def_9, type, set_Sum_sum_c_c: $tType).
% 3.14/1.73 thf(type_def_10, type, set_Pr754230471real_c: $tType).
% 3.14/1.73 thf(type_def_11, type, produc190496183real_c: $tType).
% 3.14/1.73 thf(type_def_12, type, hp_a_b_c: $tType).
% 3.14/1.73 thf(type_def_13, type, denota231621370t_unit: $tType).
% 3.14/1.73 thf(type_def_14, type, produc640052711real_c: $tType).
% 3.14/1.73 thf(type_def_15, type, produc1360640805um_b_c: $tType).
% 3.14/1.73 thf(type_def_16, type, produc793920321um_c_c: $tType).
% 3.14/1.73 thf(type_def_17, type, produc1415638375um_b_c: $tType).
% 3.14/1.73 thf(type_def_18, type, produc1573491071um_c_c: $tType).
% 3.14/1.73 thf(type_def_19, type, produc1470506001real_c: $tType).
% 3.14/1.73 thf(type_def_20, type, produc777402865um_c_c: $tType).
% 3.14/1.73 thf(type_def_21, type, produc263671631um_b_c: $tType).
% 3.14/1.73 thf(type_def_22, type, produc214722967um_c_c: $tType).
% 3.14/1.73 thf(type_def_23, type, set_Pr242060487real_c: $tType).
% 3.14/1.73 thf(type_def_24, type, produc1037099239real_c: $tType).
% 3.14/1.73 thf(type_def_25, type, sum_su737395349um_b_c: $tType).
% 3.14/1.73 thf(type_def_26, type, sum_sum_c_c: $tType).
% 3.14/1.73 thf(func_def_0, type, set_Pr242060487real_c: $tType).
% 3.14/1.73 thf(func_def_1, type, produc1037099239real_c: $tType).
% 3.14/1.73 thf(func_def_2, type, set_Pr754230471real_c: $tType).
% 3.14/1.73 thf(func_def_3, type, produc640052711real_c: $tType).
% 3.14/1.73 thf(func_def_4, type, produc1360640805um_b_c: $tType).
% 3.14/1.73 thf(func_def_5, type, produc1470506001real_c: $tType).
% 3.14/1.73 thf(func_def_6, type, produc793920321um_c_c: $tType).
% 3.14/1.73 thf(func_def_7, type, produc777402865um_c_c: $tType).
% 3.14/1.73 thf(func_def_8, type, produc1415638375um_b_c: $tType).
% 3.14/1.73 thf(func_def_9, type, set_Pr1389752855real_c: $tType).
% 3.14/1.73 thf(func_def_10, type, produc263671631um_b_c: $tType).
% 3.14/1.73 thf(func_def_11, type, produc1573491071um_c_c: $tType).
% 3.14/1.73 thf(func_def_12, type, produc190496183real_c: $tType).
% 3.14/1.73 thf(func_def_13, type, produc214722967um_c_c: $tType).
% 3.14/1.73 thf(func_def_14, type, denota231621370t_unit: $tType).
% 3.14/1.73 thf(func_def_15, type, set_Su1783761653um_b_c: $tType).
% 3.14/1.73 thf(func_def_16, type, sum_su737395349um_b_c: $tType).
% 3.14/1.73 thf(func_def_17, type, finite1398487019real_c: $tType).
% 3.14/1.73 thf(func_def_18, type, set_Sum_sum_c_c: $tType).
% 3.14/1.73 thf(func_def_19, type, hp_a_b_c: $tType).
% 3.14/1.73 thf(func_def_20, type, sum_sum_c_c: $tType).
% 3.14/1.73 thf(func_def_21, type, bNF_Ca318582436um_b_c: set_Pr1389752855real_c > (finite1398487019real_c > set_Su1783761653um_b_c) > $o).
% 3.14/1.73 thf(func_def_22, type, bNF_Ca1693016812um_c_c: set_Pr1389752855real_c > (finite1398487019real_c > set_Sum_sum_c_c) > $o).
% 3.14/1.73 thf(func_def_23, type, bNF_Ca419199138um_b_c: set_Pr754230471real_c > (produc190496183real_c > set_Su1783761653um_b_c) > $o).
% 3.14/1.73 thf(func_def_24, type, bNF_Ca1667803246um_c_c: set_Pr754230471real_c > (produc190496183real_c > set_Sum_sum_c_c) > $o).
% 3.14/1.73 thf(func_def_25, type, coinci354700372_a_b_c: hp_a_b_c > denota231621370t_unit > denota231621370t_unit > $o).
% 3.14/1.73 thf(func_def_26, type, coinci1852866155_a_b_c: hp_a_b_c > $o).
% 3.14/1.73 thf(func_def_27, type, coinci772602909_a_b_c: hp_a_b_c > denota231621370t_unit > $o).
% 3.14/1.73 thf(func_def_28, type, denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o).
% 3.14/1.73 thf(func_def_29, type, denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o).
% 3.14/1.73 thf(func_def_30, type, denota904684656_a_b_c: denota231621370t_unit > hp_a_b_c > set_Pr754230471real_c).
% 3.14/1.73 thf(func_def_31, type, sup_su2141622551real_c: finite1398487019real_c > finite1398487019real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_32, type, sup_su1639086475real_c: produc190496183real_c > produc190496183real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_33, type, sup_su1399591867real_c: produc640052711real_c > produc640052711real_c > produc640052711real_c).
% 3.14/1.73 thf(func_def_34, type, sup_su1009753337um_b_c: produc1360640805um_b_c > produc1360640805um_b_c > produc1360640805um_b_c).
% 3.14/1.73 thf(func_def_35, type, sup_su1347303021um_c_c: produc793920321um_c_c > produc793920321um_c_c > produc793920321um_c_c).
% 3.14/1.73 thf(func_def_36, type, sup_su1580927803um_b_c: produc1415638375um_b_c > produc1415638375um_b_c > produc1415638375um_b_c).
% 3.14/1.73 thf(func_def_37, type, sup_su1731217579um_c_c: produc1573491071um_c_c > produc1573491071um_c_c > produc1573491071um_c_c).
% 3.14/1.73 thf(func_def_38, type, sup_su2023888701real_c: produc1470506001real_c > produc1470506001real_c > produc1470506001real_c).
% 3.14/1.73 thf(func_def_39, type, sup_su505296157um_c_c: produc777402865um_c_c > produc777402865um_c_c > produc777402865um_c_c).
% 3.14/1.73 thf(func_def_40, type, sup_su421398139um_b_c: produc263671631um_b_c > produc263671631um_b_c > produc263671631um_b_c).
% 3.14/1.73 thf(func_def_41, type, sup_su1672617323um_c_c: produc214722967um_c_c > produc214722967um_c_c > produc214722967um_c_c).
% 3.14/1.73 thf(func_def_42, type, sup_su1857314283real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > set_Pr1389752855real_c).
% 3.14/1.73 thf(func_def_43, type, sup_su588839579real_c: set_Pr754230471real_c > set_Pr754230471real_c > set_Pr754230471real_c).
% 3.14/1.73 thf(func_def_44, type, sup_su880588443real_c: set_Pr242060487real_c > set_Pr242060487real_c > set_Pr242060487real_c).
% 3.14/1.73 thf(func_def_45, type, sup_su1968964297um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_46, type, sup_su1349021703um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_47, type, ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o).
% 3.14/1.73 thf(func_def_48, type, ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o).
% 3.14/1.73 thf(func_def_49, type, ord_le652477831real_c: produc640052711real_c > produc640052711real_c > $o).
% 3.14/1.73 thf(func_def_50, type, ord_le907560199um_b_c: produc1415638375um_b_c > produc1415638375um_b_c > $o).
% 3.14/1.73 thf(func_def_51, type, ord_le1852514783um_c_c: produc1573491071um_c_c > produc1573491071um_c_c > $o).
% 3.14/1.73 thf(func_def_52, type, ord_le542695343um_b_c: produc263671631um_b_c > produc263671631um_b_c > $o).
% 3.14/1.73 thf(func_def_53, type, ord_le684454199um_c_c: produc214722967um_c_c > produc214722967um_c_c > $o).
% 3.14/1.73 thf(func_def_54, type, ord_le977353143real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > $o).
% 3.14/1.73 thf(func_def_55, type, ord_le1988344935real_c: set_Pr754230471real_c > set_Pr754230471real_c > $o).
% 3.14/1.73 thf(func_def_56, type, ord_le100418663real_c: set_Pr242060487real_c > set_Pr242060487real_c > $o).
% 3.14/1.73 thf(func_def_57, type, ord_le929608341um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > $o).
% 3.14/1.73 thf(func_def_58, type, ord_le1772180283um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > $o).
% 3.14/1.73 thf(func_def_59, type, order_365181262um_b_c: (set_Su1783761653um_b_c > $o) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_60, type, order_1776530114um_c_c: (set_Sum_sum_c_c > $o) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_61, type, produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_62, type, produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c).
% 3.14/1.73 thf(func_def_63, type, produc2010919061um_b_c: produc190496183real_c > set_Su1783761653um_b_c > produc1360640805um_b_c).
% 3.14/1.73 thf(func_def_64, type, produc639456571um_c_c: produc190496183real_c > set_Sum_sum_c_c > produc793920321um_c_c).
% 3.14/1.73 thf(func_def_65, type, produc544496471real_c: produc640052711real_c > produc640052711real_c > produc1037099239real_c).
% 3.14/1.73 thf(func_def_66, type, produc754249687um_b_c: set_Su1783761653um_b_c > set_Su1783761653um_b_c > produc1415638375um_b_c).
% 3.14/1.73 thf(func_def_67, type, produc616453753um_c_c: set_Su1783761653um_b_c > set_Sum_sum_c_c > produc1573491071um_c_c).
% 3.14/1.73 thf(func_def_68, type, produc439851843real_c: set_Sum_sum_c_c > produc190496183real_c > produc1470506001real_c).
% 3.14/1.73 thf(func_def_69, type, produc1333497635um_c_c: set_Sum_sum_c_c > produc214722967um_c_c > produc777402865um_c_c).
% 3.14/1.73 thf(func_def_70, type, produc919784577um_b_c: set_Sum_sum_c_c > set_Su1783761653um_b_c > produc263671631um_b_c).
% 3.14/1.73 thf(func_def_71, type, produc1439061071um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > produc214722967um_c_c).
% 3.14/1.73 thf(func_def_72, type, produc2010422875real_c: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_73, type, produc876006723real_c: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_74, type, produc1961869763um_b_c: produc1415638375um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_75, type, produc1455464333um_c_c: produc1573491071um_c_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_76, type, produc1758795157um_b_c: produc263671631um_b_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_77, type, produc1983230011um_c_c: produc214722967um_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_78, type, produc314122909real_c: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_79, type, produc415593093real_c: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_80, type, produc932426501um_b_c: produc1415638375um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_81, type, produc890433227um_c_c: produc1573491071um_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_82, type, produc1193764051um_b_c: produc263671631um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_83, type, produc1132019837um_c_c: produc214722967um_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_84, type, produc704157711real_c: produc190496183real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_85, type, produc350724343real_c: produc640052711real_c > produc640052711real_c).
% 3.14/1.73 thf(func_def_86, type, collec1126017874real_c: (produc640052711real_c > $o) > set_Pr754230471real_c).
% 3.14/1.73 thf(func_def_87, type, collec2086029184um_b_c: (sum_su737395349um_b_c > $o) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_88, type, collect_Sum_sum_c_c: (sum_sum_c_c > $o) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_89, type, static_FVP_a_b_c: hp_a_b_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_90, type, static_MBV_a_b_c: hp_a_b_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_91, type, static_SIGP_a_b_c: hp_a_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_92, type, choice_a_b_c: hp_a_b_c > hp_a_b_c > hp_a_b_c).
% 3.14/1.73 thf(func_def_93, type, hpsafe_a_b_c: hp_a_b_c > $o).
% 3.14/1.73 thf(func_def_94, type, same_f1974156740real_c: (finite1398487019real_c > $o) > (finite1398487019real_c > set_Pr1389752855real_c) > set_Pr754230471real_c).
% 3.14/1.73 thf(func_def_95, type, same_f598810924real_c: (produc190496183real_c > $o) > (produc190496183real_c > set_Pr754230471real_c) > set_Pr242060487real_c).
% 3.14/1.73 thf(func_def_96, type, member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o).
% 3.14/1.73 thf(func_def_97, type, member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o).
% 3.14/1.73 thf(func_def_98, type, member616151824real_c: produc1037099239real_c > set_Pr242060487real_c > $o).
% 3.14/1.73 thf(func_def_99, type, member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o).
% 3.14/1.73 thf(func_def_100, type, member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o).
% 3.14/1.73 thf(func_def_101, type, i: denota231621370t_unit).
% 3.14/1.73 thf(func_def_102, type, j: denota231621370t_unit).
% 3.14/1.73 thf(func_def_103, type, v: set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_104, type, mu: produc190496183real_c).
% 3.14/1.73 thf(func_def_105, type, mu2: finite1398487019real_c).
% 3.14/1.73 thf(func_def_106, type, mu3: finite1398487019real_c).
% 3.14/1.73 thf(func_def_107, type, nu_1: finite1398487019real_c).
% 3.14/1.73 thf(func_def_108, type, nu_12: finite1398487019real_c).
% 3.14/1.73 thf(func_def_109, type, nu_2: finite1398487019real_c).
% 3.14/1.73 thf(func_def_110, type, nu_22: finite1398487019real_c).
% 3.14/1.73 thf(func_def_111, type, a: hp_a_b_c).
% 3.14/1.73 thf(func_def_112, type, b: hp_a_b_c).
% 3.14/1.73 thf(func_def_130, type, sK0: (set_Su1783761653um_b_c > $o) > (set_Su1783761653um_b_c > $o) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_131, type, sK1: set_Su1783761653um_b_c > (set_Su1783761653um_b_c > $o) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_132, type, sK2: set_Su1783761653um_b_c > set_Su1783761653um_b_c > sum_su737395349um_b_c).
% 3.14/1.73 thf(func_def_133, type, sK3: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_134, type, sK4: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_135, type, sK5: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_136, type, sK6: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_137, type, sK7: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_138, type, sK8: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_139, type, sK9: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_140, type, sK10: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_141, type, sK11: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_142, type, sK12: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_143, type, sK13: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_144, type, sK14: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_145, type, sK15: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_146, type, sK16: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_147, type, sK17: (set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_148, type, sK18: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_149, type, sK19: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_150, type, sK20: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_151, type, sK21: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_152, type, sK22: set_Su1783761653um_b_c > (set_Su1783761653um_b_c > $o) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_153, type, sK23: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_154, type, sK24: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_155, type, sK25: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_156, type, sK26: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_157, type, sK27: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_158, type, sK28: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_159, type, sK29: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_160, type, sK30: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_161, type, sK31: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_162, type, sK32: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_163, type, sK33: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_164, type, sK34: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_165, type, sK35: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_166, type, sK36: (set_Su1783761653um_b_c > set_Sum_sum_c_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_167, type, sK37: set_Pr242060487real_c > set_Pr242060487real_c > produc1037099239real_c).
% 3.14/1.73 thf(func_def_168, type, sK38: produc190496183real_c > set_Sum_sum_c_c > produc190496183real_c > denota231621370t_unit > produc190496183real_c).
% 3.14/1.73 thf(func_def_169, type, sK39: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_170, type, sK40: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_171, type, sK41: produc190496183real_c > set_Sum_sum_c_c > produc190496183real_c > denota231621370t_unit > produc190496183real_c).
% 3.14/1.73 thf(func_def_172, type, sK42: set_Sum_sum_c_c > (set_Sum_sum_c_c > $o) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_173, type, sK43: (set_Sum_sum_c_c > $o) > (set_Sum_sum_c_c > $o) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_174, type, sK44: (sum_sum_c_c > $o) > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_175, type, sK45: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_176, type, sK46: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_177, type, sK47: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_178, type, sK48: produc190496183real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_179, type, sK49: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_180, type, sK50: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_181, type, sK51: (sum_su737395349um_b_c > $o) > (sum_su737395349um_b_c > $o) > sum_su737395349um_b_c).
% 3.14/1.73 thf(func_def_182, type, sK52: set_Sum_sum_c_c > set_Sum_sum_c_c > sum_sum_c_c).
% 3.14/1.73 thf(func_def_183, type, sK53: (set_Sum_sum_c_c > $o) > set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_184, type, sK54: produc190496183real_c > produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_185, type, sK55: produc640052711real_c > produc190496183real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_186, type, sK56: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_187, type, sK57: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_188, type, sK58: set_Sum_sum_c_c > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_189, type, sK59: set_Sum_sum_c_c > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_190, type, sK60: set_Sum_sum_c_c > set_Sum_sum_c_c > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_191, type, sK61: (sum_sum_c_c > $o) > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_192, type, sK62: set_Sum_sum_c_c > (sum_sum_c_c > $o) > sum_sum_c_c).
% 3.14/1.73 thf(func_def_193, type, sK63: (sum_sum_c_c > $o) > set_Sum_sum_c_c > sum_sum_c_c).
% 3.14/1.73 thf(func_def_194, type, sK64: set_Sum_sum_c_c > (sum_sum_c_c > $o) > set_Sum_sum_c_c > sum_sum_c_c).
% 3.14/1.73 thf(func_def_195, type, sK65: set_Pr1389752855real_c > set_Pr1389752855real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_196, type, sK66: (produc640052711real_c > $o) > produc190496183real_c).
% 3.14/1.73 thf(func_def_197, type, sK67: (produc640052711real_c > $o) > produc190496183real_c).
% 3.14/1.73 thf(func_def_198, type, sK68: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_199, type, sK69: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_200, type, sK70: produc190496183real_c > finite1398487019real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_201, type, sK71: produc190496183real_c).
% 3.14/1.73 thf(func_def_202, type, sK72: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_203, type, sK73: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_204, type, sK74: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_205, type, sK75: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_206, type, sK76: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_207, type, sK77: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_208, type, sK78: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_209, type, sK79: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_210, type, sK80: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_211, type, sK81: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_212, type, sK82: (set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_213, type, sK83: (produc640052711real_c > $o) > produc190496183real_c).
% 3.14/1.73 thf(func_def_214, type, sK84: (produc640052711real_c > $o) > produc190496183real_c).
% 3.14/1.73 thf(func_def_215, type, sK85: produc640052711real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_216, type, sK86: produc640052711real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_217, type, sK87: produc640052711real_c > produc190496183real_c).
% 3.14/1.73 thf(func_def_218, type, sK88: produc190496183real_c > finite1398487019real_c > finite1398487019real_c).
% 3.14/1.73 thf(func_def_219, type, sK89: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_220, type, sK90: (set_Sum_sum_c_c > set_Su1783761653um_b_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_221, type, sK91: (sum_su737395349um_b_c > $o) > (sum_su737395349um_b_c > $o) > sum_su737395349um_b_c).
% 3.14/1.73 thf(func_def_222, type, sK92: (produc640052711real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_223, type, sK93: (produc640052711real_c > $o) > produc190496183real_c).
% 3.14/1.73 thf(func_def_224, type, sK94: (produc640052711real_c > $o) > finite1398487019real_c).
% 3.14/1.73 thf(func_def_225, type, sK95: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_226, type, sK96: (set_Sum_sum_c_c > set_Sum_sum_c_c) > set_Sum_sum_c_c).
% 3.14/1.73 thf(func_def_227, type, sK97: set_Pr754230471real_c > set_Pr754230471real_c > produc640052711real_c).
% 3.14/1.73 thf(func_def_228, type, sK98: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_229, type, sK99: (set_Su1783761653um_b_c > set_Su1783761653um_b_c) > set_Su1783761653um_b_c).
% 3.14/1.73 thf(func_def_231, type, ph101: !>[X0: $tType]:(X0)).
% 3.14/1.73 thf(f2060,plain,(
% 3.14/1.73 $false),
% 3.14/1.73 inference(trivial_inequality_removal,[status(thm)],[f2055])).
% 3.14/1.73 thf(f2055,plain,(
% 3.14/1.73 ($true != $true)),
% 3.14/1.73 inference(superposition,[status(thm)],[f2010,f1871])).
% 3.14/1.73 thf(f1871,plain,(
% 3.14/1.73 ((member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))) = $true)),
% 3.14/1.73 inference(cnf_transformation,[status(thm)],[f531])).
% 3.14/1.73 thf(f531,plain,(
% 3.14/1.73 ((member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))) = $true)),
% 3.14/1.73 inference(fool_elimination,[status(thm)],[f530])).
% 3.14/1.73 thf(f530,plain,(
% 3.14/1.73 (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b)))),
% 3.14/1.73 inference(rectify,[status(thm)],[f3])).
% 3.14/1.73 thf(f3,axiom,(
% 3.14/1.73 (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b)))),
% 3.14/1.73 file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',fact_2_prog__sem_H)).
% 3.14/1.73 thf(f2010,plain,(
% 3.14/1.73 ((member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))) != $true)),
% 3.14/1.73 inference(trivial_inequality_removal,[status(thm)],[f2003])).
% 3.14/1.73 thf(f2003,plain,(
% 3.14/1.73 ($true != $true) | ((member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ mu) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))) != $true)),
% 3.14/1.73 inference(superposition,[status(thm)],[f1557,f1708])).
% 3.14/1.73 thf(f1708,plain,(
% 3.14/1.73 ((denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ mu @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v)) = $true)),
% 3.14/1.73 inference(cnf_transformation,[status(thm)],[f479])).
% 3.14/1.73 thf(f479,plain,(
% 3.14/1.73 ((denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ mu @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v)) = $true)),
% 3.14/1.73 inference(fool_elimination,[status(thm)],[f478])).
% 3.14/1.73 thf(f478,plain,(
% 3.14/1.73 (denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ mu @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v))),
% 3.14/1.73 inference(rectify,[status(thm)],[f4])).
% 3.14/1.73 thf(f4,axiom,(
% 3.14/1.73 (denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ mu @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v))),
% 3.14/1.73 file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',fact_3_agree_H)).
% 3.14/1.73 thf(f1557,plain,(
% 3.14/1.73 ( ! [X0 : produc190496183real_c] : (($true != (denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X0 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v))) | ($true != (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X0) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))))) )),
% 3.14/1.73 inference(cnf_transformation,[status(thm)],[f1183])).
% 3.14/1.73 thf(f1183,plain,(
% 3.14/1.73 ! [X0 : produc190496183real_c] : (($true != (denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X0 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v))) | ($true != (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X0) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b)))))),
% 3.14/1.73 inference(ennf_transformation,[status(thm)],[f717])).
% 3.14/1.73 thf(f717,plain,(
% 3.14/1.73 ~? [X0 : produc190496183real_c] : (($true = (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X0) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b)))) & ($true = (denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X0 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v))))),
% 3.14/1.73 inference(fool_elimination,[status(thm)],[f716])).
% 3.14/1.73 thf(f716,plain,(
% 3.14/1.73 ~? [X0 : produc190496183real_c] : ((denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X0 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v)) & (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X0) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))))),
% 3.14/1.73 inference(rectify,[status(thm)],[f356])).
% 3.14/1.73 thf(f356,negated_conjecture,(
% 3.14/1.73 ~? [X79 : produc190496183real_c] : ((denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X79 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v)) & (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X79) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))))),
% 3.14/1.73 inference(negated_conjecture,[status(cth)],[f355])).
% 3.14/1.73 thf(f355,conjecture,(
% 3.14/1.73 ? [X79 : produc190496183real_c] : ((denota1997846518gree_c @ (produc394644079real_c @ mu3 @ mu2) @ X79 @ (sup_su1349021703um_c_c @ (static_MBV_a_b_c @ (choice_a_b_c @ a @ b)) @ v)) & (member346808080real_c @ (produc1687028567real_c @ (produc394644079real_c @ nu_22 @ nu_2) @ X79) @ (denota904684656_a_b_c @ j @ (choice_a_b_c @ a @ b))))),
% 3.14/1.73 file('/export/starexec/sandbox/tmp/tmp.bcQ9LxgT6J/DTF2THF_24065.p',conj_0)).
% 3.14/1.73 % SZS output end Proof for DTF2THF_24065
% 3.14/1.73 % (24417)------------------------------
% 3.14/1.73 % (24417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (24417)Termination reason: Refutation
% 3.14/1.73
% 3.14/1.73 % (24417)Memory used [KB]: 7419
% 3.14/1.73 % (24417)Time elapsed: 0.045 s
% 3.14/1.73 % (24417)Instructions burned: 137 (million)
% 3.14/1.73 % (24417)------------------------------
% 3.14/1.73 % (24417)------------------------------
% 3.14/1.73 % (24364)Success in time 0.132 s
%------------------------------------------------------------------------------