%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP042^1 : 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 : n026.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 08:55:05 AM UTC 2026
% Result : Theorem 2.75s 1.78s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 36 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 269 ( 8 ~; 3 |; 22 &; 220 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 29 ( 28 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 170 ( 166 usr; 15 con; 0-5 aty)
% ( 0 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 54 ( 35 ^; 10 !; 9 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
denota723907260t_unit: $tType ).
thf(type_def_6,type,
set_Su111624115um_c_b: $tType ).
thf(type_def_8,type,
produc133005365real_b: $tType ).
thf(type_def_9,type,
set_Sum_sum_b_b: $tType ).
thf(type_def_10,type,
produc1149990247eal_sz: $tType ).
thf(type_def_11,type,
set_Sum_sum_sz_sz: $tType ).
thf(type_def_12,type,
a: $tType ).
thf(type_def_13,type,
finite1390225514real_b: $tType ).
thf(type_def_14,type,
real: $tType ).
thf(type_def_15,type,
denota610675952t_unit: $tType ).
thf(type_def_16,type,
trm_a_b: $tType ).
thf(type_def_17,type,
trm_sf_sz: $tType ).
thf(type_def_18,type,
finite824932053eal_sz: $tType ).
thf(type_def_19,type,
freche2095075217_sc_sz: $tType ).
thf(type_def_20,type,
frechet_strm_sf_sz: $tType ).
thf(type_def_21,type,
bounde472938360z_real: $tType ).
thf(type_def_22,type,
frechet_strm_a_b: $tType ).
thf(type_def_23,type,
freche1734198479_a_c_b: $tType ).
thf(type_def_24,type,
sum_su1965225555um_c_b: $tType ).
thf(type_def_25,type,
sum_sum_b_b: $tType ).
thf(type_def_26,type,
set_Fi291318197eal_sz: $tType ).
thf(type_def_27,type,
set_a: $tType ).
thf(type_def_28,type,
set_sf: $tType ).
thf(type_def_29,type,
set_trm_a_b: $tType ).
thf(type_def_30,type,
set_trm_sf_sz: $tType ).
thf(type_def_31,type,
set_Fi268318752real_b: $tType ).
thf(type_def_32,type,
set_De153000604t_unit: $tType ).
thf(type_def_33,type,
set_De208295462t_unit: $tType ).
thf(func_def_0,type,
produc1149990247eal_sz: $tType ).
thf(func_def_1,type,
produc133005365real_b: $tType ).
thf(func_def_2,type,
bounde472938360z_real: $tType ).
thf(func_def_3,type,
set_De208295462t_unit: $tType ).
thf(func_def_4,type,
set_De153000604t_unit: $tType ).
thf(func_def_5,type,
denota610675952t_unit: $tType ).
thf(func_def_6,type,
denota723907260t_unit: $tType ).
thf(func_def_7,type,
set_Su111624115um_c_b: $tType ).
thf(func_def_8,type,
set_Fi291318197eal_sz: $tType ).
thf(func_def_9,type,
set_Fi268318752real_b: $tType ).
thf(func_def_10,type,
freche2095075217_sc_sz: $tType ).
thf(func_def_11,type,
freche1734198479_a_c_b: $tType ).
thf(func_def_12,type,
sum_su1965225555um_c_b: $tType ).
thf(func_def_13,type,
finite824932053eal_sz: $tType ).
thf(func_def_14,type,
finite1390225514real_b: $tType ).
thf(func_def_15,type,
frechet_strm_sf_sz: $tType ).
thf(func_def_16,type,
set_Sum_sum_sz_sz: $tType ).
thf(func_def_17,type,
frechet_strm_a_b: $tType ).
thf(func_def_18,type,
set_Sum_sum_b_b: $tType ).
thf(func_def_19,type,
set_trm_sf_sz: $tType ).
thf(func_def_20,type,
set_trm_a_b: $tType ).
thf(func_def_21,type,
sum_sum_b_b: $tType ).
thf(func_def_22,type,
trm_sf_sz: $tType ).
thf(func_def_23,type,
trm_a_b: $tType ).
thf(func_def_24,type,
set_sf: $tType ).
thf(func_def_25,type,
set_a: $tType ).
thf(func_def_26,type,
real: $tType ).
thf(func_def_27,type,
a: $tType ).
thf(func_def_28,type,
denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o ).
thf(func_def_29,type,
denota1997846517gree_b: produc133005365real_b > produc133005365real_b > set_Sum_sum_b_b > $o ).
thf(func_def_30,type,
denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
thf(func_def_31,type,
denota102976244t_unit: denota723907260t_unit > a > finite1390225514real_b > real ).
thf(func_def_32,type,
denota1086158987_a_c_b: denota723907260t_unit > $o ).
thf(func_def_33,type,
denota1579475975_sc_sz: denota610675952t_unit > $o ).
thf(func_def_34,type,
denota722380397_a_c_b: denota723907260t_unit > trm_a_b > finite1390225514real_b > real ).
thf(func_def_35,type,
denota1179238309_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > real ).
thf(func_def_36,type,
freche585307148_sc_sz: freche2095075217_sc_sz > frechet_strm_sf_sz > finite824932053eal_sz > bounde472938360z_real ).
thf(func_def_37,type,
freche58918398_sc_sz: denota610675952t_unit > freche2095075217_sc_sz > $o ).
thf(func_def_38,type,
frechet_cr_strm_a_b: trm_a_b > frechet_strm_a_b > $o ).
thf(func_def_39,type,
freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
thf(func_def_40,type,
freche153761090_a_c_b: denota723907260t_unit > freche1734198479_a_c_b ).
thf(func_def_41,type,
freche1784963216_sc_sz: denota610675952t_unit > freche2095075217_sc_sz ).
thf(func_def_42,type,
freche288321865_a_c_b: freche1734198479_a_c_b > denota723907260t_unit ).
thf(func_def_43,type,
freche1421597129_sc_sz: freche2095075217_sc_sz > denota610675952t_unit ).
thf(func_def_44,type,
frechet_raw_term_a_b: frechet_strm_a_b > trm_a_b ).
thf(func_def_45,type,
freche782854530_sf_sz: frechet_strm_sf_sz > trm_sf_sz ).
thf(func_def_46,type,
freche665377491rm_a_b: trm_a_b > frechet_strm_a_b ).
thf(func_def_47,type,
freche1046279700_sf_sz: trm_sf_sz > frechet_strm_sf_sz ).
thf(func_def_48,type,
if_Bou1785791806z_real: $o > bounde472938360z_real > bounde472938360z_real > bounde472938360z_real ).
thf(func_def_49,type,
sup_su1211201046_c_b_o: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b > $o ).
thf(func_def_50,type,
sup_su2024788734_b_b_o: ( sum_sum_b_b > $o ) > ( sum_sum_b_b > $o ) > sum_sum_b_b > $o ).
thf(func_def_51,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_52,type,
sup_sup_o: $o > $o > $o ).
thf(func_def_53,type,
sup_su2133361046real_b: finite1390225514real_b > finite1390225514real_b > finite1390225514real_b ).
thf(func_def_54,type,
sup_su1581595657real_b: produc133005365real_b > produc133005365real_b > produc133005365real_b ).
thf(func_def_55,type,
sup_su1321388937eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > set_Fi291318197eal_sz ).
thf(func_def_56,type,
sup_su296826759um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b ).
thf(func_def_57,type,
sup_su2137030215um_b_b: set_Sum_sum_b_b > set_Sum_sum_b_b > set_Sum_sum_b_b ).
thf(func_def_58,type,
sup_su1670953621_sz_sz: set_Sum_sum_sz_sz > set_Sum_sum_sz_sz > set_Sum_sum_sz_sz ).
thf(func_def_59,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_60,type,
sup_sup_set_sf: set_sf > set_sf > set_sf ).
thf(func_def_61,type,
ord_le1534094666_c_b_o: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > $o ).
thf(func_def_62,type,
ord_le1306331338_b_b_o: ( sum_sum_b_b > $o ) > ( sum_sum_b_b > $o ) > $o ).
thf(func_def_63,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_64,type,
ord_le767445194real_b: finite1390225514real_b > finite1390225514real_b > $o ).
thf(func_def_65,type,
ord_le793200597real_b: produc133005365real_b > produc133005365real_b > $o ).
thf(func_def_66,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_67,type,
ord_le41263445eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o ).
thf(func_def_68,type,
ord_le1404954451um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > $o ).
thf(func_def_69,type,
ord_le412705147um_b_b: set_Sum_sum_b_b > set_Sum_sum_b_b > $o ).
thf(func_def_70,type,
ord_le230080206rm_a_b: set_trm_a_b > set_trm_a_b > $o ).
thf(func_def_71,type,
ord_le1697056455_sf_sz: set_trm_sf_sz > set_trm_sf_sz > $o ).
thf(func_def_72,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_73,type,
top_to646513176l_sz_o: finite824932053eal_sz > $o ).
thf(func_def_74,type,
top_to1849113498_c_b_o: sum_su1965225555um_c_b > $o ).
thf(func_def_75,type,
top_top_a_o: a > $o ).
thf(func_def_76,type,
top_to502572752real_b: set_Fi268318752real_b ).
thf(func_def_77,type,
top_to1873962757eal_sz: set_Fi291318197eal_sz ).
thf(func_def_78,type,
top_to999478531um_c_b: set_Su111624115um_c_b ).
thf(func_def_79,type,
top_to301096907um_b_b: set_Sum_sum_b_b ).
thf(func_def_80,type,
top_top_set_a: set_a ).
thf(func_def_81,type,
produc936751193real_b: produc133005365real_b > finite1390225514real_b ).
thf(func_def_82,type,
produc1111759555eal_sz: produc1149990247eal_sz > finite824932053eal_sz ).
thf(func_def_83,type,
domain413207655_sc_sz: ( denota610675952t_unit > freche2095075217_sc_sz > $o ) > denota610675952t_unit > $o ).
thf(func_def_84,type,
domain134596861rm_a_b: ( trm_a_b > frechet_strm_a_b > $o ) > trm_a_b > $o ).
thf(func_def_85,type,
domain512309999_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > trm_sf_sz > $o ).
thf(func_def_86,type,
collec944067751t_unit: ( denota723907260t_unit > $o ) > set_De153000604t_unit ).
thf(func_def_87,type,
collec1767975749t_unit: ( denota610675952t_unit > $o ) > set_De208295462t_unit ).
thf(func_def_88,type,
collec1002602816eal_sz: ( finite824932053eal_sz > $o ) > set_Fi291318197eal_sz ).
thf(func_def_89,type,
collec1166375742um_c_b: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b ).
thf(func_def_90,type,
collect_Sum_sum_b_b: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b ).
thf(func_def_91,type,
collect_trm_a_b: ( trm_a_b > $o ) > set_trm_a_b ).
thf(func_def_92,type,
collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
thf(func_def_93,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_94,type,
static_FVT_a_b: trm_a_b > set_Sum_sum_b_b ).
thf(func_def_95,type,
static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
thf(func_def_96,type,
static_SIGT_a_b: trm_a_b > set_a ).
thf(func_def_97,type,
static_SIGT_sf_sz: trm_sf_sz > set_sf ).
thf(func_def_98,type,
sum_In811702836um_c_b: a > sum_su1965225555um_c_b ).
thf(func_def_99,type,
dfree_a_b: trm_a_b > $o ).
thf(func_def_100,type,
dfree_sf_sz: trm_sf_sz > $o ).
thf(func_def_101,type,
times_a_b: trm_a_b > trm_a_b > trm_a_b ).
thf(func_def_102,type,
times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_103,type,
topolo238266006b_real: set_Fi268318752real_b > ( finite1390225514real_b > real ) > $o ).
thf(func_def_104,type,
topolo885751137z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > $o ).
thf(func_def_105,type,
topolo1348430467z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > real ) > $o ).
thf(func_def_106,type,
type_d1092523951t_unit: ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > set_De208295462t_unit > $o ).
thf(func_def_107,type,
type_d2045870413rm_a_b: ( frechet_strm_a_b > trm_a_b ) > ( trm_a_b > frechet_strm_a_b ) > set_trm_a_b > $o ).
thf(func_def_108,type,
type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
thf(func_def_109,type,
member122424677t_unit: denota723907260t_unit > set_De153000604t_unit > $o ).
thf(func_def_110,type,
member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
thf(func_def_111,type,
member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
thf(func_def_112,type,
member973578748um_c_b: sum_su1965225555um_c_b > set_Su111624115um_c_b > $o ).
thf(func_def_113,type,
member_Sum_sum_b_b: sum_sum_b_b > set_Sum_sum_b_b > $o ).
thf(func_def_114,type,
member_trm_a_b: trm_a_b > set_trm_a_b > $o ).
thf(func_def_115,type,
member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
thf(func_def_116,type,
member_a: a > set_a > $o ).
thf(func_def_117,type,
i: denota723907260t_unit ).
thf(func_def_118,type,
j: denota723907260t_unit ).
thf(func_def_119,type,
nu: produc133005365real_b ).
thf(func_def_120,type,
nu2: produc133005365real_b ).
thf(func_def_121,type,
theta_1: trm_a_b ).
thf(func_def_122,type,
theta_2: trm_a_b ).
thf(func_def_136,type,
sK0: ( trm_a_b > $o ) > frechet_strm_a_b ).
thf(func_def_137,type,
sK1: trm_a_b > frechet_strm_a_b ).
thf(func_def_138,type,
sK2: denota723907260t_unit > freche1734198479_a_c_b ).
thf(func_def_139,type,
sK3: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_140,type,
sK4: set_trm_a_b > set_trm_a_b > trm_a_b ).
thf(func_def_141,type,
sK5: set_a > set_a > a ).
thf(func_def_142,type,
sK6: a ).
thf(func_def_143,type,
sK7: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_144,type,
sK8: frechet_strm_a_b > trm_a_b ).
thf(func_def_145,type,
sK9: ( denota723907260t_unit > $o ) > freche1734198479_a_c_b ).
thf(func_def_146,type,
sK10: freche1734198479_a_c_b > denota723907260t_unit ).
thf(func_def_147,type,
sK11: ( trm_a_b > $o ) > ( trm_a_b > $o ) > trm_a_b ).
thf(func_def_148,type,
sK12: ( frechet_strm_a_b > $o ) > trm_a_b ).
thf(func_def_149,type,
sK13: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_150,type,
sK14: set_a > a ).
thf(func_def_151,type,
sK15: ( finite824932053eal_sz > real ) > real > set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > ( finite824932053eal_sz > bounde472938360z_real ) > finite824932053eal_sz ).
thf(func_def_152,type,
sK16: ( freche1734198479_a_c_b > $o ) > denota723907260t_unit ).
thf(func_def_153,type,
sK17: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_156,type,
sK19: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_157,type,
sK20: set_Su111624115um_c_b > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_158,type,
sK21: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_159,type,
sK22: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_161,type,
sK23: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_162,type,
sK24: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_163,type,
sK25: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_164,type,
sK26: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_165,type,
sK27: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_166,type,
sK28: set_a > set_a > set_a > a ).
thf(func_def_167,type,
sK29: set_a > set_a > a ).
thf(func_def_168,type,
sK30: set_a > set_a > a ).
thf(func_def_169,type,
sK31: set_a > set_a > a ).
thf(func_def_170,type,
sK32: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_171,type,
sK33: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_172,type,
sK34: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_173,type,
sK35: set_a > set_a > a ).
thf(func_def_174,type,
sK36: set_a > set_a > a ).
thf(func_def_175,type,
sK37: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_176,type,
sK38: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b > set_Sum_sum_b_b > sum_sum_b_b ).
thf(func_def_177,type,
sK39: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b > set_Sum_sum_b_b > sum_sum_b_b ).
thf(func_def_178,type,
sK40: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b > sum_sum_b_b ).
thf(func_def_179,type,
sK41: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b > sum_sum_b_b ).
thf(func_def_180,type,
sK42: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b > sum_sum_b_b ).
thf(func_def_181,type,
sK43: set_a > set_a > a ).
thf(func_def_182,type,
sK44: set_a > set_a > a ).
thf(func_def_183,type,
sK45: set_a > set_a > a ).
thf(func_def_184,type,
sK46: set_a > set_a > set_a > a ).
thf(func_def_185,type,
sK47: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_186,type,
sK48: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_187,type,
sK49: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_188,type,
sK50: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_189,type,
sK51: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_190,type,
sK52: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_191,type,
sK53: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_192,type,
sK54: set_a > set_a > set_a > a ).
thf(func_def_193,type,
sK55: set_a > set_a > a ).
thf(func_def_194,type,
sK56: set_a > set_a > a ).
thf(func_def_195,type,
sK57: set_a > set_a > a ).
thf(func_def_196,type,
sK58: set_a > set_a > a ).
thf(func_def_197,type,
sK59: set_a > set_a > a ).
thf(func_def_198,type,
sK60: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_199,type,
sK61: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_200,type,
sK62: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_201,type,
sK63: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_202,type,
sK64: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_203,type,
sK65: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b ).
thf(func_def_204,type,
sK66: set_Sum_sum_b_b > set_Sum_sum_b_b > ( sum_sum_b_b > $o ) > sum_sum_b_b ).
thf(func_def_205,type,
sK67: set_Sum_sum_b_b > set_Sum_sum_b_b > ( sum_sum_b_b > $o ) > sum_sum_b_b ).
thf(func_def_206,type,
sK68: set_Sum_sum_b_b > ( sum_sum_b_b > $o ) > sum_sum_b_b ).
thf(func_def_207,type,
sK69: set_Sum_sum_b_b > ( sum_sum_b_b > $o ) > sum_sum_b_b ).
thf(func_def_208,type,
sK70: set_Su111624115um_c_b > sum_su1965225555um_c_b ).
thf(func_def_210,type,
ph71:
!>[X0: $tType] : X0 ).
thf(f2273,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2271,f1116]) ).
thf(f1116,plain,
( $true
!= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f926,plain,
( $true
!= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f871]) ).
thf(f871,plain,
( $true
!= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f870]) ).
thf(f870,plain,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X0: sum_su1965225555um_c_b] :
? [X1: a] :
( ( ( sum_In811702836um_c_b @ X1 )
= X0 )
& ( member_a @ X1 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( ( sum_In811702836um_c_b @ X3 )
= X2 )
& ( member_a @ X3 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( ( sum_In811702836um_c_b @ X3 )
= X2 )
& ( member_a @ X3 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',conj_0) ).
thf(f2271,plain,
( $true
= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2269]) ).
thf(f2269,plain,
( ( $true != $true )
| ( $true
= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f1209,f1140]) ).
thf(f1140,plain,
( $true
= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sum_In811702836um_c_b @ Y1 )
= Y0 )
& ( member_a @ Y1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f845]) ).
thf(f845,plain,
( $true
= ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sum_In811702836um_c_b @ Y1 )
= Y0 )
& ( member_a @ Y1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f844]) ).
thf(f844,plain,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X0: sum_su1965225555um_c_b] :
? [X1: a] :
( ( member_a @ X1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) )
& ( ( sum_In811702836um_c_b @ X1 )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( member_a @ X3 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) )
& ( ( sum_In811702836um_c_b @ X3 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',fact_3_dfree__Times_Oprems_I2_J) ).
thf(f1209,plain,
! [X0: denota723907260t_unit,X1: denota723907260t_unit] :
( ( $true
!= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sum_In811702836um_c_b @ Y1 )
= Y0 )
& ( member_a @ Y1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ) )
| ( $true
= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f960]) ).
thf(f960,plain,
! [X0: denota723907260t_unit,X1: denota723907260t_unit] :
( ( $true
!= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sum_In811702836um_c_b @ Y1 )
= Y0 )
& ( member_a @ Y1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ) )
| ( $true
= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f531]) ).
thf(f531,plain,
! [X0: denota723907260t_unit,X1: denota723907260t_unit] :
( ( $true
= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( sum_In811702836um_c_b @ Y1 )
= Y0 )
& ( member_a @ Y1 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ) )
=> ( $true
= ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [Y0: sum_su1965225555um_c_b] :
( ?? @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ ( static_SIGT_a_b @ theta_1 ) )
& ( ( sum_In811702836um_c_b @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f530]) ).
thf(f530,plain,
! [X0: denota723907260t_unit,X1: denota723907260t_unit] :
( ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( member_a @ X3 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) )
& ( ( sum_In811702836um_c_b @ X3 )
= X2 ) ) ) )
=> ( denota896875430_a_c_b @ X1 @ X0
@ ( collec1166375742um_c_b
@ ^ [X4: sum_su1965225555um_c_b] :
? [X5: a] :
( ( ( sum_In811702836um_c_b @ X5 )
= X4 )
& ( member_a @ X5 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: denota723907260t_unit,X0: denota723907260t_unit] :
( ( denota896875430_a_c_b @ X0 @ X1
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( member_a @ X3 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) )
& ( ( sum_In811702836um_c_b @ X3 )
= X2 ) ) ) )
=> ( denota896875430_a_c_b @ X0 @ X1
@ ( collec1166375742um_c_b
@ ^ [X2: sum_su1965225555um_c_b] :
? [X3: a] :
( ( ( sum_In811702836um_c_b @ X3 )
= X2 )
& ( member_a @ X3 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP042^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : ITP042^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.48 % Domain : Interactive Theorem Proving
% 0.19/0.48 % Problem : Sledgehammer Coincidence problem prob_99__7210728_1
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.48 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Des21]
% 0.19/0.48 % Names : Coincidence/prob_99__7210728_1 [Des21]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.19/0.48 % Syntax : Number of formulae : 482 ( 196 unt; 123 typ; 0 def)
% 0.19/0.48 % Number of atoms : 940 ( 301 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 12 ( 2 avg)
% 0.19/0.48 % Number of connectives : 2316 ( 34 ~; 10 |; 49 &;1961 @)
% 0.19/0.48 % ( 0 <=>; 262 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 18 ( 5 avg)
% 0.19/0.48 % Number of types : 29 ( 28 usr)
% 0.19/0.48 % Number of type conns : 289 ( 289 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 98 ( 95 usr; 13 con; 0-3 aty)
% 0.19/0.48 % Number of variables : 876 ( 138 ^; 720 !; 18 ?; 876 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:49.138
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % Could-be-implicit typings (28)
% 0.19/0.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.19/0.48 produc1149990247eal_sz: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_J,type,
% 0.19/0.48 produc133005365real_b: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 0.19/0.48 bounde472938360z_real: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.19/0.48 set_De208295462t_unit: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J_J,type,
% 0.19/0.48 set_De153000604t_unit: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.19/0.48 denota610675952t_unit: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J,type,
% 0.19/0.48 denota723907260t_unit: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J_J,type,
% 0.19/0.48 set_Su111624115um_c_b: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.19/0.48 set_Fi291318197eal_sz: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_J,type,
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% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.19/0.48 collec1767975749t_unit: ( denota610675952t_unit > $o ) > set_De208295462t_unit ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 0.19/0.48 collec1002602816eal_sz: ( finite824932053eal_sz > $o ) > set_Fi291318197eal_sz ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J,type,
% 0.19/0.48 collec1166375742um_c_b: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__b_Mtf__b_J,type,
% 0.19/0.48 collect_Sum_sum_b_b: ( sum_sum_b_b > $o ) > set_Sum_sum_b_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 0.19/0.48 collect_trm_a_b: ( trm_a_b > $o ) > set_trm_a_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.19/0.48 collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.19/0.48 collect_a: ( a > $o ) > set_a ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Static__Semantics_OFVT_001tf__a_001tf__b,type,
% 0.19/0.48 static_FVT_a_b: trm_a_b > set_Sum_sum_b_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Static__Semantics_OFVT_001tf__sf_001tf__sz,type,
% 0.19/0.48 static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Static__Semantics_OSIGT_001tf__a_001tf__b,type,
% 0.19/0.48 static_SIGT_a_b: trm_a_b > set_a ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Static__Semantics_OSIGT_001tf__sf_001tf__sz,type,
% 0.19/0.48 static_SIGT_sf_sz: trm_sf_sz > set_sf ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Sum__Type_OInl_001tf__a_001t__Sum____Type__Osum_Itf__c_Mtf__b_J,type,
% 0.19/0.48 sum_In811702836um_c_b: a > sum_su1965225555um_c_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Syntax_Odfree_001tf__a_001tf__b,type,
% 0.19/0.48 dfree_a_b: trm_a_b > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Syntax_Odfree_001tf__sf_001tf__sz,type,
% 0.19/0.48 dfree_sf_sz: trm_sf_sz > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Syntax_Otrm_OTimes_001tf__a_001tf__b,type,
% 0.19/0.48 times_a_b: trm_a_b > trm_a_b > trm_a_b ).
% 0.19/0.48
% 0.19/0.48 thf(sy_c_Syntax_Otrm_OTimes_001tf__sf_001tf__sz,type,
% 0.32/0.48 times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_001t__Real__Oreal,type,
% 0.32/0.48 topolo238266006b_real: set_Fi268318752real_b > ( finite1390225514real_b > real ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 0.32/0.48 topolo885751137z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Real__Oreal,type,
% 0.32/0.48 topolo1348430467z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > real ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ogood____interp_Itf__sf_Mtf__sc_Mtf__sz_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.32/0.48 type_d1092523951t_unit: ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > set_De208295462t_unit > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__b_J_001t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 0.32/0.48 type_d2045870413rm_a_b: ( frechet_strm_a_b > trm_a_b ) > ( trm_a_b > frechet_strm_a_b ) > set_trm_a_b > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.32/0.48 type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J,type,
% 0.32/0.48 member122424677t_unit: denota723907260t_unit > set_De153000604t_unit > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.32/0.48 member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 0.32/0.48 member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J,type,
% 0.32/0.48 member973578748um_c_b: sum_su1965225555um_c_b > set_Su111624115um_c_b > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Sum____Type__Osum_Itf__b_Mtf__b_J,type,
% 0.32/0.48 member_Sum_sum_b_b: sum_sum_b_b > set_Sum_sum_b_b > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 0.32/0.48 member_trm_a_b: trm_a_b > set_trm_a_b > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.32/0.48 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member_001tf__a,type,
% 0.32/0.48 member_a: a > set_a > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_I,type,
% 0.32/0.48 i: denota723907260t_unit ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_J,type,
% 0.32/0.48 j: denota723907260t_unit ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v__092_060nu_062,type,
% 0.32/0.48 nu: produc133005365real_b ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v__092_060nu_062_H,type,
% 0.32/0.48 nu2: produc133005365real_b ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v__092_060theta_062_092_060_094sub_0621____,type,
% 0.32/0.48 theta_1: trm_a_b ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v__092_060theta_062_092_060_094sub_0622____,type,
% 0.32/0.48 theta_2: trm_a_b ).
% 0.32/0.48
% 0.32/0.48 % Relevant facts (355)
% 0.32/0.48 thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
% 0.32/0.48 ! [I: denota723907260t_unit,J: denota723907260t_unit] :
% 0.32/0.48 ( ( denota896875430_a_c_b @ I @ J
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
% 0.32/0.48 => ( denota896875430_a_c_b @ I @ J
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % \<open>\<And>J I. Iagree I J {Inl x |x. x \<in> SIGT (Times \<theta>\<^sub>1 \<theta>\<^sub>2)} \<Longrightarrow> Iagree I J {Inl x |x. x \<in> SIGT \<theta>\<^sub>1}\<close>
% 0.32/0.48 thf(fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062,axiom,
% 0.32/0.48 ! [I: denota723907260t_unit,J: denota723907260t_unit] :
% 0.32/0.48 ( ( denota896875430_a_c_b @ I @ J
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
% 0.32/0.48 => ( denota896875430_a_c_b @ I @ J
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % \<open>\<And>J I. Iagree I J {Inl x |x. x \<in> SIGT (Times \<theta>\<^sub>1 \<theta>\<^sub>2)} \<Longrightarrow> Iagree I J {Inl x |x. x \<in> SIGT \<theta>\<^sub>2}\<close>
% 0.32/0.48 thf(fact_2_IA,axiom,
% 0.32/0.48 ( denota896875430_a_c_b @ i @ j
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) )
% 0.32/0.48 | ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IA
% 0.32/0.48 thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
% 0.32/0.48 ( denota896875430_a_c_b @ i @ j
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dfree_Times.prems(2)
% 0.32/0.48 thf(fact_4_dfree__Times_Ohyps_I1_J,axiom,
% 0.32/0.48 dfree_a_b @ theta_1 ).
% 0.32/0.48
% 0.32/0.48 % dfree_Times.hyps(1)
% 0.32/0.48 thf(fact_5_sum_Oinject_I1_J,axiom,
% 0.32/0.48 ! [X1: a,Y1: a] :
% 0.32/0.48 ( ( ( sum_In811702836um_c_b @ X1 )
% 0.32/0.48 = ( sum_In811702836um_c_b @ Y1 ) )
% 0.32/0.48 = ( X1 = Y1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % sum.inject(1)
% 0.32/0.48 thf(fact_6_old_Osum_Oinject_I1_J,axiom,
% 0.32/0.48 ! [A: a,A2: a] :
% 0.32/0.48 ( ( ( sum_In811702836um_c_b @ A )
% 0.32/0.48 = ( sum_In811702836um_c_b @ A2 ) )
% 0.32/0.48 = ( A = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.sum.inject(1)
% 0.32/0.48 thf(fact_7_Isubs_I2_J,axiom,
% 0.32/0.48 ( ord_le1404954451um_c_b
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) )
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Isubs(2)
% 0.32/0.48 thf(fact_8_Isubs_I1_J,axiom,
% 0.32/0.48 ( ord_le1404954451um_c_b
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) )
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Isubs(1)
% 0.32/0.48 thf(fact_9_Iagree__comm,axiom,
% 0.32/0.48 ! [A3: denota723907260t_unit,B: denota723907260t_unit,V: set_Su111624115um_c_b] :
% 0.32/0.48 ( ( denota896875430_a_c_b @ A3 @ B @ V )
% 0.32/0.48 => ( denota896875430_a_c_b @ B @ A3 @ V ) ) ).
% 0.32/0.48
% 0.32/0.48 % Iagree_comm
% 0.32/0.48 thf(fact_10_Iagree__refl,axiom,
% 0.32/0.48 ! [I: denota723907260t_unit,A3: set_Su111624115um_c_b] : ( denota896875430_a_c_b @ I @ I @ A3 ) ).
% 0.32/0.48
% 0.32/0.48 % Iagree_refl
% 0.32/0.48 thf(fact_11_Inl__inject,axiom,
% 0.32/0.48 ! [X2: a,Y: a] :
% 0.32/0.48 ( ( ( sum_In811702836um_c_b @ X2 )
% 0.32/0.48 = ( sum_In811702836um_c_b @ Y ) )
% 0.32/0.48 => ( X2 = Y ) ) ).
% 0.32/0.48
% 0.32/0.48 % Inl_inject
% 0.32/0.48 thf(fact_12_IH1,axiom,
% 0.32/0.48 ( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) )
% 0.32/0.48 => ( ( denota896875430_a_c_b @ i @ j
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) )
% 0.32/0.48 => ( ( denota722380397_a_c_b @ i @ theta_1 @ ( produc936751193real_b @ nu ) )
% 0.32/0.48 = ( denota722380397_a_c_b @ j @ theta_1 @ ( produc936751193real_b @ nu2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IH1
% 0.32/0.48 thf(fact_13_IH2,axiom,
% 0.32/0.48 ( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) )
% 0.32/0.48 => ( ( denota896875430_a_c_b @ i @ j
% 0.32/0.48 @ ( collec1166375742um_c_b
% 0.32/0.48 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.48 ? [X: a] :
% 0.32/0.48 ( ( Uu
% 0.32/0.48 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.48 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) )
% 0.32/0.48 => ( ( denota722380397_a_c_b @ i @ theta_2 @ ( produc936751193real_b @ nu ) )
% 0.32/0.48 = ( denota722380397_a_c_b @ j @ theta_2 @ ( produc936751193real_b @ nu2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IH2
% 0.32/0.48 thf(fact_14_Iagree__Func,axiom,
% 0.32/0.48 ! [I: denota723907260t_unit,J: denota723907260t_unit,V: set_Su111624115um_c_b,F: a] :
% 0.32/0.48 ( ( denota896875430_a_c_b @ I @ J @ V )
% 0.32/0.48 => ( ( member973578748um_c_b @ ( sum_In811702836um_c_b @ F ) @ V )
% 0.32/0.48 => ( ( denota102976244t_unit @ I @ F )
% 0.32/0.48 = ( denota102976244t_unit @ J @ F ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Iagree_Func
% 0.32/0.48 thf(fact_15_raw__interp__inject,axiom,
% 0.32/0.48 ! [X2: freche2095075217_sc_sz,Y: freche2095075217_sc_sz] :
% 0.32/0.48 ( ( ( freche1421597129_sc_sz @ X2 )
% 0.32/0.48 = ( freche1421597129_sc_sz @ Y ) )
% 0.32/0.48 = ( X2 = Y ) ) ).
% 0.32/0.48
% 0.32/0.48 % raw_interp_inject
% 0.32/0.48 thf(fact_16_dfree__Times_Ohyps_I2_J,axiom,
% 0.32/0.48 dfree_a_b @ theta_2 ).
% 0.32/0.48
% 0.32/0.48 % dfree_Times.hyps(2)
% 0.32/0.48 thf(fact_17_coincidence__sterm,axiom,
% 0.32/0.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Theta: trm_sf_sz,I: denota610675952t_unit] :
% 0.32/0.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ Theta ) )
% 0.32/0.48 => ( ( denota1179238309_sc_sz @ I @ Theta @ ( produc1111759555eal_sz @ Nu ) )
% 0.32/0.48 = ( denota1179238309_sc_sz @ I @ Theta @ ( produc1111759555eal_sz @ Nu2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % coincidence_sterm
% 0.32/0.48 thf(fact_18_coincidence__sterm,axiom,
% 0.32/0.48 ! [Nu: produc133005365real_b,Nu2: produc133005365real_b,Theta: trm_a_b,I: denota723907260t_unit] :
% 0.32/0.48 ( ( denota1997846517gree_b @ Nu @ Nu2 @ ( static_FVT_a_b @ Theta ) )
% 0.32/0.48 => ( ( denota722380397_a_c_b @ I @ Theta @ ( produc936751193real_b @ Nu ) )
% 0.32/0.48 = ( denota722380397_a_c_b @ I @ Theta @ ( produc936751193real_b @ Nu2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % coincidence_sterm
% 0.32/0.48 thf(fact_19_dfree__Times_Oprems_I1_J,axiom,
% 0.32/0.49 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % dfree_Times.prems(1)
% 0.32/0.49 thf(fact_20_VAs_I2_J,axiom,
% 0.32/0.49 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) ).
% 0.32/0.49
% 0.32/0.49 % VAs(2)
% 0.32/0.49 thf(fact_21_VAs_I1_J,axiom,
% 0.32/0.49 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) ).
% 0.32/0.49
% 0.32/0.49 % VAs(1)
% 0.32/0.49 thf(fact_22_VA,axiom,
% 0.32/0.49 denota1997846517gree_b @ nu @ nu2 @ ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ theta_1 ) @ ( static_FVT_a_b @ theta_2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % VA
% 0.32/0.49 thf(fact_23_agree__sub,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,Nu: produc133005365real_b,Omega: produc133005365real_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A3 @ B )
% 0.32/0.49 => ( ( denota1997846517gree_b @ Nu @ Omega @ B )
% 0.32/0.49 => ( denota1997846517gree_b @ Nu @ Omega @ A3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % agree_sub
% 0.32/0.49 thf(fact_24_agree__comm,axiom,
% 0.32/0.49 ! [A3: produc133005365real_b,B: produc133005365real_b,V: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( denota1997846517gree_b @ A3 @ B @ V )
% 0.32/0.49 => ( denota1997846517gree_b @ B @ A3 @ V ) ) ).
% 0.32/0.49
% 0.32/0.49 % agree_comm
% 0.32/0.49 thf(fact_25_agree__refl,axiom,
% 0.32/0.49 ! [Nu: produc133005365real_b,A3: set_Sum_sum_b_b] : ( denota1997846517gree_b @ Nu @ Nu @ A3 ) ).
% 0.32/0.49
% 0.32/0.49 % agree_refl
% 0.32/0.49 thf(fact_26_agree__supset,axiom,
% 0.32/0.49 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b,Nu: produc133005365real_b,Nu2: produc133005365real_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B @ A3 )
% 0.32/0.49 => ( ( denota1997846517gree_b @ Nu @ Nu2 @ A3 )
% 0.32/0.49 => ( denota1997846517gree_b @ Nu @ Nu2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % agree_supset
% 0.32/0.49 thf(fact_27_cr__good__interp__def,axiom,
% 0.32/0.49 ( freche58918398_sc_sz
% 0.32/0.49 = ( ^ [X: denota610675952t_unit,Y2: freche2095075217_sc_sz] :
% 0.32/0.49 ( X
% 0.32/0.49 = ( freche1421597129_sc_sz @ Y2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % cr_good_interp_def
% 0.32/0.49 thf(fact_28_dfree__Times__simps,axiom,
% 0.32/0.49 ! [A: trm_sf_sz,B2: trm_sf_sz] :
% 0.32/0.49 ( ( dfree_sf_sz @ ( times_sf_sz @ A @ B2 ) )
% 0.32/0.49 = ( ( dfree_sf_sz @ A )
% 0.32/0.49 & ( dfree_sf_sz @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dfree_Times_simps
% 0.32/0.49 thf(fact_29_dfree__Times__simps,axiom,
% 0.32/0.49 ! [A: trm_a_b,B2: trm_a_b] :
% 0.32/0.49 ( ( dfree_a_b @ ( times_a_b @ A @ B2 ) )
% 0.32/0.49 = ( ( dfree_a_b @ A )
% 0.32/0.49 & ( dfree_a_b @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dfree_Times_simps
% 0.32/0.49 thf(fact_30_simple__term__inject,axiom,
% 0.32/0.49 ! [X2: trm_a_b,Y: trm_a_b] :
% 0.32/0.49 ( ( member_trm_a_b @ X2 @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ( ( ( freche665377491rm_a_b @ X2 )
% 0.32/0.49 = ( freche665377491rm_a_b @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_inject
% 0.32/0.49 thf(fact_31_simple__term__inject,axiom,
% 0.32/0.49 ! [X2: trm_sf_sz,Y: trm_sf_sz] :
% 0.32/0.49 ( ( member_trm_sf_sz @ X2 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ( ( ( freche1046279700_sf_sz @ X2 )
% 0.32/0.49 = ( freche1046279700_sf_sz @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_inject
% 0.32/0.49 thf(fact_32_simple__term__induct,axiom,
% 0.32/0.49 ! [P: frechet_strm_a_b > $o,X2: frechet_strm_a_b] :
% 0.32/0.49 ( ! [Y3: trm_a_b] :
% 0.32/0.49 ( ( member_trm_a_b @ Y3 @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ( P @ ( freche665377491rm_a_b @ Y3 ) ) )
% 0.32/0.49 => ( P @ X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_induct
% 0.32/0.49 thf(fact_33_simple__term__induct,axiom,
% 0.32/0.49 ! [P: frechet_strm_sf_sz > $o,X2: frechet_strm_sf_sz] :
% 0.32/0.49 ( ! [Y3: trm_sf_sz] :
% 0.32/0.49 ( ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ( P @ ( freche1046279700_sf_sz @ Y3 ) ) )
% 0.32/0.49 => ( P @ X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_induct
% 0.32/0.49 thf(fact_34_simple__term__cases,axiom,
% 0.32/0.49 ! [X2: frechet_strm_a_b] :
% 0.32/0.49 ~ ! [Y3: trm_a_b] :
% 0.32/0.49 ( ( X2
% 0.32/0.49 = ( freche665377491rm_a_b @ Y3 ) )
% 0.32/0.49 => ~ ( member_trm_a_b @ Y3 @ ( collect_trm_a_b @ dfree_a_b ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_cases
% 0.32/0.49 thf(fact_35_simple__term__cases,axiom,
% 0.32/0.49 ! [X2: frechet_strm_sf_sz] :
% 0.32/0.49 ~ ! [Y3: trm_sf_sz] :
% 0.32/0.49 ( ( X2
% 0.32/0.49 = ( freche1046279700_sf_sz @ Y3 ) )
% 0.32/0.49 => ~ ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_cases
% 0.32/0.49 thf(fact_36_raw__interp__inverse,axiom,
% 0.32/0.49 ! [X2: freche2095075217_sc_sz] :
% 0.32/0.49 ( ( freche1784963216_sc_sz @ ( freche1421597129_sc_sz @ X2 ) )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp_inverse
% 0.32/0.49 thf(fact_37_raw__term__induct,axiom,
% 0.32/0.49 ! [Y: trm_a_b,P: trm_a_b > $o] :
% 0.32/0.49 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ( ! [X3: frechet_strm_a_b] : ( P @ ( frechet_raw_term_a_b @ X3 ) )
% 0.32/0.49 => ( P @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_induct
% 0.32/0.49 thf(fact_38_raw__term__induct,axiom,
% 0.32/0.49 ! [Y: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.32/0.49 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ( ! [X3: frechet_strm_sf_sz] : ( P @ ( freche782854530_sf_sz @ X3 ) )
% 0.32/0.49 => ( P @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_induct
% 0.32/0.49 thf(fact_39_raw__term__cases,axiom,
% 0.32/0.49 ! [Y: trm_a_b] :
% 0.32/0.49 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ~ ! [X3: frechet_strm_a_b] :
% 0.32/0.49 ( Y
% 0.32/0.49 != ( frechet_raw_term_a_b @ X3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_cases
% 0.32/0.49 thf(fact_40_raw__term__cases,axiom,
% 0.32/0.49 ! [Y: trm_sf_sz] :
% 0.32/0.49 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ~ ! [X3: frechet_strm_sf_sz] :
% 0.32/0.49 ( Y
% 0.32/0.49 != ( freche782854530_sf_sz @ X3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_cases
% 0.32/0.49 thf(fact_41_raw__term,axiom,
% 0.32/0.49 ! [X2: frechet_strm_a_b] : ( member_trm_a_b @ ( frechet_raw_term_a_b @ X2 ) @ ( collect_trm_a_b @ dfree_a_b ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term
% 0.32/0.49 thf(fact_42_raw__term,axiom,
% 0.32/0.49 ! [X2: frechet_strm_sf_sz] : ( member_trm_sf_sz @ ( freche782854530_sf_sz @ X2 ) @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term
% 0.32/0.49 thf(fact_43_trm_Oinject_I5_J,axiom,
% 0.32/0.49 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 0.32/0.49 ( ( ( times_sf_sz @ X51 @ X52 )
% 0.32/0.49 = ( times_sf_sz @ Y51 @ Y52 ) )
% 0.32/0.49 = ( ( X51 = Y51 )
% 0.32/0.49 & ( X52 = Y52 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % trm.inject(5)
% 0.32/0.49 thf(fact_44_trm_Oinject_I5_J,axiom,
% 0.32/0.49 ! [X51: trm_a_b,X52: trm_a_b,Y51: trm_a_b,Y52: trm_a_b] :
% 0.32/0.49 ( ( ( times_a_b @ X51 @ X52 )
% 0.32/0.49 = ( times_a_b @ Y51 @ Y52 ) )
% 0.32/0.49 = ( ( X51 = Y51 )
% 0.32/0.49 & ( X52 = Y52 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % trm.inject(5)
% 0.32/0.49 thf(fact_45_raw__term__inject,axiom,
% 0.32/0.49 ! [X2: frechet_strm_sf_sz,Y: frechet_strm_sf_sz] :
% 0.32/0.49 ( ( ( freche782854530_sf_sz @ X2 )
% 0.32/0.49 = ( freche782854530_sf_sz @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_inject
% 0.32/0.49 thf(fact_46_raw__term__inject,axiom,
% 0.32/0.49 ! [X2: frechet_strm_a_b,Y: frechet_strm_a_b] :
% 0.32/0.49 ( ( ( frechet_raw_term_a_b @ X2 )
% 0.32/0.49 = ( frechet_raw_term_a_b @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_inject
% 0.32/0.49 thf(fact_47_raw__term__inverse,axiom,
% 0.32/0.49 ! [X2: frechet_strm_a_b] :
% 0.32/0.49 ( ( freche665377491rm_a_b @ ( frechet_raw_term_a_b @ X2 ) )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_inverse
% 0.32/0.49 thf(fact_48_raw__term__inverse,axiom,
% 0.32/0.49 ! [X2: frechet_strm_sf_sz] :
% 0.32/0.49 ( ( freche1046279700_sf_sz @ ( freche782854530_sf_sz @ X2 ) )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % raw_term_inverse
% 0.32/0.49 thf(fact_49_simple__term__inverse,axiom,
% 0.32/0.49 ! [Y: trm_a_b] :
% 0.32/0.49 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 0.32/0.49 => ( ( frechet_raw_term_a_b @ ( freche665377491rm_a_b @ Y ) )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_inverse
% 0.32/0.49 thf(fact_50_simple__term__inverse,axiom,
% 0.32/0.49 ! [Y: trm_sf_sz] :
% 0.32/0.49 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 0.32/0.49 => ( ( freche782854530_sf_sz @ ( freche1046279700_sf_sz @ Y ) )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % simple_term_inverse
% 0.32/0.49 thf(fact_51_agree__union,axiom,
% 0.32/0.49 ! [Nu: produc133005365real_b,Omega: produc133005365real_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( denota1997846517gree_b @ Nu @ Omega @ A3 )
% 0.32/0.49 => ( ( denota1997846517gree_b @ Nu @ Omega @ B )
% 0.32/0.49 => ( denota1997846517gree_b @ Nu @ Omega @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % agree_union
% 0.32/0.49 thf(fact_52_Iagree__sub,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,I: denota723907260t_unit,J: denota723907260t_unit] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( denota896875430_a_c_b @ I @ J @ B )
% 0.32/0.49 => ( denota896875430_a_c_b @ I @ J @ A3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Iagree_sub
% 0.32/0.49 thf(fact_53_dfree_Odfree__Times,axiom,
% 0.32/0.49 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.32/0.49 ( ( dfree_sf_sz @ Theta_1 )
% 0.32/0.49 => ( ( dfree_sf_sz @ Theta_2 )
% 0.32/0.49 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dfree.dfree_Times
% 0.32/0.49 thf(fact_54_dfree_Odfree__Times,axiom,
% 0.32/0.49 ! [Theta_1: trm_a_b,Theta_2: trm_a_b] :
% 0.32/0.49 ( ( dfree_a_b @ Theta_1 )
% 0.32/0.49 => ( ( dfree_a_b @ Theta_2 )
% 0.32/0.49 => ( dfree_a_b @ ( times_a_b @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dfree.dfree_Times
% 0.32/0.49 thf(fact_55_cr__strm__def,axiom,
% 0.32/0.49 ( freche1244000341_sf_sz
% 0.32/0.49 = ( ^ [X: trm_sf_sz,Y2: frechet_strm_sf_sz] :
% 0.32/0.49 ( X
% 0.32/0.49 = ( freche782854530_sf_sz @ Y2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % cr_strm_def
% 0.32/0.49 thf(fact_56_cr__strm__def,axiom,
% 0.32/0.49 ( frechet_cr_strm_a_b
% 0.32/0.49 = ( ^ [X: trm_a_b,Y2: frechet_strm_a_b] :
% 0.32/0.49 ( X
% 0.32/0.49 = ( frechet_raw_term_a_b @ Y2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % cr_strm_def
% 0.32/0.49 thf(fact_57_fst__sup,axiom,
% 0.32/0.49 ! [X2: produc133005365real_b,Y: produc133005365real_b] :
% 0.32/0.49 ( ( produc936751193real_b @ ( sup_su1581595657real_b @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su2133361046real_b @ ( produc936751193real_b @ X2 ) @ ( produc936751193real_b @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % fst_sup
% 0.32/0.49 thf(fact_58_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: finite824932053eal_sz,P: finite824932053eal_sz > $o] :
% 0.32/0.49 ( ( member1693951742eal_sz @ A @ ( collec1002602816eal_sz @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_59_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: sum_sum_b_b,P: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ A @ ( collect_Sum_sum_b_b @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_60_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.32/0.49 ( ( member_trm_sf_sz @ A @ ( collect_trm_sf_sz @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_61_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: trm_a_b,P: trm_a_b > $o] :
% 0.32/0.49 ( ( member_trm_a_b @ A @ ( collect_trm_a_b @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_62_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: a,P: a > $o] :
% 0.32/0.49 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_63_mem__Collect__eq,axiom,
% 0.32/0.49 ! [A: sum_su1965225555um_c_b,P: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( member973578748um_c_b @ A @ ( collec1166375742um_c_b @ P ) )
% 0.32/0.49 = ( P @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % mem_Collect_eq
% 0.32/0.49 thf(fact_64_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( collec1002602816eal_sz
% 0.32/0.49 @ ^ [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_65_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( collect_Sum_sum_b_b
% 0.32/0.49 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_66_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_trm_sf_sz] :
% 0.32/0.49 ( ( collect_trm_sf_sz
% 0.32/0.49 @ ^ [X: trm_sf_sz] : ( member_trm_sf_sz @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_67_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_trm_a_b] :
% 0.32/0.49 ( ( collect_trm_a_b
% 0.32/0.49 @ ^ [X: trm_a_b] : ( member_trm_a_b @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_68_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_a] :
% 0.32/0.49 ( ( collect_a
% 0.32/0.49 @ ^ [X: a] : ( member_a @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_69_Collect__mem__eq,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( collec1166375742um_c_b
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A3 ) )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mem_eq
% 0.32/0.49 thf(fact_70_Collect__cong,axiom,
% 0.32/0.49 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 0.32/0.49 ( ! [X3: finite824932053eal_sz] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collec1002602816eal_sz @ P )
% 0.32/0.49 = ( collec1002602816eal_sz @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_71_Collect__cong,axiom,
% 0.32/0.49 ! [P: sum_sum_b_b > $o,Q: sum_sum_b_b > $o] :
% 0.32/0.49 ( ! [X3: sum_sum_b_b] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collect_Sum_sum_b_b @ P )
% 0.32/0.49 = ( collect_Sum_sum_b_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_72_Collect__cong,axiom,
% 0.32/0.49 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 0.32/0.49 ( ! [X3: trm_sf_sz] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collect_trm_sf_sz @ P )
% 0.32/0.49 = ( collect_trm_sf_sz @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_73_Collect__cong,axiom,
% 0.32/0.49 ! [P: trm_a_b > $o,Q: trm_a_b > $o] :
% 0.32/0.49 ( ! [X3: trm_a_b] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collect_trm_a_b @ P )
% 0.32/0.49 = ( collect_trm_a_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_74_Collect__cong,axiom,
% 0.32/0.49 ! [P: a > $o,Q: a > $o] :
% 0.32/0.49 ( ! [X3: a] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collect_a @ P )
% 0.32/0.49 = ( collect_a @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_75_Collect__cong,axiom,
% 0.32/0.49 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ! [X3: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 = ( Q @ X3 ) )
% 0.32/0.49 => ( ( collec1166375742um_c_b @ P )
% 0.32/0.49 = ( collec1166375742um_c_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_cong
% 0.32/0.49 thf(fact_76_Un__subset__iff,axiom,
% 0.32/0.49 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz,C: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ A3 @ B ) @ C )
% 0.32/0.49 = ( ( ord_le41263445eal_sz @ A3 @ C )
% 0.32/0.49 & ( ord_le41263445eal_sz @ B @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_subset_iff
% 0.32/0.49 thf(fact_77_Un__subset__iff,axiom,
% 0.32/0.49 ! [A3: set_a,B: set_a,C: set_a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A3 @ B ) @ C )
% 0.32/0.49 = ( ( ord_less_eq_set_a @ A3 @ C )
% 0.32/0.49 & ( ord_less_eq_set_a @ B @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_subset_iff
% 0.32/0.49 thf(fact_78_Un__subset__iff,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C )
% 0.32/0.49 = ( ( ord_le412705147um_b_b @ A3 @ C )
% 0.32/0.49 & ( ord_le412705147um_b_b @ B @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_subset_iff
% 0.32/0.49 thf(fact_79_Un__subset__iff,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ C )
% 0.32/0.49 = ( ( ord_le1404954451um_c_b @ A3 @ C )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ B @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_subset_iff
% 0.32/0.49 thf(fact_80_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: sum_sum_b_b > $o,C2: sum_sum_b_b > $o,A: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( ord_le1306331338_b_b_o @ ( sup_su2024788734_b_b_o @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_le1306331338_b_b_o @ B2 @ A )
% 0.32/0.49 & ( ord_le1306331338_b_b_o @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_81_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: set_Fi291318197eal_sz,C2: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_le41263445eal_sz @ B2 @ A )
% 0.32/0.49 & ( ord_le41263445eal_sz @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_82_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: set_a,C2: set_a,A: set_a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_less_eq_set_a @ B2 @ A )
% 0.32/0.49 & ( ord_less_eq_set_a @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_83_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: sum_su1965225555um_c_b > $o,C2: sum_su1965225555um_c_b > $o,A: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_le1534094666_c_b_o @ B2 @ A )
% 0.32/0.49 & ( ord_le1534094666_c_b_o @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_84_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: a > $o,C2: a > $o,A: a > $o] :
% 0.32/0.49 ( ( ord_less_eq_a_o @ ( sup_sup_a_o @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_less_eq_a_o @ B2 @ A )
% 0.32/0.49 & ( ord_less_eq_a_o @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_85_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_le412705147um_b_b @ B2 @ A )
% 0.32/0.49 & ( ord_le412705147um_b_b @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_86_sup_Obounded__iff,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A )
% 0.32/0.49 = ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.bounded_iff
% 0.32/0.49 thf(fact_87_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: sum_sum_b_b > $o,Y: sum_sum_b_b > $o,Z: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( ord_le1306331338_b_b_o @ ( sup_su2024788734_b_b_o @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_le1306331338_b_b_o @ X2 @ Z )
% 0.32/0.49 & ( ord_le1306331338_b_b_o @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_88_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,Z: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_le41263445eal_sz @ X2 @ Z )
% 0.32/0.49 & ( ord_le41263445eal_sz @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_89_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: set_a,Y: set_a,Z: set_a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_less_eq_set_a @ X2 @ Z )
% 0.32/0.49 & ( ord_less_eq_set_a @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_90_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: sum_su1965225555um_c_b > $o,Y: sum_su1965225555um_c_b > $o,Z: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_le1534094666_c_b_o @ X2 @ Z )
% 0.32/0.49 & ( ord_le1534094666_c_b_o @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_91_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: a > $o,Y: a > $o,Z: a > $o] :
% 0.32/0.49 ( ( ord_less_eq_a_o @ ( sup_sup_a_o @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_less_eq_a_o @ X2 @ Z )
% 0.32/0.49 & ( ord_less_eq_a_o @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_92_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_le412705147um_b_b @ X2 @ Z )
% 0.32/0.49 & ( ord_le412705147um_b_b @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_93_le__sup__iff,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( ( ord_le1404954451um_c_b @ X2 @ Z )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_sup_iff
% 0.32/0.49 thf(fact_94_FVT_Osimps_I5_J,axiom,
% 0.32/0.49 ! [F: trm_sf_sz,G: trm_sf_sz] :
% 0.32/0.49 ( ( static_FVT_sf_sz @ ( times_sf_sz @ F @ G ) )
% 0.32/0.49 = ( sup_su1670953621_sz_sz @ ( static_FVT_sf_sz @ F ) @ ( static_FVT_sf_sz @ G ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % FVT.simps(5)
% 0.32/0.49 thf(fact_95_FVT_Osimps_I5_J,axiom,
% 0.32/0.49 ! [F: trm_a_b,G: trm_a_b] :
% 0.32/0.49 ( ( static_FVT_a_b @ ( times_a_b @ F @ G ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ F ) @ ( static_FVT_a_b @ G ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % FVT.simps(5)
% 0.32/0.49 thf(fact_96_SIGT_Osimps_I5_J,axiom,
% 0.32/0.49 ! [T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.32/0.49 ( ( static_SIGT_sf_sz @ ( times_sf_sz @ T1 @ T2 ) )
% 0.32/0.49 = ( sup_sup_set_sf @ ( static_SIGT_sf_sz @ T1 ) @ ( static_SIGT_sf_sz @ T2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % SIGT.simps(5)
% 0.32/0.49 thf(fact_97_SIGT_Osimps_I5_J,axiom,
% 0.32/0.49 ! [T1: trm_a_b,T2: trm_a_b] :
% 0.32/0.49 ( ( static_SIGT_a_b @ ( times_a_b @ T1 @ T2 ) )
% 0.32/0.49 = ( sup_sup_set_a @ ( static_SIGT_a_b @ T1 ) @ ( static_SIGT_a_b @ T2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % SIGT.simps(5)
% 0.32/0.49 thf(fact_98_type__definition__strm,axiom,
% 0.32/0.49 type_d2045870413rm_a_b @ frechet_raw_term_a_b @ freche665377491rm_a_b @ ( collect_trm_a_b @ dfree_a_b ) ).
% 0.32/0.49
% 0.32/0.49 % type_definition_strm
% 0.32/0.49 thf(fact_99_type__definition__strm,axiom,
% 0.32/0.49 type_d46389773_sf_sz @ freche782854530_sf_sz @ freche1046279700_sf_sz @ ( collect_trm_sf_sz @ dfree_sf_sz ) ).
% 0.32/0.49
% 0.32/0.49 % type_definition_strm
% 0.32/0.49 thf(fact_100_good__interp__inverse,axiom,
% 0.32/0.49 ! [Y: denota723907260t_unit] :
% 0.32/0.49 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ( ( freche288321865_a_c_b @ ( freche153761090_a_c_b @ Y ) )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_inverse
% 0.32/0.49 thf(fact_101_good__interp__inverse,axiom,
% 0.32/0.49 ! [Y: denota610675952t_unit] :
% 0.32/0.49 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ( ( freche1421597129_sc_sz @ ( freche1784963216_sc_sz @ Y ) )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_inverse
% 0.32/0.49 thf(fact_102_raw__interp__induct,axiom,
% 0.32/0.49 ! [Y: denota723907260t_unit,P: denota723907260t_unit > $o] :
% 0.32/0.49 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ( ! [X3: freche1734198479_a_c_b] : ( P @ ( freche288321865_a_c_b @ X3 ) )
% 0.32/0.49 => ( P @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp_induct
% 0.32/0.49 thf(fact_103_raw__interp__induct,axiom,
% 0.32/0.49 ! [Y: denota610675952t_unit,P: denota610675952t_unit > $o] :
% 0.32/0.49 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ( ! [X3: freche2095075217_sc_sz] : ( P @ ( freche1421597129_sc_sz @ X3 ) )
% 0.32/0.49 => ( P @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp_induct
% 0.32/0.49 thf(fact_104_raw__interp__cases,axiom,
% 0.32/0.49 ! [Y: denota723907260t_unit] :
% 0.32/0.49 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ~ ! [X3: freche1734198479_a_c_b] :
% 0.32/0.49 ( Y
% 0.32/0.49 != ( freche288321865_a_c_b @ X3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp_cases
% 0.32/0.49 thf(fact_105_raw__interp__cases,axiom,
% 0.32/0.49 ! [Y: denota610675952t_unit] :
% 0.32/0.49 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ~ ! [X3: freche2095075217_sc_sz] :
% 0.32/0.49 ( Y
% 0.32/0.49 != ( freche1421597129_sc_sz @ X3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp_cases
% 0.32/0.49 thf(fact_106_raw__interp,axiom,
% 0.32/0.49 ! [X2: freche1734198479_a_c_b] : ( member122424677t_unit @ ( freche288321865_a_c_b @ X2 ) @ ( collec944067751t_unit @ denota1086158987_a_c_b ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp
% 0.32/0.49 thf(fact_107_raw__interp,axiom,
% 0.32/0.49 ! [X2: freche2095075217_sc_sz] : ( member754147591t_unit @ ( freche1421597129_sc_sz @ X2 ) @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ).
% 0.32/0.49
% 0.32/0.49 % raw_interp
% 0.32/0.49 thf(fact_108_good__interp__inject,axiom,
% 0.32/0.49 ! [X2: denota723907260t_unit,Y: denota723907260t_unit] :
% 0.32/0.49 ( ( member122424677t_unit @ X2 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ( ( ( freche153761090_a_c_b @ X2 )
% 0.32/0.49 = ( freche153761090_a_c_b @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_inject
% 0.32/0.49 thf(fact_109_good__interp__inject,axiom,
% 0.32/0.49 ! [X2: denota610675952t_unit,Y: denota610675952t_unit] :
% 0.32/0.49 ( ( member754147591t_unit @ X2 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ( ( ( freche1784963216_sc_sz @ X2 )
% 0.32/0.49 = ( freche1784963216_sc_sz @ Y ) )
% 0.32/0.49 = ( X2 = Y ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_inject
% 0.32/0.49 thf(fact_110_good__interp__induct,axiom,
% 0.32/0.49 ! [P: freche1734198479_a_c_b > $o,X2: freche1734198479_a_c_b] :
% 0.32/0.49 ( ! [Y3: denota723907260t_unit] :
% 0.32/0.49 ( ( member122424677t_unit @ Y3 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 0.32/0.49 => ( P @ ( freche153761090_a_c_b @ Y3 ) ) )
% 0.32/0.49 => ( P @ X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_induct
% 0.32/0.49 thf(fact_111_good__interp__induct,axiom,
% 0.32/0.49 ! [P: freche2095075217_sc_sz > $o,X2: freche2095075217_sc_sz] :
% 0.32/0.49 ( ! [Y3: denota610675952t_unit] :
% 0.32/0.49 ( ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 0.32/0.49 => ( P @ ( freche1784963216_sc_sz @ Y3 ) ) )
% 0.32/0.49 => ( P @ X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_induct
% 0.32/0.49 thf(fact_112_good__interp__cases,axiom,
% 0.32/0.49 ! [X2: freche1734198479_a_c_b] :
% 0.32/0.49 ~ ! [Y3: denota723907260t_unit] :
% 0.32/0.49 ( ( X2
% 0.32/0.49 = ( freche153761090_a_c_b @ Y3 ) )
% 0.32/0.49 => ~ ( member122424677t_unit @ Y3 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_cases
% 0.32/0.49 thf(fact_113_good__interp__cases,axiom,
% 0.32/0.49 ! [X2: freche2095075217_sc_sz] :
% 0.32/0.49 ~ ! [Y3: denota610675952t_unit] :
% 0.32/0.49 ( ( X2
% 0.32/0.49 = ( freche1784963216_sc_sz @ Y3 ) )
% 0.32/0.49 => ~ ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp_cases
% 0.32/0.49 thf(fact_114_subsetI,axiom,
% 0.32/0.49 ! [A3: set_trm_sf_sz,B: set_trm_sf_sz] :
% 0.32/0.49 ( ! [X3: trm_sf_sz] :
% 0.32/0.49 ( ( member_trm_sf_sz @ X3 @ A3 )
% 0.32/0.49 => ( member_trm_sf_sz @ X3 @ B ) )
% 0.32/0.49 => ( ord_le1697056455_sf_sz @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_115_subsetI,axiom,
% 0.32/0.49 ! [A3: set_trm_a_b,B: set_trm_a_b] :
% 0.32/0.49 ( ! [X3: trm_a_b] :
% 0.32/0.49 ( ( member_trm_a_b @ X3 @ A3 )
% 0.32/0.49 => ( member_trm_a_b @ X3 @ B ) )
% 0.32/0.49 => ( ord_le230080206rm_a_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_116_subsetI,axiom,
% 0.32/0.49 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ! [X3: finite824932053eal_sz] :
% 0.32/0.49 ( ( member1693951742eal_sz @ X3 @ A3 )
% 0.32/0.49 => ( member1693951742eal_sz @ X3 @ B ) )
% 0.32/0.49 => ( ord_le41263445eal_sz @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_117_subsetI,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ! [X3: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X3 @ A3 )
% 0.32/0.49 => ( member_Sum_sum_b_b @ X3 @ B ) )
% 0.32/0.49 => ( ord_le412705147um_b_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_118_subsetI,axiom,
% 0.32/0.49 ! [A3: set_a,B: set_a] :
% 0.32/0.49 ( ! [X3: a] :
% 0.32/0.49 ( ( member_a @ X3 @ A3 )
% 0.32/0.49 => ( member_a @ X3 @ B ) )
% 0.32/0.49 => ( ord_less_eq_set_a @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_119_subsetI,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ! [X3: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( member973578748um_c_b @ X3 @ A3 )
% 0.32/0.49 => ( member973578748um_c_b @ X3 @ B ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetI
% 0.32/0.49 thf(fact_120_subset__antisym,axiom,
% 0.32/0.49 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( ord_le41263445eal_sz @ A3 @ B )
% 0.32/0.49 => ( ( ord_le41263445eal_sz @ B @ A3 )
% 0.32/0.49 => ( A3 = B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_antisym
% 0.32/0.49 thf(fact_121_subset__antisym,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A3 @ B )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ B @ A3 )
% 0.32/0.49 => ( A3 = B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_antisym
% 0.32/0.49 thf(fact_122_subset__antisym,axiom,
% 0.32/0.49 ! [A3: set_a,B: set_a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ A3 @ B )
% 0.32/0.49 => ( ( ord_less_eq_set_a @ B @ A3 )
% 0.32/0.49 => ( A3 = B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_antisym
% 0.32/0.49 thf(fact_123_subset__antisym,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B @ A3 )
% 0.32/0.49 => ( A3 = B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_antisym
% 0.32/0.49 thf(fact_124_sup__apply,axiom,
% 0.32/0.49 ( sup_su2024788734_b_b_o
% 0.32/0.49 = ( ^ [F2: sum_sum_b_b > $o,G2: sum_sum_b_b > $o,X: sum_sum_b_b] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_apply
% 0.32/0.49 thf(fact_125_sup__apply,axiom,
% 0.32/0.49 ( sup_su1211201046_c_b_o
% 0.32/0.49 = ( ^ [F2: sum_su1965225555um_c_b > $o,G2: sum_su1965225555um_c_b > $o,X: sum_su1965225555um_c_b] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_apply
% 0.32/0.49 thf(fact_126_sup__apply,axiom,
% 0.32/0.49 ( sup_sup_a_o
% 0.32/0.49 = ( ^ [F2: a > $o,G2: a > $o,X: a] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_apply
% 0.32/0.49 thf(fact_127_sup_Oidem,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_128_sup_Oidem,axiom,
% 0.32/0.49 ! [A: set_a] :
% 0.32/0.49 ( ( sup_sup_set_a @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_129_sup_Oidem,axiom,
% 0.32/0.49 ! [A: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( sup_su2024788734_b_b_o @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_130_sup_Oidem,axiom,
% 0.32/0.49 ! [A: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( sup_su1211201046_c_b_o @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_131_sup_Oidem,axiom,
% 0.32/0.49 ! [A: a > $o] :
% 0.32/0.49 ( ( sup_sup_a_o @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_132_sup_Oidem,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A @ A )
% 0.32/0.49 = A ) ).
% 0.32/0.49
% 0.32/0.49 % sup.idem
% 0.32/0.49 thf(fact_133_sup__idem,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_134_sup__idem,axiom,
% 0.32/0.49 ! [X2: set_a] :
% 0.32/0.49 ( ( sup_sup_set_a @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_135_sup__idem,axiom,
% 0.32/0.49 ! [X2: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( sup_su2024788734_b_b_o @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_136_sup__idem,axiom,
% 0.32/0.49 ! [X2: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( sup_su1211201046_c_b_o @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_137_sup__idem,axiom,
% 0.32/0.49 ! [X2: a > $o] :
% 0.32/0.49 ( ( sup_sup_a_o @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_138_sup__idem,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X2 @ X2 )
% 0.32/0.49 = X2 ) ).
% 0.32/0.49
% 0.32/0.49 % sup_idem
% 0.32/0.49 thf(fact_139_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B2 ) )
% 0.32/0.49 = ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_140_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: set_a,B2: set_a] :
% 0.32/0.49 ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B2 ) )
% 0.32/0.49 = ( sup_sup_set_a @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_141_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: sum_sum_b_b > $o,B2: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( sup_su2024788734_b_b_o @ A @ ( sup_su2024788734_b_b_o @ A @ B2 ) )
% 0.32/0.49 = ( sup_su2024788734_b_b_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_142_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: sum_su1965225555um_c_b > $o,B2: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B2 ) )
% 0.32/0.49 = ( sup_su1211201046_c_b_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_143_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: a > $o,B2: a > $o] :
% 0.32/0.49 ( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B2 ) )
% 0.32/0.49 = ( sup_sup_a_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_144_sup_Oleft__idem,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B2 ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_idem
% 0.32/0.49 thf(fact_145_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_146_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: set_a,Y: set_a] :
% 0.32/0.49 ( ( sup_sup_set_a @ X2 @ ( sup_sup_set_a @ X2 @ Y ) )
% 0.32/0.49 = ( sup_sup_set_a @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_147_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: sum_sum_b_b > $o,Y: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( sup_su2024788734_b_b_o @ X2 @ ( sup_su2024788734_b_b_o @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su2024788734_b_b_o @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_148_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: sum_su1965225555um_c_b > $o,Y: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( sup_su1211201046_c_b_o @ X2 @ ( sup_su1211201046_c_b_o @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su1211201046_c_b_o @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_149_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: a > $o,Y: a > $o] :
% 0.32/0.49 ( ( sup_sup_a_o @ X2 @ ( sup_sup_a_o @ X2 @ Y ) )
% 0.32/0.49 = ( sup_sup_a_o @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_150_sup__left__idem,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_idem
% 0.32/0.49 thf(fact_151_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_152_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: set_a,B2: set_a] :
% 0.32/0.49 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_sup_set_a @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_153_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: sum_sum_b_b > $o,B2: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( sup_su2024788734_b_b_o @ ( sup_su2024788734_b_b_o @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_su2024788734_b_b_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_154_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: sum_su1965225555um_c_b > $o,B2: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( sup_su1211201046_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_su1211201046_c_b_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_155_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: a > $o,B2: a > $o] :
% 0.32/0.49 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_sup_a_o @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_156_sup_Oright__idem,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ B2 )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.right_idem
% 0.32/0.49 thf(fact_157_UnCI,axiom,
% 0.32/0.49 ! [C2: a,B: set_a,A3: set_a] :
% 0.32/0.49 ( ( ~ ( member_a @ C2 @ B )
% 0.32/0.49 => ( member_a @ C2 @ A3 ) )
% 0.32/0.49 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnCI
% 0.32/0.49 thf(fact_158_UnCI,axiom,
% 0.32/0.49 ! [C2: sum_sum_b_b,B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ~ ( member_Sum_sum_b_b @ C2 @ B )
% 0.32/0.49 => ( member_Sum_sum_b_b @ C2 @ A3 ) )
% 0.32/0.49 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnCI
% 0.32/0.49 thf(fact_159_Un__iff,axiom,
% 0.32/0.49 ! [C2: a,A3: set_a,B: set_a] :
% 0.32/0.49 ( ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) )
% 0.32/0.49 = ( ( member_a @ C2 @ A3 )
% 0.32/0.49 | ( member_a @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_iff
% 0.32/0.49 thf(fact_160_Un__iff,axiom,
% 0.32/0.49 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 = ( ( member_Sum_sum_b_b @ C2 @ A3 )
% 0.32/0.49 | ( member_Sum_sum_b_b @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_iff
% 0.32/0.49 thf(fact_161_sup__set__def,axiom,
% 0.32/0.49 ( sup_sup_set_a
% 0.32/0.49 = ( ^ [A4: set_a,B3: set_a] :
% 0.32/0.49 ( collect_a
% 0.32/0.49 @ ( sup_sup_a_o
% 0.32/0.49 @ ^ [X: a] : ( member_a @ X @ A4 )
% 0.32/0.49 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_set_def
% 0.32/0.49 thf(fact_162_sup__set__def,axiom,
% 0.32/0.49 ( sup_su296826759um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ( collec1166375742um_c_b
% 0.32/0.49 @ ( sup_su1211201046_c_b_o
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A4 )
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_set_def
% 0.32/0.49 thf(fact_163_sup__set__def,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 0.32/0.49 ( collect_Sum_sum_b_b
% 0.32/0.49 @ ( sup_su2024788734_b_b_o
% 0.32/0.49 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ A4 )
% 0.32/0.49 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_set_def
% 0.32/0.49 thf(fact_164_less__eq__set__def,axiom,
% 0.32/0.49 ( ord_less_eq_set_a
% 0.32/0.49 = ( ^ [A4: set_a,B3: set_a] :
% 0.32/0.49 ( ord_less_eq_a_o
% 0.32/0.49 @ ^ [X: a] : ( member_a @ X @ A4 )
% 0.32/0.49 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % less_eq_set_def
% 0.32/0.49 thf(fact_165_less__eq__set__def,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ord_le1534094666_c_b_o
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A4 )
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % less_eq_set_def
% 0.32/0.49 thf(fact_166_in__mono,axiom,
% 0.32/0.49 ! [A3: set_a,B: set_a,X2: a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ A3 @ B )
% 0.32/0.49 => ( ( member_a @ X2 @ A3 )
% 0.32/0.49 => ( member_a @ X2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % in_mono
% 0.32/0.49 thf(fact_167_in__mono,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,X2: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( member973578748um_c_b @ X2 @ A3 )
% 0.32/0.49 => ( member973578748um_c_b @ X2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % in_mono
% 0.32/0.49 thf(fact_168_subsetD,axiom,
% 0.32/0.49 ! [A3: set_a,B: set_a,C2: a] :
% 0.32/0.49 ( ( ord_less_eq_set_a @ A3 @ B )
% 0.32/0.49 => ( ( member_a @ C2 @ A3 )
% 0.32/0.49 => ( member_a @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetD
% 0.32/0.49 thf(fact_169_subsetD,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C2: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( member973578748um_c_b @ C2 @ A3 )
% 0.32/0.49 => ( member973578748um_c_b @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subsetD
% 0.32/0.49 thf(fact_170_equalityE,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A3 = B )
% 0.32/0.49 => ~ ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ~ ( ord_le1404954451um_c_b @ B @ A3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % equalityE
% 0.32/0.49 thf(fact_171_subset__eq,axiom,
% 0.32/0.49 ( ord_less_eq_set_a
% 0.32/0.49 = ( ^ [A4: set_a,B3: set_a] :
% 0.32/0.49 ! [X: a] :
% 0.32/0.49 ( ( member_a @ X @ A4 )
% 0.32/0.49 => ( member_a @ X @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_eq
% 0.32/0.49 thf(fact_172_subset__eq,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ! [X: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( member973578748um_c_b @ X @ A4 )
% 0.32/0.49 => ( member973578748um_c_b @ X @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_eq
% 0.32/0.49 thf(fact_173_equalityD1,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A3 = B )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % equalityD1
% 0.32/0.49 thf(fact_174_equalityD2,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A3 = B )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ B @ A3 ) ) ).
% 0.32/0.49
% 0.32/0.49 % equalityD2
% 0.32/0.49 thf(fact_175_subset__iff,axiom,
% 0.32/0.49 ( ord_less_eq_set_a
% 0.32/0.49 = ( ^ [A4: set_a,B3: set_a] :
% 0.32/0.49 ! [T: a] :
% 0.32/0.49 ( ( member_a @ T @ A4 )
% 0.32/0.49 => ( member_a @ T @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_iff
% 0.32/0.49 thf(fact_176_subset__iff,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ! [T: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( member973578748um_c_b @ T @ A4 )
% 0.32/0.49 => ( member973578748um_c_b @ T @ B3 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_iff
% 0.32/0.49 thf(fact_177_subset__refl,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ A3 ) ).
% 0.32/0.49
% 0.32/0.49 % subset_refl
% 0.32/0.49 thf(fact_178_Collect__mono,axiom,
% 0.32/0.49 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ! [X3: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( P @ X3 )
% 0.32/0.49 => ( Q @ X3 ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mono
% 0.32/0.49 thf(fact_179_subset__trans,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B @ C )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A3 @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_trans
% 0.32/0.49 thf(fact_180_set__eq__subset,axiom,
% 0.32/0.49 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A4 @ B3 )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ B3 @ A4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % set_eq_subset
% 0.32/0.49 thf(fact_181_Collect__mono__iff,axiom,
% 0.32/0.49 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) )
% 0.32/0.49 = ( ! [X: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( P @ X )
% 0.32/0.49 => ( Q @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_mono_iff
% 0.32/0.49 thf(fact_182_inf__sup__aci_I8_J,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_aci(8)
% 0.32/0.49 thf(fact_183_inf__sup__aci_I7_J,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_aci(7)
% 0.32/0.49 thf(fact_184_inf__sup__aci_I6_J,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_aci(6)
% 0.32/0.49 thf(fact_185_inf__sup__aci_I5_J,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ Y2 @ X ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_aci(5)
% 0.32/0.49 thf(fact_186_boolean__algebra__cancel_Osup1,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,K: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( A3
% 0.32/0.49 = ( sup_su2137030215um_b_b @ K @ A ) )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A3 @ B2 )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ K @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % boolean_algebra_cancel.sup1
% 0.32/0.49 thf(fact_187_boolean__algebra__cancel_Osup2,axiom,
% 0.32/0.49 ! [B: set_Sum_sum_b_b,K: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( B
% 0.32/0.49 = ( sup_su2137030215um_b_b @ K @ B2 ) )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A @ B )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ K @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % boolean_algebra_cancel.sup2
% 0.32/0.49 thf(fact_188_sup_Oassoc,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ C2 )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B2 @ C2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.assoc
% 0.32/0.49 thf(fact_189_sup__assoc,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_assoc
% 0.32/0.49 thf(fact_190_sup_Ocommute,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [A5: set_Sum_sum_b_b,B4: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B4 @ A5 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.commute
% 0.32/0.49 thf(fact_191_sup__commute,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ Y2 @ X ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_commute
% 0.32/0.49 thf(fact_192_sup_Oleft__commute,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ B2 @ ( sup_su2137030215um_b_b @ A @ C2 ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B2 @ C2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.left_commute
% 0.32/0.49 thf(fact_193_sup__left__commute,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_left_commute
% 0.32/0.49 thf(fact_194_UnE,axiom,
% 0.32/0.49 ! [C2: a,A3: set_a,B: set_a] :
% 0.32/0.49 ( ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) )
% 0.32/0.49 => ( ~ ( member_a @ C2 @ A3 )
% 0.32/0.49 => ( member_a @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnE
% 0.32/0.49 thf(fact_195_UnE,axiom,
% 0.32/0.49 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 => ( ~ ( member_Sum_sum_b_b @ C2 @ A3 )
% 0.32/0.49 => ( member_Sum_sum_b_b @ C2 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnE
% 0.32/0.49 thf(fact_196_UnI1,axiom,
% 0.32/0.49 ! [C2: a,A3: set_a,B: set_a] :
% 0.32/0.49 ( ( member_a @ C2 @ A3 )
% 0.32/0.49 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnI1
% 0.32/0.49 thf(fact_197_UnI1,axiom,
% 0.32/0.49 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ C2 @ A3 )
% 0.32/0.49 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnI1
% 0.32/0.49 thf(fact_198_UnI2,axiom,
% 0.32/0.49 ! [C2: a,B: set_a,A3: set_a] :
% 0.32/0.49 ( ( member_a @ C2 @ B )
% 0.32/0.49 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnI2
% 0.32/0.49 thf(fact_199_UnI2,axiom,
% 0.32/0.49 ! [C2: sum_sum_b_b,B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ C2 @ B )
% 0.32/0.49 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % UnI2
% 0.32/0.49 thf(fact_200_bex__Un,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,P: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( ? [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 & ( P @ X ) ) )
% 0.32/0.49 = ( ? [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ A3 )
% 0.32/0.49 & ( P @ X ) )
% 0.32/0.49 | ? [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ B )
% 0.32/0.49 & ( P @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % bex_Un
% 0.32/0.49 thf(fact_201_ball__Un,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,P: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( ! [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 => ( P @ X ) ) )
% 0.32/0.49 = ( ! [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ A3 )
% 0.32/0.49 => ( P @ X ) )
% 0.32/0.49 & ! [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ B )
% 0.32/0.49 => ( P @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % ball_Un
% 0.32/0.49 thf(fact_202_Un__assoc,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ B @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_assoc
% 0.32/0.49 thf(fact_203_Un__absorb,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A3 @ A3 )
% 0.32/0.49 = A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Un_absorb
% 0.32/0.49 thf(fact_204_Un__commute,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B3 @ A4 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_commute
% 0.32/0.49 thf(fact_205_Un__left__absorb,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_left_absorb
% 0.32/0.49 thf(fact_206_Un__left__commute,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ B @ C ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A3 @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_left_commute
% 0.32/0.49 thf(fact_207_Collect__subset,axiom,
% 0.32/0.49 ! [A3: set_a,P: a > $o] :
% 0.32/0.49 ( ord_less_eq_set_a
% 0.32/0.49 @ ( collect_a
% 0.32/0.49 @ ^ [X: a] :
% 0.32/0.49 ( ( member_a @ X @ A3 )
% 0.32/0.49 & ( P @ X ) ) )
% 0.32/0.49 @ A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_subset
% 0.32/0.49 thf(fact_208_Collect__subset,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,P: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 @ ( collec1166375742um_c_b
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( member973578748um_c_b @ X @ A3 )
% 0.32/0.49 & ( P @ X ) ) )
% 0.32/0.49 @ A3 ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_subset
% 0.32/0.49 thf(fact_209_Un__def,axiom,
% 0.32/0.49 ( sup_sup_set_a
% 0.32/0.49 = ( ^ [A4: set_a,B3: set_a] :
% 0.32/0.49 ( collect_a
% 0.32/0.49 @ ^ [X: a] :
% 0.32/0.49 ( ( member_a @ X @ A4 )
% 0.32/0.49 | ( member_a @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_def
% 0.32/0.49 thf(fact_210_Un__def,axiom,
% 0.32/0.49 ( sup_su296826759um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ( collec1166375742um_c_b
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( member973578748um_c_b @ X @ A4 )
% 0.32/0.49 | ( member973578748um_c_b @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_def
% 0.32/0.49 thf(fact_211_Un__def,axiom,
% 0.32/0.49 ( sup_su2137030215um_b_b
% 0.32/0.49 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 0.32/0.49 ( collect_Sum_sum_b_b
% 0.32/0.49 @ ^ [X: sum_sum_b_b] :
% 0.32/0.49 ( ( member_Sum_sum_b_b @ X @ A4 )
% 0.32/0.49 | ( member_Sum_sum_b_b @ X @ B3 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_def
% 0.32/0.49 thf(fact_212_Collect__disj__eq,axiom,
% 0.32/0.49 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 0.32/0.49 ( ( collec1166375742um_c_b
% 0.32/0.49 @ ^ [X: sum_su1965225555um_c_b] :
% 0.32/0.49 ( ( P @ X )
% 0.32/0.49 | ( Q @ X ) ) )
% 0.32/0.49 = ( sup_su296826759um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_disj_eq
% 0.32/0.49 thf(fact_213_Collect__disj__eq,axiom,
% 0.32/0.49 ! [P: sum_sum_b_b > $o,Q: sum_sum_b_b > $o] :
% 0.32/0.49 ( ( collect_Sum_sum_b_b
% 0.32/0.49 @ ^ [X: sum_sum_b_b] :
% 0.32/0.49 ( ( P @ X )
% 0.32/0.49 | ( Q @ X ) ) )
% 0.32/0.49 = ( sup_su2137030215um_b_b @ ( collect_Sum_sum_b_b @ P ) @ ( collect_Sum_sum_b_b @ Q ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Collect_disj_eq
% 0.32/0.49 thf(fact_214_inf__sup__ord_I4_J,axiom,
% 0.32/0.49 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_ord(4)
% 0.32/0.49 thf(fact_215_inf__sup__ord_I4_J,axiom,
% 0.32/0.49 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_ord(4)
% 0.32/0.49 thf(fact_216_inf__sup__ord_I3_J,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_ord(3)
% 0.32/0.49 thf(fact_217_inf__sup__ord_I3_J,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % inf_sup_ord(3)
% 0.32/0.49 thf(fact_218_le__supE,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ X2 )
% 0.32/0.49 => ~ ( ( ord_le412705147um_b_b @ A @ X2 )
% 0.32/0.49 => ~ ( ord_le412705147um_b_b @ B2 @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supE
% 0.32/0.49 thf(fact_219_le__supE,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ X2 )
% 0.32/0.49 => ~ ( ( ord_le1404954451um_c_b @ A @ X2 )
% 0.32/0.49 => ~ ( ord_le1404954451um_c_b @ B2 @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supE
% 0.32/0.49 thf(fact_220_le__supI,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,X2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A @ X2 )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ B2 @ X2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI
% 0.32/0.49 thf(fact_221_le__supI,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,X2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ X2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ X2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI
% 0.32/0.49 thf(fact_222_sup__ge1,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_ge1
% 0.32/0.49 thf(fact_223_sup__ge1,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_ge1
% 0.32/0.49 thf(fact_224_sup__ge2,axiom,
% 0.32/0.49 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_ge2
% 0.32/0.49 thf(fact_225_sup__ge2,axiom,
% 0.32/0.49 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_ge2
% 0.32/0.49 thf(fact_226_le__supI1,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ X2 @ A )
% 0.32/0.49 => ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI1
% 0.32/0.49 thf(fact_227_le__supI1,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X2 @ A )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI1
% 0.32/0.49 thf(fact_228_le__supI2,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ X2 @ B2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI2
% 0.32/0.49 thf(fact_229_le__supI2,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X2 @ B2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_supI2
% 0.32/0.49 thf(fact_230_sup_Omono,axiom,
% 0.32/0.49 ! [C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,D: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ C2 @ A )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ D @ B2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ C2 @ D ) @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.mono
% 0.32/0.49 thf(fact_231_sup_Omono,axiom,
% 0.32/0.49 ! [C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,D: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ C2 @ A )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ D @ B2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ C2 @ D ) @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.mono
% 0.32/0.49 thf(fact_232_sup__mono,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A @ C2 )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ B2 @ D )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ ( sup_su2137030215um_b_b @ C2 @ D ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_mono
% 0.32/0.49 thf(fact_233_sup__mono,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ C2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ D )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ ( sup_su296826759um_c_b @ C2 @ D ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_mono
% 0.32/0.49 thf(fact_234_sup__least,axiom,
% 0.32/0.49 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ Y @ X2 )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ Z @ X2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ Y @ Z ) @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_least
% 0.32/0.49 thf(fact_235_sup__least,axiom,
% 0.32/0.49 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ Z @ X2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ Y @ Z ) @ X2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_least
% 0.32/0.49 thf(fact_236_le__iff__sup,axiom,
% 0.32/0.49 ( ord_le412705147um_b_b
% 0.32/0.49 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ X @ Y2 )
% 0.32/0.49 = Y2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_iff_sup
% 0.32/0.49 thf(fact_237_le__iff__sup,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [X: set_Su111624115um_c_b,Y2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ X @ Y2 )
% 0.32/0.49 = Y2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % le_iff_sup
% 0.32/0.49 thf(fact_238_sup_OorderE,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B2 @ A )
% 0.32/0.49 => ( A
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.orderE
% 0.32/0.49 thf(fact_239_sup_OorderE,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( A
% 0.32/0.49 = ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.orderE
% 0.32/0.49 thf(fact_240_sup_OorderI,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( A
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A @ B2 ) )
% 0.32/0.49 => ( ord_le412705147um_b_b @ B2 @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.orderI
% 0.32/0.49 thf(fact_241_sup_OorderI,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A
% 0.32/0.49 = ( sup_su296826759um_c_b @ A @ B2 ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ B2 @ A ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.orderI
% 0.32/0.49 thf(fact_242_sup__unique,axiom,
% 0.32/0.49 ! [F: set_Sum_sum_b_b > set_Sum_sum_b_b > set_Sum_sum_b_b,X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 0.32/0.49 ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X3 @ ( F @ X3 @ Y3 ) )
% 0.32/0.49 => ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y3 @ ( F @ X3 @ Y3 ) )
% 0.32/0.49 => ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b,Z3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ Y3 @ X3 )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ Z3 @ X3 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( F @ Y3 @ Z3 ) @ X3 ) ) )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 0.32/0.49 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_unique
% 0.32/0.49 thf(fact_243_sup__unique,axiom,
% 0.32/0.49 ! [F: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b,X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 0.32/0.49 ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X3 @ ( F @ X3 @ Y3 ) )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y3 @ ( F @ X3 @ Y3 ) )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b,Z3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ Y3 @ X3 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ Z3 @ X3 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ Y3 @ Z3 ) @ X3 ) ) )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 0.32/0.49 = ( F @ X2 @ Y ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_unique
% 0.32/0.49 thf(fact_244_sup_Oabsorb1,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B2 @ A )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A @ B2 )
% 0.32/0.49 = A ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb1
% 0.32/0.49 thf(fact_245_sup_Oabsorb1,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ A @ B2 )
% 0.32/0.49 = A ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb1
% 0.32/0.49 thf(fact_246_sup_Oabsorb2,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A @ B2 )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A @ B2 )
% 0.32/0.49 = B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb2
% 0.32/0.49 thf(fact_247_sup_Oabsorb2,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ A @ B2 )
% 0.32/0.49 = B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb2
% 0.32/0.49 thf(fact_248_sup__absorb1,axiom,
% 0.32/0.49 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ Y @ X2 )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 0.32/0.49 = X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_absorb1
% 0.32/0.49 thf(fact_249_sup__absorb1,axiom,
% 0.32/0.49 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 0.32/0.49 = X2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_absorb1
% 0.32/0.49 thf(fact_250_sup__absorb2,axiom,
% 0.32/0.49 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ X2 @ Y )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_absorb2
% 0.32/0.49 thf(fact_251_sup__absorb2,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 0.32/0.49 = Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup_absorb2
% 0.32/0.49 thf(fact_252_sup_OboundedE,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A )
% 0.32/0.49 => ~ ( ( ord_le412705147um_b_b @ B2 @ A )
% 0.32/0.49 => ~ ( ord_le412705147um_b_b @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.boundedE
% 0.32/0.49 thf(fact_253_sup_OboundedE,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A )
% 0.32/0.49 => ~ ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ~ ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.boundedE
% 0.32/0.49 thf(fact_254_sup_OboundedI,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B2 @ A )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ C2 @ A )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.boundedI
% 0.32/0.49 thf(fact_255_sup_OboundedI,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ C2 @ A )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.boundedI
% 0.32/0.49 thf(fact_256_sup_Oorder__iff,axiom,
% 0.32/0.49 ( ord_le412705147um_b_b
% 0.32/0.49 = ( ^ [B4: set_Sum_sum_b_b,A5: set_Sum_sum_b_b] :
% 0.32/0.49 ( A5
% 0.32/0.49 = ( sup_su2137030215um_b_b @ A5 @ B4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.order_iff
% 0.32/0.49 thf(fact_257_sup_Oorder__iff,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [B4: set_Su111624115um_c_b,A5: set_Su111624115um_c_b] :
% 0.32/0.49 ( A5
% 0.32/0.49 = ( sup_su296826759um_c_b @ A5 @ B4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.order_iff
% 0.32/0.49 thf(fact_258_sup_Ocobounded1,axiom,
% 0.32/0.49 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.cobounded1
% 0.32/0.49 thf(fact_259_sup_Ocobounded1,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.cobounded1
% 0.32/0.49 thf(fact_260_sup_Ocobounded2,axiom,
% 0.32/0.49 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ B2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.cobounded2
% 0.32/0.49 thf(fact_261_sup_Ocobounded2,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ B2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.cobounded2
% 0.32/0.49 thf(fact_262_sup_Oabsorb__iff1,axiom,
% 0.32/0.49 ( ord_le412705147um_b_b
% 0.32/0.49 = ( ^ [B4: set_Sum_sum_b_b,A5: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A5 @ B4 )
% 0.32/0.49 = A5 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb_iff1
% 0.32/0.49 thf(fact_263_sup_Oabsorb__iff1,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [B4: set_Su111624115um_c_b,A5: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ A5 @ B4 )
% 0.32/0.49 = A5 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb_iff1
% 0.32/0.49 thf(fact_264_sup_Oabsorb__iff2,axiom,
% 0.32/0.49 ( ord_le412705147um_b_b
% 0.32/0.49 = ( ^ [A5: set_Sum_sum_b_b,B4: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A5 @ B4 )
% 0.32/0.49 = B4 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb_iff2
% 0.32/0.49 thf(fact_265_sup_Oabsorb__iff2,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ A5 @ B4 )
% 0.32/0.49 = B4 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.absorb_iff2
% 0.32/0.49 thf(fact_266_sup_OcoboundedI1,axiom,
% 0.32/0.49 ! [C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ C2 @ A )
% 0.32/0.49 => ( ord_le412705147um_b_b @ C2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.coboundedI1
% 0.32/0.49 thf(fact_267_sup_OcoboundedI1,axiom,
% 0.32/0.49 ! [C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ C2 @ A )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ C2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.coboundedI1
% 0.32/0.49 thf(fact_268_sup_OcoboundedI2,axiom,
% 0.32/0.49 ! [C2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ C2 @ B2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ C2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.coboundedI2
% 0.32/0.49 thf(fact_269_sup_OcoboundedI2,axiom,
% 0.32/0.49 ! [C2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ C2 @ B2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ C2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sup.coboundedI2
% 0.32/0.49 thf(fact_270_fst__mono,axiom,
% 0.32/0.49 ! [X2: produc133005365real_b,Y: produc133005365real_b] :
% 0.32/0.49 ( ( ord_le793200597real_b @ X2 @ Y )
% 0.32/0.49 => ( ord_le767445194real_b @ ( produc936751193real_b @ X2 ) @ ( produc936751193real_b @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % fst_mono
% 0.32/0.49 thf(fact_271_Un__mono,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,C: set_Sum_sum_b_b,B: set_Sum_sum_b_b,D2: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A3 @ C )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ B @ D2 )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ ( sup_su2137030215um_b_b @ C @ D2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_mono
% 0.32/0.49 thf(fact_272_Un__mono,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,C: set_Su111624115um_c_b,B: set_Su111624115um_c_b,D2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ C )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B @ D2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ ( sup_su296826759um_c_b @ C @ D2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_mono
% 0.32/0.49 thf(fact_273_Un__least,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,C: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A3 @ C )
% 0.32/0.49 => ( ( ord_le412705147um_b_b @ B @ C )
% 0.32/0.49 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_least
% 0.32/0.49 thf(fact_274_Un__least,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,C: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ C )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B @ C )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ C ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_least
% 0.32/0.49 thf(fact_275_Un__upper1,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ A3 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_upper1
% 0.32/0.49 thf(fact_276_Un__upper1,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ ( sup_su296826759um_c_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_upper1
% 0.32/0.49 thf(fact_277_Un__upper2,axiom,
% 0.32/0.49 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ B @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_upper2
% 0.32/0.49 thf(fact_278_Un__upper2,axiom,
% 0.32/0.49 ! [B: set_Su111624115um_c_b,A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ B @ ( sup_su296826759um_c_b @ A3 @ B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_upper2
% 0.32/0.49 thf(fact_279_Un__absorb1,axiom,
% 0.32/0.49 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A3 @ B )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A3 @ B )
% 0.32/0.49 = B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_absorb1
% 0.32/0.49 thf(fact_280_Un__absorb1,axiom,
% 0.32/0.49 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ A3 @ B )
% 0.32/0.49 = B ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_absorb1
% 0.32/0.49 thf(fact_281_Un__absorb2,axiom,
% 0.32/0.49 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B @ A3 )
% 0.32/0.49 => ( ( sup_su2137030215um_b_b @ A3 @ B )
% 0.32/0.49 = A3 ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_absorb2
% 0.32/0.49 thf(fact_282_Un__absorb2,axiom,
% 0.32/0.49 ! [B: set_Su111624115um_c_b,A3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B @ A3 )
% 0.32/0.49 => ( ( sup_su296826759um_c_b @ A3 @ B )
% 0.32/0.49 = A3 ) ) ).
% 0.32/0.49
% 0.32/0.49 % Un_absorb2
% 0.32/0.49 thf(fact_283_subset__UnE,axiom,
% 0.32/0.49 ! [C: set_Sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ C @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 0.32/0.49 => ~ ! [A6: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ A6 @ A3 )
% 0.32/0.49 => ! [B5: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( ord_le412705147um_b_b @ B5 @ B )
% 0.32/0.49 => ( C
% 0.32/0.49 != ( sup_su2137030215um_b_b @ A6 @ B5 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_UnE
% 0.32/0.49 thf(fact_284_subset__UnE,axiom,
% 0.32/0.49 ! [C: set_Su111624115um_c_b,A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ C @ ( sup_su296826759um_c_b @ A3 @ B ) )
% 0.32/0.49 => ~ ! [A6: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A6 @ A3 )
% 0.32/0.49 => ! [B5: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B5 @ B )
% 0.32/0.49 => ( C
% 0.32/0.49 != ( sup_su296826759um_c_b @ A6 @ B5 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_UnE
% 0.32/0.49 thf(fact_285_subset__Un__eq,axiom,
% 0.32/0.49 ( ord_le412705147um_b_b
% 0.32/0.49 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 0.32/0.49 ( ( sup_su2137030215um_b_b @ A4 @ B3 )
% 0.32/0.49 = B3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_Un_eq
% 0.32/0.49 thf(fact_286_subset__Un__eq,axiom,
% 0.32/0.49 ( ord_le1404954451um_c_b
% 0.32/0.49 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( sup_su296826759um_c_b @ A4 @ B3 )
% 0.32/0.49 = B3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % subset_Un_eq
% 0.32/0.49 thf(fact_287_type__definition__good__interp,axiom,
% 0.32/0.49 type_d1092523951t_unit @ freche1421597129_sc_sz @ freche1784963216_sc_sz @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ).
% 0.32/0.49
% 0.32/0.49 % type_definition_good_interp
% 0.32/0.49 thf(fact_288_order__refl,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ X2 ) ).
% 0.32/0.49
% 0.32/0.49 % order_refl
% 0.32/0.49 thf(fact_289_sterm__continuous_H,axiom,
% 0.32/0.49 ! [I: denota610675952t_unit,Theta: trm_sf_sz,S: set_Fi291318197eal_sz] :
% 0.32/0.49 ( ( denota1579475975_sc_sz @ I )
% 0.32/0.49 => ( ( dfree_sf_sz @ Theta )
% 0.32/0.49 => ( topolo1348430467z_real @ S @ ( denota1179238309_sc_sz @ I @ Theta ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sterm_continuous'
% 0.32/0.49 thf(fact_290_sterm__continuous_H,axiom,
% 0.32/0.49 ! [I: denota723907260t_unit,Theta: trm_a_b,S: set_Fi268318752real_b] :
% 0.32/0.49 ( ( denota1086158987_a_c_b @ I )
% 0.32/0.49 => ( ( dfree_a_b @ Theta )
% 0.32/0.49 => ( topolo238266006b_real @ S @ ( denota722380397_a_c_b @ I @ Theta ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % sterm_continuous'
% 0.32/0.49 thf(fact_291_good__interp_Odomain,axiom,
% 0.32/0.49 ( ( domain413207655_sc_sz @ freche58918398_sc_sz )
% 0.32/0.49 = denota1579475975_sc_sz ) ).
% 0.32/0.49
% 0.32/0.49 % good_interp.domain
% 0.32/0.49 thf(fact_292_strm_Odomain,axiom,
% 0.32/0.49 ( ( domain134596861rm_a_b @ frechet_cr_strm_a_b )
% 0.32/0.49 = dfree_a_b ) ).
% 0.32/0.49
% 0.32/0.49 % strm.domain
% 0.32/0.49 thf(fact_293_strm_Odomain,axiom,
% 0.32/0.49 ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 0.32/0.49 = dfree_sf_sz ) ).
% 0.32/0.49
% 0.32/0.49 % strm.domain
% 0.32/0.49 thf(fact_294_dual__order_Oantisym,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( A = B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dual_order.antisym
% 0.32/0.49 thf(fact_295_dual__order_Oeq__iff,axiom,
% 0.32/0.49 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 0.32/0.49 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B4 @ A5 )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ A5 @ B4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dual_order.eq_iff
% 0.32/0.49 thf(fact_296_dual__order_Otrans,axiom,
% 0.32/0.49 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ C2 @ B2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % dual_order.trans
% 0.32/0.49 thf(fact_297_dual__order_Orefl,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ) ).
% 0.32/0.49
% 0.32/0.49 % dual_order.refl
% 0.32/0.49 thf(fact_298_order__trans,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ Y @ Z )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ X2 @ Z ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order_trans
% 0.32/0.49 thf(fact_299_order__class_Oorder_Oantisym,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ A )
% 0.32/0.49 => ( A = B2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order_class.order.antisym
% 0.32/0.49 thf(fact_300_ord__le__eq__trans,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( B2 = C2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % ord_le_eq_trans
% 0.32/0.49 thf(fact_301_ord__eq__le__trans,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A = B2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % ord_eq_le_trans
% 0.32/0.49 thf(fact_302_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.49 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 0.32/0.49 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A5 @ B4 )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ B4 @ A5 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order_class.order.eq_iff
% 0.32/0.49 thf(fact_303_antisym__conv,axiom,
% 0.32/0.49 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 0.32/0.49 = ( X2 = Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % antisym_conv
% 0.32/0.49 thf(fact_304_order_Otrans,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order.trans
% 0.32/0.49 thf(fact_305_eq__refl,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( X2 = Y )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ X2 @ Y ) ) ).
% 0.32/0.49
% 0.32/0.49 % eq_refl
% 0.32/0.49 thf(fact_306_antisym,axiom,
% 0.32/0.49 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 0.32/0.49 => ( X2 = Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % antisym
% 0.32/0.49 thf(fact_307_eq__iff,axiom,
% 0.32/0.49 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 0.32/0.49 = ( ^ [X: set_Su111624115um_c_b,Y2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X @ Y2 )
% 0.32/0.49 & ( ord_le1404954451um_c_b @ Y2 @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % eq_iff
% 0.32/0.49 thf(fact_308_ord__le__eq__subst,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( ( F @ B2 )
% 0.32/0.49 = C2 )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % ord_le_eq_subst
% 0.32/0.49 thf(fact_309_ord__eq__le__subst,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( A
% 0.32/0.49 = ( F @ B2 ) )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % ord_eq_le_subst
% 0.32/0.49 thf(fact_310_order__subst2,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ ( F @ B2 ) @ C2 )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order_subst2
% 0.32/0.49 thf(fact_311_order__subst1,axiom,
% 0.32/0.49 ! [A: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ A @ ( F @ B2 ) )
% 0.32/0.49 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 0.32/0.49 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 0.32/0.49 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.32/0.49 => ( ord_le1404954451um_c_b @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % order_subst1
% 0.32/0.50 thf(fact_312_sterm__continuous,axiom,
% 0.32/0.50 ! [I: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.32/0.50 ( ( denota1579475975_sc_sz @ I )
% 0.32/0.50 => ( ( dfree_sf_sz @ Theta )
% 0.32/0.50 => ( topolo1348430467z_real @ top_to1873962757eal_sz @ ( denota1179238309_sc_sz @ I @ Theta ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % sterm_continuous
% 0.32/0.50 thf(fact_313_sterm__continuous,axiom,
% 0.32/0.50 ! [I: denota723907260t_unit,Theta: trm_a_b] :
% 0.32/0.50 ( ( denota1086158987_a_c_b @ I )
% 0.32/0.50 => ( ( dfree_a_b @ Theta )
% 0.32/0.50 => ( topolo238266006b_real @ top_to502572752real_b @ ( denota722380397_a_c_b @ I @ Theta ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % sterm_continuous
% 0.32/0.50 thf(fact_314_sup__Un__eq,axiom,
% 0.32/0.50 ! [R: set_a,S: set_a] :
% 0.32/0.50 ( ( sup_sup_a_o
% 0.32/0.50 @ ^ [X: a] : ( member_a @ X @ R )
% 0.32/0.50 @ ^ [X: a] : ( member_a @ X @ S ) )
% 0.32/0.50 = ( ^ [X: a] : ( member_a @ X @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % sup_Un_eq
% 0.32/0.50 thf(fact_315_sup__Un__eq,axiom,
% 0.32/0.50 ! [R: set_Sum_sum_b_b,S: set_Sum_sum_b_b] :
% 0.32/0.50 ( ( sup_su2024788734_b_b_o
% 0.32/0.50 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ R )
% 0.32/0.50 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ S ) )
% 0.32/0.50 = ( ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ R @ S ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % sup_Un_eq
% 0.32/0.50 thf(fact_316_pred__subset__eq,axiom,
% 0.32/0.50 ! [R: set_a,S: set_a] :
% 0.32/0.50 ( ( ord_less_eq_a_o
% 0.32/0.50 @ ^ [X: a] : ( member_a @ X @ R )
% 0.32/0.50 @ ^ [X: a] : ( member_a @ X @ S ) )
% 0.32/0.50 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 0.32/0.50
% 0.32/0.50 % pred_subset_eq
% 0.32/0.50 thf(fact_317_pred__subset__eq,axiom,
% 0.32/0.50 ! [R: set_Su111624115um_c_b,S: set_Su111624115um_c_b] :
% 0.32/0.50 ( ( ord_le1534094666_c_b_o
% 0.32/0.50 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ R )
% 0.32/0.50 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ S ) )
% 0.32/0.50 = ( ord_le1404954451um_c_b @ R @ S ) ) ).
% 0.32/0.50
% 0.32/0.50 % pred_subset_eq
% 0.32/0.50 thf(fact_318_UNIV__I,axiom,
% 0.32/0.50 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_I
% 0.32/0.50 thf(fact_319_UNIV__I,axiom,
% 0.32/0.50 ! [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_I
% 0.32/0.50 thf(fact_320_sup__top__right,axiom,
% 0.32/0.50 ! [X2: set_Sum_sum_b_b] :
% 0.32/0.50 ( ( sup_su2137030215um_b_b @ X2 @ top_to301096907um_b_b )
% 0.32/0.50 = top_to301096907um_b_b ) ).
% 0.32/0.50
% 0.32/0.50 % sup_top_right
% 0.32/0.50 thf(fact_321_sup__top__right,axiom,
% 0.32/0.50 ! [X2: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( sup_su1321388937eal_sz @ X2 @ top_to1873962757eal_sz )
% 0.32/0.50 = top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % sup_top_right
% 0.32/0.50 thf(fact_322_sup__top__left,axiom,
% 0.32/0.50 ! [X2: set_Sum_sum_b_b] :
% 0.32/0.50 ( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ X2 )
% 0.32/0.50 = top_to301096907um_b_b ) ).
% 0.32/0.50
% 0.32/0.50 % sup_top_left
% 0.32/0.50 thf(fact_323_sup__top__left,axiom,
% 0.32/0.50 ! [X2: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( sup_su1321388937eal_sz @ top_to1873962757eal_sz @ X2 )
% 0.32/0.50 = top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % sup_top_left
% 0.32/0.50 thf(fact_324_top_Oextremum__uniqueI,axiom,
% 0.32/0.50 ! [A: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A )
% 0.32/0.50 => ( A = top_to1873962757eal_sz ) ) ).
% 0.32/0.50
% 0.32/0.50 % top.extremum_uniqueI
% 0.32/0.50 thf(fact_325_top_Oextremum__uniqueI,axiom,
% 0.32/0.50 ! [A: set_Su111624115um_c_b] :
% 0.32/0.50 ( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
% 0.32/0.50 => ( A = top_to999478531um_c_b ) ) ).
% 0.32/0.50
% 0.32/0.50 % top.extremum_uniqueI
% 0.32/0.50 thf(fact_326_top_Oextremum__unique,axiom,
% 0.32/0.50 ! [A: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A )
% 0.32/0.50 = ( A = top_to1873962757eal_sz ) ) ).
% 0.32/0.50
% 0.32/0.50 % top.extremum_unique
% 0.32/0.50 thf(fact_327_top_Oextremum__unique,axiom,
% 0.32/0.50 ! [A: set_Su111624115um_c_b] :
% 0.32/0.50 ( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
% 0.32/0.50 = ( A = top_to999478531um_c_b ) ) ).
% 0.32/0.50
% 0.32/0.50 % top.extremum_unique
% 0.32/0.50 thf(fact_328_top__greatest,axiom,
% 0.32/0.50 ! [A: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A @ top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % top_greatest
% 0.32/0.50 thf(fact_329_top__greatest,axiom,
% 0.32/0.50 ! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ) ).
% 0.32/0.50
% 0.32/0.50 % top_greatest
% 0.32/0.50 thf(fact_330_subset__UNIV,axiom,
% 0.32/0.50 ! [A3: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A3 @ top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % subset_UNIV
% 0.32/0.50 thf(fact_331_subset__UNIV,axiom,
% 0.32/0.50 ! [A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ top_to999478531um_c_b ) ).
% 0.32/0.50
% 0.32/0.50 % subset_UNIV
% 0.32/0.50 thf(fact_332_Un__UNIV__left,axiom,
% 0.32/0.50 ! [B: set_Sum_sum_b_b] :
% 0.32/0.50 ( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ B )
% 0.32/0.50 = top_to301096907um_b_b ) ).
% 0.32/0.50
% 0.32/0.50 % Un_UNIV_left
% 0.32/0.50 thf(fact_333_Un__UNIV__left,axiom,
% 0.32/0.50 ! [B: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( sup_su1321388937eal_sz @ top_to1873962757eal_sz @ B )
% 0.32/0.50 = top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % Un_UNIV_left
% 0.32/0.50 thf(fact_334_Un__UNIV__right,axiom,
% 0.32/0.50 ! [A3: set_Sum_sum_b_b] :
% 0.32/0.50 ( ( sup_su2137030215um_b_b @ A3 @ top_to301096907um_b_b )
% 0.32/0.50 = top_to301096907um_b_b ) ).
% 0.32/0.50
% 0.32/0.50 % Un_UNIV_right
% 0.32/0.50 thf(fact_335_Un__UNIV__right,axiom,
% 0.32/0.50 ! [A3: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( sup_su1321388937eal_sz @ A3 @ top_to1873962757eal_sz )
% 0.32/0.50 = top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % Un_UNIV_right
% 0.32/0.50 thf(fact_336_UNIV__witness,axiom,
% 0.32/0.50 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_witness
% 0.32/0.50 thf(fact_337_UNIV__witness,axiom,
% 0.32/0.50 ? [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_witness
% 0.32/0.50 thf(fact_338_UNIV__eq__I,axiom,
% 0.32/0.50 ! [A3: set_a] :
% 0.32/0.50 ( ! [X3: a] : ( member_a @ X3 @ A3 )
% 0.32/0.50 => ( top_top_set_a = A3 ) ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_eq_I
% 0.32/0.50 thf(fact_339_UNIV__eq__I,axiom,
% 0.32/0.50 ! [A3: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ! [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ A3 )
% 0.32/0.50 => ( top_to1873962757eal_sz = A3 ) ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_eq_I
% 0.32/0.50 thf(fact_340_UNIV__def,axiom,
% 0.32/0.50 ( top_to999478531um_c_b
% 0.32/0.50 = ( collec1166375742um_c_b
% 0.32/0.50 @ ^ [X: sum_su1965225555um_c_b] : $true ) ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_def
% 0.32/0.50 thf(fact_341_UNIV__def,axiom,
% 0.32/0.50 ( top_to1873962757eal_sz
% 0.32/0.50 = ( collec1002602816eal_sz
% 0.32/0.50 @ ^ [X: finite824932053eal_sz] : $true ) ) ).
% 0.32/0.50
% 0.32/0.50 % UNIV_def
% 0.32/0.50 thf(fact_342_continuous__on__cases__le,axiom,
% 0.32/0.50 ! [S2: set_Fi291318197eal_sz,H: finite824932053eal_sz > real,A: real,F: finite824932053eal_sz > bounde472938360z_real,G: finite824932053eal_sz > bounde472938360z_real] :
% 0.32/0.50 ( ( topolo885751137z_real
% 0.32/0.50 @ ( collec1002602816eal_sz
% 0.32/0.50 @ ^ [T: finite824932053eal_sz] :
% 0.32/0.50 ( ( member1693951742eal_sz @ T @ S2 )
% 0.32/0.50 & ( ord_less_eq_real @ ( H @ T ) @ A ) ) )
% 0.32/0.50 @ F )
% 0.32/0.50 => ( ( topolo885751137z_real
% 0.32/0.50 @ ( collec1002602816eal_sz
% 0.32/0.50 @ ^ [T: finite824932053eal_sz] :
% 0.32/0.50 ( ( member1693951742eal_sz @ T @ S2 )
% 0.32/0.50 & ( ord_less_eq_real @ A @ ( H @ T ) ) ) )
% 0.32/0.50 @ G )
% 0.32/0.50 => ( ( topolo1348430467z_real @ S2 @ H )
% 0.32/0.50 => ( ! [T3: finite824932053eal_sz] :
% 0.32/0.50 ( ( member1693951742eal_sz @ T3 @ S2 )
% 0.32/0.50 => ( ( ( H @ T3 )
% 0.32/0.50 = A )
% 0.32/0.50 => ( ( F @ T3 )
% 0.32/0.50 = ( G @ T3 ) ) ) )
% 0.32/0.50 => ( topolo885751137z_real @ S2
% 0.32/0.50 @ ^ [T: finite824932053eal_sz] : ( if_Bou1785791806z_real @ ( ord_less_eq_real @ ( H @ T ) @ A ) @ ( F @ T ) @ ( G @ T ) ) ) ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % continuous_on_cases_le
% 0.32/0.50 thf(fact_343_agree__UNIV__eq,axiom,
% 0.32/0.50 ! [Nu: produc133005365real_b,Omega: produc133005365real_b] :
% 0.32/0.50 ( ( denota1997846517gree_b @ Nu @ Omega @ top_to301096907um_b_b )
% 0.32/0.50 => ( Nu = Omega ) ) ).
% 0.32/0.50
% 0.32/0.50 % agree_UNIV_eq
% 0.32/0.50 thf(fact_344_top__empty__eq,axiom,
% 0.32/0.50 ( top_top_a_o
% 0.32/0.50 = ( ^ [X: a] : ( member_a @ X @ top_top_set_a ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % top_empty_eq
% 0.32/0.50 thf(fact_345_top__empty__eq,axiom,
% 0.32/0.50 ( top_to646513176l_sz_o
% 0.32/0.50 = ( ^ [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ top_to1873962757eal_sz ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % top_empty_eq
% 0.32/0.50 thf(fact_346_top__set__def,axiom,
% 0.32/0.50 ( top_to999478531um_c_b
% 0.32/0.50 = ( collec1166375742um_c_b @ top_to1849113498_c_b_o ) ) ).
% 0.32/0.50
% 0.32/0.50 % top_set_def
% 0.32/0.50 thf(fact_347_top__set__def,axiom,
% 0.32/0.50 ( top_to1873962757eal_sz
% 0.32/0.50 = ( collec1002602816eal_sz @ top_to646513176l_sz_o ) ) ).
% 0.32/0.50
% 0.32/0.50 % top_set_def
% 0.32/0.50 thf(fact_348_frechet__continuous,axiom,
% 0.32/0.50 ! [I: denota610675952t_unit,Theta: trm_sf_sz] :
% 0.32/0.50 ( ( denota1579475975_sc_sz @ I )
% 0.32/0.50 => ( ( dfree_sf_sz @ Theta )
% 0.32/0.50 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % frechet_continuous
% 0.32/0.50 thf(fact_349_iso__tuple__UNIV__I,axiom,
% 0.32/0.50 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 0.32/0.50
% 0.32/0.50 % iso_tuple_UNIV_I
% 0.32/0.50 thf(fact_350_iso__tuple__UNIV__I,axiom,
% 0.32/0.50 ! [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ top_to1873962757eal_sz ) ).
% 0.32/0.50
% 0.32/0.50 % iso_tuple_UNIV_I
% 0.32/0.50 thf(fact_351_continuous__on__cong,axiom,
% 0.32/0.50 ! [S2: set_Fi291318197eal_sz,T4: set_Fi291318197eal_sz,F: finite824932053eal_sz > bounde472938360z_real,G: finite824932053eal_sz > bounde472938360z_real] :
% 0.32/0.50 ( ( S2 = T4 )
% 0.32/0.50 => ( ! [X3: finite824932053eal_sz] :
% 0.32/0.50 ( ( member1693951742eal_sz @ X3 @ T4 )
% 0.32/0.50 => ( ( F @ X3 )
% 0.32/0.50 = ( G @ X3 ) ) )
% 0.32/0.50 => ( ( topolo885751137z_real @ S2 @ F )
% 0.32/0.50 = ( topolo885751137z_real @ T4 @ G ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % continuous_on_cong
% 0.32/0.50 thf(fact_352_continuous__on__const,axiom,
% 0.32/0.50 ! [S2: set_Fi291318197eal_sz,C2: bounde472938360z_real] :
% 0.32/0.50 ( topolo885751137z_real @ S2
% 0.32/0.50 @ ^ [X: finite824932053eal_sz] : C2 ) ).
% 0.32/0.50
% 0.32/0.50 % continuous_on_const
% 0.32/0.50 thf(fact_353_continuous__on__subset,axiom,
% 0.32/0.50 ! [S2: set_Fi291318197eal_sz,F: finite824932053eal_sz > bounde472938360z_real,T4: set_Fi291318197eal_sz] :
% 0.32/0.50 ( ( topolo885751137z_real @ S2 @ F )
% 0.32/0.50 => ( ( ord_le41263445eal_sz @ T4 @ S2 )
% 0.32/0.50 => ( topolo885751137z_real @ T4 @ F ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % continuous_on_subset
% 0.32/0.50 thf(fact_354_conj__subset__def,axiom,
% 0.32/0.50 ! [A3: set_Su111624115um_c_b,P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 0.32/0.50 ( ( ord_le1404954451um_c_b @ A3
% 0.32/0.50 @ ( collec1166375742um_c_b
% 0.32/0.50 @ ^ [X: sum_su1965225555um_c_b] :
% 0.32/0.50 ( ( P @ X )
% 0.32/0.50 & ( Q @ X ) ) ) )
% 0.32/0.50 = ( ( ord_le1404954451um_c_b @ A3 @ ( collec1166375742um_c_b @ P ) )
% 0.32/0.50 & ( ord_le1404954451um_c_b @ A3 @ ( collec1166375742um_c_b @ Q ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 % conj_subset_def
% 0.32/0.50
% 0.32/0.50 % Helper facts (3)
% 0.32/0.50 thf(help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.32/0.50 ! [P: $o] :
% 0.32/0.50 ( ( P = $true )
% 0.32/0.50 | ( P = $false ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.32/0.50 ! [X2: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.32/0.50 ( ( if_Bou1785791806z_real @ $false @ X2 @ Y )
% 0.32/0.50 = Y ) ).
% 0.32/0.50
% 0.32/0.50 thf(help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 0.32/0.50 ! [X2: bounde472938360z_real,Y: bounde472938360z_real] :
% 0.32/0.50 ( ( if_Bou1785791806z_real @ $true @ X2 @ Y )
% 0.32/0.50 = X2 ) ).
% 0.32/0.50
% 0.32/0.50 % Conjectures (1)
% 0.32/0.50 thf(conj_0,conjecture,
% 0.32/0.50 ( denota896875430_a_c_b @ i @ j
% 0.32/0.50 @ ( collec1166375742um_c_b
% 0.32/0.50 @ ^ [Uu: sum_su1965225555um_c_b] :
% 0.32/0.50 ? [X: a] :
% 0.32/0.50 ( ( Uu
% 0.32/0.50 = ( sum_In811702836um_c_b @ X ) )
% 0.32/0.50 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 ------------------------
% 2.42/1.48 ---- Embedded in THF ---
% 2.42/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.42/1.48 %%% Generated on Tue Feb 24 08:24:26 EST 2026
% 2.42/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.42/1.48 %%% Logic specification used:
% 2.42/1.48 %%% thf(spec, logic, $$dhol).
% 2.42/1.48
% 2.42/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2DTF20266.p
% See solution above
% 2.42/1.48 ------------------------
% 2.71/1.53 ---- Cleaned THF ---
% 2.71/1.53 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 2.71/1.53 produc1149990247eal_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_J,type,
% 2.71/1.53 produc133005365real_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 2.71/1.53 bounde472938360z_real: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 2.71/1.53 set_De208295462t_unit: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J_J,type,
% 2.71/1.53 set_De153000604t_unit: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.71/1.53 denota610675952t_unit: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J,type,
% 2.71/1.53 denota723907260t_unit: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J_J,type,
% 2.71/1.53 set_Su111624115um_c_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 2.71/1.53 set_Fi291318197eal_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_J,type,
% 2.71/1.53 set_Fi268318752real_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Frechet____Correctness__Oids__Ogood____interp_Itf__sf_Mtf__sc_Mtf__sz_J,type,
% 2.71/1.53 freche2095075217_sc_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Frechet____Correctness__Oids__Ogood____interp_Itf__a_Mtf__c_Mtf__b_J,type,
% 2.71/1.53 freche1734198479_a_c_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J,type,
% 2.71/1.53 sum_su1965225555um_c_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 2.71/1.53 finite824932053eal_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J,type,
% 2.71/1.53 finite1390225514real_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 2.71/1.53 frechet_strm_sf_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__sz_Mtf__sz_J_J,type,
% 2.71/1.53 set_Sum_sum_sz_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__b_J,type,
% 2.71/1.53 frechet_strm_a_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__b_Mtf__b_J_J,type,
% 2.71/1.53 set_Sum_sum_b_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_J,type,
% 2.71/1.53 set_trm_sf_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__a_Mtf__b_J_J,type,
% 2.71/1.53 set_trm_a_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Sum____Type__Osum_Itf__b_Mtf__b_J,type,
% 2.71/1.53 sum_sum_b_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.71/1.53 trm_sf_sz: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 2.71/1.53 trm_a_b: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_Itf__sf_J,type,
% 2.71/1.53 set_sf: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.71/1.53 set_a: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Real__Oreal,type,
% 2.71/1.53 real: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_tf__a,type,
% 2.71/1.53 a: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Denotational__Semantics_OIagree_001tf__a_001tf__c_001tf__b,type,
% 2.71/1.53 denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Denotational__Semantics_OVagree_001tf__b,type,
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% 2.71/1.53
% 2.71/1.53 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__b_J_001t__Real__Oreal,type,
% 2.71/1.53 topolo238266006b_real: set_Fi268318752real_b > ( finite1390225514real_b > real ) > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J,type,
% 2.71/1.53 topolo885751137z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > bounde472938360z_real ) > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Real__Oreal,type,
% 2.71/1.53 topolo1348430467z_real: set_Fi291318197eal_sz > ( finite824932053eal_sz > real ) > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ogood____interp_Itf__sf_Mtf__sc_Mtf__sz_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.71/1.53 type_d1092523951t_unit: ( freche2095075217_sc_sz > denota610675952t_unit ) > ( denota610675952t_unit > freche2095075217_sc_sz ) > set_De208295462t_unit > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__b_J_001t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 2.71/1.53 type_d2045870413rm_a_b: ( frechet_strm_a_b > trm_a_b ) > ( trm_a_b > frechet_strm_a_b ) > set_trm_a_b > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Typedef_Otype__definition_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.71/1.53 type_d46389773_sf_sz: ( frechet_strm_sf_sz > trm_sf_sz ) > ( trm_sf_sz > frechet_strm_sf_sz ) > set_trm_sf_sz > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__c_Mtf__b_Mt__Product____Type__Ounit_J,type,
% 2.71/1.53 member122424677t_unit: denota723907260t_unit > set_De153000604t_unit > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.71/1.53 member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 2.71/1.53 member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__c_Mtf__b_J_J,type,
% 2.71/1.53 member973578748um_c_b: sum_su1965225555um_c_b > set_Su111624115um_c_b > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Sum____Type__Osum_Itf__b_Mtf__b_J,type,
% 2.71/1.53 member_Sum_sum_b_b: sum_sum_b_b > set_Sum_sum_b_b > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__b_J,type,
% 2.71/1.53 member_trm_a_b: trm_a_b > set_trm_a_b > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.71/1.53 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001tf__a,type,
% 2.71/1.53 member_a: a > set_a > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_I,type,
% 2.71/1.53 i: denota723907260t_unit ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_J,type,
% 2.71/1.53 j: denota723907260t_unit ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v__092_060nu_062,type,
% 2.71/1.53 nu: produc133005365real_b ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v__092_060nu_062_H,type,
% 2.71/1.53 nu2: produc133005365real_b ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v__092_060theta_062_092_060_094sub_0621____,type,
% 2.71/1.53 theta_1: trm_a_b ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v__092_060theta_062_092_060_094sub_0622____,type,
% 2.71/1.53 theta_2: trm_a_b ).
% 2.71/1.53
% 2.71/1.53 thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
% 2.71/1.53 ! [I: denota723907260t_unit,J: denota723907260t_unit] :
% 2.71/1.53 ( ( denota896875430_a_c_b @ I @ J
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
% 2.71/1.53 => ( denota896875430_a_c_b @ I @ J
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062,axiom,
% 2.71/1.53 ! [I: denota723907260t_unit,J: denota723907260t_unit] :
% 2.71/1.53 ( ( denota896875430_a_c_b @ I @ J
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
% 2.71/1.53 => ( denota896875430_a_c_b @ I @ J
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_2_IA,axiom,
% 2.71/1.53 ( denota896875430_a_c_b @ i @ j
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) )
% 2.71/1.53 | ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
% 2.71/1.53 ( denota896875430_a_c_b @ i @ j
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_4_dfree__Times_Ohyps_I1_J,axiom,
% 2.71/1.53 dfree_a_b @ theta_1 ).
% 2.71/1.53
% 2.71/1.53 thf(fact_5_sum_Oinject_I1_J,axiom,
% 2.71/1.53 ! [X1: a,Y1: a] :
% 2.71/1.53 ( ( ( sum_In811702836um_c_b @ X1 )
% 2.71/1.53 = ( sum_In811702836um_c_b @ Y1 ) )
% 2.71/1.53 = ( X1 = Y1 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_6_old_Osum_Oinject_I1_J,axiom,
% 2.71/1.53 ! [A: a,A2: a] :
% 2.71/1.53 ( ( ( sum_In811702836um_c_b @ A )
% 2.71/1.53 = ( sum_In811702836um_c_b @ A2 ) )
% 2.71/1.53 = ( A = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_7_Isubs_I2_J,axiom,
% 2.71/1.53 ( ord_le1404954451um_c_b
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) )
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_8_Isubs_I1_J,axiom,
% 2.71/1.53 ( ord_le1404954451um_c_b
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) )
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_9_Iagree__comm,axiom,
% 2.71/1.53 ! [A3: denota723907260t_unit,B: denota723907260t_unit,V: set_Su111624115um_c_b] :
% 2.71/1.53 ( ( denota896875430_a_c_b @ A3 @ B @ V )
% 2.71/1.53 => ( denota896875430_a_c_b @ B @ A3 @ V ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_10_Iagree__refl,axiom,
% 2.71/1.53 ! [I: denota723907260t_unit,A3: set_Su111624115um_c_b] : ( denota896875430_a_c_b @ I @ I @ A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_11_Inl__inject,axiom,
% 2.71/1.53 ! [X2: a,Y: a] :
% 2.71/1.53 ( ( ( sum_In811702836um_c_b @ X2 )
% 2.71/1.53 = ( sum_In811702836um_c_b @ Y ) )
% 2.71/1.53 => ( X2 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_12_IH1,axiom,
% 2.71/1.53 ( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) )
% 2.71/1.53 => ( ( denota896875430_a_c_b @ i @ j
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) )
% 2.71/1.53 => ( ( denota722380397_a_c_b @ i @ theta_1 @ ( produc936751193real_b @ nu ) )
% 2.71/1.53 = ( denota722380397_a_c_b @ j @ theta_1 @ ( produc936751193real_b @ nu2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_13_IH2,axiom,
% 2.71/1.53 ( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) )
% 2.71/1.53 => ( ( denota896875430_a_c_b @ i @ j
% 2.71/1.53 @ ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.53 ? [X: a] :
% 2.71/1.53 ( ( Uu
% 2.71/1.53 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.53 & ( member_a @ X @ ( static_SIGT_a_b @ theta_2 ) ) ) ) )
% 2.71/1.53 => ( ( denota722380397_a_c_b @ i @ theta_2 @ ( produc936751193real_b @ nu ) )
% 2.71/1.53 = ( denota722380397_a_c_b @ j @ theta_2 @ ( produc936751193real_b @ nu2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_14_Iagree__Func,axiom,
% 2.71/1.53 ! [I: denota723907260t_unit,J: denota723907260t_unit,V: set_Su111624115um_c_b,F: a] :
% 2.71/1.53 ( ( denota896875430_a_c_b @ I @ J @ V )
% 2.71/1.53 => ( ( member973578748um_c_b @ ( sum_In811702836um_c_b @ F ) @ V )
% 2.71/1.53 => ( ( denota102976244t_unit @ I @ F )
% 2.71/1.53 = ( denota102976244t_unit @ J @ F ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_15_raw__interp__inject,axiom,
% 2.71/1.53 ! [X2: freche2095075217_sc_sz,Y: freche2095075217_sc_sz] :
% 2.71/1.53 ( ( ( freche1421597129_sc_sz @ X2 )
% 2.71/1.53 = ( freche1421597129_sc_sz @ Y ) )
% 2.71/1.53 = ( X2 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_16_dfree__Times_Ohyps_I2_J,axiom,
% 2.71/1.53 dfree_a_b @ theta_2 ).
% 2.71/1.53
% 2.71/1.53 thf(fact_17_coincidence__sterm,axiom,
% 2.71/1.53 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Theta: trm_sf_sz,I: denota610675952t_unit] :
% 2.71/1.53 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVT_sf_sz @ Theta ) )
% 2.71/1.53 => ( ( denota1179238309_sc_sz @ I @ Theta @ ( produc1111759555eal_sz @ Nu ) )
% 2.71/1.53 = ( denota1179238309_sc_sz @ I @ Theta @ ( produc1111759555eal_sz @ Nu2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_18_coincidence__sterm,axiom,
% 2.71/1.53 ! [Nu: produc133005365real_b,Nu2: produc133005365real_b,Theta: trm_a_b,I: denota723907260t_unit] :
% 2.71/1.53 ( ( denota1997846517gree_b @ Nu @ Nu2 @ ( static_FVT_a_b @ Theta ) )
% 2.71/1.53 => ( ( denota722380397_a_c_b @ I @ Theta @ ( produc936751193real_b @ Nu ) )
% 2.71/1.53 = ( denota722380397_a_c_b @ I @ Theta @ ( produc936751193real_b @ Nu2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_19_dfree__Times_Oprems_I1_J,axiom,
% 2.71/1.53 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_20_VAs_I2_J,axiom,
% 2.71/1.53 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_21_VAs_I1_J,axiom,
% 2.71/1.53 denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_22_VA,axiom,
% 2.71/1.53 denota1997846517gree_b @ nu @ nu2 @ ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ theta_1 ) @ ( static_FVT_a_b @ theta_2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_23_agree__sub,axiom,
% 2.71/1.53 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,Nu: produc133005365real_b,Omega: produc133005365real_b] :
% 2.71/1.53 ( ( ord_le412705147um_b_b @ A3 @ B )
% 2.71/1.53 => ( ( denota1997846517gree_b @ Nu @ Omega @ B )
% 2.71/1.53 => ( denota1997846517gree_b @ Nu @ Omega @ A3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_24_agree__comm,axiom,
% 2.71/1.53 ! [A3: produc133005365real_b,B: produc133005365real_b,V: set_Sum_sum_b_b] :
% 2.71/1.53 ( ( denota1997846517gree_b @ A3 @ B @ V )
% 2.71/1.53 => ( denota1997846517gree_b @ B @ A3 @ V ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_25_agree__refl,axiom,
% 2.71/1.53 ! [Nu: produc133005365real_b,A3: set_Sum_sum_b_b] : ( denota1997846517gree_b @ Nu @ Nu @ A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_26_agree__supset,axiom,
% 2.71/1.53 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b,Nu: produc133005365real_b,Nu2: produc133005365real_b] :
% 2.71/1.53 ( ( ord_le412705147um_b_b @ B @ A3 )
% 2.71/1.53 => ( ( denota1997846517gree_b @ Nu @ Nu2 @ A3 )
% 2.71/1.53 => ( denota1997846517gree_b @ Nu @ Nu2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_27_cr__good__interp__def,axiom,
% 2.71/1.53 ( freche58918398_sc_sz
% 2.71/1.53 = ( ^ [X: denota610675952t_unit,Y2: freche2095075217_sc_sz] :
% 2.71/1.53 ( X
% 2.71/1.53 = ( freche1421597129_sc_sz @ Y2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_28_dfree__Times__simps,axiom,
% 2.71/1.53 ! [A: trm_sf_sz,B2: trm_sf_sz] :
% 2.71/1.53 ( ( dfree_sf_sz @ ( times_sf_sz @ A @ B2 ) )
% 2.71/1.53 = ( ( dfree_sf_sz @ A )
% 2.71/1.53 & ( dfree_sf_sz @ B2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_29_dfree__Times__simps,axiom,
% 2.71/1.53 ! [A: trm_a_b,B2: trm_a_b] :
% 2.71/1.53 ( ( dfree_a_b @ ( times_a_b @ A @ B2 ) )
% 2.71/1.53 = ( ( dfree_a_b @ A )
% 2.71/1.53 & ( dfree_a_b @ B2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_30_simple__term__inject,axiom,
% 2.71/1.53 ! [X2: trm_a_b,Y: trm_a_b] :
% 2.71/1.53 ( ( member_trm_a_b @ X2 @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ( ( ( freche665377491rm_a_b @ X2 )
% 2.71/1.53 = ( freche665377491rm_a_b @ Y ) )
% 2.71/1.53 = ( X2 = Y ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_31_simple__term__inject,axiom,
% 2.71/1.53 ! [X2: trm_sf_sz,Y: trm_sf_sz] :
% 2.71/1.53 ( ( member_trm_sf_sz @ X2 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ( ( ( freche1046279700_sf_sz @ X2 )
% 2.71/1.53 = ( freche1046279700_sf_sz @ Y ) )
% 2.71/1.53 = ( X2 = Y ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_32_simple__term__induct,axiom,
% 2.71/1.53 ! [P: frechet_strm_a_b > $o,X2: frechet_strm_a_b] :
% 2.71/1.53 ( ! [Y3: trm_a_b] :
% 2.71/1.53 ( ( member_trm_a_b @ Y3 @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ( P @ ( freche665377491rm_a_b @ Y3 ) ) )
% 2.71/1.53 => ( P @ X2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_33_simple__term__induct,axiom,
% 2.71/1.53 ! [P: frechet_strm_sf_sz > $o,X2: frechet_strm_sf_sz] :
% 2.71/1.53 ( ! [Y3: trm_sf_sz] :
% 2.71/1.53 ( ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ( P @ ( freche1046279700_sf_sz @ Y3 ) ) )
% 2.71/1.53 => ( P @ X2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_34_simple__term__cases,axiom,
% 2.71/1.53 ! [X2: frechet_strm_a_b] :
% 2.71/1.53 ~ ! [Y3: trm_a_b] :
% 2.71/1.53 ( ( X2
% 2.71/1.53 = ( freche665377491rm_a_b @ Y3 ) )
% 2.71/1.53 => ~ ( member_trm_a_b @ Y3 @ ( collect_trm_a_b @ dfree_a_b ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_35_simple__term__cases,axiom,
% 2.71/1.53 ! [X2: frechet_strm_sf_sz] :
% 2.71/1.53 ~ ! [Y3: trm_sf_sz] :
% 2.71/1.53 ( ( X2
% 2.71/1.53 = ( freche1046279700_sf_sz @ Y3 ) )
% 2.71/1.53 => ~ ( member_trm_sf_sz @ Y3 @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_36_raw__interp__inverse,axiom,
% 2.71/1.53 ! [X2: freche2095075217_sc_sz] :
% 2.71/1.53 ( ( freche1784963216_sc_sz @ ( freche1421597129_sc_sz @ X2 ) )
% 2.71/1.53 = X2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_37_raw__term__induct,axiom,
% 2.71/1.53 ! [Y: trm_a_b,P: trm_a_b > $o] :
% 2.71/1.53 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ( ! [X3: frechet_strm_a_b] : ( P @ ( frechet_raw_term_a_b @ X3 ) )
% 2.71/1.53 => ( P @ Y ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_38_raw__term__induct,axiom,
% 2.71/1.53 ! [Y: trm_sf_sz,P: trm_sf_sz > $o] :
% 2.71/1.53 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ( ! [X3: frechet_strm_sf_sz] : ( P @ ( freche782854530_sf_sz @ X3 ) )
% 2.71/1.53 => ( P @ Y ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_39_raw__term__cases,axiom,
% 2.71/1.53 ! [Y: trm_a_b] :
% 2.71/1.53 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ~ ! [X3: frechet_strm_a_b] :
% 2.71/1.53 ( Y
% 2.71/1.53 != ( frechet_raw_term_a_b @ X3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_40_raw__term__cases,axiom,
% 2.71/1.53 ! [Y: trm_sf_sz] :
% 2.71/1.53 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ~ ! [X3: frechet_strm_sf_sz] :
% 2.71/1.53 ( Y
% 2.71/1.53 != ( freche782854530_sf_sz @ X3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_41_raw__term,axiom,
% 2.71/1.53 ! [X2: frechet_strm_a_b] : ( member_trm_a_b @ ( frechet_raw_term_a_b @ X2 ) @ ( collect_trm_a_b @ dfree_a_b ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_42_raw__term,axiom,
% 2.71/1.53 ! [X2: frechet_strm_sf_sz] : ( member_trm_sf_sz @ ( freche782854530_sf_sz @ X2 ) @ ( collect_trm_sf_sz @ dfree_sf_sz ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_43_trm_Oinject_I5_J,axiom,
% 2.71/1.53 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 2.71/1.53 ( ( ( times_sf_sz @ X51 @ X52 )
% 2.71/1.53 = ( times_sf_sz @ Y51 @ Y52 ) )
% 2.71/1.53 = ( ( X51 = Y51 )
% 2.71/1.53 & ( X52 = Y52 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_44_trm_Oinject_I5_J,axiom,
% 2.71/1.53 ! [X51: trm_a_b,X52: trm_a_b,Y51: trm_a_b,Y52: trm_a_b] :
% 2.71/1.53 ( ( ( times_a_b @ X51 @ X52 )
% 2.71/1.53 = ( times_a_b @ Y51 @ Y52 ) )
% 2.71/1.53 = ( ( X51 = Y51 )
% 2.71/1.53 & ( X52 = Y52 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_45_raw__term__inject,axiom,
% 2.71/1.53 ! [X2: frechet_strm_sf_sz,Y: frechet_strm_sf_sz] :
% 2.71/1.53 ( ( ( freche782854530_sf_sz @ X2 )
% 2.71/1.53 = ( freche782854530_sf_sz @ Y ) )
% 2.71/1.53 = ( X2 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_46_raw__term__inject,axiom,
% 2.71/1.53 ! [X2: frechet_strm_a_b,Y: frechet_strm_a_b] :
% 2.71/1.53 ( ( ( frechet_raw_term_a_b @ X2 )
% 2.71/1.53 = ( frechet_raw_term_a_b @ Y ) )
% 2.71/1.53 = ( X2 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_47_raw__term__inverse,axiom,
% 2.71/1.53 ! [X2: frechet_strm_a_b] :
% 2.71/1.53 ( ( freche665377491rm_a_b @ ( frechet_raw_term_a_b @ X2 ) )
% 2.71/1.53 = X2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_48_raw__term__inverse,axiom,
% 2.71/1.53 ! [X2: frechet_strm_sf_sz] :
% 2.71/1.53 ( ( freche1046279700_sf_sz @ ( freche782854530_sf_sz @ X2 ) )
% 2.71/1.53 = X2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_49_simple__term__inverse,axiom,
% 2.71/1.53 ! [Y: trm_a_b] :
% 2.71/1.53 ( ( member_trm_a_b @ Y @ ( collect_trm_a_b @ dfree_a_b ) )
% 2.71/1.53 => ( ( frechet_raw_term_a_b @ ( freche665377491rm_a_b @ Y ) )
% 2.71/1.53 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_50_simple__term__inverse,axiom,
% 2.71/1.53 ! [Y: trm_sf_sz] :
% 2.71/1.53 ( ( member_trm_sf_sz @ Y @ ( collect_trm_sf_sz @ dfree_sf_sz ) )
% 2.71/1.53 => ( ( freche782854530_sf_sz @ ( freche1046279700_sf_sz @ Y ) )
% 2.71/1.53 = Y ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_51_agree__union,axiom,
% 2.71/1.53 ! [Nu: produc133005365real_b,Omega: produc133005365real_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.53 ( ( denota1997846517gree_b @ Nu @ Omega @ A3 )
% 2.71/1.53 => ( ( denota1997846517gree_b @ Nu @ Omega @ B )
% 2.71/1.53 => ( denota1997846517gree_b @ Nu @ Omega @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_52_Iagree__sub,axiom,
% 2.71/1.53 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,I: denota723907260t_unit,J: denota723907260t_unit] :
% 2.71/1.53 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.53 => ( ( denota896875430_a_c_b @ I @ J @ B )
% 2.71/1.53 => ( denota896875430_a_c_b @ I @ J @ A3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_53_dfree_Odfree__Times,axiom,
% 2.71/1.53 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 2.71/1.53 ( ( dfree_sf_sz @ Theta_1 )
% 2.71/1.53 => ( ( dfree_sf_sz @ Theta_2 )
% 2.71/1.53 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_54_dfree_Odfree__Times,axiom,
% 2.71/1.53 ! [Theta_1: trm_a_b,Theta_2: trm_a_b] :
% 2.71/1.53 ( ( dfree_a_b @ Theta_1 )
% 2.71/1.53 => ( ( dfree_a_b @ Theta_2 )
% 2.71/1.53 => ( dfree_a_b @ ( times_a_b @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_55_cr__strm__def,axiom,
% 2.71/1.53 ( freche1244000341_sf_sz
% 2.71/1.53 = ( ^ [X: trm_sf_sz,Y2: frechet_strm_sf_sz] :
% 2.71/1.53 ( X
% 2.71/1.53 = ( freche782854530_sf_sz @ Y2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_56_cr__strm__def,axiom,
% 2.71/1.53 ( frechet_cr_strm_a_b
% 2.71/1.53 = ( ^ [X: trm_a_b,Y2: frechet_strm_a_b] :
% 2.71/1.53 ( X
% 2.71/1.53 = ( frechet_raw_term_a_b @ Y2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_57_fst__sup,axiom,
% 2.71/1.53 ! [X2: produc133005365real_b,Y: produc133005365real_b] :
% 2.71/1.53 ( ( produc936751193real_b @ ( sup_su1581595657real_b @ X2 @ Y ) )
% 2.71/1.53 = ( sup_su2133361046real_b @ ( produc936751193real_b @ X2 ) @ ( produc936751193real_b @ Y ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_58_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: finite824932053eal_sz,P: finite824932053eal_sz > $o] :
% 2.71/1.53 ( ( member1693951742eal_sz @ A @ ( collec1002602816eal_sz @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_59_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: sum_sum_b_b,P: sum_sum_b_b > $o] :
% 2.71/1.53 ( ( member_Sum_sum_b_b @ A @ ( collect_Sum_sum_b_b @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_60_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: trm_sf_sz,P: trm_sf_sz > $o] :
% 2.71/1.53 ( ( member_trm_sf_sz @ A @ ( collect_trm_sf_sz @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_61_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: trm_a_b,P: trm_a_b > $o] :
% 2.71/1.53 ( ( member_trm_a_b @ A @ ( collect_trm_a_b @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_62_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: a,P: a > $o] :
% 2.71/1.53 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_63_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A: sum_su1965225555um_c_b,P: sum_su1965225555um_c_b > $o] :
% 2.71/1.53 ( ( member973578748um_c_b @ A @ ( collec1166375742um_c_b @ P ) )
% 2.71/1.53 = ( P @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_64_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_Fi291318197eal_sz] :
% 2.71/1.53 ( ( collec1002602816eal_sz
% 2.71/1.53 @ ^ [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_65_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_Sum_sum_b_b] :
% 2.71/1.53 ( ( collect_Sum_sum_b_b
% 2.71/1.53 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_66_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_trm_sf_sz] :
% 2.71/1.53 ( ( collect_trm_sf_sz
% 2.71/1.53 @ ^ [X: trm_sf_sz] : ( member_trm_sf_sz @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_67_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_trm_a_b] :
% 2.71/1.53 ( ( collect_trm_a_b
% 2.71/1.53 @ ^ [X: trm_a_b] : ( member_trm_a_b @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_68_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_a] :
% 2.71/1.53 ( ( collect_a
% 2.71/1.53 @ ^ [X: a] : ( member_a @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_69_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A3: set_Su111624115um_c_b] :
% 2.71/1.53 ( ( collec1166375742um_c_b
% 2.71/1.53 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A3 ) )
% 2.71/1.53 = A3 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_70_Collect__cong,axiom,
% 2.71/1.53 ! [P: finite824932053eal_sz > $o,Q: finite824932053eal_sz > $o] :
% 2.71/1.53 ( ! [X3: finite824932053eal_sz] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collec1002602816eal_sz @ P )
% 2.71/1.53 = ( collec1002602816eal_sz @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_71_Collect__cong,axiom,
% 2.71/1.53 ! [P: sum_sum_b_b > $o,Q: sum_sum_b_b > $o] :
% 2.71/1.53 ( ! [X3: sum_sum_b_b] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collect_Sum_sum_b_b @ P )
% 2.71/1.53 = ( collect_Sum_sum_b_b @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_72_Collect__cong,axiom,
% 2.71/1.53 ! [P: trm_sf_sz > $o,Q: trm_sf_sz > $o] :
% 2.71/1.53 ( ! [X3: trm_sf_sz] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collect_trm_sf_sz @ P )
% 2.71/1.53 = ( collect_trm_sf_sz @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_73_Collect__cong,axiom,
% 2.71/1.53 ! [P: trm_a_b > $o,Q: trm_a_b > $o] :
% 2.71/1.53 ( ! [X3: trm_a_b] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collect_trm_a_b @ P )
% 2.71/1.53 = ( collect_trm_a_b @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_74_Collect__cong,axiom,
% 2.71/1.53 ! [P: a > $o,Q: a > $o] :
% 2.71/1.53 ( ! [X3: a] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collect_a @ P )
% 2.71/1.53 = ( collect_a @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_75_Collect__cong,axiom,
% 2.71/1.53 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 2.71/1.53 ( ! [X3: sum_su1965225555um_c_b] :
% 2.71/1.53 ( ( P @ X3 )
% 2.71/1.53 = ( Q @ X3 ) )
% 2.71/1.53 => ( ( collec1166375742um_c_b @ P )
% 2.71/1.53 = ( collec1166375742um_c_b @ Q ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_76_Un__subset__iff,axiom,
% 2.71/1.53 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz,C: set_Fi291318197eal_sz] :
% 2.71/1.53 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ A3 @ B ) @ C )
% 2.71/1.53 = ( ( ord_le41263445eal_sz @ A3 @ C )
% 2.71/1.53 & ( ord_le41263445eal_sz @ B @ C ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_77_Un__subset__iff,axiom,
% 2.71/1.53 ! [A3: set_a,B: set_a,C: set_a] :
% 2.71/1.53 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A3 @ B ) @ C )
% 2.71/1.53 = ( ( ord_less_eq_set_a @ A3 @ C )
% 2.71/1.54 & ( ord_less_eq_set_a @ B @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_78_Un__subset__iff,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C )
% 2.71/1.54 = ( ( ord_le412705147um_b_b @ A3 @ C )
% 2.71/1.54 & ( ord_le412705147um_b_b @ B @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_79_Un__subset__iff,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ C )
% 2.71/1.54 = ( ( ord_le1404954451um_c_b @ A3 @ C )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ B @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_80_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: sum_sum_b_b > $o,C2: sum_sum_b_b > $o,A: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( ord_le1306331338_b_b_o @ ( sup_su2024788734_b_b_o @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_le1306331338_b_b_o @ B2 @ A )
% 2.71/1.54 & ( ord_le1306331338_b_b_o @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_81_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: set_Fi291318197eal_sz,C2: set_Fi291318197eal_sz,A: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_le41263445eal_sz @ B2 @ A )
% 2.71/1.54 & ( ord_le41263445eal_sz @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_82_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: set_a,C2: set_a,A: set_a] :
% 2.71/1.54 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_less_eq_set_a @ B2 @ A )
% 2.71/1.54 & ( ord_less_eq_set_a @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_83_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: sum_su1965225555um_c_b > $o,C2: sum_su1965225555um_c_b > $o,A: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_le1534094666_c_b_o @ B2 @ A )
% 2.71/1.54 & ( ord_le1534094666_c_b_o @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_84_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: a > $o,C2: a > $o,A: a > $o] :
% 2.71/1.54 ( ( ord_less_eq_a_o @ ( sup_sup_a_o @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_less_eq_a_o @ B2 @ A )
% 2.71/1.54 & ( ord_less_eq_a_o @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_85_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_le412705147um_b_b @ B2 @ A )
% 2.71/1.54 & ( ord_le412705147um_b_b @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_86_sup_Obounded__iff,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A )
% 2.71/1.54 = ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_87_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: sum_sum_b_b > $o,Y: sum_sum_b_b > $o,Z: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( ord_le1306331338_b_b_o @ ( sup_su2024788734_b_b_o @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_le1306331338_b_b_o @ X2 @ Z )
% 2.71/1.54 & ( ord_le1306331338_b_b_o @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_88_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: set_Fi291318197eal_sz,Y: set_Fi291318197eal_sz,Z: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( ord_le41263445eal_sz @ ( sup_su1321388937eal_sz @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_le41263445eal_sz @ X2 @ Z )
% 2.71/1.54 & ( ord_le41263445eal_sz @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_89_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: set_a,Y: set_a,Z: set_a] :
% 2.71/1.54 ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_less_eq_set_a @ X2 @ Z )
% 2.71/1.54 & ( ord_less_eq_set_a @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_90_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: sum_su1965225555um_c_b > $o,Y: sum_su1965225555um_c_b > $o,Z: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_le1534094666_c_b_o @ X2 @ Z )
% 2.71/1.54 & ( ord_le1534094666_c_b_o @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_91_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: a > $o,Y: a > $o,Z: a > $o] :
% 2.71/1.54 ( ( ord_less_eq_a_o @ ( sup_sup_a_o @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_less_eq_a_o @ X2 @ Z )
% 2.71/1.54 & ( ord_less_eq_a_o @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_92_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_le412705147um_b_b @ X2 @ Z )
% 2.71/1.54 & ( ord_le412705147um_b_b @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_93_le__sup__iff,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( ( ord_le1404954451um_c_b @ X2 @ Z )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_94_FVT_Osimps_I5_J,axiom,
% 2.71/1.54 ! [F: trm_sf_sz,G: trm_sf_sz] :
% 2.71/1.54 ( ( static_FVT_sf_sz @ ( times_sf_sz @ F @ G ) )
% 2.71/1.54 = ( sup_su1670953621_sz_sz @ ( static_FVT_sf_sz @ F ) @ ( static_FVT_sf_sz @ G ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_95_FVT_Osimps_I5_J,axiom,
% 2.71/1.54 ! [F: trm_a_b,G: trm_a_b] :
% 2.71/1.54 ( ( static_FVT_a_b @ ( times_a_b @ F @ G ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ F ) @ ( static_FVT_a_b @ G ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_96_SIGT_Osimps_I5_J,axiom,
% 2.71/1.54 ! [T1: trm_sf_sz,T2: trm_sf_sz] :
% 2.71/1.54 ( ( static_SIGT_sf_sz @ ( times_sf_sz @ T1 @ T2 ) )
% 2.71/1.54 = ( sup_sup_set_sf @ ( static_SIGT_sf_sz @ T1 ) @ ( static_SIGT_sf_sz @ T2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_97_SIGT_Osimps_I5_J,axiom,
% 2.71/1.54 ! [T1: trm_a_b,T2: trm_a_b] :
% 2.71/1.54 ( ( static_SIGT_a_b @ ( times_a_b @ T1 @ T2 ) )
% 2.71/1.54 = ( sup_sup_set_a @ ( static_SIGT_a_b @ T1 ) @ ( static_SIGT_a_b @ T2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_98_type__definition__strm,axiom,
% 2.71/1.54 type_d2045870413rm_a_b @ frechet_raw_term_a_b @ freche665377491rm_a_b @ ( collect_trm_a_b @ dfree_a_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_99_type__definition__strm,axiom,
% 2.71/1.54 type_d46389773_sf_sz @ freche782854530_sf_sz @ freche1046279700_sf_sz @ ( collect_trm_sf_sz @ dfree_sf_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_100_good__interp__inverse,axiom,
% 2.71/1.54 ! [Y: denota723907260t_unit] :
% 2.71/1.54 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ( ( freche288321865_a_c_b @ ( freche153761090_a_c_b @ Y ) )
% 2.71/1.54 = Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_101_good__interp__inverse,axiom,
% 2.71/1.54 ! [Y: denota610675952t_unit] :
% 2.71/1.54 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ( ( freche1421597129_sc_sz @ ( freche1784963216_sc_sz @ Y ) )
% 2.71/1.54 = Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_102_raw__interp__induct,axiom,
% 2.71/1.54 ! [Y: denota723907260t_unit,P: denota723907260t_unit > $o] :
% 2.71/1.54 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ( ! [X3: freche1734198479_a_c_b] : ( P @ ( freche288321865_a_c_b @ X3 ) )
% 2.71/1.54 => ( P @ Y ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_103_raw__interp__induct,axiom,
% 2.71/1.54 ! [Y: denota610675952t_unit,P: denota610675952t_unit > $o] :
% 2.71/1.54 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ( ! [X3: freche2095075217_sc_sz] : ( P @ ( freche1421597129_sc_sz @ X3 ) )
% 2.71/1.54 => ( P @ Y ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_104_raw__interp__cases,axiom,
% 2.71/1.54 ! [Y: denota723907260t_unit] :
% 2.71/1.54 ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ~ ! [X3: freche1734198479_a_c_b] :
% 2.71/1.54 ( Y
% 2.71/1.54 != ( freche288321865_a_c_b @ X3 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_105_raw__interp__cases,axiom,
% 2.71/1.54 ! [Y: denota610675952t_unit] :
% 2.71/1.54 ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ~ ! [X3: freche2095075217_sc_sz] :
% 2.71/1.54 ( Y
% 2.71/1.54 != ( freche1421597129_sc_sz @ X3 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_106_raw__interp,axiom,
% 2.71/1.54 ! [X2: freche1734198479_a_c_b] : ( member122424677t_unit @ ( freche288321865_a_c_b @ X2 ) @ ( collec944067751t_unit @ denota1086158987_a_c_b ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_107_raw__interp,axiom,
% 2.71/1.54 ! [X2: freche2095075217_sc_sz] : ( member754147591t_unit @ ( freche1421597129_sc_sz @ X2 ) @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_108_good__interp__inject,axiom,
% 2.71/1.54 ! [X2: denota723907260t_unit,Y: denota723907260t_unit] :
% 2.71/1.54 ( ( member122424677t_unit @ X2 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ( ( member122424677t_unit @ Y @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ( ( ( freche153761090_a_c_b @ X2 )
% 2.71/1.54 = ( freche153761090_a_c_b @ Y ) )
% 2.71/1.54 = ( X2 = Y ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_109_good__interp__inject,axiom,
% 2.71/1.54 ! [X2: denota610675952t_unit,Y: denota610675952t_unit] :
% 2.71/1.54 ( ( member754147591t_unit @ X2 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ( ( member754147591t_unit @ Y @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ( ( ( freche1784963216_sc_sz @ X2 )
% 2.71/1.54 = ( freche1784963216_sc_sz @ Y ) )
% 2.71/1.54 = ( X2 = Y ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_110_good__interp__induct,axiom,
% 2.71/1.54 ! [P: freche1734198479_a_c_b > $o,X2: freche1734198479_a_c_b] :
% 2.71/1.54 ( ! [Y3: denota723907260t_unit] :
% 2.71/1.54 ( ( member122424677t_unit @ Y3 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) )
% 2.71/1.54 => ( P @ ( freche153761090_a_c_b @ Y3 ) ) )
% 2.71/1.54 => ( P @ X2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_111_good__interp__induct,axiom,
% 2.71/1.54 ! [P: freche2095075217_sc_sz > $o,X2: freche2095075217_sc_sz] :
% 2.71/1.54 ( ! [Y3: denota610675952t_unit] :
% 2.71/1.54 ( ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) )
% 2.71/1.54 => ( P @ ( freche1784963216_sc_sz @ Y3 ) ) )
% 2.71/1.54 => ( P @ X2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_112_good__interp__cases,axiom,
% 2.71/1.54 ! [X2: freche1734198479_a_c_b] :
% 2.71/1.54 ~ ! [Y3: denota723907260t_unit] :
% 2.71/1.54 ( ( X2
% 2.71/1.54 = ( freche153761090_a_c_b @ Y3 ) )
% 2.71/1.54 => ~ ( member122424677t_unit @ Y3 @ ( collec944067751t_unit @ denota1086158987_a_c_b ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_113_good__interp__cases,axiom,
% 2.71/1.54 ! [X2: freche2095075217_sc_sz] :
% 2.71/1.54 ~ ! [Y3: denota610675952t_unit] :
% 2.71/1.54 ( ( X2
% 2.71/1.54 = ( freche1784963216_sc_sz @ Y3 ) )
% 2.71/1.54 => ~ ( member754147591t_unit @ Y3 @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_114_subsetI,axiom,
% 2.71/1.54 ! [A3: set_trm_sf_sz,B: set_trm_sf_sz] :
% 2.71/1.54 ( ! [X3: trm_sf_sz] :
% 2.71/1.54 ( ( member_trm_sf_sz @ X3 @ A3 )
% 2.71/1.54 => ( member_trm_sf_sz @ X3 @ B ) )
% 2.71/1.54 => ( ord_le1697056455_sf_sz @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_115_subsetI,axiom,
% 2.71/1.54 ! [A3: set_trm_a_b,B: set_trm_a_b] :
% 2.71/1.54 ( ! [X3: trm_a_b] :
% 2.71/1.54 ( ( member_trm_a_b @ X3 @ A3 )
% 2.71/1.54 => ( member_trm_a_b @ X3 @ B ) )
% 2.71/1.54 => ( ord_le230080206rm_a_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_116_subsetI,axiom,
% 2.71/1.54 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ! [X3: finite824932053eal_sz] :
% 2.71/1.54 ( ( member1693951742eal_sz @ X3 @ A3 )
% 2.71/1.54 => ( member1693951742eal_sz @ X3 @ B ) )
% 2.71/1.54 => ( ord_le41263445eal_sz @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_117_subsetI,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ! [X3: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X3 @ A3 )
% 2.71/1.54 => ( member_Sum_sum_b_b @ X3 @ B ) )
% 2.71/1.54 => ( ord_le412705147um_b_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_118_subsetI,axiom,
% 2.71/1.54 ! [A3: set_a,B: set_a] :
% 2.71/1.54 ( ! [X3: a] :
% 2.71/1.54 ( ( member_a @ X3 @ A3 )
% 2.71/1.54 => ( member_a @ X3 @ B ) )
% 2.71/1.54 => ( ord_less_eq_set_a @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_119_subsetI,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ! [X3: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( member973578748um_c_b @ X3 @ A3 )
% 2.71/1.54 => ( member973578748um_c_b @ X3 @ B ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_120_subset__antisym,axiom,
% 2.71/1.54 ! [A3: set_Fi291318197eal_sz,B: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( ord_le41263445eal_sz @ A3 @ B )
% 2.71/1.54 => ( ( ord_le41263445eal_sz @ B @ A3 )
% 2.71/1.54 => ( A3 = B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_121_subset__antisym,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A3 @ B )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ B @ A3 )
% 2.71/1.54 => ( A3 = B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_122_subset__antisym,axiom,
% 2.71/1.54 ! [A3: set_a,B: set_a] :
% 2.71/1.54 ( ( ord_less_eq_set_a @ A3 @ B )
% 2.71/1.54 => ( ( ord_less_eq_set_a @ B @ A3 )
% 2.71/1.54 => ( A3 = B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_123_subset__antisym,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B @ A3 )
% 2.71/1.54 => ( A3 = B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_124_sup__apply,axiom,
% 2.71/1.54 ( sup_su2024788734_b_b_o
% 2.71/1.54 = ( ^ [F2: sum_sum_b_b > $o,G2: sum_sum_b_b > $o,X: sum_sum_b_b] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_125_sup__apply,axiom,
% 2.71/1.54 ( sup_su1211201046_c_b_o
% 2.71/1.54 = ( ^ [F2: sum_su1965225555um_c_b > $o,G2: sum_su1965225555um_c_b > $o,X: sum_su1965225555um_c_b] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_126_sup__apply,axiom,
% 2.71/1.54 ( sup_sup_a_o
% 2.71/1.54 = ( ^ [F2: a > $o,G2: a > $o,X: a] : ( sup_sup_o @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_127_sup_Oidem,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_128_sup_Oidem,axiom,
% 2.71/1.54 ! [A: set_a] :
% 2.71/1.54 ( ( sup_sup_set_a @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_129_sup_Oidem,axiom,
% 2.71/1.54 ! [A: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_130_sup_Oidem,axiom,
% 2.71/1.54 ! [A: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( sup_su1211201046_c_b_o @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_131_sup_Oidem,axiom,
% 2.71/1.54 ! [A: a > $o] :
% 2.71/1.54 ( ( sup_sup_a_o @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_132_sup_Oidem,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A @ A )
% 2.71/1.54 = A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_133_sup__idem,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_134_sup__idem,axiom,
% 2.71/1.54 ! [X2: set_a] :
% 2.71/1.54 ( ( sup_sup_set_a @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_135_sup__idem,axiom,
% 2.71/1.54 ! [X2: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_136_sup__idem,axiom,
% 2.71/1.54 ! [X2: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( sup_su1211201046_c_b_o @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_137_sup__idem,axiom,
% 2.71/1.54 ! [X2: a > $o] :
% 2.71/1.54 ( ( sup_sup_a_o @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_138_sup__idem,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ X2 )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_139_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B2 ) )
% 2.71/1.54 = ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_140_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: set_a,B2: set_a] :
% 2.71/1.54 ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B2 ) )
% 2.71/1.54 = ( sup_sup_set_a @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_141_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: sum_sum_b_b > $o,B2: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o @ A @ ( sup_su2024788734_b_b_o @ A @ B2 ) )
% 2.71/1.54 = ( sup_su2024788734_b_b_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_142_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: sum_su1965225555um_c_b > $o,B2: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B2 ) )
% 2.71/1.54 = ( sup_su1211201046_c_b_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_143_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: a > $o,B2: a > $o] :
% 2.71/1.54 ( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B2 ) )
% 2.71/1.54 = ( sup_sup_a_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_144_sup_Oleft__idem,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B2 ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_145_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) )
% 2.71/1.54 = ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_146_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: set_a,Y: set_a] :
% 2.71/1.54 ( ( sup_sup_set_a @ X2 @ ( sup_sup_set_a @ X2 @ Y ) )
% 2.71/1.54 = ( sup_sup_set_a @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_147_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: sum_sum_b_b > $o,Y: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o @ X2 @ ( sup_su2024788734_b_b_o @ X2 @ Y ) )
% 2.71/1.54 = ( sup_su2024788734_b_b_o @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_148_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: sum_su1965225555um_c_b > $o,Y: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( sup_su1211201046_c_b_o @ X2 @ ( sup_su1211201046_c_b_o @ X2 @ Y ) )
% 2.71/1.54 = ( sup_su1211201046_c_b_o @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_149_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: a > $o,Y: a > $o] :
% 2.71/1.54 ( ( sup_sup_a_o @ X2 @ ( sup_sup_a_o @ X2 @ Y ) )
% 2.71/1.54 = ( sup_sup_a_o @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_150_sup__left__idem,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_151_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_152_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: set_a,B2: set_a] :
% 2.71/1.54 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_sup_set_a @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_153_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: sum_sum_b_b > $o,B2: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o @ ( sup_su2024788734_b_b_o @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_su2024788734_b_b_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_154_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: sum_su1965225555um_c_b > $o,B2: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( sup_su1211201046_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_su1211201046_c_b_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_155_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: a > $o,B2: a > $o] :
% 2.71/1.54 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_sup_a_o @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_156_sup_Oright__idem,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ B2 )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_157_UnCI,axiom,
% 2.71/1.54 ! [C2: a,B: set_a,A3: set_a] :
% 2.71/1.54 ( ( ~ ( member_a @ C2 @ B )
% 2.71/1.54 => ( member_a @ C2 @ A3 ) )
% 2.71/1.54 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_158_UnCI,axiom,
% 2.71/1.54 ! [C2: sum_sum_b_b,B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ~ ( member_Sum_sum_b_b @ C2 @ B )
% 2.71/1.54 => ( member_Sum_sum_b_b @ C2 @ A3 ) )
% 2.71/1.54 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_159_Un__iff,axiom,
% 2.71/1.54 ! [C2: a,A3: set_a,B: set_a] :
% 2.71/1.54 ( ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) )
% 2.71/1.54 = ( ( member_a @ C2 @ A3 )
% 2.71/1.54 | ( member_a @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_160_Un__iff,axiom,
% 2.71/1.54 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 = ( ( member_Sum_sum_b_b @ C2 @ A3 )
% 2.71/1.54 | ( member_Sum_sum_b_b @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_161_sup__set__def,axiom,
% 2.71/1.54 ( sup_sup_set_a
% 2.71/1.54 = ( ^ [A4: set_a,B3: set_a] :
% 2.71/1.54 ( collect_a
% 2.71/1.54 @ ( sup_sup_a_o
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ A4 )
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_162_sup__set__def,axiom,
% 2.71/1.54 ( sup_su296826759um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ( collec1166375742um_c_b
% 2.71/1.54 @ ( sup_su1211201046_c_b_o
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A4 )
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_163_sup__set__def,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 2.71/1.54 ( collect_Sum_sum_b_b
% 2.71/1.54 @ ( sup_su2024788734_b_b_o
% 2.71/1.54 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ A4 )
% 2.71/1.54 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_164_less__eq__set__def,axiom,
% 2.71/1.54 ( ord_less_eq_set_a
% 2.71/1.54 = ( ^ [A4: set_a,B3: set_a] :
% 2.71/1.54 ( ord_less_eq_a_o
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ A4 )
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_165_less__eq__set__def,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ord_le1534094666_c_b_o
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ A4 )
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_166_in__mono,axiom,
% 2.71/1.54 ! [A3: set_a,B: set_a,X2: a] :
% 2.71/1.54 ( ( ord_less_eq_set_a @ A3 @ B )
% 2.71/1.54 => ( ( member_a @ X2 @ A3 )
% 2.71/1.54 => ( member_a @ X2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_167_in__mono,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,X2: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ( ( member973578748um_c_b @ X2 @ A3 )
% 2.71/1.54 => ( member973578748um_c_b @ X2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_168_subsetD,axiom,
% 2.71/1.54 ! [A3: set_a,B: set_a,C2: a] :
% 2.71/1.54 ( ( ord_less_eq_set_a @ A3 @ B )
% 2.71/1.54 => ( ( member_a @ C2 @ A3 )
% 2.71/1.54 => ( member_a @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_169_subsetD,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C2: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ( ( member973578748um_c_b @ C2 @ A3 )
% 2.71/1.54 => ( member973578748um_c_b @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_170_equalityE,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A3 = B )
% 2.71/1.54 => ~ ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ~ ( ord_le1404954451um_c_b @ B @ A3 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_171_subset__eq,axiom,
% 2.71/1.54 ( ord_less_eq_set_a
% 2.71/1.54 = ( ^ [A4: set_a,B3: set_a] :
% 2.71/1.54 ! [X: a] :
% 2.71/1.54 ( ( member_a @ X @ A4 )
% 2.71/1.54 => ( member_a @ X @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_172_subset__eq,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ! [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( member973578748um_c_b @ X @ A4 )
% 2.71/1.54 => ( member973578748um_c_b @ X @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_173_equalityD1,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A3 = B )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_174_equalityD2,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A3 = B )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ B @ A3 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_175_subset__iff,axiom,
% 2.71/1.54 ( ord_less_eq_set_a
% 2.71/1.54 = ( ^ [A4: set_a,B3: set_a] :
% 2.71/1.54 ! [T: a] :
% 2.71/1.54 ( ( member_a @ T @ A4 )
% 2.71/1.54 => ( member_a @ T @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_176_subset__iff,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ! [T: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( member973578748um_c_b @ T @ A4 )
% 2.71/1.54 => ( member973578748um_c_b @ T @ B3 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_177_subset__refl,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ A3 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_178_Collect__mono,axiom,
% 2.71/1.54 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ! [X3: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( P @ X3 )
% 2.71/1.54 => ( Q @ X3 ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_179_subset__trans,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B @ C )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A3 @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_180_set__eq__subset,axiom,
% 2.71/1.54 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A4 @ B3 )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ B3 @ A4 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_181_Collect__mono__iff,axiom,
% 2.71/1.54 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) )
% 2.71/1.54 = ( ! [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( P @ X )
% 2.71/1.54 => ( Q @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_182_inf__sup__aci_I8_J,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_183_inf__sup__aci_I7_J,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_184_inf__sup__aci_I6_J,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_185_inf__sup__aci_I5_J,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ Y2 @ X ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_186_boolean__algebra__cancel_Osup1,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,K: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( A3
% 2.71/1.54 = ( sup_su2137030215um_b_b @ K @ A ) )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A3 @ B2 )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ K @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_187_boolean__algebra__cancel_Osup2,axiom,
% 2.71/1.54 ! [B: set_Sum_sum_b_b,K: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( B
% 2.71/1.54 = ( sup_su2137030215um_b_b @ K @ B2 ) )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A @ B )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ K @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_188_sup_Oassoc,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ C2 )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B2 @ C2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_189_sup__assoc,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ X2 @ Y ) @ Z )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_190_sup_Ocommute,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [A5: set_Sum_sum_b_b,B4: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B4 @ A5 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_191_sup__commute,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ Y2 @ X ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_192_sup_Oleft__commute,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ B2 @ ( sup_su2137030215um_b_b @ A @ C2 ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B2 @ C2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_193_sup__left__commute,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ ( sup_su2137030215um_b_b @ Y @ Z ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_194_UnE,axiom,
% 2.71/1.54 ! [C2: a,A3: set_a,B: set_a] :
% 2.71/1.54 ( ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) )
% 2.71/1.54 => ( ~ ( member_a @ C2 @ A3 )
% 2.71/1.54 => ( member_a @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_195_UnE,axiom,
% 2.71/1.54 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 => ( ~ ( member_Sum_sum_b_b @ C2 @ A3 )
% 2.71/1.54 => ( member_Sum_sum_b_b @ C2 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_196_UnI1,axiom,
% 2.71/1.54 ! [C2: a,A3: set_a,B: set_a] :
% 2.71/1.54 ( ( member_a @ C2 @ A3 )
% 2.71/1.54 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_197_UnI1,axiom,
% 2.71/1.54 ! [C2: sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ C2 @ A3 )
% 2.71/1.54 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_198_UnI2,axiom,
% 2.71/1.54 ! [C2: a,B: set_a,A3: set_a] :
% 2.71/1.54 ( ( member_a @ C2 @ B )
% 2.71/1.54 => ( member_a @ C2 @ ( sup_sup_set_a @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_199_UnI2,axiom,
% 2.71/1.54 ! [C2: sum_sum_b_b,B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ C2 @ B )
% 2.71/1.54 => ( member_Sum_sum_b_b @ C2 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_200_bex__Un,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,P: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( ? [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 & ( P @ X ) ) )
% 2.71/1.54 = ( ? [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ A3 )
% 2.71/1.54 & ( P @ X ) )
% 2.71/1.54 | ? [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ B )
% 2.71/1.54 & ( P @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_201_ball__Un,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,P: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( ! [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 => ( P @ X ) ) )
% 2.71/1.54 = ( ! [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ A3 )
% 2.71/1.54 => ( P @ X ) )
% 2.71/1.54 & ! [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ B )
% 2.71/1.54 => ( P @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_202_Un__assoc,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ B @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_203_Un__absorb,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A3 @ A3 )
% 2.71/1.54 = A3 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_204_Un__commute,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B3 @ A4 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_205_Un__left__absorb,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_206_Un__left__commute,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A3 @ ( sup_su2137030215um_b_b @ B @ C ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A3 @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_207_Collect__subset,axiom,
% 2.71/1.54 ! [A3: set_a,P: a > $o] :
% 2.71/1.54 ( ord_less_eq_set_a
% 2.71/1.54 @ ( collect_a
% 2.71/1.54 @ ^ [X: a] :
% 2.71/1.54 ( ( member_a @ X @ A3 )
% 2.71/1.54 & ( P @ X ) ) )
% 2.71/1.54 @ A3 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_208_Collect__subset,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,P: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 @ ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( member973578748um_c_b @ X @ A3 )
% 2.71/1.54 & ( P @ X ) ) )
% 2.71/1.54 @ A3 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_209_Un__def,axiom,
% 2.71/1.54 ( sup_sup_set_a
% 2.71/1.54 = ( ^ [A4: set_a,B3: set_a] :
% 2.71/1.54 ( collect_a
% 2.71/1.54 @ ^ [X: a] :
% 2.71/1.54 ( ( member_a @ X @ A4 )
% 2.71/1.54 | ( member_a @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_210_Un__def,axiom,
% 2.71/1.54 ( sup_su296826759um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( member973578748um_c_b @ X @ A4 )
% 2.71/1.54 | ( member973578748um_c_b @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_211_Un__def,axiom,
% 2.71/1.54 ( sup_su2137030215um_b_b
% 2.71/1.54 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 2.71/1.54 ( collect_Sum_sum_b_b
% 2.71/1.54 @ ^ [X: sum_sum_b_b] :
% 2.71/1.54 ( ( member_Sum_sum_b_b @ X @ A4 )
% 2.71/1.54 | ( member_Sum_sum_b_b @ X @ B3 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_212_Collect__disj__eq,axiom,
% 2.71/1.54 ! [P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( P @ X )
% 2.71/1.54 | ( Q @ X ) ) )
% 2.71/1.54 = ( sup_su296826759um_c_b @ ( collec1166375742um_c_b @ P ) @ ( collec1166375742um_c_b @ Q ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_213_Collect__disj__eq,axiom,
% 2.71/1.54 ! [P: sum_sum_b_b > $o,Q: sum_sum_b_b > $o] :
% 2.71/1.54 ( ( collect_Sum_sum_b_b
% 2.71/1.54 @ ^ [X: sum_sum_b_b] :
% 2.71/1.54 ( ( P @ X )
% 2.71/1.54 | ( Q @ X ) ) )
% 2.71/1.54 = ( sup_su2137030215um_b_b @ ( collect_Sum_sum_b_b @ P ) @ ( collect_Sum_sum_b_b @ Q ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_214_inf__sup__ord_I4_J,axiom,
% 2.71/1.54 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_215_inf__sup__ord_I4_J,axiom,
% 2.71/1.54 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_216_inf__sup__ord_I3_J,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_217_inf__sup__ord_I3_J,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_218_le__supE,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ X2 )
% 2.71/1.54 => ~ ( ( ord_le412705147um_b_b @ A @ X2 )
% 2.71/1.54 => ~ ( ord_le412705147um_b_b @ B2 @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_219_le__supE,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ X2 )
% 2.71/1.54 => ~ ( ( ord_le1404954451um_c_b @ A @ X2 )
% 2.71/1.54 => ~ ( ord_le1404954451um_c_b @ B2 @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_220_le__supI,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,X2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A @ X2 )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ B2 @ X2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_221_le__supI,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,X2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ X2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ X2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_222_sup__ge1,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_223_sup__ge1,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_224_sup__ge2,axiom,
% 2.71/1.54 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y @ ( sup_su2137030215um_b_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_225_sup__ge2,axiom,
% 2.71/1.54 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y @ ( sup_su296826759um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_226_le__supI1,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ X2 @ A )
% 2.71/1.54 => ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_227_le__supI1,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X2 @ A )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_228_le__supI2,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ X2 @ B2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ X2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_229_le__supI2,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X2 @ B2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ X2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_230_sup_Omono,axiom,
% 2.71/1.54 ! [C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,D: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ C2 @ A )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ D @ B2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ C2 @ D ) @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_231_sup_Omono,axiom,
% 2.71/1.54 ! [C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,D: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ C2 @ A )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ D @ B2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ C2 @ D ) @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_232_sup__mono,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A @ C2 )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ B2 @ D )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A @ B2 ) @ ( sup_su2137030215um_b_b @ C2 @ D ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_233_sup__mono,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ C2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ D )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B2 ) @ ( sup_su296826759um_c_b @ C2 @ D ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_234_sup__least,axiom,
% 2.71/1.54 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b,Z: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ Y @ X2 )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ Z @ X2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ Y @ Z ) @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_235_sup__least,axiom,
% 2.71/1.54 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ Z @ X2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ Y @ Z ) @ X2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_236_le__iff__sup,axiom,
% 2.71/1.54 ( ord_le412705147um_b_b
% 2.71/1.54 = ( ^ [X: set_Sum_sum_b_b,Y2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X @ Y2 )
% 2.71/1.54 = Y2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_237_le__iff__sup,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [X: set_Su111624115um_c_b,Y2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ X @ Y2 )
% 2.71/1.54 = Y2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_238_sup_OorderE,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ B2 @ A )
% 2.71/1.54 => ( A
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_239_sup_OorderE,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( A
% 2.71/1.54 = ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_240_sup_OorderI,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( A
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A @ B2 ) )
% 2.71/1.54 => ( ord_le412705147um_b_b @ B2 @ A ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_241_sup_OorderI,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A
% 2.71/1.54 = ( sup_su296826759um_c_b @ A @ B2 ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ B2 @ A ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_242_sup__unique,axiom,
% 2.71/1.54 ! [F: set_Sum_sum_b_b > set_Sum_sum_b_b > set_Sum_sum_b_b,X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 2.71/1.54 ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ X3 @ ( F @ X3 @ Y3 ) )
% 2.71/1.54 => ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ Y3 @ ( F @ X3 @ Y3 ) )
% 2.71/1.54 => ( ! [X3: set_Sum_sum_b_b,Y3: set_Sum_sum_b_b,Z3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ Y3 @ X3 )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ Z3 @ X3 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( F @ Y3 @ Z3 ) @ X3 ) ) )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 2.71/1.54 = ( F @ X2 @ Y ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_243_sup__unique,axiom,
% 2.71/1.54 ! [F: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b,X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 2.71/1.54 ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X3 @ ( F @ X3 @ Y3 ) )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ Y3 @ ( F @ X3 @ Y3 ) )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b,Z3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ Y3 @ X3 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ Z3 @ X3 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ Y3 @ Z3 ) @ X3 ) ) )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 2.71/1.54 = ( F @ X2 @ Y ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_244_sup_Oabsorb1,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ B2 @ A )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A @ B2 )
% 2.71/1.54 = A ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_245_sup_Oabsorb1,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ A @ B2 )
% 2.71/1.54 = A ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_246_sup_Oabsorb2,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A @ B2 )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A @ B2 )
% 2.71/1.54 = B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_247_sup_Oabsorb2,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ A @ B2 )
% 2.71/1.54 = B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_248_sup__absorb1,axiom,
% 2.71/1.54 ! [Y: set_Sum_sum_b_b,X2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ Y @ X2 )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 2.71/1.54 = X2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_249_sup__absorb1,axiom,
% 2.71/1.54 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 2.71/1.54 = X2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_250_sup__absorb2,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b,Y: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ X2 @ Y )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ X2 @ Y )
% 2.71/1.54 = Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_251_sup__absorb2,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ X2 @ Y )
% 2.71/1.54 = Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_252_sup_OboundedE,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A )
% 2.71/1.54 => ~ ( ( ord_le412705147um_b_b @ B2 @ A )
% 2.71/1.54 => ~ ( ord_le412705147um_b_b @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_253_sup_OboundedE,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A )
% 2.71/1.54 => ~ ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ~ ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_254_sup_OboundedI,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,C2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ B2 @ A )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ C2 @ A )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ B2 @ C2 ) @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_255_sup_OboundedI,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ C2 @ A )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ B2 @ C2 ) @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_256_sup_Oorder__iff,axiom,
% 2.71/1.54 ( ord_le412705147um_b_b
% 2.71/1.54 = ( ^ [B4: set_Sum_sum_b_b,A5: set_Sum_sum_b_b] :
% 2.71/1.54 ( A5
% 2.71/1.54 = ( sup_su2137030215um_b_b @ A5 @ B4 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_257_sup_Oorder__iff,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [B4: set_Su111624115um_c_b,A5: set_Su111624115um_c_b] :
% 2.71/1.54 ( A5
% 2.71/1.54 = ( sup_su296826759um_c_b @ A5 @ B4 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_258_sup_Ocobounded1,axiom,
% 2.71/1.54 ! [A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_259_sup_Ocobounded1,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_260_sup_Ocobounded2,axiom,
% 2.71/1.54 ! [B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ B2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_261_sup_Ocobounded2,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ B2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_262_sup_Oabsorb__iff1,axiom,
% 2.71/1.54 ( ord_le412705147um_b_b
% 2.71/1.54 = ( ^ [B4: set_Sum_sum_b_b,A5: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A5 @ B4 )
% 2.71/1.54 = A5 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_263_sup_Oabsorb__iff1,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [B4: set_Su111624115um_c_b,A5: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ A5 @ B4 )
% 2.71/1.54 = A5 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_264_sup_Oabsorb__iff2,axiom,
% 2.71/1.54 ( ord_le412705147um_b_b
% 2.71/1.54 = ( ^ [A5: set_Sum_sum_b_b,B4: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A5 @ B4 )
% 2.71/1.54 = B4 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_265_sup_Oabsorb__iff2,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ A5 @ B4 )
% 2.71/1.54 = B4 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_266_sup_OcoboundedI1,axiom,
% 2.71/1.54 ! [C2: set_Sum_sum_b_b,A: set_Sum_sum_b_b,B2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ C2 @ A )
% 2.71/1.54 => ( ord_le412705147um_b_b @ C2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_267_sup_OcoboundedI1,axiom,
% 2.71/1.54 ! [C2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ C2 @ A )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ C2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_268_sup_OcoboundedI2,axiom,
% 2.71/1.54 ! [C2: set_Sum_sum_b_b,B2: set_Sum_sum_b_b,A: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ C2 @ B2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ C2 @ ( sup_su2137030215um_b_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_269_sup_OcoboundedI2,axiom,
% 2.71/1.54 ! [C2: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ C2 @ B2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ C2 @ ( sup_su296826759um_c_b @ A @ B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_270_fst__mono,axiom,
% 2.71/1.54 ! [X2: produc133005365real_b,Y: produc133005365real_b] :
% 2.71/1.54 ( ( ord_le793200597real_b @ X2 @ Y )
% 2.71/1.54 => ( ord_le767445194real_b @ ( produc936751193real_b @ X2 ) @ ( produc936751193real_b @ Y ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_271_Un__mono,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,C: set_Sum_sum_b_b,B: set_Sum_sum_b_b,D2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A3 @ C )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ B @ D2 )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ ( sup_su2137030215um_b_b @ C @ D2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_272_Un__mono,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,C: set_Su111624115um_c_b,B: set_Su111624115um_c_b,D2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ C )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B @ D2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ ( sup_su296826759um_c_b @ C @ D2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_273_Un__least,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,C: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A3 @ C )
% 2.71/1.54 => ( ( ord_le412705147um_b_b @ B @ C )
% 2.71/1.54 => ( ord_le412705147um_b_b @ ( sup_su2137030215um_b_b @ A3 @ B ) @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_274_Un__least,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,C: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ C )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B @ C )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A3 @ B ) @ C ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_275_Un__upper1,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ A3 @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_276_Un__upper1,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ ( sup_su296826759um_c_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_277_Un__upper2,axiom,
% 2.71/1.54 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] : ( ord_le412705147um_b_b @ B @ ( sup_su2137030215um_b_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_278_Un__upper2,axiom,
% 2.71/1.54 ! [B: set_Su111624115um_c_b,A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ B @ ( sup_su296826759um_c_b @ A3 @ B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_279_Un__absorb1,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A3 @ B )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A3 @ B )
% 2.71/1.54 = B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_280_Un__absorb1,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3 @ B )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ A3 @ B )
% 2.71/1.54 = B ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_281_Un__absorb2,axiom,
% 2.71/1.54 ! [B: set_Sum_sum_b_b,A3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ B @ A3 )
% 2.71/1.54 => ( ( sup_su2137030215um_b_b @ A3 @ B )
% 2.71/1.54 = A3 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_282_Un__absorb2,axiom,
% 2.71/1.54 ! [B: set_Su111624115um_c_b,A3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B @ A3 )
% 2.71/1.54 => ( ( sup_su296826759um_c_b @ A3 @ B )
% 2.71/1.54 = A3 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_283_subset__UnE,axiom,
% 2.71/1.54 ! [C: set_Sum_sum_b_b,A3: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ C @ ( sup_su2137030215um_b_b @ A3 @ B ) )
% 2.71/1.54 => ~ ! [A6: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ A6 @ A3 )
% 2.71/1.54 => ! [B5: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( ord_le412705147um_b_b @ B5 @ B )
% 2.71/1.54 => ( C
% 2.71/1.54 != ( sup_su2137030215um_b_b @ A6 @ B5 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_284_subset__UnE,axiom,
% 2.71/1.54 ! [C: set_Su111624115um_c_b,A3: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ C @ ( sup_su296826759um_c_b @ A3 @ B ) )
% 2.71/1.54 => ~ ! [A6: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A6 @ A3 )
% 2.71/1.54 => ! [B5: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B5 @ B )
% 2.71/1.54 => ( C
% 2.71/1.54 != ( sup_su296826759um_c_b @ A6 @ B5 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_285_subset__Un__eq,axiom,
% 2.71/1.54 ( ord_le412705147um_b_b
% 2.71/1.54 = ( ^ [A4: set_Sum_sum_b_b,B3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A4 @ B3 )
% 2.71/1.54 = B3 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_286_subset__Un__eq,axiom,
% 2.71/1.54 ( ord_le1404954451um_c_b
% 2.71/1.54 = ( ^ [A4: set_Su111624115um_c_b,B3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( sup_su296826759um_c_b @ A4 @ B3 )
% 2.71/1.54 = B3 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_287_type__definition__good__interp,axiom,
% 2.71/1.54 type_d1092523951t_unit @ freche1421597129_sc_sz @ freche1784963216_sc_sz @ ( collec1767975749t_unit @ denota1579475975_sc_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_288_order__refl,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ X2 @ X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_289_sterm__continuous_H,axiom,
% 2.71/1.54 ! [I: denota610675952t_unit,Theta: trm_sf_sz,S: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( denota1579475975_sc_sz @ I )
% 2.71/1.54 => ( ( dfree_sf_sz @ Theta )
% 2.71/1.54 => ( topolo1348430467z_real @ S @ ( denota1179238309_sc_sz @ I @ Theta ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_290_sterm__continuous_H,axiom,
% 2.71/1.54 ! [I: denota723907260t_unit,Theta: trm_a_b,S: set_Fi268318752real_b] :
% 2.71/1.54 ( ( denota1086158987_a_c_b @ I )
% 2.71/1.54 => ( ( dfree_a_b @ Theta )
% 2.71/1.54 => ( topolo238266006b_real @ S @ ( denota722380397_a_c_b @ I @ Theta ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_291_good__interp_Odomain,axiom,
% 2.71/1.54 ( ( domain413207655_sc_sz @ freche58918398_sc_sz )
% 2.71/1.54 = denota1579475975_sc_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_292_strm_Odomain,axiom,
% 2.71/1.54 ( ( domain134596861rm_a_b @ frechet_cr_strm_a_b )
% 2.71/1.54 = dfree_a_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_293_strm_Odomain,axiom,
% 2.71/1.54 ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 2.71/1.54 = dfree_sf_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_294_dual__order_Oantisym,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( A = B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_295_dual__order_Oeq__iff,axiom,
% 2.71/1.54 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 2.71/1.54 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B4 @ A5 )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ A5 @ B4 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_296_dual__order_Otrans,axiom,
% 2.71/1.54 ! [B2: set_Su111624115um_c_b,A: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ C2 @ B2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ C2 @ A ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_297_dual__order_Orefl,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_298_order__trans,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b,Z: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ Y @ Z )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ X2 @ Z ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_299_order__class_Oorder_Oantisym,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ A )
% 2.71/1.54 => ( A = B2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_300_ord__le__eq__trans,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( B2 = C2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_301_ord__eq__le__trans,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A = B2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_302_order__class_Oorder_Oeq__iff,axiom,
% 2.71/1.54 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 2.71/1.54 = ( ^ [A5: set_Su111624115um_c_b,B4: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A5 @ B4 )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ B4 @ A5 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_303_antisym__conv,axiom,
% 2.71/1.54 ! [Y: set_Su111624115um_c_b,X2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 2.71/1.54 = ( X2 = Y ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_304_order_Otrans,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A @ C2 ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_305_eq__refl,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( X2 = Y )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ X2 @ Y ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_306_antisym,axiom,
% 2.71/1.54 ! [X2: set_Su111624115um_c_b,Y: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X2 @ Y )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ Y @ X2 )
% 2.71/1.54 => ( X2 = Y ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_307_eq__iff,axiom,
% 2.71/1.54 ( ( ^ [Y4: set_Su111624115um_c_b,Z2: set_Su111624115um_c_b] : ( Y4 = Z2 ) )
% 2.71/1.54 = ( ^ [X: set_Su111624115um_c_b,Y2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X @ Y2 )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ Y2 @ X ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_308_ord__le__eq__subst,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( ( F @ B2 )
% 2.71/1.54 = C2 )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ A ) @ C2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_309_ord__eq__le__subst,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( A
% 2.71/1.54 = ( F @ B2 ) )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A @ ( F @ C2 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_310_order__subst2,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,B2: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ B2 )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ ( F @ B2 ) @ C2 )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ A ) @ C2 ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_311_order__subst1,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b,F: set_Su111624115um_c_b > set_Su111624115um_c_b,B2: set_Su111624115um_c_b,C2: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A @ ( F @ B2 ) )
% 2.71/1.54 => ( ( ord_le1404954451um_c_b @ B2 @ C2 )
% 2.71/1.54 => ( ! [X3: set_Su111624115um_c_b,Y3: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ X3 @ Y3 )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.71/1.54 => ( ord_le1404954451um_c_b @ A @ ( F @ C2 ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_312_sterm__continuous,axiom,
% 2.71/1.54 ! [I: denota610675952t_unit,Theta: trm_sf_sz] :
% 2.71/1.54 ( ( denota1579475975_sc_sz @ I )
% 2.71/1.54 => ( ( dfree_sf_sz @ Theta )
% 2.71/1.54 => ( topolo1348430467z_real @ top_to1873962757eal_sz @ ( denota1179238309_sc_sz @ I @ Theta ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_313_sterm__continuous,axiom,
% 2.71/1.54 ! [I: denota723907260t_unit,Theta: trm_a_b] :
% 2.71/1.54 ( ( denota1086158987_a_c_b @ I )
% 2.71/1.54 => ( ( dfree_a_b @ Theta )
% 2.71/1.54 => ( topolo238266006b_real @ top_to502572752real_b @ ( denota722380397_a_c_b @ I @ Theta ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_314_sup__Un__eq,axiom,
% 2.71/1.54 ! [R: set_a,S: set_a] :
% 2.71/1.54 ( ( sup_sup_a_o
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ R )
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ S ) )
% 2.71/1.54 = ( ^ [X: a] : ( member_a @ X @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_315_sup__Un__eq,axiom,
% 2.71/1.54 ! [R: set_Sum_sum_b_b,S: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2024788734_b_b_o
% 2.71/1.54 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ R )
% 2.71/1.54 @ ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ S ) )
% 2.71/1.54 = ( ^ [X: sum_sum_b_b] : ( member_Sum_sum_b_b @ X @ ( sup_su2137030215um_b_b @ R @ S ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_316_pred__subset__eq,axiom,
% 2.71/1.54 ! [R: set_a,S: set_a] :
% 2.71/1.54 ( ( ord_less_eq_a_o
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ R )
% 2.71/1.54 @ ^ [X: a] : ( member_a @ X @ S ) )
% 2.71/1.54 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_317_pred__subset__eq,axiom,
% 2.71/1.54 ! [R: set_Su111624115um_c_b,S: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1534094666_c_b_o
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ R )
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : ( member973578748um_c_b @ X @ S ) )
% 2.71/1.54 = ( ord_le1404954451um_c_b @ R @ S ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_318_UNIV__I,axiom,
% 2.71/1.54 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_319_UNIV__I,axiom,
% 2.71/1.54 ! [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_320_sup__top__right,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ X2 @ top_to301096907um_b_b )
% 2.71/1.54 = top_to301096907um_b_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_321_sup__top__right,axiom,
% 2.71/1.54 ! [X2: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( sup_su1321388937eal_sz @ X2 @ top_to1873962757eal_sz )
% 2.71/1.54 = top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_322_sup__top__left,axiom,
% 2.71/1.54 ! [X2: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ X2 )
% 2.71/1.54 = top_to301096907um_b_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_323_sup__top__left,axiom,
% 2.71/1.54 ! [X2: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( sup_su1321388937eal_sz @ top_to1873962757eal_sz @ X2 )
% 2.71/1.54 = top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_324_top_Oextremum__uniqueI,axiom,
% 2.71/1.54 ! [A: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A )
% 2.71/1.54 => ( A = top_to1873962757eal_sz ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_325_top_Oextremum__uniqueI,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
% 2.71/1.54 => ( A = top_to999478531um_c_b ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_326_top_Oextremum__unique,axiom,
% 2.71/1.54 ! [A: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( ord_le41263445eal_sz @ top_to1873962757eal_sz @ A )
% 2.71/1.54 = ( A = top_to1873962757eal_sz ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_327_top_Oextremum__unique,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
% 2.71/1.54 = ( A = top_to999478531um_c_b ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_328_top__greatest,axiom,
% 2.71/1.54 ! [A: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A @ top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_329_top__greatest,axiom,
% 2.71/1.54 ! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_330_subset__UNIV,axiom,
% 2.71/1.54 ! [A3: set_Fi291318197eal_sz] : ( ord_le41263445eal_sz @ A3 @ top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_331_subset__UNIV,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A3 @ top_to999478531um_c_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_332_Un__UNIV__left,axiom,
% 2.71/1.54 ! [B: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ B )
% 2.71/1.54 = top_to301096907um_b_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_333_Un__UNIV__left,axiom,
% 2.71/1.54 ! [B: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( sup_su1321388937eal_sz @ top_to1873962757eal_sz @ B )
% 2.71/1.54 = top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_334_Un__UNIV__right,axiom,
% 2.71/1.54 ! [A3: set_Sum_sum_b_b] :
% 2.71/1.54 ( ( sup_su2137030215um_b_b @ A3 @ top_to301096907um_b_b )
% 2.71/1.54 = top_to301096907um_b_b ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_335_Un__UNIV__right,axiom,
% 2.71/1.54 ! [A3: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( sup_su1321388937eal_sz @ A3 @ top_to1873962757eal_sz )
% 2.71/1.54 = top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_336_UNIV__witness,axiom,
% 2.71/1.54 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_337_UNIV__witness,axiom,
% 2.71/1.54 ? [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_338_UNIV__eq__I,axiom,
% 2.71/1.54 ! [A3: set_a] :
% 2.71/1.54 ( ! [X3: a] : ( member_a @ X3 @ A3 )
% 2.71/1.54 => ( top_top_set_a = A3 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_339_UNIV__eq__I,axiom,
% 2.71/1.54 ! [A3: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ! [X3: finite824932053eal_sz] : ( member1693951742eal_sz @ X3 @ A3 )
% 2.71/1.54 => ( top_to1873962757eal_sz = A3 ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_340_UNIV__def,axiom,
% 2.71/1.54 ( top_to999478531um_c_b
% 2.71/1.54 = ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] : $true ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_341_UNIV__def,axiom,
% 2.71/1.54 ( top_to1873962757eal_sz
% 2.71/1.54 = ( collec1002602816eal_sz
% 2.71/1.54 @ ^ [X: finite824932053eal_sz] : $true ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_342_continuous__on__cases__le,axiom,
% 2.71/1.54 ! [S2: set_Fi291318197eal_sz,H: finite824932053eal_sz > real,A: real,F: finite824932053eal_sz > bounde472938360z_real,G: finite824932053eal_sz > bounde472938360z_real] :
% 2.71/1.54 ( ( topolo885751137z_real
% 2.71/1.54 @ ( collec1002602816eal_sz
% 2.71/1.54 @ ^ [T: finite824932053eal_sz] :
% 2.71/1.54 ( ( member1693951742eal_sz @ T @ S2 )
% 2.71/1.54 & ( ord_less_eq_real @ ( H @ T ) @ A ) ) )
% 2.71/1.54 @ F )
% 2.71/1.54 => ( ( topolo885751137z_real
% 2.71/1.54 @ ( collec1002602816eal_sz
% 2.71/1.54 @ ^ [T: finite824932053eal_sz] :
% 2.71/1.54 ( ( member1693951742eal_sz @ T @ S2 )
% 2.71/1.54 & ( ord_less_eq_real @ A @ ( H @ T ) ) ) )
% 2.71/1.54 @ G )
% 2.71/1.54 => ( ( topolo1348430467z_real @ S2 @ H )
% 2.71/1.54 => ( ! [T3: finite824932053eal_sz] :
% 2.71/1.54 ( ( member1693951742eal_sz @ T3 @ S2 )
% 2.71/1.54 => ( ( ( H @ T3 )
% 2.71/1.54 = A )
% 2.71/1.54 => ( ( F @ T3 )
% 2.71/1.54 = ( G @ T3 ) ) ) )
% 2.71/1.54 => ( topolo885751137z_real @ S2
% 2.71/1.54 @ ^ [T: finite824932053eal_sz] : ( if_Bou1785791806z_real @ ( ord_less_eq_real @ ( H @ T ) @ A ) @ ( F @ T ) @ ( G @ T ) ) ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_343_agree__UNIV__eq,axiom,
% 2.71/1.54 ! [Nu: produc133005365real_b,Omega: produc133005365real_b] :
% 2.71/1.54 ( ( denota1997846517gree_b @ Nu @ Omega @ top_to301096907um_b_b )
% 2.71/1.54 => ( Nu = Omega ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_344_top__empty__eq,axiom,
% 2.71/1.54 ( top_top_a_o
% 2.71/1.54 = ( ^ [X: a] : ( member_a @ X @ top_top_set_a ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_345_top__empty__eq,axiom,
% 2.71/1.54 ( top_to646513176l_sz_o
% 2.71/1.54 = ( ^ [X: finite824932053eal_sz] : ( member1693951742eal_sz @ X @ top_to1873962757eal_sz ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_346_top__set__def,axiom,
% 2.71/1.54 ( top_to999478531um_c_b
% 2.71/1.54 = ( collec1166375742um_c_b @ top_to1849113498_c_b_o ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_347_top__set__def,axiom,
% 2.71/1.54 ( top_to1873962757eal_sz
% 2.71/1.54 = ( collec1002602816eal_sz @ top_to646513176l_sz_o ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_348_frechet__continuous,axiom,
% 2.71/1.54 ! [I: denota610675952t_unit,Theta: trm_sf_sz] :
% 2.71/1.54 ( ( denota1579475975_sc_sz @ I )
% 2.71/1.54 => ( ( dfree_sf_sz @ Theta )
% 2.71/1.54 => ( topolo885751137z_real @ top_to1873962757eal_sz @ ( freche585307148_sc_sz @ ( freche1784963216_sc_sz @ I ) @ ( freche1046279700_sf_sz @ Theta ) ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_349_iso__tuple__UNIV__I,axiom,
% 2.71/1.54 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_350_iso__tuple__UNIV__I,axiom,
% 2.71/1.54 ! [X2: finite824932053eal_sz] : ( member1693951742eal_sz @ X2 @ top_to1873962757eal_sz ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_351_continuous__on__cong,axiom,
% 2.71/1.54 ! [S2: set_Fi291318197eal_sz,T4: set_Fi291318197eal_sz,F: finite824932053eal_sz > bounde472938360z_real,G: finite824932053eal_sz > bounde472938360z_real] :
% 2.71/1.54 ( ( S2 = T4 )
% 2.71/1.54 => ( ! [X3: finite824932053eal_sz] :
% 2.71/1.54 ( ( member1693951742eal_sz @ X3 @ T4 )
% 2.71/1.54 => ( ( F @ X3 )
% 2.71/1.54 = ( G @ X3 ) ) )
% 2.71/1.54 => ( ( topolo885751137z_real @ S2 @ F )
% 2.71/1.54 = ( topolo885751137z_real @ T4 @ G ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_352_continuous__on__const,axiom,
% 2.71/1.54 ! [S2: set_Fi291318197eal_sz,C2: bounde472938360z_real] :
% 2.71/1.54 ( topolo885751137z_real @ S2
% 2.71/1.54 @ ^ [X: finite824932053eal_sz] : C2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_353_continuous__on__subset,axiom,
% 2.71/1.54 ! [S2: set_Fi291318197eal_sz,F: finite824932053eal_sz > bounde472938360z_real,T4: set_Fi291318197eal_sz] :
% 2.71/1.54 ( ( topolo885751137z_real @ S2 @ F )
% 2.71/1.54 => ( ( ord_le41263445eal_sz @ T4 @ S2 )
% 2.71/1.54 => ( topolo885751137z_real @ T4 @ F ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(fact_354_conj__subset__def,axiom,
% 2.71/1.54 ! [A3: set_Su111624115um_c_b,P: sum_su1965225555um_c_b > $o,Q: sum_su1965225555um_c_b > $o] :
% 2.71/1.54 ( ( ord_le1404954451um_c_b @ A3
% 2.71/1.54 @ ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [X: sum_su1965225555um_c_b] :
% 2.71/1.54 ( ( P @ X )
% 2.71/1.54 & ( Q @ X ) ) ) )
% 2.71/1.54 = ( ( ord_le1404954451um_c_b @ A3 @ ( collec1166375742um_c_b @ P ) )
% 2.71/1.54 & ( ord_le1404954451um_c_b @ A3 @ ( collec1166375742um_c_b @ Q ) ) ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 2.71/1.54 ! [P: $o] :
% 2.71/1.54 ( ( P = $true )
% 2.71/1.54 | ( P = $false ) ) ).
% 2.71/1.54
% 2.71/1.54 thf(help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 2.71/1.54 ! [X2: bounde472938360z_real,Y: bounde472938360z_real] :
% 2.71/1.54 ( ( if_Bou1785791806z_real @ $false @ X2 @ Y )
% 2.71/1.54 = Y ) ).
% 2.71/1.54
% 2.71/1.54 thf(help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T,axiom,
% 2.71/1.54 ! [X2: bounde472938360z_real,Y: bounde472938360z_real] :
% 2.71/1.54 ( ( if_Bou1785791806z_real @ $true @ X2 @ Y )
% 2.71/1.54 = X2 ) ).
% 2.71/1.54
% 2.71/1.54 thf(conj_0,conjecture,
% 2.71/1.54 ( denota896875430_a_c_b @ i @ j
% 2.71/1.54 @ ( collec1166375742um_c_b
% 2.71/1.54 @ ^ [Uu: sum_su1965225555um_c_b] :
% 2.71/1.54 ? [X: a] :
% 2.71/1.54 ( ( Uu
% 2.71/1.54 = ( sum_In811702836um_c_b @ X ) )
% 2.71/1.54 & ( member_a @ X @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ).
% 2.71/1.54 ------------------------
% 2.71/1.57 % (20373)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_20266 for (2999ds/4Mi)
% 2.71/1.57 % (20375)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/2Mi)
% 2.71/1.57 % (20375)Instruction limit reached!
% 2.71/1.57 % (20375)------------------------------
% 2.71/1.57 % (20375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.57 % (20375)Termination reason: Unknown
% 2.71/1.57 % (20375)Termination phase: shuffling
% 2.71/1.57
% 2.71/1.57 % (20375)Memory used [KB]: 1407
% 2.71/1.57 % (20375)Time elapsed: 0.002 s
% 2.71/1.57 % (20375)Instructions burned: 2 (million)
% 2.71/1.57 % (20375)------------------------------
% 2.71/1.57 % (20375)------------------------------
% 2.71/1.57 % (20377)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_20266 for (2999ds/275Mi)
% 2.71/1.57 % (20373)Instruction limit reached!
% 2.71/1.57 % (20373)------------------------------
% 2.71/1.57 % (20373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.57 % (20373)Termination reason: Unknown
% 2.71/1.57 % (20373)Termination phase: shuffling
% 2.71/1.57
% 2.71/1.57 % (20373)Memory used [KB]: 1535
% 2.71/1.57 % (20373)Time elapsed: 0.003 s
% 2.71/1.57 % (20373)Instructions burned: 5 (million)
% 2.71/1.57 % (20373)------------------------------
% 2.71/1.57 % (20373)------------------------------
% 2.71/1.58 % (20372)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/183Mi)
% 2.71/1.58 % (20374)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_20266 for (2999ds/27Mi)
% 2.71/1.58 % (20376)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_20266 for (2999ds/2Mi)
% 2.71/1.58 % (20376)Instruction limit reached!
% 2.71/1.58 % (20376)------------------------------
% 2.71/1.58 % (20376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.58 % (20376)Termination reason: Unknown
% 2.71/1.58 % (20376)Termination phase: shuffling
% 2.71/1.58
% 2.71/1.58 % (20376)Memory used [KB]: 1407
% 2.71/1.58 % (20376)Time elapsed: 0.004 s
% 2.71/1.58 % (20376)Instructions burned: 3 (million)
% 2.71/1.58 % (20376)------------------------------
% 2.71/1.58 % (20376)------------------------------
% 2.71/1.58 % (20379)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/3Mi)
% 2.71/1.58 % (20379)Instruction limit reached!
% 2.71/1.58 % (20379)------------------------------
% 2.71/1.58 % (20379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.58 % (20379)Termination reason: Unknown
% 2.71/1.58 % (20379)Termination phase: shuffling
% 2.71/1.58
% 2.71/1.58 % (20379)Memory used [KB]: 1407
% 2.71/1.58 % (20379)Time elapsed: 0.002 s
% 2.71/1.58 % (20379)Instructions burned: 3 (million)
% 2.71/1.58 % (20379)------------------------------
% 2.71/1.58 % (20379)------------------------------
% 2.71/1.58 % (20378)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/18Mi)
% 2.71/1.59 % (20380)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_20266 for (2999ds/37Mi)
% 2.71/1.59 % (20382)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_20266 for (2999ds/3Mi)
% 2.71/1.59 % (20382)Instruction limit reached!
% 2.71/1.59 % (20382)------------------------------
% 2.71/1.59 % (20382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (20382)Termination reason: Unknown
% 2.71/1.59 % (20382)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (20382)Memory used [KB]: 1407
% 2.71/1.59 % (20382)Time elapsed: 0.002 s
% 2.71/1.59 % (20382)Instructions burned: 3 (million)
% 2.71/1.59 % (20382)------------------------------
% 2.71/1.59 % (20382)------------------------------
% 2.71/1.59 % (20378)Instruction limit reached!
% 2.71/1.59 % (20378)------------------------------
% 2.71/1.59 % (20378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (20378)Termination reason: Unknown
% 2.71/1.59 % (20378)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (20378)Memory used [KB]: 1791
% 2.71/1.59 % (20378)Time elapsed: 0.013 s
% 2.71/1.59 % (20378)Instructions burned: 18 (million)
% 2.71/1.59 % (20378)------------------------------
% 2.71/1.59 % (20378)------------------------------
% 2.71/1.59 % (20374)Instruction limit reached!
% 2.71/1.59 % (20374)------------------------------
% 2.71/1.59 % (20374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (20374)Termination reason: Unknown
% 2.71/1.59 % (20374)Termination phase: Property scanning
% 2.71/1.59
% 2.71/1.59 % (20374)Memory used [KB]: 1791
% 2.71/1.59 % (20374)Time elapsed: 0.018 s
% 2.71/1.59 % (20374)Instructions burned: 27 (million)
% 2.71/1.59 % (20374)------------------------------
% 2.71/1.59 % (20374)------------------------------
% 2.75/1.60 % (20381)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_20266 for (2999ds/15Mi)
% 2.75/1.60 % (20383)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_20266 for (2999ds/1041Mi)
% 2.75/1.61 % (20380)Instruction limit reached!
% 2.75/1.61 % (20380)------------------------------
% 2.75/1.61 % (20380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.61 % (20380)Termination reason: Unknown
% 2.75/1.61 % (20380)Termination phase: shuffling
% 2.75/1.61
% 2.75/1.61 % (20380)Memory used [KB]: 2174
% 2.75/1.61 % (20380)Time elapsed: 0.020 s
% 2.75/1.61 % (20380)Instructions burned: 37 (million)
% 2.75/1.61 % (20380)------------------------------
% 2.75/1.61 % (20380)------------------------------
% 2.75/1.61 % (20381)Instruction limit reached!
% 2.75/1.61 % (20381)------------------------------
% 2.75/1.61 % (20381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.61 % (20381)Termination reason: Unknown
% 2.75/1.61 % (20381)Termination phase: shuffling
% 2.75/1.61
% 2.75/1.61 % (20381)Memory used [KB]: 1791
% 2.75/1.61 % (20381)Time elapsed: 0.012 s
% 2.75/1.61 % (20381)Instructions burned: 16 (million)
% 2.75/1.61 % (20381)------------------------------
% 2.75/1.61 % (20381)------------------------------
% 2.75/1.61 % (20384)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/7Mi)
% 2.75/1.61 % (20385)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/16Mi)
% 2.75/1.61 % (20384)Instruction limit reached!
% 2.75/1.61 % (20384)------------------------------
% 2.75/1.61 % (20384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.62 % (20384)Termination reason: Unknown
% 2.75/1.62 % (20384)Termination phase: shuffling
% 2.75/1.62
% 2.75/1.62 % (20384)Memory used [KB]: 1535
% 2.75/1.62 % (20384)Time elapsed: 0.006 s
% 2.75/1.62 % (20384)Instructions burned: 7 (million)
% 2.75/1.62 % (20384)------------------------------
% 2.75/1.62 % (20384)------------------------------
% 2.75/1.62 % (20386)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_20266 for (2999ds/3Mi)
% 2.75/1.62 % (20386)Instruction limit reached!
% 2.75/1.62 % (20386)------------------------------
% 2.75/1.62 % (20386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.62 % (20386)Termination reason: Unknown
% 2.75/1.62 % (20386)Termination phase: shuffling
% 2.75/1.62
% 2.75/1.62 % (20386)Memory used [KB]: 1407
% 2.75/1.62 % (20386)Time elapsed: 0.002 s
% 2.75/1.62 % (20386)Instructions burned: 3 (million)
% 2.75/1.62 % (20386)------------------------------
% 2.75/1.62 % (20386)------------------------------
% 2.75/1.62 % (20385)Instruction limit reached!
% 2.75/1.62 % (20385)------------------------------
% 2.75/1.62 % (20385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.62 % (20385)Termination reason: Unknown
% 2.75/1.62 % (20385)Termination phase: shuffling
% 2.75/1.62
% 2.75/1.62 % (20385)Memory used [KB]: 1791
% 2.75/1.62 % (20385)Time elapsed: 0.012 s
% 2.75/1.62 % (20385)Instructions burned: 16 (million)
% 2.75/1.62 % (20385)------------------------------
% 2.75/1.62 % (20385)------------------------------
% 2.75/1.63 % (20387)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_20266 for (2999ds/3Mi)
% 2.75/1.63 % (20389)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/3Mi)
% 2.75/1.63 % (20387)Instruction limit reached!
% 2.75/1.63 % (20387)------------------------------
% 2.75/1.63 % (20387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.63 % (20387)Termination reason: Unknown
% 2.75/1.63 % (20387)Termination phase: shuffling
% 2.75/1.63
% 2.75/1.63 % (20387)Memory used [KB]: 1535
% 2.75/1.63 % (20387)Time elapsed: 0.004 s
% 2.75/1.63 % (20387)Instructions burned: 4 (million)
% 2.75/1.63 % (20387)------------------------------
% 2.75/1.63 % (20387)------------------------------
% 2.75/1.63 % (20389)Instruction limit reached!
% 2.75/1.63 % (20389)------------------------------
% 2.75/1.63 % (20389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.63 % (20389)Termination reason: Unknown
% 2.75/1.63 % (20389)Termination phase: shuffling
% 2.75/1.63
% 2.75/1.63 % (20389)Memory used [KB]: 1535
% 2.75/1.63 % (20389)Time elapsed: 0.002 s
% 2.75/1.63 % (20389)Instructions burned: 4 (million)
% 2.75/1.63 % (20389)------------------------------
% 2.75/1.63 % (20389)------------------------------
% 2.75/1.63 % (20388)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/7Mi)
% 2.75/1.64 % (20388)Instruction limit reached!
% 2.75/1.64 % (20388)------------------------------
% 2.75/1.64 % (20388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.64 % (20388)Termination reason: Unknown
% 2.75/1.64 % (20388)Termination phase: shuffling
% 2.75/1.64
% 2.75/1.64 % (20388)Memory used [KB]: 1535
% 2.75/1.64 % (20388)Time elapsed: 0.006 s
% 2.75/1.64 % (20388)Instructions burned: 7 (million)
% 2.75/1.64 % (20388)------------------------------
% 2.75/1.64 % (20388)------------------------------
% 2.75/1.64 % (20392)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/710Mi)
% 2.75/1.64 % (20390)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/4Mi)
% 2.75/1.64 % (20390)Instruction limit reached!
% 2.75/1.64 % (20390)------------------------------
% 2.75/1.64 % (20390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.64 % (20390)Termination reason: Unknown
% 2.75/1.64 % (20390)Termination phase: shuffling
% 2.75/1.64
% 2.75/1.64 % (20390)Memory used [KB]: 1535
% 2.75/1.64 % (20390)Time elapsed: 0.004 s
% 2.75/1.64 % (20390)Instructions burned: 4 (million)
% 2.75/1.64 % (20390)------------------------------
% 2.75/1.64 % (20390)------------------------------
% 2.75/1.64 % (20391)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/18Mi)
% 2.75/1.65 % (20394)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_20266 for (2999ds/902Mi)
% 2.75/1.65 % (20391)Instruction limit reached!
% 2.75/1.65 % (20391)------------------------------
% 2.75/1.65 % (20391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.65 % (20391)Termination reason: Unknown
% 2.75/1.65 % (20391)Termination phase: shuffling
% 2.75/1.65
% 2.75/1.65 % (20391)Memory used [KB]: 1791
% 2.75/1.65 % (20391)Time elapsed: 0.010 s
% 2.75/1.65 % (20391)Instructions burned: 18 (million)
% 2.75/1.65 % (20391)------------------------------
% 2.75/1.65 % (20391)------------------------------
% 2.75/1.65 % (20393)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20266 for (2999ds/6Mi)
% 2.75/1.66 % (20377)Instruction limit reached!
% 2.75/1.66 % (20377)------------------------------
% 2.75/1.66 % (20377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.66 % (20377)Termination reason: Unknown
% 2.75/1.66 % (20377)Termination phase: Saturation
% 2.75/1.66
% 2.75/1.66 % (20377)Memory used [KB]: 7291
% 2.75/1.66 % (20377)Time elapsed: 0.085 s
% 2.75/1.66 % (20377)Instructions burned: 276 (million)
% 2.75/1.66 % (20377)------------------------------
% 2.75/1.66 % (20377)------------------------------
% 2.75/1.66 % (20393)Instruction limit reached!
% 2.75/1.66 % (20393)------------------------------
% 2.75/1.66 % (20393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.66 % (20393)Termination reason: Unknown
% 2.75/1.66 % (20393)Termination phase: shuffling
% 2.75/1.66
% 2.75/1.66 % (20393)Memory used [KB]: 1535
% 2.75/1.66 % (20393)Time elapsed: 0.005 s
% 2.75/1.66 % (20393)Instructions burned: 6 (million)
% 2.75/1.66 % (20393)------------------------------
% 2.75/1.66 % (20393)------------------------------
% 2.75/1.66 % (20372)Instruction limit reached!
% 2.75/1.66 % (20372)------------------------------
% 2.75/1.66 % (20372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.66 % (20372)Termination reason: Unknown
% 2.75/1.66 % (20372)Termination phase: Saturation
% 2.75/1.66
% 2.75/1.66 % (20372)Memory used [KB]: 7291
% 2.75/1.66 % (20372)Time elapsed: 0.081 s
% 2.75/1.66 % (20372)Instructions burned: 183 (million)
% 2.75/1.66 % (20372)------------------------------
% 2.75/1.66 % (20372)------------------------------
% 2.75/1.67 % (20395)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_20266 for (2999ds/21Mi)
% 2.75/1.67 % (20396)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/5Mi)
% 2.75/1.67 % (20398)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/377Mi)
% 2.75/1.67 % (20396)Instruction limit reached!
% 2.75/1.67 % (20396)------------------------------
% 2.75/1.67 % (20396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (20396)Termination reason: Unknown
% 2.75/1.67 % (20396)Termination phase: shuffling
% 2.75/1.67
% 2.75/1.67 % (20396)Memory used [KB]: 1663
% 2.75/1.67 % (20396)Time elapsed: 0.004 s
% 2.75/1.67 % (20396)Instructions burned: 7 (million)
% 2.75/1.67 % (20396)------------------------------
% 2.75/1.67 % (20396)------------------------------
% 2.75/1.67 % (20397)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_20266 for (2998ds/6Mi)
% 2.75/1.67 % (20397)Instruction limit reached!
% 2.75/1.67 % (20397)------------------------------
% 2.75/1.67 % (20397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (20397)Termination reason: Unknown
% 2.75/1.67 % (20397)Termination phase: shuffling
% 2.75/1.67
% 2.75/1.67 % (20397)Memory used [KB]: 1535
% 2.75/1.67 % (20397)Time elapsed: 0.003 s
% 2.75/1.67 % (20397)Instructions burned: 7 (million)
% 2.75/1.67 % (20397)------------------------------
% 2.75/1.67 % (20397)------------------------------
% 2.75/1.67 % (20395)Instruction limit reached!
% 2.75/1.67 % (20395)------------------------------
% 2.75/1.67 % (20395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.67 % (20395)Termination reason: Unknown
% 2.75/1.67 % (20395)Termination phase: shuffling
% 2.75/1.67
% 2.75/1.67 % (20395)Memory used [KB]: 1791
% 2.75/1.67 % (20395)Time elapsed: 0.009 s
% 2.75/1.67 % (20395)Instructions burned: 21 (million)
% 2.75/1.67 % (20395)------------------------------
% 2.75/1.67 % (20395)------------------------------
% 2.75/1.68 % (20399)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_20266 for (2998ds/779Mi)
% 2.75/1.68 % (20400)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_20266 for (2998ds/19Mi)
% 2.75/1.68 % (20401)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/879Mi)
% 2.75/1.69 % (20400)Instruction limit reached!
% 2.75/1.69 % (20400)------------------------------
% 2.75/1.69 % (20400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.69 % (20400)Termination reason: Unknown
% 2.75/1.69 % (20400)Termination phase: shuffling
% 2.75/1.69
% 2.75/1.69 % (20400)Memory used [KB]: 1791
% 2.75/1.69 % (20400)Time elapsed: 0.008 s
% 2.75/1.69 % (20400)Instructions burned: 21 (million)
% 2.75/1.69 % (20400)------------------------------
% 2.75/1.69 % (20400)------------------------------
% 2.75/1.70 % (20402)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/17Mi)
% 2.75/1.70 % (20402)Instruction limit reached!
% 2.75/1.70 % (20402)------------------------------
% 2.75/1.70 % (20402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.70 % (20402)Termination reason: Unknown
% 2.75/1.70 % (20402)Termination phase: shuffling
% 2.75/1.70
% 2.75/1.70 % (20402)Memory used [KB]: 1791
% 2.75/1.70 % (20402)Time elapsed: 0.007 s
% 2.75/1.70 % (20402)Instructions burned: 17 (million)
% 2.75/1.70 % (20402)------------------------------
% 2.75/1.70 % (20402)------------------------------
% 2.75/1.71 % (20403)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/3Mi)
% 2.75/1.72 % (20403)Instruction limit reached!
% 2.75/1.72 % (20403)------------------------------
% 2.75/1.72 % (20403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.72 % (20403)Termination reason: Unknown
% 2.75/1.72 % (20403)Termination phase: shuffling
% 2.75/1.72
% 2.75/1.72 % (20403)Memory used [KB]: 1407
% 2.75/1.72 % (20403)Time elapsed: 0.003 s
% 2.75/1.72 % (20403)Instructions burned: 4 (million)
% 2.75/1.72 % (20403)------------------------------
% 2.75/1.72 % (20403)------------------------------
% 2.75/1.73 % (20404)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/30Mi)
% 2.75/1.74 % (20404)Instruction limit reached!
% 2.75/1.74 % (20404)------------------------------
% 2.75/1.74 % (20404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.74 % (20404)Termination reason: Unknown
% 2.75/1.74 % (20404)Termination phase: Property scanning
% 2.75/1.74
% 2.75/1.74 % (20404)Memory used [KB]: 1918
% 2.75/1.74 % (20404)Time elapsed: 0.012 s
% 2.75/1.74 % (20404)Instructions burned: 31 (million)
% 2.75/1.74 % (20404)------------------------------
% 2.75/1.74 % (20404)------------------------------
% 2.75/1.75 % (20405)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20266 for (2998ds/127Mi)
% 2.75/1.78 % (20401)First to succeed.
% 2.75/1.78 % (20401)Refutation found. Thanks to Tanya!
% 2.75/1.78 % SZS status Theorem for DTF2THF_20266
% 2.75/1.78 % SZS output start Proof for DTF2THF_20266
% 2.75/1.78 thf(type_def_5, type, denota723907260t_unit: $tType).
% 2.75/1.78 thf(type_def_6, type, set_Su111624115um_c_b: $tType).
% 2.75/1.78 thf(type_def_8, type, produc133005365real_b: $tType).
% 2.75/1.78 thf(type_def_9, type, set_Sum_sum_b_b: $tType).
% 2.75/1.78 thf(type_def_10, type, produc1149990247eal_sz: $tType).
% 2.75/1.78 thf(type_def_11, type, set_Sum_sum_sz_sz: $tType).
% 2.75/1.78 thf(type_def_12, type, a: $tType).
% 2.75/1.78 thf(type_def_13, type, finite1390225514real_b: $tType).
% 2.75/1.78 thf(type_def_14, type, real: $tType).
% 2.75/1.78 thf(type_def_15, type, denota610675952t_unit: $tType).
% 2.75/1.78 thf(type_def_16, type, trm_a_b: $tType).
% 2.75/1.78 thf(type_def_17, type, trm_sf_sz: $tType).
% 2.75/1.78 thf(type_def_18, type, finite824932053eal_sz: $tType).
% 2.75/1.78 thf(type_def_19, type, freche2095075217_sc_sz: $tType).
% 2.75/1.78 thf(type_def_20, type, frechet_strm_sf_sz: $tType).
% 2.75/1.78 thf(type_def_21, type, bounde472938360z_real: $tType).
% 2.75/1.78 thf(type_def_22, type, frechet_strm_a_b: $tType).
% 2.75/1.78 thf(type_def_23, type, freche1734198479_a_c_b: $tType).
% 2.75/1.78 thf(type_def_24, type, sum_su1965225555um_c_b: $tType).
% 2.75/1.78 thf(type_def_25, type, sum_sum_b_b: $tType).
% 2.75/1.78 thf(type_def_26, type, set_Fi291318197eal_sz: $tType).
% 2.75/1.78 thf(type_def_27, type, set_a: $tType).
% 2.75/1.78 thf(type_def_28, type, set_sf: $tType).
% 2.75/1.78 thf(type_def_29, type, set_trm_a_b: $tType).
% 2.75/1.78 thf(type_def_30, type, set_trm_sf_sz: $tType).
% 2.75/1.78 thf(type_def_31, type, set_Fi268318752real_b: $tType).
% 2.75/1.78 thf(type_def_32, type, set_De153000604t_unit: $tType).
% 2.75/1.78 thf(type_def_33, type, set_De208295462t_unit: $tType).
% 2.75/1.78 thf(func_def_0, type, produc1149990247eal_sz: $tType).
% 2.75/1.78 thf(func_def_1, type, produc133005365real_b: $tType).
% 2.75/1.78 thf(func_def_2, type, bounde472938360z_real: $tType).
% 2.75/1.78 thf(func_def_3, type, set_De208295462t_unit: $tType).
% 2.75/1.78 thf(func_def_4, type, set_De153000604t_unit: $tType).
% 2.75/1.78 thf(func_def_5, type, denota610675952t_unit: $tType).
% 2.75/1.78 thf(func_def_6, type, denota723907260t_unit: $tType).
% 2.75/1.78 thf(func_def_7, type, set_Su111624115um_c_b: $tType).
% 2.75/1.78 thf(func_def_8, type, set_Fi291318197eal_sz: $tType).
% 2.75/1.78 thf(func_def_9, type, set_Fi268318752real_b: $tType).
% 2.75/1.78 thf(func_def_10, type, freche2095075217_sc_sz: $tType).
% 2.75/1.78 thf(func_def_11, type, freche1734198479_a_c_b: $tType).
% 2.75/1.78 thf(func_def_12, type, sum_su1965225555um_c_b: $tType).
% 2.75/1.78 thf(func_def_13, type, finite824932053eal_sz: $tType).
% 2.75/1.78 thf(func_def_14, type, finite1390225514real_b: $tType).
% 2.75/1.78 thf(func_def_15, type, frechet_strm_sf_sz: $tType).
% 2.75/1.78 thf(func_def_16, type, set_Sum_sum_sz_sz: $tType).
% 2.75/1.78 thf(func_def_17, type, frechet_strm_a_b: $tType).
% 2.75/1.78 thf(func_def_18, type, set_Sum_sum_b_b: $tType).
% 2.75/1.78 thf(func_def_19, type, set_trm_sf_sz: $tType).
% 2.75/1.78 thf(func_def_20, type, set_trm_a_b: $tType).
% 2.75/1.78 thf(func_def_21, type, sum_sum_b_b: $tType).
% 2.75/1.78 thf(func_def_22, type, trm_sf_sz: $tType).
% 2.75/1.78 thf(func_def_23, type, trm_a_b: $tType).
% 2.75/1.78 thf(func_def_24, type, set_sf: $tType).
% 2.75/1.78 thf(func_def_25, type, set_a: $tType).
% 2.75/1.78 thf(func_def_26, type, real: $tType).
% 2.75/1.78 thf(func_def_27, type, a: $tType).
% 2.75/1.78 thf(func_def_28, type, denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o).
% 2.75/1.78 thf(func_def_29, type, denota1997846517gree_b: produc133005365real_b > produc133005365real_b > set_Sum_sum_b_b > $o).
% 2.75/1.78 thf(func_def_30, type, denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o).
% 2.75/1.78 thf(func_def_31, type, denota102976244t_unit: denota723907260t_unit > a > finite1390225514real_b > real).
% 2.75/1.78 thf(func_def_32, type, denota1086158987_a_c_b: denota723907260t_unit > $o).
% 2.75/1.78 thf(func_def_33, type, denota1579475975_sc_sz: denota610675952t_unit > $o).
% 2.75/1.78 thf(func_def_34, type, denota722380397_a_c_b: denota723907260t_unit > trm_a_b > finite1390225514real_b > real).
% 2.75/1.78 thf(func_def_35, type, denota1179238309_sc_sz: denota610675952t_unit > trm_sf_sz > finite824932053eal_sz > real).
% 2.75/1.78 thf(func_def_36, type, freche585307148_sc_sz: freche2095075217_sc_sz > frechet_strm_sf_sz > finite824932053eal_sz > bounde472938360z_real).
% 2.75/1.78 thf(func_def_37, type, freche58918398_sc_sz: denota610675952t_unit > freche2095075217_sc_sz > $o).
% 2.75/1.78 thf(func_def_38, type, frechet_cr_strm_a_b: trm_a_b > frechet_strm_a_b > $o).
% 2.75/1.78 thf(func_def_39, type, freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o).
% 2.75/1.78 thf(func_def_40, type, freche153761090_a_c_b: denota723907260t_unit > freche1734198479_a_c_b).
% 2.75/1.78 thf(func_def_41, type, freche1784963216_sc_sz: denota610675952t_unit > freche2095075217_sc_sz).
% 2.75/1.78 thf(func_def_42, type, freche288321865_a_c_b: freche1734198479_a_c_b > denota723907260t_unit).
% 2.75/1.78 thf(func_def_43, type, freche1421597129_sc_sz: freche2095075217_sc_sz > denota610675952t_unit).
% 2.75/1.78 thf(func_def_44, type, frechet_raw_term_a_b: frechet_strm_a_b > trm_a_b).
% 2.75/1.78 thf(func_def_45, type, freche782854530_sf_sz: frechet_strm_sf_sz > trm_sf_sz).
% 2.75/1.78 thf(func_def_46, type, freche665377491rm_a_b: trm_a_b > frechet_strm_a_b).
% 2.75/1.78 thf(func_def_47, type, freche1046279700_sf_sz: trm_sf_sz > frechet_strm_sf_sz).
% 2.75/1.78 thf(func_def_48, type, if_Bou1785791806z_real: $o > bounde472938360z_real > bounde472938360z_real > bounde472938360z_real).
% 2.75/1.78 thf(func_def_49, type, sup_su1211201046_c_b_o: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b > $o).
% 2.75/1.78 thf(func_def_50, type, sup_su2024788734_b_b_o: (sum_sum_b_b > $o) > (sum_sum_b_b > $o) > sum_sum_b_b > $o).
% 2.75/1.78 thf(func_def_51, type, sup_sup_a_o: (a > $o) > (a > $o) > a > $o).
% 2.75/1.78 thf(func_def_52, type, sup_sup_o: $o > $o > $o).
% 2.75/1.78 thf(func_def_53, type, sup_su2133361046real_b: finite1390225514real_b > finite1390225514real_b > finite1390225514real_b).
% 2.75/1.78 thf(func_def_54, type, sup_su1581595657real_b: produc133005365real_b > produc133005365real_b > produc133005365real_b).
% 2.75/1.78 thf(func_def_55, type, sup_su1321388937eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > set_Fi291318197eal_sz).
% 2.75/1.78 thf(func_def_56, type, sup_su296826759um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b).
% 2.75/1.78 thf(func_def_57, type, sup_su2137030215um_b_b: set_Sum_sum_b_b > set_Sum_sum_b_b > set_Sum_sum_b_b).
% 2.75/1.78 thf(func_def_58, type, sup_su1670953621_sz_sz: set_Sum_sum_sz_sz > set_Sum_sum_sz_sz > set_Sum_sum_sz_sz).
% 2.75/1.78 thf(func_def_59, type, sup_sup_set_a: set_a > set_a > set_a).
% 2.75/1.78 thf(func_def_60, type, sup_sup_set_sf: set_sf > set_sf > set_sf).
% 2.75/1.78 thf(func_def_61, type, ord_le1534094666_c_b_o: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > $o).
% 2.75/1.78 thf(func_def_62, type, ord_le1306331338_b_b_o: (sum_sum_b_b > $o) > (sum_sum_b_b > $o) > $o).
% 2.75/1.78 thf(func_def_63, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 2.75/1.78 thf(func_def_64, type, ord_le767445194real_b: finite1390225514real_b > finite1390225514real_b > $o).
% 2.75/1.78 thf(func_def_65, type, ord_le793200597real_b: produc133005365real_b > produc133005365real_b > $o).
% 2.75/1.78 thf(func_def_66, type, ord_less_eq_real: real > real > $o).
% 2.75/1.78 thf(func_def_67, type, ord_le41263445eal_sz: set_Fi291318197eal_sz > set_Fi291318197eal_sz > $o).
% 2.75/1.78 thf(func_def_68, type, ord_le1404954451um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > $o).
% 2.75/1.78 thf(func_def_69, type, ord_le412705147um_b_b: set_Sum_sum_b_b > set_Sum_sum_b_b > $o).
% 2.75/1.78 thf(func_def_70, type, ord_le230080206rm_a_b: set_trm_a_b > set_trm_a_b > $o).
% 2.75/1.78 thf(func_def_71, type, ord_le1697056455_sf_sz: set_trm_sf_sz > set_trm_sf_sz > $o).
% 2.75/1.78 thf(func_def_72, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.75/1.78 thf(func_def_73, type, top_to646513176l_sz_o: finite824932053eal_sz > $o).
% 2.75/1.78 thf(func_def_74, type, top_to1849113498_c_b_o: sum_su1965225555um_c_b > $o).
% 2.75/1.78 thf(func_def_75, type, top_top_a_o: a > $o).
% 2.75/1.78 thf(func_def_76, type, top_to502572752real_b: set_Fi268318752real_b).
% 2.75/1.78 thf(func_def_77, type, top_to1873962757eal_sz: set_Fi291318197eal_sz).
% 2.75/1.78 thf(func_def_78, type, top_to999478531um_c_b: set_Su111624115um_c_b).
% 2.75/1.78 thf(func_def_79, type, top_to301096907um_b_b: set_Sum_sum_b_b).
% 2.75/1.78 thf(func_def_80, type, top_top_set_a: set_a).
% 2.75/1.78 thf(func_def_81, type, produc936751193real_b: produc133005365real_b > finite1390225514real_b).
% 2.75/1.78 thf(func_def_82, type, produc1111759555eal_sz: produc1149990247eal_sz > finite824932053eal_sz).
% 2.75/1.78 thf(func_def_83, type, domain413207655_sc_sz: (denota610675952t_unit > freche2095075217_sc_sz > $o) > denota610675952t_unit > $o).
% 2.75/1.78 thf(func_def_84, type, domain134596861rm_a_b: (trm_a_b > frechet_strm_a_b > $o) > trm_a_b > $o).
% 2.75/1.78 thf(func_def_85, type, domain512309999_sf_sz: (trm_sf_sz > frechet_strm_sf_sz > $o) > trm_sf_sz > $o).
% 2.75/1.78 thf(func_def_86, type, collec944067751t_unit: (denota723907260t_unit > $o) > set_De153000604t_unit).
% 2.75/1.78 thf(func_def_87, type, collec1767975749t_unit: (denota610675952t_unit > $o) > set_De208295462t_unit).
% 2.75/1.78 thf(func_def_88, type, collec1002602816eal_sz: (finite824932053eal_sz > $o) > set_Fi291318197eal_sz).
% 2.75/1.78 thf(func_def_89, type, collec1166375742um_c_b: (sum_su1965225555um_c_b > $o) > set_Su111624115um_c_b).
% 2.75/1.78 thf(func_def_90, type, collect_Sum_sum_b_b: (sum_sum_b_b > $o) > set_Sum_sum_b_b).
% 2.75/1.78 thf(func_def_91, type, collect_trm_a_b: (trm_a_b > $o) > set_trm_a_b).
% 2.75/1.78 thf(func_def_92, type, collect_trm_sf_sz: (trm_sf_sz > $o) > set_trm_sf_sz).
% 2.75/1.78 thf(func_def_93, type, collect_a: (a > $o) > set_a).
% 2.75/1.78 thf(func_def_94, type, static_FVT_a_b: trm_a_b > set_Sum_sum_b_b).
% 2.75/1.78 thf(func_def_95, type, static_FVT_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz).
% 2.75/1.78 thf(func_def_96, type, static_SIGT_a_b: trm_a_b > set_a).
% 2.75/1.78 thf(func_def_97, type, static_SIGT_sf_sz: trm_sf_sz > set_sf).
% 2.75/1.78 thf(func_def_98, type, sum_In811702836um_c_b: a > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_99, type, dfree_a_b: trm_a_b > $o).
% 2.75/1.78 thf(func_def_100, type, dfree_sf_sz: trm_sf_sz > $o).
% 2.75/1.78 thf(func_def_101, type, times_a_b: trm_a_b > trm_a_b > trm_a_b).
% 2.75/1.78 thf(func_def_102, type, times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 2.75/1.78 thf(func_def_103, type, topolo238266006b_real: set_Fi268318752real_b > (finite1390225514real_b > real) > $o).
% 2.75/1.78 thf(func_def_104, type, topolo885751137z_real: set_Fi291318197eal_sz > (finite824932053eal_sz > bounde472938360z_real) > $o).
% 2.75/1.78 thf(func_def_105, type, topolo1348430467z_real: set_Fi291318197eal_sz > (finite824932053eal_sz > real) > $o).
% 2.75/1.78 thf(func_def_106, type, type_d1092523951t_unit: (freche2095075217_sc_sz > denota610675952t_unit) > (denota610675952t_unit > freche2095075217_sc_sz) > set_De208295462t_unit > $o).
% 2.75/1.78 thf(func_def_107, type, type_d2045870413rm_a_b: (frechet_strm_a_b > trm_a_b) > (trm_a_b > frechet_strm_a_b) > set_trm_a_b > $o).
% 2.75/1.78 thf(func_def_108, type, type_d46389773_sf_sz: (frechet_strm_sf_sz > trm_sf_sz) > (trm_sf_sz > frechet_strm_sf_sz) > set_trm_sf_sz > $o).
% 2.75/1.78 thf(func_def_109, type, member122424677t_unit: denota723907260t_unit > set_De153000604t_unit > $o).
% 2.75/1.78 thf(func_def_110, type, member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o).
% 2.75/1.78 thf(func_def_111, type, member1693951742eal_sz: finite824932053eal_sz > set_Fi291318197eal_sz > $o).
% 2.75/1.78 thf(func_def_112, type, member973578748um_c_b: sum_su1965225555um_c_b > set_Su111624115um_c_b > $o).
% 2.75/1.78 thf(func_def_113, type, member_Sum_sum_b_b: sum_sum_b_b > set_Sum_sum_b_b > $o).
% 2.75/1.78 thf(func_def_114, type, member_trm_a_b: trm_a_b > set_trm_a_b > $o).
% 2.75/1.78 thf(func_def_115, type, member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o).
% 2.75/1.78 thf(func_def_116, type, member_a: a > set_a > $o).
% 2.75/1.78 thf(func_def_117, type, i: denota723907260t_unit).
% 2.75/1.78 thf(func_def_118, type, j: denota723907260t_unit).
% 2.75/1.78 thf(func_def_119, type, nu: produc133005365real_b).
% 2.75/1.78 thf(func_def_120, type, nu2: produc133005365real_b).
% 2.75/1.78 thf(func_def_121, type, theta_1: trm_a_b).
% 2.75/1.78 thf(func_def_122, type, theta_2: trm_a_b).
% 2.75/1.78 thf(func_def_136, type, sK0: (trm_a_b > $o) > frechet_strm_a_b).
% 2.75/1.78 thf(func_def_137, type, sK1: trm_a_b > frechet_strm_a_b).
% 2.75/1.78 thf(func_def_138, type, sK2: denota723907260t_unit > freche1734198479_a_c_b).
% 2.75/1.78 thf(func_def_139, type, sK3: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_140, type, sK4: set_trm_a_b > set_trm_a_b > trm_a_b).
% 2.75/1.78 thf(func_def_141, type, sK5: set_a > set_a > a).
% 2.75/1.78 thf(func_def_142, type, sK6: a).
% 2.75/1.78 thf(func_def_143, type, sK7: (a > $o) > (a > $o) > a).
% 2.75/1.78 thf(func_def_144, type, sK8: frechet_strm_a_b > trm_a_b).
% 2.75/1.78 thf(func_def_145, type, sK9: (denota723907260t_unit > $o) > freche1734198479_a_c_b).
% 2.75/1.78 thf(func_def_146, type, sK10: freche1734198479_a_c_b > denota723907260t_unit).
% 2.75/1.78 thf(func_def_147, type, sK11: (trm_a_b > $o) > (trm_a_b > $o) > trm_a_b).
% 2.75/1.78 thf(func_def_148, type, sK12: (frechet_strm_a_b > $o) > trm_a_b).
% 2.75/1.78 thf(func_def_149, type, sK13: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_150, type, sK14: set_a > a).
% 2.75/1.78 thf(func_def_151, type, sK15: (finite824932053eal_sz > real) > real > set_Fi291318197eal_sz > (finite824932053eal_sz > bounde472938360z_real) > (finite824932053eal_sz > bounde472938360z_real) > finite824932053eal_sz).
% 2.75/1.78 thf(func_def_152, type, sK16: (freche1734198479_a_c_b > $o) > denota723907260t_unit).
% 2.75/1.78 thf(func_def_153, type, sK17: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_156, type, sK19: (sum_su1965225555um_c_b > $o) > set_Su111624115um_c_b > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_157, type, sK20: set_Su111624115um_c_b > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_158, type, sK21: (sum_su1965225555um_c_b > $o) > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_159, type, sK22: (sum_su1965225555um_c_b > $o) > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_161, type, sK23: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_162, type, sK24: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_163, type, sK25: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_164, type, sK26: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_165, type, sK27: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_166, type, sK28: set_a > set_a > set_a > a).
% 2.75/1.78 thf(func_def_167, type, sK29: set_a > set_a > a).
% 2.75/1.78 thf(func_def_168, type, sK30: set_a > set_a > a).
% 2.75/1.78 thf(func_def_169, type, sK31: set_a > set_a > a).
% 2.75/1.78 thf(func_def_170, type, sK32: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_171, type, sK33: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_172, type, sK34: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_173, type, sK35: set_a > set_a > a).
% 2.75/1.78 thf(func_def_174, type, sK36: set_a > set_a > a).
% 2.75/1.78 thf(func_def_175, type, sK37: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_176, type, sK38: (sum_sum_b_b > $o) > set_Sum_sum_b_b > set_Sum_sum_b_b > sum_sum_b_b).
% 2.75/1.78 thf(func_def_177, type, sK39: (sum_sum_b_b > $o) > set_Sum_sum_b_b > set_Sum_sum_b_b > sum_sum_b_b).
% 2.75/1.78 thf(func_def_178, type, sK40: (sum_sum_b_b > $o) > set_Sum_sum_b_b > sum_sum_b_b).
% 2.75/1.78 thf(func_def_179, type, sK41: (sum_sum_b_b > $o) > set_Sum_sum_b_b > sum_sum_b_b).
% 2.75/1.78 thf(func_def_180, type, sK42: (sum_sum_b_b > $o) > set_Sum_sum_b_b > sum_sum_b_b).
% 2.75/1.78 thf(func_def_181, type, sK43: set_a > set_a > a).
% 2.75/1.78 thf(func_def_182, type, sK44: set_a > set_a > a).
% 2.75/1.78 thf(func_def_183, type, sK45: set_a > set_a > a).
% 2.75/1.78 thf(func_def_184, type, sK46: set_a > set_a > set_a > a).
% 2.75/1.78 thf(func_def_185, type, sK47: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_186, type, sK48: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_187, type, sK49: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_188, type, sK50: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_189, type, sK51: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_190, type, sK52: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_191, type, sK53: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_192, type, sK54: set_a > set_a > set_a > a).
% 2.75/1.78 thf(func_def_193, type, sK55: set_a > set_a > a).
% 2.75/1.78 thf(func_def_194, type, sK56: set_a > set_a > a).
% 2.75/1.78 thf(func_def_195, type, sK57: set_a > set_a > a).
% 2.75/1.78 thf(func_def_196, type, sK58: set_a > set_a > a).
% 2.75/1.78 thf(func_def_197, type, sK59: set_a > set_a > a).
% 2.75/1.78 thf(func_def_198, type, sK60: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_199, type, sK61: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_200, type, sK62: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_201, type, sK63: set_Su111624115um_c_b > set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_202, type, sK64: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_203, type, sK65: (sum_su1965225555um_c_b > $o) > (sum_su1965225555um_c_b > $o) > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_204, type, sK66: set_Sum_sum_b_b > set_Sum_sum_b_b > (sum_sum_b_b > $o) > sum_sum_b_b).
% 2.75/1.78 thf(func_def_205, type, sK67: set_Sum_sum_b_b > set_Sum_sum_b_b > (sum_sum_b_b > $o) > sum_sum_b_b).
% 2.75/1.78 thf(func_def_206, type, sK68: set_Sum_sum_b_b > (sum_sum_b_b > $o) > sum_sum_b_b).
% 2.75/1.78 thf(func_def_207, type, sK69: set_Sum_sum_b_b > (sum_sum_b_b > $o) > sum_sum_b_b).
% 2.75/1.78 thf(func_def_208, type, sK70: set_Su111624115um_c_b > sum_su1965225555um_c_b).
% 2.75/1.78 thf(func_def_210, type, ph71: !>[X0: $tType]:(X0)).
% 2.75/1.78 thf(f2273,plain,(
% 2.75/1.78 $false),
% 2.75/1.78 inference(subsumption_resolution,[status(thm)],[f2271,f1116])).
% 2.75/1.78 thf(f1116,plain,(
% 2.75/1.78 ($true != (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))),
% 2.75/1.78 inference(cnf_transformation,[status(thm)],[f926])).
% 2.75/1.78 thf(f926,plain,(
% 2.75/1.78 ($true != (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))),
% 2.75/1.78 inference(flattening,[status(thm)],[f871])).
% 2.75/1.78 thf(f871,plain,(
% 2.75/1.78 ~($true = (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))),
% 2.75/1.78 inference(fool_elimination,[status(thm)],[f870])).
% 2.75/1.78 thf(f870,plain,(
% 2.75/1.78 ~(denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[X0 : sum_su1965225555um_c_b] : (? [X1 : a] : (((sum_In811702836um_c_b @ X1) = X0) & (member_a @ X1 @ (static_SIGT_a_b @ theta_1)))))))),
% 2.75/1.78 inference(rectify,[status(thm)],[f360])).
% 2.75/1.78 thf(f360,negated_conjecture,(
% 2.75/1.78 ~(denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : (((sum_In811702836um_c_b @ X3) = X2) & (member_a @ X3 @ (static_SIGT_a_b @ theta_1)))))))),
% 2.75/1.78 inference(negated_conjecture,[status(cth)],[f359])).
% 2.75/1.78 thf(f359,conjecture,(
% 2.75/1.78 (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : (((sum_In811702836um_c_b @ X3) = X2) & (member_a @ X3 @ (static_SIGT_a_b @ theta_1)))))))),
% 2.75/1.78 file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',conj_0)).
% 2.75/1.78 thf(f2271,plain,(
% 2.75/1.78 ($true = (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))),
% 2.75/1.78 inference(trivial_inequality_removal,[status(thm)],[f2269])).
% 2.75/1.78 thf(f2269,plain,(
% 2.75/1.78 ($true != $true) | ($true = (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))),
% 2.75/1.78 inference(superposition,[status(thm)],[f1209,f1140])).
% 2.75/1.78 thf(f1140,plain,(
% 2.75/1.78 ($true = (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: (((sum_In811702836um_c_b @ Y1) = Y0) & (member_a @ Y1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))))))))))),
% 2.75/1.78 inference(cnf_transformation,[status(thm)],[f845])).
% 2.75/1.78 thf(f845,plain,(
% 2.75/1.78 ($true = (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: (((sum_In811702836um_c_b @ Y1) = Y0) & (member_a @ Y1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))))))))))),
% 2.75/1.78 inference(fool_elimination,[status(thm)],[f844])).
% 2.75/1.78 thf(f844,plain,(
% 2.75/1.78 (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[X0 : sum_su1965225555um_c_b] : (? [X1 : a] : ((member_a @ X1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))) & ((sum_In811702836um_c_b @ X1) = X0))))))),
% 2.75/1.78 inference(rectify,[status(thm)],[f4])).
% 2.75/1.78 thf(f4,axiom,(
% 2.75/1.78 (denota896875430_a_c_b @ i @ j @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : ((member_a @ X3 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))) & ((sum_In811702836um_c_b @ X3) = X2))))))),
% 2.75/1.78 file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',fact_3_dfree__Times_Oprems_I2_J)).
% 2.75/1.78 thf(f1209,plain,(
% 2.75/1.78 ( ! [X0 : denota723907260t_unit,X1 : denota723907260t_unit] : (($true != (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: (((sum_In811702836um_c_b @ Y1) = Y0) & (member_a @ Y1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2)))))))))) | ($true = (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0))))))))) )),
% 2.75/1.78 inference(cnf_transformation,[status(thm)],[f960])).
% 2.75/1.78 thf(f960,plain,(
% 2.75/1.78 ! [X0 : denota723907260t_unit,X1 : denota723907260t_unit] : (($true != (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: (((sum_In811702836um_c_b @ Y1) = Y0) & (member_a @ Y1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2)))))))))) | ($true = (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0)))))))))),
% 2.75/1.78 inference(ennf_transformation,[status(thm)],[f531])).
% 2.75/1.78 thf(f531,plain,(
% 2.75/1.78 ! [X0 : denota723907260t_unit,X1 : denota723907260t_unit] : (($true = (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: (((sum_In811702836um_c_b @ Y1) = Y0) & (member_a @ Y1 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2)))))))))) => ($true = (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[Y0 : sum_su1965225555um_c_b]: (?? @ a @ (^[Y1 : a]: ((member_a @ Y1 @ (static_SIGT_a_b @ theta_1)) & ((sum_In811702836um_c_b @ Y1) = Y0)))))))))),
% 2.75/1.78 inference(fool_elimination,[status(thm)],[f530])).
% 2.75/1.78 thf(f530,plain,(
% 2.75/1.78 ! [X0 : denota723907260t_unit,X1 : denota723907260t_unit] : ((denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : ((member_a @ X3 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))) & ((sum_In811702836um_c_b @ X3) = X2)))))) => (denota896875430_a_c_b @ X1 @ X0 @ (collec1166375742um_c_b @ (^[X4 : sum_su1965225555um_c_b] : (? [X5 : a] : (((sum_In811702836um_c_b @ X5) = X4) & (member_a @ X5 @ (static_SIGT_a_b @ theta_1))))))))),
% 2.75/1.78 inference(rectify,[status(thm)],[f1])).
% 2.75/1.78 thf(f1,axiom,(
% 2.75/1.78 ! [X1 : denota723907260t_unit,X0 : denota723907260t_unit] : ((denota896875430_a_c_b @ X0 @ X1 @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : ((member_a @ X3 @ (static_SIGT_a_b @ (times_a_b @ theta_1 @ theta_2))) & ((sum_In811702836um_c_b @ X3) = X2)))))) => (denota896875430_a_c_b @ X0 @ X1 @ (collec1166375742um_c_b @ (^[X2 : sum_su1965225555um_c_b] : (? [X3 : a] : (((sum_In811702836um_c_b @ X3) = X2) & (member_a @ X3 @ (static_SIGT_a_b @ theta_1))))))))),
% 2.75/1.78 file('/export/starexec/sandbox/tmp/tmp.NhliTiQjPu/DTF2THF_20266.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062)).
% 2.75/1.78 % SZS output end Proof for DTF2THF_20266
% 2.75/1.78 % (20401)------------------------------
% 2.75/1.78 % (20401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.78 % (20401)Termination reason: Refutation
% 2.75/1.78
% 2.75/1.78 % (20401)Memory used [KB]: 7419
% 2.75/1.78 % (20401)Time elapsed: 0.120 s
% 2.75/1.78 % (20401)Instructions burned: 292 (million)
% 2.75/1.78 % (20401)------------------------------
% 2.75/1.78 % (20401)------------------------------
% 2.75/1.78 % (20371)Success in time 0.244 s
%------------------------------------------------------------------------------