%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP040^1 : 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 : n003.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 08:55:04 AM UTC 2026
% Result : ContradictoryAxioms 3.12s 1.71s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 86 ( 8 ~; 3 |; 0 &; 72 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 34 ( 33 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 163 ( 160 usr; 18 con; 0-4 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
formula_a_b_c: $tType ).
thf(type_def_7,type,
denota231621370t_unit: $tType ).
thf(type_def_8,type,
oDE_a_c: $tType ).
thf(type_def_9,type,
finite1398487019real_c: $tType ).
thf(type_def_10,type,
set_c: $tType ).
thf(type_def_11,type,
produc190496183real_c: $tType ).
thf(type_def_12,type,
set_Sum_sum_c_c: $tType ).
thf(type_def_13,type,
set_Pr1389752855real_c: $tType ).
thf(type_def_14,type,
c: $tType ).
thf(type_def_15,type,
real: $tType ).
thf(type_def_16,type,
set_re2066790124real_c: $tType ).
thf(type_def_17,type,
set_re1692486081real_c: $tType ).
thf(type_def_18,type,
set_re844416664real_c: $tType ).
thf(type_def_19,type,
set_re366411824um_c_c: $tType ).
thf(type_def_20,type,
set_Sum_sum_c_d: $tType ).
thf(type_def_21,type,
set_re1812065969um_c_d: $tType ).
thf(type_def_22,type,
set_re141277793al_c_c: $tType ).
thf(type_def_23,type,
set_real: $tType ).
thf(type_def_24,type,
set_Fi1407883041real_c: $tType ).
thf(type_def_25,type,
sum_sum_c_c: $tType ).
thf(type_def_26,type,
set_Su1710027039um_c_c: $tType ).
thf(type_def_27,type,
set_Su1008197536um_c_d: $tType ).
thf(type_def_28,type,
set_Sum_sum_c_c_c: $tType ).
thf(type_def_29,type,
sum_sum_c_d: $tType ).
thf(type_def_30,type,
set_Su1997276704um_c_c: $tType ).
thf(type_def_31,type,
set_Sum_sum_c_d_c: $tType ).
thf(type_def_32,type,
set_c_655950471real_c: $tType ).
thf(type_def_33,type,
set_c_Sum_sum_c_c: $tType ).
thf(type_def_34,type,
set_c_Sum_sum_c_d: $tType ).
thf(type_def_35,type,
set_c_c: $tType ).
thf(type_def_36,type,
produc214722967um_c_c: $tType ).
thf(type_def_37,type,
produc957004601l_real: $tType ).
thf(type_def_38,type,
d: $tType ).
thf(func_def_0,type,
set_re844416664real_c: $tType ).
thf(func_def_1,type,
set_re1692486081real_c: $tType ).
thf(func_def_2,type,
set_Pr1389752855real_c: $tType ).
thf(func_def_3,type,
produc190496183real_c: $tType ).
thf(func_def_4,type,
set_re1812065969um_c_d: $tType ).
thf(func_def_5,type,
set_re366411824um_c_c: $tType ).
thf(func_def_6,type,
produc214722967um_c_c: $tType ).
thf(func_def_7,type,
set_c_655950471real_c: $tType ).
thf(func_def_8,type,
set_re141277793al_c_c: $tType ).
thf(func_def_9,type,
set_re2066790124real_c: $tType ).
thf(func_def_10,type,
denota231621370t_unit: $tType ).
thf(func_def_11,type,
set_Su1997276704um_c_c: $tType ).
thf(func_def_12,type,
set_Su1008197536um_c_d: $tType ).
thf(func_def_13,type,
set_Su1710027039um_c_c: $tType ).
thf(func_def_14,type,
set_Fi1407883041real_c: $tType ).
thf(func_def_15,type,
set_c_Sum_sum_c_d: $tType ).
thf(func_def_16,type,
set_c_Sum_sum_c_c: $tType ).
thf(func_def_17,type,
set_Sum_sum_c_d_c: $tType ).
thf(func_def_18,type,
set_Sum_sum_c_c_c: $tType ).
thf(func_def_19,type,
finite1398487019real_c: $tType ).
thf(func_def_20,type,
produc957004601l_real: $tType ).
thf(func_def_21,type,
set_Sum_sum_c_d: $tType ).
thf(func_def_22,type,
set_Sum_sum_c_c: $tType ).
thf(func_def_23,type,
formula_a_b_c: $tType ).
thf(func_def_24,type,
sum_sum_c_d: $tType ).
thf(func_def_25,type,
sum_sum_c_c: $tType ).
thf(func_def_26,type,
set_c_c: $tType ).
thf(func_def_27,type,
oDE_a_c: $tType ).
thf(func_def_28,type,
set_real: $tType ).
thf(func_def_29,type,
set_c: $tType ).
thf(func_def_30,type,
real: $tType ).
thf(func_def_31,type,
d: $tType ).
thf(func_def_32,type,
c: $tType ).
thf(func_def_33,type,
coinci501627771_a_b_c: formula_a_b_c > $o ).
thf(func_def_34,type,
denota1275485728_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > finite1398487019real_c ).
thf(func_def_35,type,
denota540094197_a_b_c: denota231621370t_unit > oDE_a_c > set_c ).
thf(func_def_36,type,
denota256060419gree_c: finite1398487019real_c > finite1398487019real_c > set_c > $o ).
thf(func_def_37,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(func_def_38,type,
denota310462944_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_39,type,
denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
thf(func_def_40,type,
denota161327353_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_41,type,
denota1896987029_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_42,type,
denotational_repd_c: produc190496183real_c > c > real > produc190496183real_c ).
thf(func_def_43,type,
denota1293057250_a_b_c: denota231621370t_unit > oDE_a_c > set_Sum_sum_c_c ).
thf(func_def_44,type,
finite557796307c_real: ( c > real ) > finite1398487019real_c ).
thf(func_def_45,type,
finite772340578real_c: finite1398487019real_c > c > real ).
thf(func_def_46,type,
pi_rea1386151481real_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_re2066790124real_c ) > set_re1692486081real_c ).
thf(func_def_47,type,
pi_rea1379668980real_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Pr1389752855real_c ) > set_re844416664real_c ).
thf(func_def_48,type,
pi_rea1500330408um_c_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Sum_sum_c_c ) > set_re366411824um_c_c ).
thf(func_def_49,type,
pi_rea1508591913um_c_d: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Sum_sum_c_d ) > set_re1812065969um_c_d ).
thf(func_def_50,type,
pi_rea1228756413al_c_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_c ) > set_re141277793al_c_c ).
thf(func_def_51,type,
pi_rea1111636068real_c: set_real > ( real > set_Fi1407883041real_c ) > set_re2066790124real_c ).
thf(func_def_52,type,
pi_Sum253006871um_c_c: set_Sum_sum_c_c > ( sum_sum_c_c > set_Sum_sum_c_c ) > set_Su1710027039um_c_c ).
thf(func_def_53,type,
pi_Sum261268376um_c_d: set_Sum_sum_c_c > ( sum_sum_c_c > set_Sum_sum_c_d ) > set_Su1008197536um_c_d ).
thf(func_def_54,type,
pi_Sum_sum_c_c_c: set_Sum_sum_c_c > ( sum_sum_c_c > set_c ) > set_Sum_sum_c_c_c ).
thf(func_def_55,type,
pi_Sum1145067928um_c_c: set_Sum_sum_c_d > ( sum_sum_c_d > set_Sum_sum_c_c ) > set_Su1997276704um_c_c ).
thf(func_def_56,type,
pi_Sum_sum_c_d_c: set_Sum_sum_c_d > ( sum_sum_c_d > set_c ) > set_Sum_sum_c_d_c ).
thf(func_def_57,type,
pi_c_r41638571real_c: set_c > ( c > set_re2066790124real_c ) > set_c_655950471real_c ).
thf(func_def_58,type,
pi_c_Sum_sum_c_c: set_c > ( c > set_Sum_sum_c_c ) > set_c_Sum_sum_c_c ).
thf(func_def_59,type,
pi_c_Sum_sum_c_d: set_c > ( c > set_Sum_sum_c_d ) > set_c_Sum_sum_c_d ).
thf(func_def_60,type,
pi_c_c: set_c > ( c > set_c ) > set_c_c ).
thf(func_def_61,type,
uminus1756072592al_c_o: ( ( real > finite1398487019real_c ) > $o ) > ( real > finite1398487019real_c ) > $o ).
thf(func_def_62,type,
uminus23580315al_c_o: ( finite1398487019real_c > $o ) > finite1398487019real_c > $o ).
thf(func_def_63,type,
uminus32155087al_c_o: ( produc190496183real_c > $o ) > produc190496183real_c > $o ).
thf(func_def_64,type,
uminus88729697_c_c_o: ( sum_sum_c_c > $o ) > sum_sum_c_c > $o ).
thf(func_def_65,type,
uminus916499104_c_d_o: ( sum_sum_c_d > $o ) > sum_sum_c_d > $o ).
thf(func_def_66,type,
uminus_uminus_c_o: ( c > $o ) > c > $o ).
thf(func_def_67,type,
uminus1737280820real_c: finite1398487019real_c > finite1398487019real_c ).
thf(func_def_68,type,
uminus17964590real_c: produc190496183real_c > produc190496183real_c ).
thf(func_def_69,type,
uminus1225118734um_c_c: produc214722967um_c_c > produc214722967um_c_c ).
thf(func_def_70,type,
uminus_uminus_real: real > real ).
thf(func_def_71,type,
uminus946614837real_c: set_re2066790124real_c > set_re2066790124real_c ).
thf(func_def_72,type,
uminus102402154real_c: set_Fi1407883041real_c > set_Fi1407883041real_c ).
thf(func_def_73,type,
uminus232257166real_c: set_Pr1389752855real_c > set_Pr1389752855real_c ).
thf(func_def_74,type,
uminus1381786404um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_75,type,
uminus373867045um_c_d: set_Sum_sum_c_d > set_Sum_sum_c_d ).
thf(func_def_76,type,
uminus_uminus_set_c: set_c > set_c ).
thf(func_def_77,type,
zero_z109254132real_c: finite1398487019real_c ).
thf(func_def_78,type,
zero_z1506780526real_c: produc190496183real_c ).
thf(func_def_79,type,
zero_z659284464l_real: produc957004601l_real ).
thf(func_def_80,type,
zero_zero_real: real ).
thf(func_def_81,type,
if_Fin36944805real_c: $o > finite1398487019real_c > finite1398487019real_c > finite1398487019real_c ).
thf(func_def_82,type,
if_real: $o > real > real > real ).
thf(func_def_83,type,
initia1631504802real_c: ( real > finite1398487019real_c ) > ( real > finite1398487019real_c > finite1398487019real_c ) > set_real > set_Fi1407883041real_c > $o ).
thf(func_def_84,type,
ord_le818951225al_c_o: ( ( real > finite1398487019real_c ) > $o ) > ( ( real > finite1398487019real_c ) > $o ) > $o ).
thf(func_def_85,type,
ord_le1132241894al_c_o: ( produc190496183real_c > $o ) > ( produc190496183real_c > $o ) > $o ).
thf(func_def_86,type,
ord_le584953750real_c: ( real > finite1398487019real_c ) > ( real > finite1398487019real_c ) > $o ).
thf(func_def_87,type,
ord_le1315653386_c_c_o: ( sum_sum_c_c > $o ) > ( sum_sum_c_c > $o ) > $o ).
thf(func_def_88,type,
ord_le2143422793_c_d_o: ( sum_sum_c_d > $o ) > ( sum_sum_c_d > $o ) > $o ).
thf(func_def_89,type,
ord_less_eq_c_o: ( c > $o ) > ( c > $o ) > $o ).
thf(func_def_90,type,
ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o ).
thf(func_def_91,type,
ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o ).
thf(func_def_92,type,
ord_le1342644953l_real: produc957004601l_real > produc957004601l_real > $o ).
thf(func_def_93,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_94,type,
ord_le35002188real_c: set_re2066790124real_c > set_re2066790124real_c > $o ).
thf(func_def_95,type,
ord_le1327118209real_c: set_Fi1407883041real_c > set_Fi1407883041real_c > $o ).
thf(func_def_96,type,
ord_le977353143real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > $o ).
thf(func_def_97,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(func_def_98,type,
ord_le1772180283um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > $o ).
thf(func_def_99,type,
ord_le764260924um_c_d: set_Sum_sum_c_d > set_Sum_sum_c_d > $o ).
thf(func_def_100,type,
ord_less_eq_set_c: set_c > set_c > $o ).
thf(func_def_101,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_102,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(func_def_103,type,
produc1439061071um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > produc214722967um_c_c ).
thf(func_def_104,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_105,type,
produc1422991709l_real: produc957004601l_real > real ).
thf(func_def_106,type,
produc1983230011um_c_c: produc214722967um_c_c > set_Sum_sum_c_c ).
thf(func_def_107,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_108,type,
produc1407670175l_real: produc957004601l_real > real ).
thf(func_def_109,type,
produc1132019837um_c_c: produc214722967um_c_c > set_Sum_sum_c_c ).
thf(func_def_110,type,
collec913357835real_c: ( ( real > finite1398487019real_c ) > $o ) > set_re2066790124real_c ).
thf(func_def_111,type,
collec230941376real_c: ( finite1398487019real_c > $o ) > set_Fi1407883041real_c ).
thf(func_def_112,type,
collec1643251106real_c: ( produc190496183real_c > $o ) > set_Pr1389752855real_c ).
thf(func_def_113,type,
collect_Sum_sum_c_c: ( sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
thf(func_def_114,type,
collect_Sum_sum_c_d: ( sum_sum_c_d > $o ) > set_Sum_sum_c_d ).
thf(func_def_115,type,
collect_c: ( c > $o ) > set_c ).
thf(func_def_116,type,
image_266490115al_c_c: ( ( real > finite1398487019real_c ) > c ) > set_re2066790124real_c > set_c ).
thf(func_def_117,type,
image_1260608398al_c_c: ( finite1398487019real_c > c ) > set_Fi1407883041real_c > set_c ).
thf(func_def_118,type,
image_327677598real_c: ( real > finite1398487019real_c ) > set_real > set_Fi1407883041real_c ).
thf(func_def_119,type,
image_real_real: ( real > real ) > set_real > set_real ).
thf(func_def_120,type,
image_666880337um_c_c: ( sum_sum_c_c > sum_sum_c_c ) > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(func_def_121,type,
image_675141842um_c_d: ( sum_sum_c_c > sum_sum_c_d ) > set_Sum_sum_c_c > set_Sum_sum_c_d ).
thf(func_def_122,type,
image_Sum_sum_c_c_c: ( sum_sum_c_c > c ) > set_Sum_sum_c_c > set_c ).
thf(func_def_123,type,
image_1558941394um_c_c: ( sum_sum_c_d > sum_sum_c_c ) > set_Sum_sum_c_d > set_Sum_sum_c_c ).
thf(func_def_124,type,
image_1567202899um_c_d: ( sum_sum_c_d > sum_sum_c_d ) > set_Sum_sum_c_d > set_Sum_sum_c_d ).
thf(func_def_125,type,
image_Sum_sum_c_d_c: ( sum_sum_c_d > c ) > set_Sum_sum_c_d > set_c ).
thf(func_def_126,type,
image_1226855921real_c: ( c > real > finite1398487019real_c ) > set_c > set_re2066790124real_c ).
thf(func_def_127,type,
image_687300774real_c: ( c > finite1398487019real_c ) > set_c > set_Fi1407883041real_c ).
thf(func_def_128,type,
image_c_Sum_sum_c_c: ( c > sum_sum_c_c ) > set_c > set_Sum_sum_c_c ).
thf(func_def_129,type,
image_c_Sum_sum_c_d: ( c > sum_sum_c_d ) > set_c > set_Sum_sum_c_d ).
thf(func_def_130,type,
image_c_c: ( c > c ) > set_c > set_c ).
thf(func_def_131,type,
set_or1308937537real_c: ( real > finite1398487019real_c ) > ( real > finite1398487019real_c ) > set_re2066790124real_c ).
thf(func_def_132,type,
set_or385782508real_c: produc190496183real_c > produc190496183real_c > set_Pr1389752855real_c ).
thf(func_def_133,type,
set_or656347191t_real: real > real > set_real ).
thf(func_def_134,type,
static_BVO_a_c: oDE_a_c > set_Sum_sum_c_c ).
thf(func_def_135,type,
static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
thf(func_def_136,type,
static_FVO_a_c: oDE_a_c > set_c ).
thf(func_def_137,type,
sum_Inl_c_c: c > sum_sum_c_c ).
thf(func_def_138,type,
sum_Inl_c_d: c > sum_sum_c_d ).
thf(func_def_139,type,
sum_Inr_c_c: c > sum_sum_c_c ).
thf(func_def_140,type,
sum_Inr_d_c: d > sum_sum_c_d ).
thf(func_def_141,type,
equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
thf(func_def_142,type,
fsafe_a_b_c: formula_a_b_c > $o ).
thf(func_def_143,type,
osafe_a_c: oDE_a_c > $o ).
thf(func_def_144,type,
member1851015714real_c: ( ( real > finite1398487019real_c ) > real > finite1398487019real_c ) > set_re1692486081real_c > $o ).
thf(func_def_145,type,
member954762593real_c: ( ( real > finite1398487019real_c ) > produc190496183real_c ) > set_re844416664real_c > $o ).
thf(func_def_146,type,
member354622481um_c_c: ( ( real > finite1398487019real_c ) > sum_sum_c_c ) > set_re366411824um_c_c > $o ).
thf(func_def_147,type,
member1494186770um_c_d: ( ( real > finite1398487019real_c ) > sum_sum_c_d ) > set_re1812065969um_c_d > $o ).
thf(func_def_148,type,
member527957930al_c_c: ( ( real > finite1398487019real_c ) > c ) > set_re141277793al_c_c > $o ).
thf(func_def_149,type,
member1321351885real_c: ( real > finite1398487019real_c ) > set_re2066790124real_c > $o ).
thf(func_def_150,type,
member1326674048um_c_c: ( sum_sum_c_c > sum_sum_c_c ) > set_Su1710027039um_c_c > $o ).
thf(func_def_151,type,
member318754689um_c_d: ( sum_sum_c_c > sum_sum_c_d ) > set_Su1008197536um_c_d > $o ).
thf(func_def_152,type,
member_Sum_sum_c_c_c: ( sum_sum_c_c > c ) > set_Sum_sum_c_c_c > $o ).
thf(func_def_153,type,
member71251457um_c_c: ( sum_sum_c_d > sum_sum_c_c ) > set_Su1997276704um_c_c > $o ).
thf(func_def_154,type,
member_Sum_sum_c_d_c: ( sum_sum_c_d > c ) > set_Sum_sum_c_d_c > $o ).
thf(func_def_155,type,
member469531344real_c: ( c > real > finite1398487019real_c ) > set_c_655950471real_c > $o ).
thf(func_def_156,type,
member_c_Sum_sum_c_c: ( c > sum_sum_c_c ) > set_c_Sum_sum_c_c > $o ).
thf(func_def_157,type,
member_c_Sum_sum_c_d: ( c > sum_sum_c_d ) > set_c_Sum_sum_c_d > $o ).
thf(func_def_158,type,
member_c_c: ( c > c ) > set_c_c > $o ).
thf(func_def_159,type,
member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o ).
thf(func_def_160,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(func_def_161,type,
member_real: real > set_real > $o ).
thf(func_def_162,type,
member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
thf(func_def_163,type,
member_Sum_sum_c_d: sum_sum_c_d > set_Sum_sum_c_d > $o ).
thf(func_def_164,type,
member_c: c > set_c > $o ).
thf(func_def_165,type,
i: denota231621370t_unit ).
thf(func_def_166,type,
ode: oDE_a_c ).
thf(func_def_167,type,
oDEa: oDE_a_c ).
thf(func_def_168,type,
p: formula_a_b_c ).
thf(func_def_169,type,
phi: formula_a_b_c ).
thf(func_def_170,type,
aa: finite1398487019real_c ).
thf(func_def_171,type,
ab: finite1398487019real_c ).
thf(func_def_172,type,
ba: finite1398487019real_c ).
thf(func_def_173,type,
bb: finite1398487019real_c ).
thf(func_def_174,type,
i2: c ).
thf(func_def_175,type,
sol: real > finite1398487019real_c ).
thf(func_def_176,type,
t: real ).
thf(func_def_177,type,
x: real ).
thf(func_def_193,type,
sK0: produc190496183real_c > finite1398487019real_c ).
thf(func_def_194,type,
sK1: produc190496183real_c > finite1398487019real_c ).
thf(func_def_195,type,
sK2: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_196,type,
sK3: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_197,type,
sK4: ( sum_sum_c_c > $o ) > set_c > ( c > sum_sum_c_c ) > c ).
thf(func_def_198,type,
sK5: ( c > sum_sum_c_c ) > set_c > sum_sum_c_c > c ).
thf(func_def_199,type,
sK6: finite1398487019real_c > ( c > real ) > c ).
thf(func_def_200,type,
sK7: ( c > sum_sum_c_c ) > ( c > sum_sum_c_c ) > set_c > c ).
thf(func_def_201,type,
sK8: ( sum_sum_c_c > $o ) > ( c > sum_sum_c_c ) > set_c > sum_sum_c_c ).
thf(func_def_202,type,
sK9: produc190496183real_c > finite1398487019real_c ).
thf(func_def_203,type,
sK10: produc190496183real_c > finite1398487019real_c ).
thf(func_def_204,type,
sK11: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_205,type,
sK12: ( produc190496183real_c > $o ) > finite1398487019real_c ).
thf(func_def_206,type,
sK13: set_c > ( c > sum_sum_c_c ) > sum_sum_c_c > c ).
thf(func_def_208,type,
ph15:
!>[X0: $tType] : X0 ).
thf(f1255,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1254,f1162]) ).
thf(f1162,plain,
( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1001]) ).
thf(f1001,plain,
( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
!= $true ),
inference(flattening,[status(thm)],[f497]) ).
thf(f497,plain,
( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f496]) ).
thf(f496,plain,
~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,axiom,
~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ),
file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',conj_2) ).
thf(f1254,plain,
( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1253]) ).
thf(f1253,plain,
( ( $true != $true )
| ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
= $true ) ),
inference(superposition,[status(thm)],[f1096,f1132]) ).
thf(f1132,plain,
( ( member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ) )
= $true ),
inference(fool_elimination,[status(thm)],[f422]) ).
thf(f422,plain,
member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ),
inference(rectify,[status(thm)],[f359]) ).
thf(f359,axiom,
member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ),
file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',conj_1) ).
thf(f1096,plain,
! [X2: oDE_a_c,X0: c,X1: denota231621370t_unit] :
( ( ( member_c @ X0 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
!= $true )
| ( ( member_c @ X0 @ ( static_FVO_a_c @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1047]) ).
thf(f1047,plain,
! [X0: c,X1: denota231621370t_unit,X2: oDE_a_c] :
( ( ( member_c @ X0 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
!= $true )
| ( ( member_c @ X0 @ ( static_FVO_a_c @ X2 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f451]) ).
thf(f451,plain,
! [X0: c,X1: denota231621370t_unit,X2: oDE_a_c] :
( ( ( member_c @ X0 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
= $true )
=> ( ( member_c @ X0 @ ( static_FVO_a_c @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f450]) ).
thf(f450,plain,
! [X0: c,X1: denota231621370t_unit,X2: oDE_a_c] :
( ( member_c @ X0 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
=> ( member_c @ X0 @ ( static_FVO_a_c @ X2 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: c,X1: denota231621370t_unit,X2: oDE_a_c] :
( ( member_c @ X0 @ ( denota540094197_a_b_c @ X1 @ X2 ) )
=> ( member_c @ X0 @ ( static_FVO_a_c @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',fact_0_ode__to__fvo) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP040^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:26:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP040^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer Coincidence problem prob_718__7224732_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : Coincidence/prob_718__7224732_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : ContradictoryAxioms
% 0.29/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 547 ( 170 unt; 178 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1039 ( 297 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.29/0.46 % Number of connectives : 3951 ( 92 ~; 9 |; 68 &;3407 @)
% 0.29/0.46 % ( 0 <=>; 375 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 17 ( 6 avg)
% 0.29/0.46 % Number of types : 34 ( 33 usr)
% 0.29/0.46 % Number of type conns : 622 ( 622 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 148 ( 145 usr; 18 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 1129 ( 213 ^; 905 !; 11 ?;1129 :)
% 0.29/0.46 % SPC : TH0_CAX_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:42:28.764
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (33)
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.29/0.46 set_re844416664real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.29/0.46 set_re1692486081real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.29/0.46 set_Pr1389752855real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.29/0.46 produc190496183real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 0.29/0.46 set_re1812065969um_c_d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.29/0.46 set_re366411824um_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.29/0.46 produc214722967um_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_Itf__c_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.29/0.46 set_c_655950471real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mtf__c_J_J,type,
% 0.29/0.46 set_re141277793al_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.29/0.46 set_re2066790124real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 0.29/0.46 denota231621370t_unit: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.29/0.46 set_Su1997276704um_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 0.29/0.46 set_Su1008197536um_c_d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.29/0.46 set_Su1710027039um_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.29/0.46 set_Fi1407883041real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 0.29/0.46 set_c_Sum_sum_c_d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.29/0.46 set_c_Sum_sum_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mtf__c_J_J,type,
% 0.29/0.46 set_Sum_sum_c_d_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mtf__c_J_J,type,
% 0.29/0.46 set_Sum_sum_c_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.29/0.46 finite1398487019real_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.29/0.46 produc957004601l_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__d_J_J,type,
% 0.29/0.46 set_Sum_sum_c_d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.29/0.46 set_Sum_sum_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Syntax__Oformula_Itf__a_Mtf__b_Mtf__c_J,type,
% 0.29/0.46 formula_a_b_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 0.29/0.46 sum_sum_c_d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 0.29/0.46 sum_sum_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mtf__c_J_J,type,
% 0.29/0.46 set_c_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Syntax__OODE_Itf__a_Mtf__c_J,type,
% 0.29/0.46 oDE_a_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.46 set_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_Itf__c_J,type,
% 0.29/0.46 set_c: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Real__Oreal,type,
% 0.29/0.46 real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_tf__d,type,
% 0.29/0.46 d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_tf__c,type,
% 0.29/0.46 c: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (145)
% 0.29/0.46 thf(sy_c_Coincidence__Mirabelle__veeocdlawq_Oids_Ocoincide__fml_001tf__a_001tf__b_001tf__c,type,
% 0.29/0.46 coinci501627771_a_b_c: formula_a_b_c > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_OODE__sem_001tf__a_001tf__b_001tf__c,type,
% 0.29/0.46 denota1275485728_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > finite1398487019real_c ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_OODE__vars_001tf__a_001tf__b_001tf__c,type,
% 0.29/0.46 denota540094197_a_b_c: denota231621370t_unit > oDE_a_c > set_c ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_OVSagree_001tf__c,type,
% 0.29/0.46 denota256060419gree_c: finite1398487019real_c > finite1398487019real_c > set_c > $o ).
% 0.29/0.46
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% 0.29/0.46 % x
% 0.29/0.46 thf(fact_4_fsafe,axiom,
% 0.29/0.46 fsafe_a_b_c @ phi ).
% 0.29/0.46
% 0.29/0.46 % fsafe
% 0.29/0.46 thf(fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,axiom,
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) )
% 0.29/0.46 = ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>(Inl i \<in> semBV I ODE) = (Inr i \<in> semBV I ODE)\<close>
% 0.29/0.46 thf(fact_6_VA,axiom,
% 0.29/0.46 ! [X: real] :
% 0.29/0.46 ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ X ) )
% 0.29/0.46 @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ X ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.46 @ ( static_FVF_a_b_c @ phi ) ) ).
% 0.29/0.46
% 0.29/0.46 % VA
% 0.29/0.46 thf(fact_7_prod_Ocollapse,axiom,
% 0.29/0.46 ! [Prod: produc190496183real_c] :
% 0.29/0.46 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.29/0.46 = Prod ) ).
% 0.29/0.46
% 0.29/0.46 % prod.collapse
% 0.29/0.46 thf(fact_8_bvo__to__fvo,axiom,
% 0.29/0.46 ! [X: c,ODE: oDE_a_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X ) @ ( static_BVO_a_c @ ODE ) )
% 0.29/0.46 => ( member_c @ X @ ( static_FVO_a_c @ ODE ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bvo_to_fvo
% 0.29/0.46 thf(fact_9_vec__lambda__eta,axiom,
% 0.29/0.46 ! [G: finite1398487019real_c] :
% 0.29/0.46 ( ( finite557796307c_real @ ( finite772340578real_c @ G ) )
% 0.29/0.46 = G ) ).
% 0.29/0.46
% 0.29/0.46 % vec_lambda_eta
% 0.29/0.46 thf(fact_10_Inl__Inr__False,axiom,
% 0.29/0.46 ! [X: c,Y: d] :
% 0.29/0.46 ( ( sum_Inl_c_d @ X )
% 0.29/0.46 != ( sum_Inr_d_c @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % Inl_Inr_False
% 0.29/0.46 thf(fact_11_Inl__Inr__False,axiom,
% 0.29/0.46 ! [X: c,Y: c] :
% 0.29/0.46 ( ( sum_Inl_c_c @ X )
% 0.29/0.46 != ( sum_Inr_c_c @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % Inl_Inr_False
% 0.29/0.46 thf(fact_12_Inr__Inl__False,axiom,
% 0.29/0.46 ! [X: d,Y: c] :
% 0.29/0.46 ( ( sum_Inr_d_c @ X )
% 0.29/0.46 != ( sum_Inl_c_d @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % Inr_Inl_False
% 0.29/0.46 thf(fact_13_Inr__Inl__False,axiom,
% 0.29/0.46 ! [X: c,Y: c] :
% 0.29/0.46 ( ( sum_Inr_c_c @ X )
% 0.29/0.46 != ( sum_Inl_c_c @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % Inr_Inl_False
% 0.29/0.46 thf(fact_14_vec__lambda__beta,axiom,
% 0.29/0.46 ! [G: c > real,I3: c] :
% 0.29/0.46 ( ( finite772340578real_c @ ( finite557796307c_real @ G ) @ I3 )
% 0.29/0.46 = ( G @ I3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % vec_lambda_beta
% 0.29/0.46 thf(fact_15_alt__sem__lemma,axiom,
% 0.29/0.46 ! [ODE: oDE_a_c,I: denota231621370t_unit,Sol: real > finite1398487019real_c,T: real,Ab: finite1398487019real_c] :
% 0.29/0.46 ( ( osafe_a_c @ ODE )
% 0.29/0.46 => ( ( denota1275485728_a_b_c @ I @ ODE @ ( Sol @ T ) )
% 0.29/0.46 = ( denota1275485728_a_b_c @ I @ ODE
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ ODE ) ) @ ( finite772340578real_c @ ( Sol @ T ) @ I2 ) @ ( finite772340578real_c @ Ab @ I2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % alt_sem_lemma
% 0.29/0.46 thf(fact_16_snd__zero,axiom,
% 0.29/0.46 ( ( produc314122909real_c @ zero_z1506780526real_c )
% 0.29/0.46 = zero_z109254132real_c ) ).
% 0.29/0.46
% 0.29/0.46 % snd_zero
% 0.29/0.46 thf(fact_17_fst__zero,axiom,
% 0.29/0.46 ( ( produc2010422875real_c @ zero_z1506780526real_c )
% 0.29/0.46 = zero_z109254132real_c ) ).
% 0.29/0.46
% 0.29/0.46 % fst_zero
% 0.29/0.46 thf(fact_18_zero__index,axiom,
% 0.29/0.46 ! [I3: c] :
% 0.29/0.46 ( ( finite772340578real_c @ zero_z109254132real_c @ I3 )
% 0.29/0.46 = zero_zero_real ) ).
% 0.29/0.46
% 0.29/0.46 % zero_index
% 0.29/0.46 thf(fact_19_hpsafe__Evolve_OIH,axiom,
% 0.29/0.46 coinci501627771_a_b_c @ p ).
% 0.29/0.46
% 0.29/0.46 % hpsafe_Evolve.IH
% 0.29/0.46 thf(fact_20_hpsafe__Evolve_Ohyps_I1_J,axiom,
% 0.29/0.46 osafe_a_c @ ode ).
% 0.29/0.46
% 0.29/0.46 % hpsafe_Evolve.hyps(1)
% 0.29/0.46 thf(fact_21_hpsafe__Evolve_Ohyps_I2_J,axiom,
% 0.29/0.46 fsafe_a_b_c @ p ).
% 0.29/0.46
% 0.29/0.46 % hpsafe_Evolve.hyps(2)
% 0.29/0.46 thf(fact_22_old_Oprod_Oinject,axiom,
% 0.29/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.29/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.29/0.46 = ( produc394644079real_c @ A2 @ B2 ) )
% 0.29/0.46 = ( ( A = A2 )
% 0.29/0.46 & ( B = B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.prod.inject
% 0.29/0.46 thf(fact_23_prod_Oinject,axiom,
% 0.29/0.46 ! [X1: finite1398487019real_c,X2: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 0.29/0.46 ( ( ( produc394644079real_c @ X1 @ X2 )
% 0.29/0.46 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 0.29/0.46 = ( ( X1 = Y1 )
% 0.29/0.46 & ( X2 = Y2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod.inject
% 0.29/0.46 thf(fact_24_t,axiom,
% 0.29/0.46 ord_less_eq_real @ x @ t ).
% 0.29/0.46
% 0.29/0.46 % t
% 0.29/0.46 thf(fact_25_all,axiom,
% 0.29/0.46 ! [I4: c] :
% 0.29/0.46 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I4 ) @ ( static_BVO_a_c @ oDEa ) )
% 0.29/0.46 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 0.29/0.46 = ( finite772340578real_c @ ab @ I4 ) ) )
% 0.29/0.46 & ( ( member_Sum_sum_c_d @ ( sum_Inl_c_d @ I4 ) @ ( image_c_Sum_sum_c_d @ sum_Inl_c_d @ ( static_FVO_a_c @ oDEa ) ) )
% 0.29/0.46 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 0.29/0.46 = ( finite772340578real_c @ ab @ I4 ) ) )
% 0.29/0.46 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I4 ) @ ( static_FVF_a_b_c @ phi ) )
% 0.29/0.46 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 0.29/0.46 = ( finite772340578real_c @ ab @ I4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % all
% 0.29/0.46 thf(fact_26_less__eq__vec__def,axiom,
% 0.29/0.46 ( ord_le775706699real_c
% 0.29/0.46 = ( ^ [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.29/0.46 ! [I2: c] : ( ord_less_eq_real @ ( finite772340578real_c @ X3 @ I2 ) @ ( finite772340578real_c @ Y3 @ I2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eq_vec_def
% 0.29/0.46 thf(fact_27_old_Oprod_Oinducts,axiom,
% 0.29/0.46 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.29/0.46 ( ! [A3: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A3 @ B3 ) )
% 0.29/0.46 => ( P @ Prod ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.prod.inducts
% 0.29/0.46 thf(fact_28_old_Oprod_Oexhaust,axiom,
% 0.29/0.46 ! [Y: produc190496183real_c] :
% 0.29/0.46 ~ ! [A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( produc394644079real_c @ A3 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.prod.exhaust
% 0.29/0.46 thf(fact_29_Pair__inject,axiom,
% 0.29/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.29/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.29/0.46 = ( produc394644079real_c @ A2 @ B2 ) )
% 0.29/0.46 => ~ ( ( A = A2 )
% 0.29/0.46 => ( B != B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Pair_inject
% 0.29/0.46 thf(fact_30_prod__cases,axiom,
% 0.29/0.46 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.29/0.46 ( ! [A3: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A3 @ B3 ) )
% 0.29/0.46 => ( P @ P2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod_cases
% 0.29/0.46 thf(fact_31_surj__pair,axiom,
% 0.29/0.46 ! [P2: produc190496183real_c] :
% 0.29/0.46 ? [X4: finite1398487019real_c,Y4: finite1398487019real_c] :
% 0.29/0.46 ( P2
% 0.29/0.46 = ( produc394644079real_c @ X4 @ Y4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % surj_pair
% 0.29/0.46 thf(fact_32_vec__nth__inject,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.29/0.46 ( ( ( finite772340578real_c @ X )
% 0.29/0.46 = ( finite772340578real_c @ Y ) )
% 0.29/0.46 = ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % vec_nth_inject
% 0.29/0.46 thf(fact_33_cond__component,axiom,
% 0.29/0.46 ! [B: $o,X: finite1398487019real_c,Y: finite1398487019real_c,I3: c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 => ( ( finite772340578real_c @ ( if_Fin36944805real_c @ B @ X @ Y ) @ I3 )
% 0.29/0.46 = ( finite772340578real_c @ X @ I3 ) ) )
% 0.29/0.46 & ( ~ B
% 0.29/0.46 => ( ( finite772340578real_c @ ( if_Fin36944805real_c @ B @ X @ Y ) @ I3 )
% 0.29/0.46 = ( finite772340578real_c @ Y @ I3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % cond_component
% 0.29/0.46 thf(fact_34_vec__eq__iff,axiom,
% 0.29/0.46 ( ( ^ [Y5: finite1398487019real_c,Z: finite1398487019real_c] : ( Y5 = Z ) )
% 0.29/0.46 = ( ^ [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.29/0.46 ! [I2: c] :
% 0.29/0.46 ( ( finite772340578real_c @ X3 @ I2 )
% 0.29/0.46 = ( finite772340578real_c @ Y3 @ I2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vec_eq_iff
% 0.29/0.46 thf(fact_35_zero__prod__def,axiom,
% 0.29/0.46 ( zero_z1506780526real_c
% 0.29/0.46 = ( produc394644079real_c @ zero_z109254132real_c @ zero_z109254132real_c ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_prod_def
% 0.29/0.46 thf(fact_36_zero__prod__def,axiom,
% 0.29/0.46 ( zero_z659284464l_real
% 0.29/0.46 = ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_prod_def
% 0.29/0.46 thf(fact_37_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ A @ ( collect_Sum_sum_c_c @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_38_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: sum_sum_c_d,P: sum_sum_c_d > $o] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ A @ ( collect_Sum_sum_c_d @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_39_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: produc190496183real_c,P: produc190496183real_c > $o] :
% 0.29/0.46 ( ( member1895684704real_c @ A @ ( collec1643251106real_c @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_40_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: real > finite1398487019real_c,P: ( real > finite1398487019real_c ) > $o] :
% 0.29/0.46 ( ( member1321351885real_c @ A @ ( collec913357835real_c @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_41_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: finite1398487019real_c,P: finite1398487019real_c > $o] :
% 0.29/0.46 ( ( member1261661570real_c @ A @ ( collec230941376real_c @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_42_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: c,P: c > $o] :
% 0.29/0.46 ( ( member_c @ A @ ( collect_c @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_43_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( collect_Sum_sum_c_c
% 0.29/0.46 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_44_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ( collect_Sum_sum_c_d
% 0.29/0.46 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_Pr1389752855real_c] :
% 0.29/0.46 ( ( collec1643251106real_c
% 0.29/0.46 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_re2066790124real_c] :
% 0.29/0.46 ( ( collec913357835real_c
% 0.29/0.46 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_47_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_Fi1407883041real_c] :
% 0.29/0.46 ( ( collec230941376real_c
% 0.29/0.46 @ ^ [X3: finite1398487019real_c] : ( member1261661570real_c @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_48_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A4: set_c] :
% 0.29/0.46 ( ( collect_c
% 0.29/0.46 @ ^ [X3: c] : ( member_c @ X3 @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_49_Collect__cong,axiom,
% 0.29/0.46 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 0.29/0.46 ( ! [X4: finite1398487019real_c] :
% 0.29/0.46 ( ( P @ X4 )
% 0.29/0.46 = ( Q @ X4 ) )
% 0.29/0.46 => ( ( collec230941376real_c @ P )
% 0.29/0.46 = ( collec230941376real_c @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_cong
% 0.29/0.46 thf(fact_50_Collect__cong,axiom,
% 0.29/0.46 ! [P: c > $o,Q: c > $o] :
% 0.29/0.46 ( ! [X4: c] :
% 0.29/0.46 ( ( P @ X4 )
% 0.29/0.46 = ( Q @ X4 ) )
% 0.29/0.46 => ( ( collect_c @ P )
% 0.29/0.46 = ( collect_c @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_cong
% 0.29/0.46 thf(fact_51_fst__conv,axiom,
% 0.29/0.46 ! [X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 0.29/0.46 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X2 ) )
% 0.29/0.46 = X1 ) ).
% 0.29/0.46
% 0.29/0.46 % fst_conv
% 0.29/0.46 thf(fact_52_fst__eqD,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.29/0.46 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.29/0.46 = A )
% 0.29/0.46 => ( X = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % fst_eqD
% 0.29/0.46 thf(fact_53_snd__conv,axiom,
% 0.29/0.46 ! [X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 0.29/0.46 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X2 ) )
% 0.29/0.46 = X2 ) ).
% 0.29/0.46
% 0.29/0.46 % snd_conv
% 0.29/0.46 thf(fact_54_snd__eqD,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.29/0.46 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.29/0.46 = A )
% 0.29/0.46 => ( Y = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % snd_eqD
% 0.29/0.46 thf(fact_55_prod__eq__iff,axiom,
% 0.29/0.46 ( ( ^ [Y5: produc190496183real_c,Z: produc190496183real_c] : ( Y5 = Z ) )
% 0.29/0.46 = ( ^ [S: produc190496183real_c,T2: produc190496183real_c] :
% 0.29/0.46 ( ( ( produc2010422875real_c @ S )
% 0.29/0.46 = ( produc2010422875real_c @ T2 ) )
% 0.29/0.46 & ( ( produc314122909real_c @ S )
% 0.29/0.46 = ( produc314122909real_c @ T2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod_eq_iff
% 0.29/0.46 thf(fact_56_prod_Oexpand,axiom,
% 0.29/0.46 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 0.29/0.46 ( ( ( ( produc2010422875real_c @ Prod )
% 0.29/0.46 = ( produc2010422875real_c @ Prod2 ) )
% 0.29/0.46 & ( ( produc314122909real_c @ Prod )
% 0.29/0.46 = ( produc314122909real_c @ Prod2 ) ) )
% 0.29/0.46 => ( Prod = Prod2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod.expand
% 0.29/0.46 thf(fact_57_prod__eqI,axiom,
% 0.29/0.46 ! [P2: produc190496183real_c,Q2: produc190496183real_c] :
% 0.29/0.46 ( ( ( produc2010422875real_c @ P2 )
% 0.29/0.46 = ( produc2010422875real_c @ Q2 ) )
% 0.29/0.46 => ( ( ( produc314122909real_c @ P2 )
% 0.29/0.46 = ( produc314122909real_c @ Q2 ) )
% 0.29/0.46 => ( P2 = Q2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod_eqI
% 0.29/0.46 thf(fact_58_vec__nth__inverse,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c] :
% 0.29/0.46 ( ( finite557796307c_real @ ( finite772340578real_c @ X ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % vec_nth_inverse
% 0.29/0.46 thf(fact_59_vec__lambda__unique,axiom,
% 0.29/0.46 ! [F: finite1398487019real_c,G: c > real] :
% 0.29/0.46 ( ( ! [I2: c] :
% 0.29/0.46 ( ( finite772340578real_c @ F @ I2 )
% 0.29/0.46 = ( G @ I2 ) ) )
% 0.29/0.46 = ( ( finite557796307c_real @ G )
% 0.29/0.46 = F ) ) ).
% 0.29/0.46
% 0.29/0.46 % vec_lambda_unique
% 0.29/0.46 thf(fact_60_zero__vec__def,axiom,
% 0.29/0.46 ( zero_z109254132real_c
% 0.29/0.46 = ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_vec_def
% 0.29/0.46 thf(fact_61_surjective__pairing,axiom,
% 0.29/0.46 ! [T: produc190496183real_c] :
% 0.29/0.46 ( T
% 0.29/0.46 = ( produc394644079real_c @ ( produc2010422875real_c @ T ) @ ( produc314122909real_c @ T ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % surjective_pairing
% 0.29/0.46 thf(fact_62_prod_Oexhaust__sel,axiom,
% 0.29/0.46 ! [Prod: produc190496183real_c] :
% 0.29/0.46 ( Prod
% 0.29/0.46 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prod.exhaust_sel
% 0.29/0.46 thf(fact_63_mk__v__concrete,axiom,
% 0.29/0.46 ( denota161327353_a_b_c
% 0.29/0.46 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Nu: produc190496183real_c,Sol2: finite1398487019real_c] :
% 0.29/0.46 ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ Sol2 @ ( produc2010422875real_c @ Nu ) ) @ I2 ) )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) @ ( produc314122909real_c @ Nu ) ) @ I2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_v_concrete
% 0.29/0.46 thf(fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
% 0.29/0.46 ( ( denota1997846518gree_c
% 0.29/0.46 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.46 @ ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.46 @ bb )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.46 @ ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.46 @ bb )
% 0.29/0.46 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
% 0.29/0.46 & ( denota1997846518gree_c
% 0.29/0.46 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.46 @ ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.46 @ bb )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.46 @ ( denota1896987029_a_b_c @ i @ oDEa
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.46 @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>Vagree (mk_v I ODE (\<chi>i. if i \<in> FVO ODE then sol 0 $ i else ab $ i, bb) (\<chi>i. if i \<in> FVO ODE then sol x $ i else ab $ i)) (\<chi>i. if i \<in> FVO ODE then sol 0 $ i else ab $ i, bb) (- semBV I ODE) \<and> Vagree (mk_v I ODE (\<chi>i. if i \<in> FVO ODE then sol 0 $ i else ab $ i, bb) (\<chi>i. if i \<in> FVO ODE then sol x $ i else ab $ i)) (mk_xode I ODE (\<chi>i. if i \<in> FVO ODE then sol x $ i else ab $ i)) (semBV I ODE)\<close>
% 0.29/0.46 thf(fact_65_Vagree__def,axiom,
% 0.29/0.46 ( denota1997846518gree_c
% 0.29/0.46 = ( ^ [Nu: produc190496183real_c,Nu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.29/0.46 ( ! [I2: c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ V )
% 0.29/0.46 => ( ( finite772340578real_c @ ( produc2010422875real_c @ Nu ) @ I2 )
% 0.29/0.46 = ( finite772340578real_c @ ( produc2010422875real_c @ Nu2 ) @ I2 ) ) )
% 0.29/0.46 & ! [I2: c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ V )
% 0.29/0.46 => ( ( finite772340578real_c @ ( produc314122909real_c @ Nu ) @ I2 )
% 0.29/0.46 = ( finite772340578real_c @ ( produc314122909real_c @ Nu2 ) @ I2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_def
% 0.29/0.46 thf(fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
% 0.29/0.46 ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( produc394644079real_c @ ab @ bb ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
% 0.29/0.46 & ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( denota1896987029_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>Vagree (mk_v I ODE (ab, bb) (sol x)) (ab, bb) (- semBV I ODE) \<and> Vagree (mk_v I ODE (ab, bb) (sol x)) (mk_xode I ODE (sol x)) (semBV I ODE)\<close>
% 0.29/0.46 thf(fact_67_concrete__v_Osimps,axiom,
% 0.29/0.46 ( denota310462944_a_b_c
% 0.29/0.46 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Nu: produc190496183real_c,Sol2: finite1398487019real_c] :
% 0.29/0.46 ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ Sol2 @ ( produc2010422875real_c @ Nu ) ) @ I2 ) )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) @ ( produc314122909real_c @ Nu ) ) @ I2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % concrete_v.simps
% 0.29/0.46 thf(fact_68_concrete__v_Oelims,axiom,
% 0.29/0.46 ! [X: denota231621370t_unit,Xa: oDE_a_c,Xb: produc190496183real_c,Xc: finite1398487019real_c,Y: produc190496183real_c] :
% 0.29/0.46 ( ( ( denota310462944_a_b_c @ X @ Xa @ Xb @ Xc )
% 0.29/0.46 = Y )
% 0.29/0.46 => ( Y
% 0.29/0.46 = ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ X @ Xa ) ) @ Xc @ ( produc2010422875real_c @ Xb ) ) @ I2 ) )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ X @ Xa ) ) @ ( denota1275485728_a_b_c @ X @ Xa @ Xc ) @ ( produc314122909real_c @ Xb ) ) @ I2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % concrete_v.elims
% 0.29/0.46 thf(fact_69_Pair__le,axiom,
% 0.29/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 0.29/0.46 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 0.29/0.46 = ( ( ord_le775706699real_c @ A @ C )
% 0.29/0.46 & ( ord_le775706699real_c @ B @ D ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Pair_le
% 0.29/0.46 thf(fact_70_Pair__le,axiom,
% 0.29/0.46 ! [A: real,B: real,C: real,D: real] :
% 0.29/0.46 ( ( ord_le1342644953l_real @ ( produc705216881l_real @ A @ B ) @ ( produc705216881l_real @ C @ D ) )
% 0.29/0.46 = ( ( ord_less_eq_real @ A @ C )
% 0.29/0.46 & ( ord_less_eq_real @ B @ D ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Pair_le
% 0.29/0.46 thf(fact_71_sem,axiom,
% 0.29/0.46 ! [Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 0.29/0.46 ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ ( static_FVF_a_b_c @ p ) )
% 0.29/0.46 => ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ i @ p ) )
% 0.29/0.46 = ( member1895684704real_c @ Nu4 @ ( denota968303861_a_b_c @ i @ p ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sem
% 0.29/0.46 thf(fact_72_aaba,axiom,
% 0.29/0.46 ( ( produc394644079real_c @ aa @ ba )
% 0.29/0.46 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % aaba
% 0.29/0.46 thf(fact_73_add_Oinverse__neutral,axiom,
% 0.29/0.46 ( ( uminus_uminus_real @ zero_zero_real )
% 0.29/0.46 = zero_zero_real ) ).
% 0.29/0.46
% 0.29/0.46 % add.inverse_neutral
% 0.29/0.46 thf(fact_74_neg__0__equal__iff__equal,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( zero_zero_real
% 0.29/0.46 = ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( zero_zero_real = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_0_equal_iff_equal
% 0.29/0.46 thf(fact_75_neg__equal__0__iff__equal,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ( uminus_uminus_real @ A )
% 0.29/0.46 = zero_zero_real )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_equal_0_iff_equal
% 0.29/0.46 thf(fact_76_equal__neg__zero,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( A
% 0.29/0.46 = ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % equal_neg_zero
% 0.29/0.46 thf(fact_77_neg__equal__zero,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ( uminus_uminus_real @ A )
% 0.29/0.46 = A )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_equal_zero
% 0.29/0.46 thf(fact_78_neg__le__iff__le,axiom,
% 0.29/0.46 ! [B: real,A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_le_iff_le
% 0.29/0.46 thf(fact_79_uminus__Pair,axiom,
% 0.29/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c] :
% 0.29/0.46 ( ( uminus17964590real_c @ ( produc394644079real_c @ A @ B ) )
% 0.29/0.46 = ( produc394644079real_c @ ( uminus1737280820real_c @ A ) @ ( uminus1737280820real_c @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_Pair
% 0.29/0.46 thf(fact_80_uminus__Pair,axiom,
% 0.29/0.46 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( uminus1225118734um_c_c @ ( produc1439061071um_c_c @ A @ B ) )
% 0.29/0.46 = ( produc1439061071um_c_c @ ( uminus1381786404um_c_c @ A ) @ ( uminus1381786404um_c_c @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_Pair
% 0.29/0.46 thf(fact_81_vector__uminus__component,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c,I3: c] :
% 0.29/0.46 ( ( finite772340578real_c @ ( uminus1737280820real_c @ X ) @ I3 )
% 0.29/0.46 = ( uminus_uminus_real @ ( finite772340578real_c @ X @ I3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vector_uminus_component
% 0.29/0.46 thf(fact_82_fst__uminus,axiom,
% 0.29/0.46 ! [X: produc190496183real_c] :
% 0.29/0.46 ( ( produc2010422875real_c @ ( uminus17964590real_c @ X ) )
% 0.29/0.46 = ( uminus1737280820real_c @ ( produc2010422875real_c @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fst_uminus
% 0.29/0.46 thf(fact_83_snd__uminus,axiom,
% 0.29/0.46 ! [X: produc190496183real_c] :
% 0.29/0.46 ( ( produc314122909real_c @ ( uminus17964590real_c @ X ) )
% 0.29/0.46 = ( uminus1737280820real_c @ ( produc314122909real_c @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % snd_uminus
% 0.29/0.46 thf(fact_84_neg__less__eq__nonneg,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.29/0.46 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_less_eq_nonneg
% 0.29/0.46 thf(fact_85_less__eq__neg__nonpos,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eq_neg_nonpos
% 0.29/0.46 thf(fact_86_neg__le__0__iff__le,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.29/0.46 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_le_0_iff_le
% 0.29/0.46 thf(fact_87_neg__0__le__iff__le,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_0_le_iff_le
% 0.29/0.46 thf(fact_88_allT,axiom,
% 0.29/0.46 ! [S2: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ zero_zero_real @ S2 )
% 0.29/0.46 => ( ( ord_less_eq_real @ S2 @ t )
% 0.29/0.46 => ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ S2 ) ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % allT
% 0.29/0.46 thf(fact_89_iff__to__impl,axiom,
% 0.29/0.46 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,A4: formula_a_b_c,B4: formula_a_b_c] :
% 0.29/0.46 ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 0.29/0.46 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) )
% 0.29/0.46 = ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 0.29/0.46 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) )
% 0.29/0.46 & ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) )
% 0.29/0.46 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % iff_to_impl
% 0.29/0.46 thf(fact_90_le__imp__neg__le,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.46 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_imp_neg_le
% 0.29/0.46 thf(fact_91_minus__le__iff,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.46 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % minus_le_iff
% 0.29/0.46 thf(fact_92_le__minus__iff,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.46 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_minus_iff
% 0.29/0.46 thf(fact_93_agree__supset,axiom,
% 0.29/0.46 ! [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c,Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ B4 @ A4 )
% 0.29/0.46 => ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ A4 )
% 0.29/0.46 => ( denota1997846518gree_c @ Nu3 @ Nu4 @ B4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % agree_supset
% 0.29/0.46 thf(fact_94_agree__sub,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.29/0.46 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B4 )
% 0.29/0.46 => ( denota1997846518gree_c @ Nu3 @ Omega @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % agree_sub
% 0.29/0.46 thf(fact_95_mk__v__exists,axiom,
% 0.29/0.46 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,ODE: oDE_a_c,Sol: finite1398487019real_c] :
% 0.29/0.46 ? [Omega2: produc190496183real_c] :
% 0.29/0.46 ( ( denota1997846518gree_c @ Omega2 @ Nu3 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ I @ ODE ) ) )
% 0.29/0.46 & ( denota1997846518gree_c @ Omega2 @ ( denota1896987029_a_b_c @ I @ ODE @ Sol ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_v_exists
% 0.29/0.46 thf(fact_96_uminus__vec__def,axiom,
% 0.29/0.46 ( uminus1737280820real_c
% 0.29/0.46 = ( ^ [X3: finite1398487019real_c] :
% 0.29/0.46 ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( uminus_uminus_real @ ( finite772340578real_c @ X3 @ I2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_vec_def
% 0.29/0.46 thf(fact_97_uminus__prod__def,axiom,
% 0.29/0.46 ( uminus17964590real_c
% 0.29/0.46 = ( ^ [X3: produc190496183real_c] : ( produc394644079real_c @ ( uminus1737280820real_c @ ( produc2010422875real_c @ X3 ) ) @ ( uminus1737280820real_c @ ( produc314122909real_c @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_prod_def
% 0.29/0.46 thf(fact_98_uminus__prod__def,axiom,
% 0.29/0.46 ( uminus1225118734um_c_c
% 0.29/0.46 = ( ^ [X3: produc214722967um_c_c] : ( produc1439061071um_c_c @ ( uminus1381786404um_c_c @ ( produc1983230011um_c_c @ X3 ) ) @ ( uminus1381786404um_c_c @ ( produc1132019837um_c_c @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_prod_def
% 0.29/0.46 thf(fact_99_mk__v__agree,axiom,
% 0.29/0.46 ! [I: denota231621370t_unit,ODE: oDE_a_c,Nu3: produc190496183real_c,Sol: finite1398487019real_c] :
% 0.29/0.46 ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ I @ ODE @ Nu3 @ Sol ) @ Nu3 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ I @ ODE ) ) )
% 0.29/0.46 & ( denota1997846518gree_c @ ( denota161327353_a_b_c @ I @ ODE @ Nu3 @ Sol ) @ ( denota1896987029_a_b_c @ I @ ODE @ Sol ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_v_agree
% 0.29/0.46 thf(fact_100_mk__xode_Oelims,axiom,
% 0.29/0.46 ! [X: denota231621370t_unit,Xa: oDE_a_c,Xb: finite1398487019real_c,Y: produc190496183real_c] :
% 0.29/0.46 ( ( ( denota1896987029_a_b_c @ X @ Xa @ Xb )
% 0.29/0.46 = Y )
% 0.29/0.46 => ( Y
% 0.29/0.46 = ( produc394644079real_c @ Xb @ ( denota1275485728_a_b_c @ X @ Xa @ Xb ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_xode.elims
% 0.29/0.46 thf(fact_101_mk__xode_Osimps,axiom,
% 0.29/0.46 ( denota1896987029_a_b_c
% 0.29/0.46 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Sol2: finite1398487019real_c] : ( produc394644079real_c @ Sol2 @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_xode.simps
% 0.29/0.46 thf(fact_102_zero__reorient,axiom,
% 0.29/0.46 ! [X: real] :
% 0.29/0.46 ( ( zero_zero_real = X )
% 0.29/0.46 = ( X = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_reorient
% 0.29/0.46 thf(fact_103_agree__refl,axiom,
% 0.29/0.46 ! [Nu3: produc190496183real_c,A4: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A4 ) ).
% 0.29/0.46
% 0.29/0.46 % agree_refl
% 0.29/0.46 thf(fact_104_agree__comm,axiom,
% 0.29/0.46 ! [A4: produc190496183real_c,B4: produc190496183real_c,V2: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( denota1997846518gree_c @ A4 @ B4 @ V2 )
% 0.29/0.46 => ( denota1997846518gree_c @ B4 @ A4 @ V2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % agree_comm
% 0.29/0.46 thf(fact_105_Pair__mono,axiom,
% 0.29/0.46 ! [X: finite1398487019real_c,X5: finite1398487019real_c,Y: finite1398487019real_c,Y6: finite1398487019real_c] :
% 0.29/0.46 ( ( ord_le775706699real_c @ X @ X5 )
% 0.29/0.46 => ( ( ord_le775706699real_c @ Y @ Y6 )
% 0.29/0.46 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X5 @ Y6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Pair_mono
% 0.29/0.46 thf(fact_106_Pair__mono,axiom,
% 0.29/0.46 ! [X: real,X5: real,Y: real,Y6: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ X @ X5 )
% 0.29/0.46 => ( ( ord_less_eq_real @ Y @ Y6 )
% 0.29/0.46 => ( ord_le1342644953l_real @ ( produc705216881l_real @ X @ Y ) @ ( produc705216881l_real @ X5 @ Y6 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Pair_mono
% 0.29/0.46 thf(fact_107_fst__mono,axiom,
% 0.29/0.46 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.29/0.46 ( ( ord_le850691415real_c @ X @ Y )
% 0.29/0.46 => ( ord_le775706699real_c @ ( produc2010422875real_c @ X ) @ ( produc2010422875real_c @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fst_mono
% 0.29/0.46 thf(fact_108_snd__mono,axiom,
% 0.29/0.46 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.29/0.46 ( ( ord_le850691415real_c @ X @ Y )
% 0.29/0.46 => ( ord_le775706699real_c @ ( produc314122909real_c @ X ) @ ( produc314122909real_c @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % snd_mono
% 0.29/0.46 thf(fact_109_less__eq__prod__def,axiom,
% 0.29/0.46 ( ord_le850691415real_c
% 0.29/0.46 = ( ^ [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 0.29/0.46 ( ( ord_le775706699real_c @ ( produc2010422875real_c @ X3 ) @ ( produc2010422875real_c @ Y3 ) )
% 0.29/0.46 & ( ord_le775706699real_c @ ( produc314122909real_c @ X3 ) @ ( produc314122909real_c @ Y3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eq_prod_def
% 0.29/0.46 thf(fact_110_less__eq__prod__def,axiom,
% 0.29/0.46 ( ord_le1342644953l_real
% 0.29/0.46 = ( ^ [X3: produc957004601l_real,Y3: produc957004601l_real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( produc1422991709l_real @ X3 ) @ ( produc1422991709l_real @ Y3 ) )
% 0.29/0.46 & ( ord_less_eq_real @ ( produc1407670175l_real @ X3 ) @ ( produc1407670175l_real @ Y3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eq_prod_def
% 0.29/0.46 thf(fact_111_ODE__vars__lr,axiom,
% 0.29/0.46 ! [X: c,I: denota231621370t_unit,ODE: oDE_a_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X ) @ ( denota1293057250_a_b_c @ I @ ODE ) )
% 0.29/0.46 = ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ X ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ODE_vars_lr
% 0.29/0.46 thf(fact_112__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Aab_A_061_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
% 0.29/0.46 ( ( osafe_a_c @ oDEa )
% 0.29/0.46 => ( ( fsafe_a_b_c @ phi )
% 0.29/0.46 => ( ( ode = oDEa )
% 0.29/0.46 => ( ( p = phi )
% 0.29/0.46 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 0.29/0.46 => ( ( ( produc394644079real_c @ aa @ ba )
% 0.29/0.46 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 0.29/0.46 => ( ( initia1631504802real_c @ sol
% 0.29/0.46 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 0.29/0.46 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 0.29/0.46 @ ( collec230941376real_c
% 0.29/0.46 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 0.29/0.46 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 0.29/0.46 @ ( collect_c
% 0.29/0.46 @ ^ [Uu: c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 0.29/0.46 => ( ab
% 0.29/0.46 = ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<lbrakk>osafe ODE; fsafe \<phi>; ODE__ = ODE; P = \<phi>; 0 \<le> t; (aa, ba) = mk_v I ODE (ab, bb) (sol t); (sol solves_ode (\<lambda>a. ODE_sem I ODE)) {0..t} {x. mk_v I ODE (ab, bb) x \<in> fml_sem I \<phi>}; VSagree (sol 0) ab {uu_. Inl uu_ \<in> BVO ODE \<or> Inl uu_ \<in> Inl ` FVO ODE \<or> Inl uu_ \<in> FVF \<phi>}\<rbrakk> \<Longrightarrow> ab = (\<chi>i. if i \<in> FVO ODE then sol 0 $ i else ab $ i)\<close>
% 0.29/0.46 thf(fact_113__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_A_061_Amk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_At_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
% 0.29/0.46 ( ( osafe_a_c @ oDEa )
% 0.29/0.46 => ( ( fsafe_a_b_c @ phi )
% 0.29/0.46 => ( ( ode = oDEa )
% 0.29/0.46 => ( ( p = phi )
% 0.29/0.46 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 0.29/0.46 => ( ( ( produc394644079real_c @ aa @ ba )
% 0.29/0.46 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 0.29/0.46 => ( ( initia1631504802real_c @ sol
% 0.29/0.46 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 0.29/0.46 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 0.29/0.46 @ ( collec230941376real_c
% 0.29/0.46 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 0.29/0.46 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 0.29/0.46 @ ( collect_c
% 0.29/0.46 @ ^ [Uu: c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 0.29/0.46 => ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
% 0.29/0.46 = ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.46 @ ( produc394644079real_c
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.46 @ bb )
% 0.29/0.46 @ ( finite557796307c_real
% 0.29/0.46 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<lbrakk>osafe ODE; fsafe \<phi>; ODE__ = ODE; P = \<phi>; 0 \<le> t; (aa, ba) = mk_v I ODE (ab, bb) (sol t); (sol solves_ode (\<lambda>a. ODE_sem I ODE)) {0..t} {x. mk_v I ODE (ab, bb) x \<in> fml_sem I \<phi>}; VSagree (sol 0) ab {uu_. Inl uu_ \<in> BVO ODE \<or> Inl uu_ \<in> Inl ` FVO ODE \<or> Inl uu_ \<in> FVF \<phi>}\<rbrakk> \<Longrightarrow> mk_v I ODE (ab, bb) (sol t) = mk_v I ODE (\<chi>i. if i \<in> FVO ODE then sol 0 $ i else ab $ i, bb) (\<chi>i. if i \<in> FVO ODE then sol t $ i else ab $ i)\<close>
% 0.29/0.46 thf(fact_114__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_A0_A_092_060le_062_At_092_060close_062,axiom,
% 0.29/0.46 ( ( osafe_a_c @ oDEa )
% 0.29/0.46 => ( ( fsafe_a_b_c @ phi )
% 0.29/0.46 => ( ( ode = oDEa )
% 0.29/0.46 => ( ( p = phi )
% 0.29/0.46 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 0.29/0.46 => ( ( ( produc394644079real_c @ aa @ ba )
% 0.29/0.46 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 0.29/0.46 => ( ( initia1631504802real_c @ sol
% 0.29/0.46 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 0.29/0.46 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 0.29/0.46 @ ( collec230941376real_c
% 0.29/0.46 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 0.29/0.46 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 0.29/0.46 @ ( collect_c
% 0.29/0.46 @ ^ [Uu: c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 0.29/0.46 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 0.29/0.46 => ( ord_less_eq_real @ zero_zero_real @ t ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<lbrakk>osafe ODE; fsafe \<phi>; ODE__ = ODE; P = \<phi>; 0 \<le> t; (aa, ba) = mk_v I ODE (ab, bb) (sol t); (sol solves_ode (\<lambda>a. ODE_sem I ODE)) {0..t} {x. mk_v I ODE (ab, bb) x \<in> fml_sem I \<phi>}; VSagree (sol 0) ab {uu_. Inl uu_ \<in> BVO ODE \<or> Inl uu_ \<in> Inl ` FVO ODE \<or> Inl uu_ \<in> FVF \<phi>}\<rbrakk> \<Longrightarrow> 0 \<le> t\<close>
% 0.29/0.46 thf(fact_115_mkV,axiom,
% 0.29/0.46 ( member1321351885real_c @ sol
% 0.29/0.46 @ ( pi_rea1111636068real_c @ ( set_or656347191t_real @ zero_zero_real @ t )
% 0.29/0.46 @ ^ [Uu: real] :
% 0.29/0.46 ( collec230941376real_c
% 0.29/0.46 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mkV
% 0.29/0.46 thf(fact_116_compl__le__compl__iff,axiom,
% 0.29/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ X ) @ ( uminus1381786404um_c_c @ Y ) )
% 0.29/0.46 = ( ord_le1772180283um_c_c @ Y @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_le_compl_iff
% 0.29/0.46 thf(fact_117_iff__sem,axiom,
% 0.29/0.46 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,A4: formula_a_b_c,B4: formula_a_b_c] :
% 0.29/0.46 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ ( equiv_a_b_c @ A4 @ B4 ) ) )
% 0.29/0.46 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 0.29/0.46 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % iff_sem
% 0.29/0.46 thf(fact_118_double__compl,axiom,
% 0.29/0.46 ! [X: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( uminus1381786404um_c_c @ ( uminus1381786404um_c_c @ X ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % double_compl
% 0.29/0.46 thf(fact_119_compl__eq__compl__iff,axiom,
% 0.29/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ( uminus1381786404um_c_c @ X )
% 0.29/0.46 = ( uminus1381786404um_c_c @ Y ) )
% 0.29/0.46 = ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_eq_compl_iff
% 0.29/0.46 thf(fact_120_VSagree__sub,axiom,
% 0.29/0.46 ! [A4: set_c,B4: set_c,Nu3: finite1398487019real_c,Omega: finite1398487019real_c] :
% 0.29/0.46 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 0.29/0.46 => ( ( denota256060419gree_c @ Nu3 @ Omega @ B4 )
% 0.29/0.46 => ( denota256060419gree_c @ Nu3 @ Omega @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % VSagree_sub
% 0.29/0.46 thf(fact_121_VSagree__supset,axiom,
% 0.29/0.46 ! [B4: set_c,A4: set_c,Nu3: finite1398487019real_c,Nu4: finite1398487019real_c] :
% 0.29/0.46 ( ( ord_less_eq_set_c @ B4 @ A4 )
% 0.29/0.46 => ( ( denota256060419gree_c @ Nu3 @ Nu4 @ A4 )
% 0.29/0.46 => ( denota256060419gree_c @ Nu3 @ Nu4 @ B4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % VSagree_supset
% 0.29/0.46 thf(fact_122_VSagree__refl,axiom,
% 0.29/0.46 ! [Nu3: finite1398487019real_c,A4: set_c] : ( denota256060419gree_c @ Nu3 @ Nu3 @ A4 ) ).
% 0.29/0.46
% 0.29/0.46 % VSagree_refl
% 0.29/0.46 thf(fact_123_VSagree__def,axiom,
% 0.29/0.46 ( denota256060419gree_c
% 0.29/0.46 = ( ^ [Nu: finite1398487019real_c,Nu2: finite1398487019real_c,V: set_c] :
% 0.29/0.46 ! [X3: c] :
% 0.29/0.46 ( ( member_c @ X3 @ V )
% 0.29/0.46 => ( ( finite772340578real_c @ Nu @ X3 )
% 0.29/0.46 = ( finite772340578real_c @ Nu2 @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % VSagree_def
% 0.29/0.46 thf(fact_124_compl__mono,axiom,
% 0.29/0.46 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.29/0.46 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ Y ) @ ( uminus1381786404um_c_c @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_mono
% 0.29/0.46 thf(fact_125_compl__le__swap1,axiom,
% 0.29/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ Y @ ( uminus1381786404um_c_c @ X ) )
% 0.29/0.46 => ( ord_le1772180283um_c_c @ X @ ( uminus1381786404um_c_c @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_le_swap1
% 0.29/0.46 thf(fact_126_compl__le__swap2,axiom,
% 0.29/0.46 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ Y ) @ X )
% 0.29/0.46 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ X ) @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_le_swap2
% 0.29/0.46 thf(fact_127_image__uminus__atLeastAtMost,axiom,
% 0.29/0.46 ! [X: real,Y: real] :
% 0.29/0.46 ( ( image_real_real @ uminus_uminus_real @ ( set_or656347191t_real @ X @ Y ) )
% 0.29/0.46 = ( set_or656347191t_real @ ( uminus_uminus_real @ Y ) @ ( uminus_uminus_real @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_uminus_atLeastAtMost
% 0.29/0.46 thf(fact_128_atLeastatMost__subset__iff,axiom,
% 0.29/0.46 ! [A: real,B: real,C: real,D: real] :
% 0.29/0.46 ( ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
% 0.29/0.46 = ( ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.46 | ( ( ord_less_eq_real @ C @ A )
% 0.29/0.46 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % atLeastatMost_subset_iff
% 0.29/0.46 thf(fact_129_Compl__subset__Compl__iff,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ A4 ) @ ( uminus1381786404um_c_c @ B4 ) )
% 0.29/0.46 = ( ord_le1772180283um_c_c @ B4 @ A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_subset_Compl_iff
% 0.29/0.46 thf(fact_130_Compl__anti__mono,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.29/0.46 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ B4 ) @ ( uminus1381786404um_c_c @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_anti_mono
% 0.29/0.46 thf(fact_131_image__eqI,axiom,
% 0.29/0.46 ! [B: c,F: c > c,X: c,A4: set_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_c @ B @ ( image_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_132_image__eqI,axiom,
% 0.29/0.46 ! [B: c,F: sum_sum_c_c > c,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_133_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_c,F: c > sum_sum_c_c,X: c,A4: set_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_134_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_d,F: c > sum_sum_c_d,X: c,A4: set_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_135_image__eqI,axiom,
% 0.29/0.46 ! [B: c,F: sum_sum_c_d > c,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_136_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_137_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_138_image__eqI,axiom,
% 0.29/0.46 ! [B: real > finite1398487019real_c,F: c > real > finite1398487019real_c,X: c,A4: set_c] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member1321351885real_c @ B @ ( image_1226855921real_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_139_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_140_image__eqI,axiom,
% 0.29/0.46 ! [B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( F @ X ) )
% 0.29/0.46 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_141_subsetI,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ! [X4: sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ X4 @ B4 ) )
% 0.29/0.46 => ( ord_le1772180283um_c_c @ A4 @ B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_142_subsetI,axiom,
% 0.29/0.46 ! [A4: set_c,B4: set_c] :
% 0.29/0.46 ( ! [X4: c] :
% 0.29/0.46 ( ( member_c @ X4 @ A4 )
% 0.29/0.46 => ( member_c @ X4 @ B4 ) )
% 0.29/0.46 => ( ord_less_eq_set_c @ A4 @ B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_143_subsetI,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ! [X4: sum_sum_c_d] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ X4 @ B4 ) )
% 0.29/0.46 => ( ord_le764260924um_c_d @ A4 @ B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_144_subsetI,axiom,
% 0.29/0.46 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c] :
% 0.29/0.46 ( ! [X4: produc190496183real_c] :
% 0.29/0.46 ( ( member1895684704real_c @ X4 @ A4 )
% 0.29/0.46 => ( member1895684704real_c @ X4 @ B4 ) )
% 0.29/0.46 => ( ord_le977353143real_c @ A4 @ B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_145_subsetI,axiom,
% 0.29/0.46 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c] :
% 0.29/0.46 ( ! [X4: real > finite1398487019real_c] :
% 0.29/0.46 ( ( member1321351885real_c @ X4 @ A4 )
% 0.29/0.46 => ( member1321351885real_c @ X4 @ B4 ) )
% 0.29/0.46 => ( ord_le35002188real_c @ A4 @ B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_146_Compl__eq__Compl__iff,axiom,
% 0.29/0.46 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( ( uminus1381786404um_c_c @ A4 )
% 0.29/0.46 = ( uminus1381786404um_c_c @ B4 ) )
% 0.29/0.46 = ( A4 = B4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_eq_Compl_iff
% 0.29/0.46 thf(fact_147_Compl__iff,axiom,
% 0.29/0.46 ! [C: c,A4: set_c] :
% 0.29/0.46 ( ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) )
% 0.29/0.46 = ( ~ ( member_c @ C @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_148_Compl__iff,axiom,
% 0.29/0.46 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) )
% 0.29/0.46 = ( ~ ( member_Sum_sum_c_d @ C @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_149_Compl__iff,axiom,
% 0.29/0.46 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 0.29/0.46 ( ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) )
% 0.29/0.46 = ( ~ ( member1895684704real_c @ C @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_150_Compl__iff,axiom,
% 0.29/0.46 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 0.29/0.46 ( ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) )
% 0.29/0.46 = ( ~ ( member1321351885real_c @ C @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_151_Compl__iff,axiom,
% 0.29/0.46 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) )
% 0.29/0.46 = ( ~ ( member_Sum_sum_c_c @ C @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_152_ComplI,axiom,
% 0.29/0.46 ! [C: c,A4: set_c] :
% 0.29/0.46 ( ~ ( member_c @ C @ A4 )
% 0.29/0.46 => ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_153_ComplI,axiom,
% 0.29/0.46 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.46 ( ~ ( member_Sum_sum_c_d @ C @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_154_ComplI,axiom,
% 0.29/0.46 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 0.29/0.46 ( ~ ( member1895684704real_c @ C @ A4 )
% 0.29/0.46 => ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_155_ComplI,axiom,
% 0.29/0.46 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 0.29/0.46 ( ~ ( member1321351885real_c @ C @ A4 )
% 0.29/0.46 => ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_156_ComplI,axiom,
% 0.29/0.46 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.46 ( ~ ( member_Sum_sum_c_c @ C @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_157_Icc__eq__Icc,axiom,
% 0.29/0.46 ! [L: real,H: real,L2: real,H2: real] :
% 0.29/0.46 ( ( ( set_or656347191t_real @ L @ H )
% 0.29/0.46 = ( set_or656347191t_real @ L2 @ H2 ) )
% 0.29/0.46 = ( ( ( L = L2 )
% 0.29/0.46 & ( H = H2 ) )
% 0.29/0.46 | ( ~ ( ord_less_eq_real @ L @ H )
% 0.29/0.46 & ~ ( ord_less_eq_real @ L2 @ H2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Icc_eq_Icc
% 0.29/0.46 thf(fact_158_atLeastAtMost__iff,axiom,
% 0.29/0.46 ! [I3: produc190496183real_c,L: produc190496183real_c,U: produc190496183real_c] :
% 0.29/0.46 ( ( member1895684704real_c @ I3 @ ( set_or385782508real_c @ L @ U ) )
% 0.29/0.46 = ( ( ord_le850691415real_c @ L @ I3 )
% 0.29/0.46 & ( ord_le850691415real_c @ I3 @ U ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % atLeastAtMost_iff
% 0.29/0.46 thf(fact_159_atLeastAtMost__iff,axiom,
% 0.29/0.46 ! [I3: real > finite1398487019real_c,L: real > finite1398487019real_c,U: real > finite1398487019real_c] :
% 0.29/0.46 ( ( member1321351885real_c @ I3 @ ( set_or1308937537real_c @ L @ U ) )
% 0.29/0.46 = ( ( ord_le584953750real_c @ L @ I3 )
% 0.29/0.46 & ( ord_le584953750real_c @ I3 @ U ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % atLeastAtMost_iff
% 0.29/0.46 thf(fact_160_atLeastAtMost__iff,axiom,
% 0.29/0.46 ! [I3: real,L: real,U: real] :
% 0.29/0.46 ( ( member_real @ I3 @ ( set_or656347191t_real @ L @ U ) )
% 0.29/0.46 = ( ( ord_less_eq_real @ L @ I3 )
% 0.29/0.46 & ( ord_less_eq_real @ I3 @ U ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % atLeastAtMost_iff
% 0.29/0.46 thf(fact_161_imageI,axiom,
% 0.29/0.46 ! [X: c,A4: set_c,F: c > c] :
% 0.29/0.46 ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_c @ ( F @ X ) @ ( image_c_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_162_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_c @ ( F @ X ) @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_163_imageI,axiom,
% 0.29/0.46 ! [X: c,A4: set_c,F: c > sum_sum_c_c] :
% 0.29/0.46 ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_164_imageI,axiom,
% 0.29/0.46 ! [X: c,A4: set_c,F: c > sum_sum_c_d] :
% 0.29/0.46 ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_165_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > c] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_c @ ( F @ X ) @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_166_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_666880337um_c_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_167_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_675141842um_c_d @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_168_imageI,axiom,
% 0.29/0.46 ! [X: c,A4: set_c,F: c > real > finite1398487019real_c] :
% 0.29/0.46 ( ( member_c @ X @ A4 )
% 0.29/0.46 => ( member1321351885real_c @ ( F @ X ) @ ( image_1226855921real_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_169_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_170_imageI,axiom,
% 0.29/0.46 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.46 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_171_image__iff,axiom,
% 0.29/0.46 ! [Z2: sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ Z2 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.46 = ( ? [X3: c] :
% 0.29/0.46 ( ( member_c @ X3 @ A4 )
% 0.29/0.46 & ( Z2
% 0.29/0.46 = ( F @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_iff
% 0.29/0.46 thf(fact_172_image__iff,axiom,
% 0.29/0.46 ! [Z2: sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ Z2 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.46 = ( ? [X3: c] :
% 0.29/0.46 ( ( member_c @ X3 @ A4 )
% 0.29/0.46 & ( Z2
% 0.29/0.46 = ( F @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_iff
% 0.29/0.46 thf(fact_173_bex__imageD,axiom,
% 0.29/0.46 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 0.29/0.46 ( ? [X7: sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X7 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.46 & ( P @ X7 ) )
% 0.29/0.46 => ? [X4: c] :
% 0.29/0.46 ( ( member_c @ X4 @ A4 )
% 0.29/0.46 & ( P @ ( F @ X4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_imageD
% 0.29/0.46 thf(fact_174_bex__imageD,axiom,
% 0.29/0.46 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 0.29/0.46 ( ? [X7: sum_sum_c_d] :
% 0.29/0.46 ( ( member_Sum_sum_c_d @ X7 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.46 & ( P @ X7 ) )
% 0.29/0.46 => ? [X4: c] :
% 0.29/0.46 ( ( member_c @ X4 @ A4 )
% 0.29/0.46 & ( P @ ( F @ X4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_imageD
% 0.29/0.46 thf(fact_175_image__cong,axiom,
% 0.29/0.46 ! [M: set_c,N: set_c,F: c > sum_sum_c_c,G: c > sum_sum_c_c] :
% 0.29/0.46 ( ( M = N )
% 0.29/0.46 => ( ! [X4: c] :
% 0.29/0.46 ( ( member_c @ X4 @ N )
% 0.29/0.46 => ( ( F @ X4 )
% 0.29/0.46 = ( G @ X4 ) ) )
% 0.29/0.46 => ( ( image_c_Sum_sum_c_c @ F @ M )
% 0.29/0.46 = ( image_c_Sum_sum_c_c @ G @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_cong
% 0.29/0.46 thf(fact_176_image__cong,axiom,
% 0.29/0.46 ! [M: set_c,N: set_c,F: c > sum_sum_c_d,G: c > sum_sum_c_d] :
% 0.29/0.46 ( ( M = N )
% 0.29/0.46 => ( ! [X4: c] :
% 0.29/0.46 ( ( member_c @ X4 @ N )
% 0.29/0.46 => ( ( F @ X4 )
% 0.29/0.46 = ( G @ X4 ) ) )
% 0.29/0.46 => ( ( image_c_Sum_sum_c_d @ F @ M )
% 0.29/0.46 = ( image_c_Sum_sum_c_d @ G @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_cong
% 0.29/0.46 thf(fact_177_ball__imageD,axiom,
% 0.29/0.46 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 0.29/0.46 ( ! [X4: sum_sum_c_c] :
% 0.29/0.46 ( ( member_Sum_sum_c_c @ X4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.46 => ( P @ X4 ) )
% 0.29/0.46 => ! [X7: c] :
% 0.29/0.46 ( ( member_c @ X7 @ A4 )
% 0.29/0.46 => ( P @ ( F @ X7 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_imageD
% 0.29/0.46 thf(fact_178_ball__imageD,axiom,
% 0.29/0.46 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 0.29/0.46 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.47 => ( P @ X4 ) )
% 0.29/0.47 => ! [X7: c] :
% 0.29/0.47 ( ( member_c @ X7 @ A4 )
% 0.29/0.47 => ( P @ ( F @ X7 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ball_imageD
% 0.29/0.47 thf(fact_179_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: c,A4: set_c,B: c,F: c > c] :
% 0.29/0.47 ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_c @ B @ ( image_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_180_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: c,F: sum_sum_c_c > c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_181_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: c,A4: set_c,B: sum_sum_c_c,F: c > sum_sum_c_c] :
% 0.29/0.47 ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_182_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: c,A4: set_c,B: sum_sum_c_d,F: c > sum_sum_c_d] :
% 0.29/0.47 ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_183_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: c,F: sum_sum_c_d > c] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_184_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_185_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_186_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: c,A4: set_c,B: real > finite1398487019real_c,F: c > real > finite1398487019real_c] :
% 0.29/0.47 ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member1321351885real_c @ B @ ( image_1226855921real_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_187_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_188_rev__image__eqI,axiom,
% 0.29/0.47 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( ( B
% 0.29/0.47 = ( F @ X ) )
% 0.29/0.47 => ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_image_eqI
% 0.29/0.47 thf(fact_189_Collect__mono__iff,axiom,
% 0.29/0.47 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 0.29/0.47 ( ( ord_le1327118209real_c @ ( collec230941376real_c @ P ) @ ( collec230941376real_c @ Q ) )
% 0.29/0.47 = ( ! [X3: finite1398487019real_c] :
% 0.29/0.47 ( ( P @ X3 )
% 0.29/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono_iff
% 0.29/0.47 thf(fact_190_Collect__mono__iff,axiom,
% 0.29/0.47 ! [P: c > $o,Q: c > $o] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ ( collect_c @ P ) @ ( collect_c @ Q ) )
% 0.29/0.47 = ( ! [X3: c] :
% 0.29/0.47 ( ( P @ X3 )
% 0.29/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono_iff
% 0.29/0.47 thf(fact_191_Collect__mono,axiom,
% 0.29/0.47 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 0.29/0.47 ( ! [X4: finite1398487019real_c] :
% 0.29/0.47 ( ( P @ X4 )
% 0.29/0.47 => ( Q @ X4 ) )
% 0.29/0.47 => ( ord_le1327118209real_c @ ( collec230941376real_c @ P ) @ ( collec230941376real_c @ Q ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono
% 0.29/0.47 thf(fact_192_Collect__mono,axiom,
% 0.29/0.47 ! [P: c > $o,Q: c > $o] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( P @ X4 )
% 0.29/0.47 => ( Q @ X4 ) )
% 0.29/0.47 => ( ord_less_eq_set_c @ ( collect_c @ P ) @ ( collect_c @ Q ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono
% 0.29/0.47 thf(fact_193_subset__iff,axiom,
% 0.29/0.47 ( ord_le1772180283um_c_c
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 0.29/0.47 ! [T2: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ T2 @ A5 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ T2 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_194_subset__iff,axiom,
% 0.29/0.47 ( ord_less_eq_set_c
% 0.29/0.47 = ( ^ [A5: set_c,B5: set_c] :
% 0.29/0.47 ! [T2: c] :
% 0.29/0.47 ( ( member_c @ T2 @ A5 )
% 0.29/0.47 => ( member_c @ T2 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_195_subset__iff,axiom,
% 0.29/0.47 ( ord_le764260924um_c_d
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 0.29/0.47 ! [T2: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ T2 @ A5 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ T2 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_196_subset__iff,axiom,
% 0.29/0.47 ( ord_le977353143real_c
% 0.29/0.47 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 0.29/0.47 ! [T2: produc190496183real_c] :
% 0.29/0.47 ( ( member1895684704real_c @ T2 @ A5 )
% 0.29/0.47 => ( member1895684704real_c @ T2 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_197_subset__iff,axiom,
% 0.29/0.47 ( ord_le35002188real_c
% 0.29/0.47 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 0.29/0.47 ! [T2: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member1321351885real_c @ T2 @ A5 )
% 0.29/0.47 => ( member1321351885real_c @ T2 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_198_subset__eq,axiom,
% 0.29/0.47 ( ord_le1772180283um_c_c
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 0.29/0.47 ! [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ A5 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_199_subset__eq,axiom,
% 0.29/0.47 ( ord_less_eq_set_c
% 0.29/0.47 = ( ^ [A5: set_c,B5: set_c] :
% 0.29/0.47 ! [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A5 )
% 0.29/0.47 => ( member_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_200_subset__eq,axiom,
% 0.29/0.47 ( ord_le764260924um_c_d
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 0.29/0.47 ! [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ A5 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_201_subset__eq,axiom,
% 0.29/0.47 ( ord_le977353143real_c
% 0.29/0.47 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 0.29/0.47 ! [X3: produc190496183real_c] :
% 0.29/0.47 ( ( member1895684704real_c @ X3 @ A5 )
% 0.29/0.47 => ( member1895684704real_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_202_subset__eq,axiom,
% 0.29/0.47 ( ord_le35002188real_c
% 0.29/0.47 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 0.29/0.47 ! [X3: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member1321351885real_c @ X3 @ A5 )
% 0.29/0.47 => ( member1321351885real_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_203_subsetD,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,C: sum_sum_c_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member_Sum_sum_c_c @ C @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ C @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_204_subsetD,axiom,
% 0.29/0.47 ! [A4: set_c,B4: set_c,C: c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member_c @ C @ A4 )
% 0.29/0.47 => ( member_c @ C @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_205_subsetD,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d,C: sum_sum_c_d] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ A4 @ B4 )
% 0.29/0.47 => ( ( member_Sum_sum_c_d @ C @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ C @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_206_subsetD,axiom,
% 0.29/0.47 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c,C: produc190496183real_c] :
% 0.29/0.47 ( ( ord_le977353143real_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member1895684704real_c @ C @ A4 )
% 0.29/0.47 => ( member1895684704real_c @ C @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_207_subsetD,axiom,
% 0.29/0.47 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c,C: real > finite1398487019real_c] :
% 0.29/0.47 ( ( ord_le35002188real_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member1321351885real_c @ C @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ C @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_208_in__mono,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,X: sum_sum_c_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ X @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_209_in__mono,axiom,
% 0.29/0.47 ! [A4: set_c,B4: set_c,X: c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( member_c @ X @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_210_in__mono,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d,X: sum_sum_c_d] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ A4 @ B4 )
% 0.29/0.47 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ X @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_211_in__mono,axiom,
% 0.29/0.47 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c,X: produc190496183real_c] :
% 0.29/0.47 ( ( ord_le977353143real_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member1895684704real_c @ X @ A4 )
% 0.29/0.47 => ( member1895684704real_c @ X @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_212_in__mono,axiom,
% 0.29/0.47 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( ord_le35002188real_c @ A4 @ B4 )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ X @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_213_double__complement,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( uminus1381786404um_c_c @ ( uminus1381786404um_c_c @ A4 ) )
% 0.29/0.47 = A4 ) ).
% 0.29/0.47
% 0.29/0.47 % double_complement
% 0.29/0.47 thf(fact_214_ComplD,axiom,
% 0.29/0.47 ! [C: c,A4: set_c] :
% 0.29/0.47 ( ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) )
% 0.29/0.47 => ~ ( member_c @ C @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % ComplD
% 0.29/0.47 thf(fact_215_ComplD,axiom,
% 0.29/0.47 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ C @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % ComplD
% 0.29/0.47 thf(fact_216_ComplD,axiom,
% 0.29/0.47 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 0.29/0.47 ( ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) )
% 0.29/0.47 => ~ ( member1895684704real_c @ C @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % ComplD
% 0.29/0.47 thf(fact_217_ComplD,axiom,
% 0.29/0.47 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 0.29/0.47 ( ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) )
% 0.29/0.47 => ~ ( member1321351885real_c @ C @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % ComplD
% 0.29/0.47 thf(fact_218_ComplD,axiom,
% 0.29/0.47 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ C @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % ComplD
% 0.29/0.47 thf(fact_219_imageE,axiom,
% 0.29/0.47 ! [B: c,F: c > c,A4: set_c] :
% 0.29/0.47 ( ( member_c @ B @ ( image_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_220_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_221_imageE,axiom,
% 0.29/0.47 ! [B: c,F: sum_sum_c_c > c,A4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_222_imageE,axiom,
% 0.29/0.47 ! [B: c,F: sum_sum_c_d > c,A4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_223_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_224_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_225_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_226_imageE,axiom,
% 0.29/0.47 ! [B: c,F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c] :
% 0.29/0.47 ( ( member_c @ B @ ( image_266490115al_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: real > finite1398487019real_c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member1321351885real_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_227_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_228_imageE,axiom,
% 0.29/0.47 ! [B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) )
% 0.29/0.47 => ~ ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( B
% 0.29/0.47 = ( F @ X4 ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % imageE
% 0.29/0.47 thf(fact_229_image__image,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_c,G: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.47 ( ( image_666880337um_c_c @ F @ ( image_c_Sum_sum_c_c @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_230_image__image,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_d,G: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.47 ( ( image_675141842um_c_d @ F @ ( image_c_Sum_sum_c_c @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_231_image__image,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > sum_sum_c_c,G: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.47 ( ( image_1558941394um_c_c @ F @ ( image_c_Sum_sum_c_d @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_232_image__image,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > sum_sum_c_d,G: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.47 ( ( image_1567202899um_c_d @ F @ ( image_c_Sum_sum_c_d @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_233_image__image,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_c,G: c > c,A4: set_c] :
% 0.29/0.47 ( ( image_c_Sum_sum_c_c @ F @ ( image_c_c @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_234_image__image,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_d,G: c > c,A4: set_c] :
% 0.29/0.47 ( ( image_c_Sum_sum_c_d @ F @ ( image_c_c @ G @ A4 ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 0.29/0.47 @ A4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_image
% 0.29/0.47 thf(fact_235_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: c > c,A4: set_c,P: c > $o] :
% 0.29/0.47 ( ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ ( image_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_c_c @ F
% 0.29/0.47 @ ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_236_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_c @ F
% 0.29/0.47 @ ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_237_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_c_Sum_sum_c_d @ F
% 0.29/0.47 @ ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_238_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: c > finite1398487019real_c,A4: set_c,P: finite1398487019real_c > $o] :
% 0.29/0.47 ( ( collec230941376real_c
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] :
% 0.29/0.47 ( ( member1261661570real_c @ X3 @ ( image_687300774real_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_687300774real_c @ F
% 0.29/0.47 @ ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_239_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,P: c > $o] :
% 0.29/0.47 ( ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ ( image_Sum_sum_c_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_Sum_sum_c_c_c @ F
% 0.29/0.47 @ ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_240_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,P: c > $o] :
% 0.29/0.47 ( ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ ( image_Sum_sum_c_d_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_Sum_sum_c_d_c @ F
% 0.29/0.47 @ ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_241_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: finite1398487019real_c > c,A4: set_Fi1407883041real_c,P: c > $o] :
% 0.29/0.47 ( ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ ( image_1260608398al_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_1260608398al_c_c @ F
% 0.29/0.47 @ ( collec230941376real_c
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] :
% 0.29/0.47 ( ( member1261661570real_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_242_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ ( image_666880337um_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_666880337um_c_c @ F
% 0.29/0.47 @ ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_243_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,P: sum_sum_c_c > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ ( image_1558941394um_c_c @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_1558941394um_c_c @ F
% 0.29/0.47 @ ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_244_Compr__image__eq,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,P: sum_sum_c_d > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ ( image_675141842um_c_d @ F @ A4 ) )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 = ( image_675141842um_c_d @ F
% 0.29/0.47 @ ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compr_image_eq
% 0.29/0.47 thf(fact_245_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_le1772180283um_c_c
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 0.29/0.47 ( ord_le1315653386_c_c_o
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A5 )
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_246_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_less_eq_set_c
% 0.29/0.47 = ( ^ [A5: set_c,B5: set_c] :
% 0.29/0.47 ( ord_less_eq_c_o
% 0.29/0.47 @ ^ [X3: c] : ( member_c @ X3 @ A5 )
% 0.29/0.47 @ ^ [X3: c] : ( member_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_247_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_le764260924um_c_d
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 0.29/0.47 ( ord_le2143422793_c_d_o
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A5 )
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_248_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_le977353143real_c
% 0.29/0.47 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 0.29/0.47 ( ord_le1132241894al_c_o
% 0.29/0.47 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A5 )
% 0.29/0.47 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_249_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_le35002188real_c
% 0.29/0.47 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 0.29/0.47 ( ord_le818951225al_c_o
% 0.29/0.47 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A5 )
% 0.29/0.47 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ B5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_250_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.29/0.47 ( ord_le1772180283um_c_c
% 0.29/0.47 @ ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_251_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,P: sum_sum_c_d > $o] :
% 0.29/0.47 ( ord_le764260924um_c_d
% 0.29/0.47 @ ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_252_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 0.29/0.47 ( ord_le977353143real_c
% 0.29/0.47 @ ( collec1643251106real_c
% 0.29/0.47 @ ^ [X3: produc190496183real_c] :
% 0.29/0.47 ( ( member1895684704real_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_253_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_re2066790124real_c,P: ( real > finite1398487019real_c ) > $o] :
% 0.29/0.47 ( ord_le35002188real_c
% 0.29/0.47 @ ( collec913357835real_c
% 0.29/0.47 @ ^ [X3: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member1321351885real_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_254_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_Fi1407883041real_c,P: finite1398487019real_c > $o] :
% 0.29/0.47 ( ord_le1327118209real_c
% 0.29/0.47 @ ( collec230941376real_c
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] :
% 0.29/0.47 ( ( member1261661570real_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_255_Collect__subset,axiom,
% 0.29/0.47 ! [A4: set_c,P: c > $o] :
% 0.29/0.47 ( ord_less_eq_set_c
% 0.29/0.47 @ ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 & ( P @ X3 ) ) )
% 0.29/0.47 @ A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_256_Collect__neg__eq,axiom,
% 0.29/0.47 ! [P: finite1398487019real_c > $o] :
% 0.29/0.47 ( ( collec230941376real_c
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] :
% 0.29/0.47 ~ ( P @ X3 ) )
% 0.29/0.47 = ( uminus102402154real_c @ ( collec230941376real_c @ P ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_neg_eq
% 0.29/0.47 thf(fact_257_Collect__neg__eq,axiom,
% 0.29/0.47 ! [P: c > $o] :
% 0.29/0.47 ( ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ~ ( P @ X3 ) )
% 0.29/0.47 = ( uminus_uminus_set_c @ ( collect_c @ P ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_neg_eq
% 0.29/0.47 thf(fact_258_Collect__neg__eq,axiom,
% 0.29/0.47 ! [P: sum_sum_c_c > $o] :
% 0.29/0.47 ( ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ~ ( P @ X3 ) )
% 0.29/0.47 = ( uminus1381786404um_c_c @ ( collect_Sum_sum_c_c @ P ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_neg_eq
% 0.29/0.47 thf(fact_259_Compl__eq,axiom,
% 0.29/0.47 ( uminus373867045um_c_d
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_d] :
% 0.29/0.47 ( collect_Sum_sum_c_d
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] :
% 0.29/0.47 ~ ( member_Sum_sum_c_d @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_260_Compl__eq,axiom,
% 0.29/0.47 ( uminus232257166real_c
% 0.29/0.47 = ( ^ [A5: set_Pr1389752855real_c] :
% 0.29/0.47 ( collec1643251106real_c
% 0.29/0.47 @ ^ [X3: produc190496183real_c] :
% 0.29/0.47 ~ ( member1895684704real_c @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_261_Compl__eq,axiom,
% 0.29/0.47 ( uminus946614837real_c
% 0.29/0.47 = ( ^ [A5: set_re2066790124real_c] :
% 0.29/0.47 ( collec913357835real_c
% 0.29/0.47 @ ^ [X3: real > finite1398487019real_c] :
% 0.29/0.47 ~ ( member1321351885real_c @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_262_Compl__eq,axiom,
% 0.29/0.47 ( uminus102402154real_c
% 0.29/0.47 = ( ^ [A5: set_Fi1407883041real_c] :
% 0.29/0.47 ( collec230941376real_c
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] :
% 0.29/0.47 ~ ( member1261661570real_c @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_263_Compl__eq,axiom,
% 0.29/0.47 ( uminus_uminus_set_c
% 0.29/0.47 = ( ^ [A5: set_c] :
% 0.29/0.47 ( collect_c
% 0.29/0.47 @ ^ [X3: c] :
% 0.29/0.47 ~ ( member_c @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_264_Compl__eq,axiom,
% 0.29/0.47 ( uminus1381786404um_c_c
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_c] :
% 0.29/0.47 ( collect_Sum_sum_c_c
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] :
% 0.29/0.47 ~ ( member_Sum_sum_c_c @ X3 @ A5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Compl_eq
% 0.29/0.47 thf(fact_265_uminus__set__def,axiom,
% 0.29/0.47 ( uminus373867045um_c_d
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_d] :
% 0.29/0.47 ( collect_Sum_sum_c_d
% 0.29/0.47 @ ( uminus916499104_c_d_o
% 0.29/0.47 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_266_uminus__set__def,axiom,
% 0.29/0.47 ( uminus232257166real_c
% 0.29/0.47 = ( ^ [A5: set_Pr1389752855real_c] :
% 0.29/0.47 ( collec1643251106real_c
% 0.29/0.47 @ ( uminus32155087al_c_o
% 0.29/0.47 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_267_uminus__set__def,axiom,
% 0.29/0.47 ( uminus946614837real_c
% 0.29/0.47 = ( ^ [A5: set_re2066790124real_c] :
% 0.29/0.47 ( collec913357835real_c
% 0.29/0.47 @ ( uminus1756072592al_c_o
% 0.29/0.47 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_268_uminus__set__def,axiom,
% 0.29/0.47 ( uminus102402154real_c
% 0.29/0.47 = ( ^ [A5: set_Fi1407883041real_c] :
% 0.29/0.47 ( collec230941376real_c
% 0.29/0.47 @ ( uminus23580315al_c_o
% 0.29/0.47 @ ^ [X3: finite1398487019real_c] : ( member1261661570real_c @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_269_uminus__set__def,axiom,
% 0.29/0.47 ( uminus_uminus_set_c
% 0.29/0.47 = ( ^ [A5: set_c] :
% 0.29/0.47 ( collect_c
% 0.29/0.47 @ ( uminus_uminus_c_o
% 0.29/0.47 @ ^ [X3: c] : ( member_c @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_270_uminus__set__def,axiom,
% 0.29/0.47 ( uminus1381786404um_c_c
% 0.29/0.47 = ( ^ [A5: set_Sum_sum_c_c] :
% 0.29/0.47 ( collect_Sum_sum_c_c
% 0.29/0.47 @ ( uminus88729697_c_c_o
% 0.29/0.47 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % uminus_set_def
% 0.29/0.47 thf(fact_271_image__mono,axiom,
% 0.29/0.47 ! [A4: set_c,B4: set_c,F: c > sum_sum_c_c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 0.29/0.47 => ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ ( image_c_Sum_sum_c_c @ F @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_mono
% 0.29/0.47 thf(fact_272_image__mono,axiom,
% 0.29/0.47 ! [A4: set_c,B4: set_c,F: c > sum_sum_c_d] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 0.29/0.47 => ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ ( image_c_Sum_sum_c_d @ F @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_mono
% 0.29/0.47 thf(fact_273_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_less_eq_set_c @ ( image_c_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_274_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_less_eq_set_c @ ( image_Sum_sum_c_c_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_275_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_276_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_277_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_less_eq_set_c @ ( image_Sum_sum_c_d_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_278_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le1772180283um_c_c @ ( image_666880337um_c_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_279_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le764260924um_c_d @ ( image_675141842um_c_d @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_280_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: set_re2066790124real_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le35002188real_c @ ( image_1226855921real_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_281_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le1772180283um_c_c @ ( image_1558941394um_c_c @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_282_image__subsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( ord_le764260924um_c_d @ ( image_1567202899um_c_d @ F @ A4 ) @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subsetI
% 0.29/0.47 thf(fact_283_subset__imageE,axiom,
% 0.29/0.47 ! [B4: set_Sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ B4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.47 => ~ ! [C2: set_c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ C2 @ A4 )
% 0.29/0.47 => ( B4
% 0.29/0.47 != ( image_c_Sum_sum_c_c @ F @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_imageE
% 0.29/0.47 thf(fact_284_subset__imageE,axiom,
% 0.29/0.47 ! [B4: set_Sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ B4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.47 => ~ ! [C2: set_c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ C2 @ A4 )
% 0.29/0.47 => ( B4
% 0.29/0.47 != ( image_c_Sum_sum_c_d @ F @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_imageE
% 0.29/0.47 thf(fact_285_image__subset__iff,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_c,A4: set_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ B4 )
% 0.29/0.47 = ( ! [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subset_iff
% 0.29/0.47 thf(fact_286_image__subset__iff,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_d,A4: set_c,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ B4 )
% 0.29/0.47 = ( ! [X3: c] :
% 0.29/0.47 ( ( member_c @ X3 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subset_iff
% 0.29/0.47 thf(fact_287_subset__image__iff,axiom,
% 0.29/0.47 ! [B4: set_Sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ B4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 0.29/0.47 = ( ? [AA: set_c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ AA @ A4 )
% 0.29/0.47 & ( B4
% 0.29/0.47 = ( image_c_Sum_sum_c_c @ F @ AA ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_image_iff
% 0.29/0.47 thf(fact_288_subset__image__iff,axiom,
% 0.29/0.47 ! [B4: set_Sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ B4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 0.29/0.47 = ( ? [AA: set_c] :
% 0.29/0.47 ( ( ord_less_eq_set_c @ AA @ A4 )
% 0.29/0.47 & ( B4
% 0.29/0.47 = ( image_c_Sum_sum_c_d @ F @ AA ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_image_iff
% 0.29/0.47 thf(fact_289_repd_Oelims,axiom,
% 0.29/0.47 ! [X: produc190496183real_c,Xa: c,Xb: real,Y: produc190496183real_c] :
% 0.29/0.47 ( ( ( denotational_repd_c @ X @ Xa @ Xb )
% 0.29/0.47 = Y )
% 0.29/0.47 => ( Y
% 0.29/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ X )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [Y3: c] : ( if_real @ ( Xa = Y3 ) @ Xb @ ( finite772340578real_c @ ( produc314122909real_c @ X ) @ Y3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % repd.elims
% 0.29/0.47 thf(fact_290_repd_Osimps,axiom,
% 0.29/0.47 ( denotational_repd_c
% 0.29/0.47 = ( ^ [V3: produc190496183real_c,X3: c,R: real] :
% 0.29/0.47 ( produc394644079real_c @ ( produc2010422875real_c @ V3 )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [Y3: c] : ( if_real @ ( X3 = Y3 ) @ R @ ( finite772340578real_c @ ( produc314122909real_c @ V3 ) @ Y3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % repd.simps
% 0.29/0.47 thf(fact_291_image__subset__iff__funcset,axiom,
% 0.29/0.47 ! [F2: c > sum_sum_c_c,A4: set_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F2 @ A4 ) @ B4 )
% 0.29/0.47 = ( member_c_Sum_sum_c_c @ F2
% 0.29/0.47 @ ( pi_c_Sum_sum_c_c @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subset_iff_funcset
% 0.29/0.47 thf(fact_292_image__subset__iff__funcset,axiom,
% 0.29/0.47 ! [F2: c > sum_sum_c_d,A4: set_c,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F2 @ A4 ) @ B4 )
% 0.29/0.47 = ( member_c_Sum_sum_c_d @ F2
% 0.29/0.47 @ ( pi_c_Sum_sum_c_d @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subset_iff_funcset
% 0.29/0.47 thf(fact_293_image__subset__iff__funcset,axiom,
% 0.29/0.47 ! [F2: real > finite1398487019real_c,A4: set_real,B4: set_Fi1407883041real_c] :
% 0.29/0.47 ( ( ord_le1327118209real_c @ ( image_327677598real_c @ F2 @ A4 ) @ B4 )
% 0.29/0.47 = ( member1321351885real_c @ F2
% 0.29/0.47 @ ( pi_rea1111636068real_c @ A4
% 0.29/0.47 @ ^ [Uu: real] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % image_subset_iff_funcset
% 0.29/0.47 thf(fact_294_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > c,B4: c > set_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_295_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_real,F: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 0.29/0.47 ( ! [X4: real] :
% 0.29/0.47 ( ( member_real @ X4 @ A4 )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_296_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: sum_sum_c_c > set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_297_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_c,B4: c > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_298_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_d,B4: c > set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_299_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: sum_sum_c_d > set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_300_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_301_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: sum_sum_c_c > set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_302_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: c > set_re2066790124real_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_303_Pi__I,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: sum_sum_c_d > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I
% 0.29/0.47 thf(fact_304_PiE,axiom,
% 0.29/0.47 ! [F: c > c,A4: set_c,B4: c > set_c,X: c] :
% 0.29/0.47 ( ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_305_PiE,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_c,A4: set_c,B4: c > set_Sum_sum_c_c,X: c] :
% 0.29/0.47 ( ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_306_PiE,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_c,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_307_PiE,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_c,X: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_308_PiE,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_d,A4: set_c,B4: c > set_Sum_sum_c_d,X: c] :
% 0.29/0.47 ( ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_309_PiE,axiom,
% 0.29/0.47 ! [F: real > finite1398487019real_c,A4: set_real,B4: real > set_Fi1407883041real_c,X: real] :
% 0.29/0.47 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member1261661570real_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_real @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_310_PiE,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_311_PiE,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_Sum_sum_c_c,X: sum_sum_c_d] :
% 0.29/0.47 ( ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_d @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_312_PiE,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c,B4: ( real > finite1398487019real_c ) > set_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member527957930al_c_c @ F @ ( pi_rea1228756413al_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member1321351885real_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_313_PiE,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_d,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) )
% 0.29/0.47 => ( ~ ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) )
% 0.29/0.47 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PiE
% 0.29/0.47 thf(fact_314_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > c,B4: c > set_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_315_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_real,F: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 0.29/0.47 ( ! [X4: real] :
% 0.29/0.47 ( ( member_real @ X4 @ A4 )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_316_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: sum_sum_c_c > set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_317_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_c,B4: c > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_318_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_d,B4: c > set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_319_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: sum_sum_c_d > set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_320_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_321_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: sum_sum_c_c > set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_322_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: c > set_re2066790124real_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_323_Pi__I_H,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: sum_sum_c_d > set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 0.29/0.47 => ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_I'
% 0.29/0.47 thf(fact_324_Pi__iff,axiom,
% 0.29/0.47 ! [F: real > finite1398487019real_c,I: set_real,X8: real > set_Fi1407883041real_c] :
% 0.29/0.47 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ I @ X8 ) )
% 0.29/0.47 = ( ! [X3: real] :
% 0.29/0.47 ( ( member_real @ X3 @ I )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X3 ) @ ( X8 @ X3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_iff
% 0.29/0.47 thf(fact_325_Pi__mem,axiom,
% 0.29/0.47 ! [F: c > c,A4: set_c,B4: c > set_c,X: c] :
% 0.29/0.47 ( ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_326_Pi__mem,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_c,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_327_Pi__mem,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_c,A4: set_c,B4: c > set_Sum_sum_c_c,X: c] :
% 0.29/0.47 ( ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_328_Pi__mem,axiom,
% 0.29/0.47 ! [F: c > sum_sum_c_d,A4: set_c,B4: c > set_Sum_sum_c_d,X: c] :
% 0.29/0.47 ( ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_329_Pi__mem,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_c,X: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_330_Pi__mem,axiom,
% 0.29/0.47 ! [F: real > finite1398487019real_c,A4: set_real,B4: real > set_Fi1407883041real_c,X: real] :
% 0.29/0.47 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_real @ X @ A4 )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_331_Pi__mem,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_332_Pi__mem,axiom,
% 0.29/0.47 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_d,X: sum_sum_c_c] :
% 0.29/0.47 ( ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_333_Pi__mem,axiom,
% 0.29/0.47 ! [F: c > real > finite1398487019real_c,A4: set_c,B4: c > set_re2066790124real_c,X: c] :
% 0.29/0.47 ( ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_c @ X @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_334_Pi__mem,axiom,
% 0.29/0.47 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_Sum_sum_c_c,X: sum_sum_c_d] :
% 0.29/0.47 ( ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) )
% 0.29/0.47 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_mem
% 0.29/0.47 thf(fact_335_Pi__cong,axiom,
% 0.29/0.47 ! [A4: set_real,F: real > finite1398487019real_c,G: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 0.29/0.47 ( ! [W: real] :
% 0.29/0.47 ( ( member_real @ W @ A4 )
% 0.29/0.47 => ( ( F @ W )
% 0.29/0.47 = ( G @ W ) ) )
% 0.29/0.47 => ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 0.29/0.47 = ( member1321351885real_c @ G @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pi_cong
% 0.29/0.47 thf(fact_336_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member_c_c @ F
% 0.29/0.47 @ ( pi_c_c @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_337_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_real,F: real > finite1398487019real_c,B4: set_Fi1407883041real_c] :
% 0.29/0.47 ( ! [X4: real] :
% 0.29/0.47 ( ( member_real @ X4 @ A4 )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member1321351885real_c @ F
% 0.29/0.47 @ ( pi_rea1111636068real_c @ A4
% 0.29/0.47 @ ^ [Uu: real] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_338_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member_Sum_sum_c_c_c @ F
% 0.29/0.47 @ ( pi_Sum_sum_c_c_c @ A4
% 0.29/0.47 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_339_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_c @ F
% 0.29/0.47 @ ( pi_c_Sum_sum_c_c @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_340_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member_c_Sum_sum_c_d @ F
% 0.29/0.47 @ ( pi_c_Sum_sum_c_d @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_341_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: set_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member_Sum_sum_c_d_c @ F
% 0.29/0.47 @ ( pi_Sum_sum_c_d_c @ A4
% 0.29/0.47 @ ^ [Uu: sum_sum_c_d] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_342_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member1326674048um_c_c @ F
% 0.29/0.47 @ ( pi_Sum253006871um_c_c @ A4
% 0.29/0.47 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_343_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 0.29/0.47 ( ! [X4: sum_sum_c_c] :
% 0.29/0.47 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member318754689um_c_d @ F
% 0.29/0.47 @ ( pi_Sum261268376um_c_d @ A4
% 0.29/0.47 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_344_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: set_re2066790124real_c] :
% 0.29/0.47 ( ! [X4: c] :
% 0.29/0.47 ( ( member_c @ X4 @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member469531344real_c @ F
% 0.29/0.47 @ ( pi_c_r41638571real_c @ A4
% 0.29/0.47 @ ^ [Uu: c] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_345_funcsetI,axiom,
% 0.29/0.47 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.29/0.47 ( ! [X4: sum_sum_c_d] :
% 0.29/0.47 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 0.29/0.47 => ( member71251457um_c_c @ F
% 0.29/0.47 @ ( pi_Sum1145067928um_c_c @ A4
% 0.29/0.47 @ ^ [Uu: sum_sum_c_d] : B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcsetI
% 0.29/0.47 thf(fact_346_funcset__mem,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > sum_sum_c_c,A4: set_re2066790124real_c,B4: set_Sum_sum_c_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member354622481um_c_c @ F
% 0.29/0.47 @ ( pi_rea1500330408um_c_c @ A4
% 0.29/0.47 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_c @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47 thf(fact_347_funcset__mem,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c,B4: set_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member527957930al_c_c @ F
% 0.29/0.47 @ ( pi_rea1228756413al_c_c @ A4
% 0.29/0.47 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member_c @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47 thf(fact_348_funcset__mem,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > sum_sum_c_d,A4: set_re2066790124real_c,B4: set_Sum_sum_c_d,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member1494186770um_c_d @ F
% 0.29/0.47 @ ( pi_rea1508591913um_c_d @ A4
% 0.29/0.47 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member_Sum_sum_c_d @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47 thf(fact_349_funcset__mem,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > produc190496183real_c,A4: set_re2066790124real_c,B4: set_Pr1389752855real_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member954762593real_c @ F
% 0.29/0.47 @ ( pi_rea1379668980real_c @ A4
% 0.29/0.47 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member1895684704real_c @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47 thf(fact_350_funcset__mem,axiom,
% 0.29/0.47 ! [F: ( real > finite1398487019real_c ) > real > finite1398487019real_c,A4: set_re2066790124real_c,B4: set_re2066790124real_c,X: real > finite1398487019real_c] :
% 0.29/0.47 ( ( member1851015714real_c @ F
% 0.29/0.47 @ ( pi_rea1386151481real_c @ A4
% 0.29/0.47 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 0.29/0.47 => ( ( member1321351885real_c @ X @ A4 )
% 0.29/0.47 => ( member1321351885real_c @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47 thf(fact_351_funcset__mem,axiom,
% 0.29/0.47 ! [F: real > finite1398487019real_c,A4: set_real,B4: set_Fi1407883041real_c,X: real] :
% 0.29/0.47 ( ( member1321351885real_c @ F
% 0.29/0.47 @ ( pi_rea1111636068real_c @ A4
% 0.29/0.47 @ ^ [Uu: real] : B4 ) )
% 0.29/0.47 => ( ( member_real @ X @ A4 )
% 0.29/0.47 => ( member1261661570real_c @ ( F @ X ) @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % funcset_mem
% 0.29/0.47
% 0.29/0.47 % Helper facts (5)
% 0.29/0.47 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.47 ! [X: real,Y: real] :
% 0.29/0.47 ( ( if_real @ $false @ X @ Y )
% 0.29/0.47 = Y ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.47 ! [X: real,Y: real] :
% 0.29/0.47 ( ( if_real @ $true @ X @ Y )
% 0.29/0.47 = X ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_3_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 0.29/0.47 ! [P: $o] :
% 0.29/0.47 ( ( P = $true )
% 0.29/0.47 | ( P = $false ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 0.29/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.29/0.47 ( ( if_Fin36944805real_c @ $false @ X @ Y )
% 0.29/0.47 = Y ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 0.29/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.29/0.47 ( ( if_Fin36944805real_c @ $true @ X @ Y )
% 0.29/0.47 = X ) ).
% 0.29/0.47
% 0.29/0.47 % Conjectures (12)
% 0.29/0.47 thf(conj_0,hypothesis,
% 0.29/0.47 member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( static_FVF_a_b_c @ phi ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_1,hypothesis,
% 0.29/0.47 member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_2,hypothesis,
% 0.29/0.47 ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_3,hypothesis,
% 0.29/0.47 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 & ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 0.29/0.47 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ) )
% 0.29/0.47 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_4,hypothesis,
% 0.29/0.47 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 & ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ab @ i2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_5,hypothesis,
% 0.29/0.47 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 & ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc314122909real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ bb @ i2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_6,hypothesis,
% 0.29/0.47 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 & ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ bb @ i2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_7,hypothesis,
% 0.29/0.47 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 0.29/0.47 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ab @ i2 ) ) ) ) )
% 0.29/0.47 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 0.29/0.47 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc2010422875real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_8,hypothesis,
% 0.29/0.47 ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc314122909real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c
% 0.29/0.47 @ ( denota1275485728_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.47 @ i2 ) ) )
% 0.29/0.47 & ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c
% 0.29/0.47 @ ( produc314122909real_c
% 0.29/0.47 @ ( denota161327353_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( produc394644079real_c
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 0.29/0.47 @ bb )
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 0.29/0.47 @ i2 )
% 0.29/0.47 = ( finite772340578real_c
% 0.29/0.47 @ ( denota1275485728_a_b_c @ i @ oDEa
% 0.29/0.47 @ ( finite557796307c_real
% 0.29/0.47 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 0.29/0.47 @ i2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_9,hypothesis,
% 0.29/0.47 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 0.29/0.47 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_10,hypothesis,
% 0.29/0.47 ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) )
% 0.29/0.47 & ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 0.29/0.47 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(conj_11,conjecture,
% 0.29/0.47 ( ( finite772340578real_c @ ab @ i2 )
% 0.29/0.47 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.88/1.57 ---- Embedded in THF ---
% 2.88/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.88/1.57 %%% Generated on Tue Feb 24 08:26:42 EST 2026
% 2.88/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.88/1.57 %%% Logic specification used:
% 2.88/1.57 %%% thf(spec, logic, $$dhol).
% 2.88/1.57
% 2.88/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2DTF22144.p
% See solution above
% 2.88/1.58 ------------------------
% 3.08/1.62 ---- Cleaned THF ---
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.08/1.62 set_re844416664real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.08/1.62 set_re1692486081real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.08/1.62 set_Pr1389752855real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 produc190496183real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 3.08/1.62 set_re1812065969um_c_d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.08/1.62 set_re366411824um_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.08/1.62 produc214722967um_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_Itf__c_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.08/1.62 set_c_655950471real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mtf__c_J_J,type,
% 3.08/1.62 set_re141277793al_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.08/1.62 set_re2066790124real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 3.08/1.62 denota231621370t_unit: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.08/1.62 set_Su1997276704um_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 3.08/1.62 set_Su1008197536um_c_d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.08/1.62 set_Su1710027039um_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 set_Fi1407883041real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J_J,type,
% 3.08/1.62 set_c_Sum_sum_c_d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 3.08/1.62 set_c_Sum_sum_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mtf__c_J_J,type,
% 3.08/1.62 set_Sum_sum_c_d_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mtf__c_J_J,type,
% 3.08/1.62 set_Sum_sum_c_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.08/1.62 finite1398487019real_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 3.08/1.62 produc957004601l_real: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__d_J_J,type,
% 3.08/1.62 set_Sum_sum_c_d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 set_Sum_sum_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Syntax__Oformula_Itf__a_Mtf__b_Mtf__c_J,type,
% 3.08/1.62 formula_a_b_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 3.08/1.62 sum_sum_c_d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 sum_sum_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_I_062_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 set_c_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Syntax__OODE_Itf__a_Mtf__c_J,type,
% 3.08/1.62 oDE_a_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 3.08/1.62 set_real: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Set__Oset_Itf__c_J,type,
% 3.08/1.62 set_c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_t__Real__Oreal,type,
% 3.08/1.62 real: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_tf__d,type,
% 3.08/1.62 d: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(ty_n_tf__c,type,
% 3.08/1.62 c: $tType ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Coincidence__Mirabelle__veeocdlawq_Oids_Ocoincide__fml_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 coinci501627771_a_b_c: formula_a_b_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_OODE__sem_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota1275485728_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_OODE__vars_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota540094197_a_b_c: denota231621370t_unit > oDE_a_c > set_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_OVSagree_001tf__c,type,
% 3.08/1.62 denota256060419gree_c: finite1398487019real_c > finite1398487019real_c > set_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_OVagree_001tf__c,type,
% 3.08/1.62 denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_Oconcrete__v_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota310462944_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_Ofml__sem_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_Omk__v_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota161327353_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_Omk__xode_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota1896987029_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > produc190496183real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_Orepd_001tf__c,type,
% 3.08/1.62 denotational_repd_c: produc190496183real_c > c > real > produc190496183real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Denotational__Semantics_OsemBV_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 denota1293057250_a_b_c: denota231621370t_unit > oDE_a_c > set_Sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Finite__Cartesian__Product_Ovec_Ovec__lambda_001tf__c_001t__Real__Oreal,type,
% 3.08/1.62 finite557796307c_real: ( c > real ) > finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Finite__Cartesian__Product_Ovec_Ovec__nth_001t__Real__Oreal_001tf__c,type,
% 3.08/1.62 finite772340578real_c: finite1398487019real_c > c > real ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 pi_rea1386151481real_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_re2066790124real_c ) > set_re1692486081real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 pi_rea1379668980real_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Pr1389752855real_c ) > set_re844416664real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 pi_rea1500330408um_c_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Sum_sum_c_c ) > set_re366411824um_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 3.08/1.62 pi_rea1508591913um_c_d: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_Sum_sum_c_d ) > set_re1812065969um_c_d ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001tf__c,type,
% 3.08/1.62 pi_rea1228756413al_c_c: set_re2066790124real_c > ( ( real > finite1398487019real_c ) > set_c ) > set_re141277793al_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Real__Oreal_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.08/1.62 pi_rea1111636068real_c: set_real > ( real > set_Fi1407883041real_c ) > set_re2066790124real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Sum____Type__Osum_Itf__c_Mtf__c_J_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 pi_Sum253006871um_c_c: set_Sum_sum_c_c > ( sum_sum_c_c > set_Sum_sum_c_c ) > set_Su1710027039um_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Sum____Type__Osum_Itf__c_Mtf__c_J_001t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 3.08/1.62 pi_Sum261268376um_c_d: set_Sum_sum_c_c > ( sum_sum_c_c > set_Sum_sum_c_d ) > set_Su1008197536um_c_d ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Sum____Type__Osum_Itf__c_Mtf__c_J_001tf__c,type,
% 3.08/1.62 pi_Sum_sum_c_c_c: set_Sum_sum_c_c > ( sum_sum_c_c > set_c ) > set_Sum_sum_c_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Sum____Type__Osum_Itf__c_Mtf__d_J_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 pi_Sum1145067928um_c_c: set_Sum_sum_c_d > ( sum_sum_c_d > set_Sum_sum_c_c ) > set_Su1997276704um_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_FuncSet_OPi_001t__Sum____Type__Osum_Itf__c_Mtf__d_J_001tf__c,type,
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% 3.08/1.62 thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_Itf__c_Mtf__d_J_001tf__c,type,
% 3.08/1.62 image_Sum_sum_c_d_c: ( sum_sum_c_d > c ) > set_Sum_sum_c_d > set_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set_Oimage_001tf__c_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 image_1226855921real_c: ( c > real > finite1398487019real_c ) > set_c > set_re2066790124real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set_Oimage_001tf__c_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.08/1.62 image_687300774real_c: ( c > finite1398487019real_c ) > set_c > set_Fi1407883041real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set_Oimage_001tf__c_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 image_c_Sum_sum_c_c: ( c > sum_sum_c_c ) > set_c > set_Sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set_Oimage_001tf__c_001t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 3.08/1.62 image_c_Sum_sum_c_d: ( c > sum_sum_c_d ) > set_c > set_Sum_sum_c_d ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set_Oimage_001tf__c_001tf__c,type,
% 3.08/1.62 image_c_c: ( c > c ) > set_c > set_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 set_or1308937537real_c: ( real > finite1398487019real_c ) > ( real > finite1398487019real_c ) > set_re2066790124real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 set_or385782508real_c: produc190496183real_c > produc190496183real_c > set_Pr1389752855real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 3.08/1.62 set_or656347191t_real: real > real > set_real ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Static__Semantics_OBVO_001tf__a_001tf__c,type,
% 3.08/1.62 static_BVO_a_c: oDE_a_c > set_Sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Static__Semantics_OFVF_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Static__Semantics_OFVO_001tf__a_001tf__c,type,
% 3.08/1.62 static_FVO_a_c: oDE_a_c > set_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Sum__Type_OInl_001tf__c_001tf__c,type,
% 3.08/1.62 sum_Inl_c_c: c > sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Sum__Type_OInl_001tf__c_001tf__d,type,
% 3.08/1.62 sum_Inl_c_d: c > sum_sum_c_d ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Sum__Type_OInr_001tf__c_001tf__c,type,
% 3.08/1.62 sum_Inr_c_c: c > sum_sum_c_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Sum__Type_OInr_001tf__d_001tf__c,type,
% 3.08/1.62 sum_Inr_d_c: d > sum_sum_c_d ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Syntax_OEquiv_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Syntax_Ofsafe_001tf__a_001tf__b_001tf__c,type,
% 3.08/1.62 fsafe_a_b_c: formula_a_b_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_Syntax_Oosafe_001tf__a_001tf__c,type,
% 3.08/1.62 osafe_a_c: oDE_a_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.08/1.62 member1851015714real_c: ( ( real > finite1398487019real_c ) > real > finite1398487019real_c ) > set_re1692486081real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.08/1.62 member954762593real_c: ( ( real > finite1398487019real_c ) > produc190496183real_c ) > set_re844416664real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 member354622481um_c_c: ( ( real > finite1398487019real_c ) > sum_sum_c_c ) > set_re366411824um_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J,type,
% 3.08/1.62 member1494186770um_c_d: ( ( real > finite1398487019real_c ) > sum_sum_c_d ) > set_re1812065969um_c_d > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_I_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mtf__c_J,type,
% 3.08/1.62 member527957930al_c_c: ( ( real > finite1398487019real_c ) > c ) > set_re141277793al_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 member1321351885real_c: ( real > finite1398487019real_c ) > set_re2066790124real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 member1326674048um_c_c: ( sum_sum_c_c > sum_sum_c_c ) > set_Su1710027039um_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J,type,
% 3.08/1.62 member318754689um_c_d: ( sum_sum_c_c > sum_sum_c_d ) > set_Su1008197536um_c_d > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Sum____Type__Osum_Itf__c_Mtf__c_J_Mtf__c_J,type,
% 3.08/1.62 member_Sum_sum_c_c_c: ( sum_sum_c_c > c ) > set_Sum_sum_c_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 member71251457um_c_c: ( sum_sum_c_d > sum_sum_c_c ) > set_Su1997276704um_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_It__Sum____Type__Osum_Itf__c_Mtf__d_J_Mtf__c_J,type,
% 3.08/1.62 member_Sum_sum_c_d_c: ( sum_sum_c_d > c ) > set_Sum_sum_c_d_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_Itf__c_M_062_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.08/1.62 member469531344real_c: ( c > real > finite1398487019real_c ) > set_c_655950471real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 3.08/1.62 member_c_Sum_sum_c_c: ( c > sum_sum_c_c ) > set_c_Sum_sum_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_Itf__c_Mt__Sum____Type__Osum_Itf__c_Mtf__d_J_J,type,
% 3.08/1.62 member_c_Sum_sum_c_d: ( c > sum_sum_c_d ) > set_c_Sum_sum_c_d > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001_062_Itf__c_Mtf__c_J,type,
% 3.08/1.62 member_c_c: ( c > c ) > set_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.08/1.62 member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.08/1.62 member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001t__Real__Oreal,type,
% 3.08/1.62 member_real: real > set_real > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 3.08/1.62 member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001t__Sum____Type__Osum_Itf__c_Mtf__d_J,type,
% 3.08/1.62 member_Sum_sum_c_d: sum_sum_c_d > set_Sum_sum_c_d > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_c_member_001tf__c,type,
% 3.08/1.62 member_c: c > set_c > $o ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_I____,type,
% 3.08/1.62 i: denota231621370t_unit ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_ODE____,type,
% 3.08/1.62 ode: oDE_a_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_ODEa____,type,
% 3.08/1.62 oDEa: oDE_a_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_P____,type,
% 3.08/1.62 p: formula_a_b_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v__092_060phi_062_H____,type,
% 3.08/1.62 phi: formula_a_b_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_aa____,type,
% 3.08/1.62 aa: finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_ab____,type,
% 3.08/1.62 ab: finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_ba____,type,
% 3.08/1.62 ba: finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_bb____,type,
% 3.08/1.62 bb: finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_i____,type,
% 3.08/1.62 i2: c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_sol____,type,
% 3.08/1.62 sol: real > finite1398487019real_c ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_t____,type,
% 3.08/1.62 t: real ).
% 3.08/1.62
% 3.08/1.62 thf(sy_v_x____,type,
% 3.08/1.62 x: real ).
% 3.08/1.62
% 3.08/1.62 thf(fact_0_ode__to__fvo,axiom,
% 3.08/1.62 ! [X: c,I: denota231621370t_unit,ODE: oDE_a_c] :
% 3.08/1.62 ( ( member_c @ X @ ( denota540094197_a_b_c @ I @ ODE ) )
% 3.08/1.62 => ( member_c @ X @ ( static_FVO_a_c @ ODE ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_1_osafe,axiom,
% 3.08/1.62 osafe_a_c @ oDEa ).
% 3.08/1.62
% 3.08/1.62 thf(fact_2_eqP,axiom,
% 3.08/1.62 p = phi ).
% 3.08/1.62
% 3.08/1.62 thf(fact_3_x,axiom,
% 3.08/1.62 ord_less_eq_real @ zero_zero_real @ x ).
% 3.08/1.62
% 3.08/1.62 thf(fact_4_fsafe,axiom,
% 3.08/1.62 fsafe_a_b_c @ phi ).
% 3.08/1.62
% 3.08/1.62 thf(fact_5__092_060open_062_IInl_Ai_A_092_060in_062_AsemBV_AI_AODE_J_A_061_A_IInr_Ai_A_092_060in_062_AsemBV_AI_AODE_J_092_060close_062,axiom,
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) )
% 3.08/1.62 = ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_6_VA,axiom,
% 3.08/1.62 ! [X: real] :
% 3.08/1.62 ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ X ) )
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ X ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ ( static_FVF_a_b_c @ phi ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_7_prod_Ocollapse,axiom,
% 3.08/1.62 ! [Prod: produc190496183real_c] :
% 3.08/1.62 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 3.08/1.62 = Prod ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_8_bvo__to__fvo,axiom,
% 3.08/1.62 ! [X: c,ODE: oDE_a_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X ) @ ( static_BVO_a_c @ ODE ) )
% 3.08/1.62 => ( member_c @ X @ ( static_FVO_a_c @ ODE ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_9_vec__lambda__eta,axiom,
% 3.08/1.62 ! [G: finite1398487019real_c] :
% 3.08/1.62 ( ( finite557796307c_real @ ( finite772340578real_c @ G ) )
% 3.08/1.62 = G ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_10_Inl__Inr__False,axiom,
% 3.08/1.62 ! [X: c,Y: d] :
% 3.08/1.62 ( ( sum_Inl_c_d @ X )
% 3.08/1.62 != ( sum_Inr_d_c @ Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_11_Inl__Inr__False,axiom,
% 3.08/1.62 ! [X: c,Y: c] :
% 3.08/1.62 ( ( sum_Inl_c_c @ X )
% 3.08/1.62 != ( sum_Inr_c_c @ Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_12_Inr__Inl__False,axiom,
% 3.08/1.62 ! [X: d,Y: c] :
% 3.08/1.62 ( ( sum_Inr_d_c @ X )
% 3.08/1.62 != ( sum_Inl_c_d @ Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_13_Inr__Inl__False,axiom,
% 3.08/1.62 ! [X: c,Y: c] :
% 3.08/1.62 ( ( sum_Inr_c_c @ X )
% 3.08/1.62 != ( sum_Inl_c_c @ Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_14_vec__lambda__beta,axiom,
% 3.08/1.62 ! [G: c > real,I3: c] :
% 3.08/1.62 ( ( finite772340578real_c @ ( finite557796307c_real @ G ) @ I3 )
% 3.08/1.62 = ( G @ I3 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_15_alt__sem__lemma,axiom,
% 3.08/1.62 ! [ODE: oDE_a_c,I: denota231621370t_unit,Sol: real > finite1398487019real_c,T: real,Ab: finite1398487019real_c] :
% 3.08/1.62 ( ( osafe_a_c @ ODE )
% 3.08/1.62 => ( ( denota1275485728_a_b_c @ I @ ODE @ ( Sol @ T ) )
% 3.08/1.62 = ( denota1275485728_a_b_c @ I @ ODE
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ ODE ) ) @ ( finite772340578real_c @ ( Sol @ T ) @ I2 ) @ ( finite772340578real_c @ Ab @ I2 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_16_snd__zero,axiom,
% 3.08/1.62 ( ( produc314122909real_c @ zero_z1506780526real_c )
% 3.08/1.62 = zero_z109254132real_c ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_17_fst__zero,axiom,
% 3.08/1.62 ( ( produc2010422875real_c @ zero_z1506780526real_c )
% 3.08/1.62 = zero_z109254132real_c ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_18_zero__index,axiom,
% 3.08/1.62 ! [I3: c] :
% 3.08/1.62 ( ( finite772340578real_c @ zero_z109254132real_c @ I3 )
% 3.08/1.62 = zero_zero_real ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_19_hpsafe__Evolve_OIH,axiom,
% 3.08/1.62 coinci501627771_a_b_c @ p ).
% 3.08/1.62
% 3.08/1.62 thf(fact_20_hpsafe__Evolve_Ohyps_I1_J,axiom,
% 3.08/1.62 osafe_a_c @ ode ).
% 3.08/1.62
% 3.08/1.62 thf(fact_21_hpsafe__Evolve_Ohyps_I2_J,axiom,
% 3.08/1.62 fsafe_a_b_c @ p ).
% 3.08/1.62
% 3.08/1.62 thf(fact_22_old_Oprod_Oinject,axiom,
% 3.08/1.62 ! [A: finite1398487019real_c,B: finite1398487019real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.08/1.62 ( ( ( produc394644079real_c @ A @ B )
% 3.08/1.62 = ( produc394644079real_c @ A2 @ B2 ) )
% 3.08/1.62 = ( ( A = A2 )
% 3.08/1.62 & ( B = B2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_23_prod_Oinject,axiom,
% 3.08/1.62 ! [X1: finite1398487019real_c,X2: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 3.08/1.62 ( ( ( produc394644079real_c @ X1 @ X2 )
% 3.08/1.62 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 3.08/1.62 = ( ( X1 = Y1 )
% 3.08/1.62 & ( X2 = Y2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_24_t,axiom,
% 3.08/1.62 ord_less_eq_real @ x @ t ).
% 3.08/1.62
% 3.08/1.62 thf(fact_25_all,axiom,
% 3.08/1.62 ! [I4: c] :
% 3.08/1.62 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I4 ) @ ( static_BVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ I4 ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_d @ ( sum_Inl_c_d @ I4 ) @ ( image_c_Sum_sum_c_d @ sum_Inl_c_d @ ( static_FVO_a_c @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ I4 ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I4 ) @ ( static_FVF_a_b_c @ phi ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I4 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ I4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_26_less__eq__vec__def,axiom,
% 3.08/1.62 ( ord_le775706699real_c
% 3.08/1.62 = ( ^ [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.08/1.62 ! [I2: c] : ( ord_less_eq_real @ ( finite772340578real_c @ X3 @ I2 ) @ ( finite772340578real_c @ Y3 @ I2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_27_old_Oprod_Oinducts,axiom,
% 3.08/1.62 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 3.08/1.62 ( ! [A3: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A3 @ B3 ) )
% 3.08/1.62 => ( P @ Prod ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_28_old_Oprod_Oexhaust,axiom,
% 3.08/1.62 ! [Y: produc190496183real_c] :
% 3.08/1.62 ~ ! [A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 3.08/1.62 ( Y
% 3.08/1.62 != ( produc394644079real_c @ A3 @ B3 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_29_Pair__inject,axiom,
% 3.08/1.62 ! [A: finite1398487019real_c,B: finite1398487019real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.08/1.62 ( ( ( produc394644079real_c @ A @ B )
% 3.08/1.62 = ( produc394644079real_c @ A2 @ B2 ) )
% 3.08/1.62 => ~ ( ( A = A2 )
% 3.08/1.62 => ( B != B2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_30_prod__cases,axiom,
% 3.08/1.62 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 3.08/1.62 ( ! [A3: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A3 @ B3 ) )
% 3.08/1.62 => ( P @ P2 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_31_surj__pair,axiom,
% 3.08/1.62 ! [P2: produc190496183real_c] :
% 3.08/1.62 ? [X4: finite1398487019real_c,Y4: finite1398487019real_c] :
% 3.08/1.62 ( P2
% 3.08/1.62 = ( produc394644079real_c @ X4 @ Y4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_32_vec__nth__inject,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.08/1.62 ( ( ( finite772340578real_c @ X )
% 3.08/1.62 = ( finite772340578real_c @ Y ) )
% 3.08/1.62 = ( X = Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_33_cond__component,axiom,
% 3.08/1.62 ! [B: $o,X: finite1398487019real_c,Y: finite1398487019real_c,I3: c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 => ( ( finite772340578real_c @ ( if_Fin36944805real_c @ B @ X @ Y ) @ I3 )
% 3.08/1.62 = ( finite772340578real_c @ X @ I3 ) ) )
% 3.08/1.62 & ( ~ B
% 3.08/1.62 => ( ( finite772340578real_c @ ( if_Fin36944805real_c @ B @ X @ Y ) @ I3 )
% 3.08/1.62 = ( finite772340578real_c @ Y @ I3 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_34_vec__eq__iff,axiom,
% 3.08/1.62 ( ( ^ [Y5: finite1398487019real_c,Z: finite1398487019real_c] : ( Y5 = Z ) )
% 3.08/1.62 = ( ^ [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.08/1.62 ! [I2: c] :
% 3.08/1.62 ( ( finite772340578real_c @ X3 @ I2 )
% 3.08/1.62 = ( finite772340578real_c @ Y3 @ I2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_35_zero__prod__def,axiom,
% 3.08/1.62 ( zero_z1506780526real_c
% 3.08/1.62 = ( produc394644079real_c @ zero_z109254132real_c @ zero_z109254132real_c ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_36_zero__prod__def,axiom,
% 3.08/1.62 ( zero_z659284464l_real
% 3.08/1.62 = ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_37_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: sum_sum_c_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ A @ ( collect_Sum_sum_c_c @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_38_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: sum_sum_c_d,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ A @ ( collect_Sum_sum_c_d @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_39_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: produc190496183real_c,P: produc190496183real_c > $o] :
% 3.08/1.62 ( ( member1895684704real_c @ A @ ( collec1643251106real_c @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_40_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: real > finite1398487019real_c,P: ( real > finite1398487019real_c ) > $o] :
% 3.08/1.62 ( ( member1321351885real_c @ A @ ( collec913357835real_c @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_41_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: finite1398487019real_c,P: finite1398487019real_c > $o] :
% 3.08/1.62 ( ( member1261661570real_c @ A @ ( collec230941376real_c @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_42_mem__Collect__eq,axiom,
% 3.08/1.62 ! [A: c,P: c > $o] :
% 3.08/1.62 ( ( member_c @ A @ ( collect_c @ P ) )
% 3.08/1.62 = ( P @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_43_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_44_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_45_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_Pr1389752855real_c] :
% 3.08/1.62 ( ( collec1643251106real_c
% 3.08/1.62 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_46_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_re2066790124real_c] :
% 3.08/1.62 ( ( collec913357835real_c
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_47_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_Fi1407883041real_c] :
% 3.08/1.62 ( ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1261661570real_c @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_48_Collect__mem__eq,axiom,
% 3.08/1.62 ! [A4: set_c] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] : ( member_c @ X3 @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_49_Collect__cong,axiom,
% 3.08/1.62 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 3.08/1.62 ( ! [X4: finite1398487019real_c] :
% 3.08/1.62 ( ( P @ X4 )
% 3.08/1.62 = ( Q @ X4 ) )
% 3.08/1.62 => ( ( collec230941376real_c @ P )
% 3.08/1.62 = ( collec230941376real_c @ Q ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_50_Collect__cong,axiom,
% 3.08/1.62 ! [P: c > $o,Q: c > $o] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( P @ X4 )
% 3.08/1.62 = ( Q @ X4 ) )
% 3.08/1.62 => ( ( collect_c @ P )
% 3.08/1.62 = ( collect_c @ Q ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_51_fst__conv,axiom,
% 3.08/1.62 ! [X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 3.08/1.62 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X2 ) )
% 3.08/1.62 = X1 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_52_fst__eqD,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 3.08/1.62 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.08/1.62 = A )
% 3.08/1.62 => ( X = A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_53_snd__conv,axiom,
% 3.08/1.62 ! [X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 3.08/1.62 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X2 ) )
% 3.08/1.62 = X2 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_54_snd__eqD,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 3.08/1.62 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.08/1.62 = A )
% 3.08/1.62 => ( Y = A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_55_prod__eq__iff,axiom,
% 3.08/1.62 ( ( ^ [Y5: produc190496183real_c,Z: produc190496183real_c] : ( Y5 = Z ) )
% 3.08/1.62 = ( ^ [S: produc190496183real_c,T2: produc190496183real_c] :
% 3.08/1.62 ( ( ( produc2010422875real_c @ S )
% 3.08/1.62 = ( produc2010422875real_c @ T2 ) )
% 3.08/1.62 & ( ( produc314122909real_c @ S )
% 3.08/1.62 = ( produc314122909real_c @ T2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_56_prod_Oexpand,axiom,
% 3.08/1.62 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 3.08/1.62 ( ( ( ( produc2010422875real_c @ Prod )
% 3.08/1.62 = ( produc2010422875real_c @ Prod2 ) )
% 3.08/1.62 & ( ( produc314122909real_c @ Prod )
% 3.08/1.62 = ( produc314122909real_c @ Prod2 ) ) )
% 3.08/1.62 => ( Prod = Prod2 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_57_prod__eqI,axiom,
% 3.08/1.62 ! [P2: produc190496183real_c,Q2: produc190496183real_c] :
% 3.08/1.62 ( ( ( produc2010422875real_c @ P2 )
% 3.08/1.62 = ( produc2010422875real_c @ Q2 ) )
% 3.08/1.62 => ( ( ( produc314122909real_c @ P2 )
% 3.08/1.62 = ( produc314122909real_c @ Q2 ) )
% 3.08/1.62 => ( P2 = Q2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_58_vec__nth__inverse,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c] :
% 3.08/1.62 ( ( finite557796307c_real @ ( finite772340578real_c @ X ) )
% 3.08/1.62 = X ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_59_vec__lambda__unique,axiom,
% 3.08/1.62 ! [F: finite1398487019real_c,G: c > real] :
% 3.08/1.62 ( ( ! [I2: c] :
% 3.08/1.62 ( ( finite772340578real_c @ F @ I2 )
% 3.08/1.62 = ( G @ I2 ) ) )
% 3.08/1.62 = ( ( finite557796307c_real @ G )
% 3.08/1.62 = F ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_60_zero__vec__def,axiom,
% 3.08/1.62 ( zero_z109254132real_c
% 3.08/1.62 = ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_61_surjective__pairing,axiom,
% 3.08/1.62 ! [T: produc190496183real_c] :
% 3.08/1.62 ( T
% 3.08/1.62 = ( produc394644079real_c @ ( produc2010422875real_c @ T ) @ ( produc314122909real_c @ T ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_62_prod_Oexhaust__sel,axiom,
% 3.08/1.62 ! [Prod: produc190496183real_c] :
% 3.08/1.62 ( Prod
% 3.08/1.62 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_63_mk__v__concrete,axiom,
% 3.08/1.62 ( denota161327353_a_b_c
% 3.08/1.62 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Nu: produc190496183real_c,Sol2: finite1398487019real_c] :
% 3.08/1.62 ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ Sol2 @ ( produc2010422875real_c @ Nu ) ) @ I2 ) )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) @ ( produc314122909real_c @ Nu ) ) @ I2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_64__092_060open_062Vagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_Imk__xode_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_Ax_A_E_Ai_Aelse_Aab_A_E_Ai_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
% 3.08/1.62 ( ( denota1997846518gree_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ( denota1997846518gree_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ ( denota1896987029_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_65_Vagree__def,axiom,
% 3.08/1.62 ( denota1997846518gree_c
% 3.08/1.62 = ( ^ [Nu: produc190496183real_c,Nu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [I2: c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ V )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc2010422875real_c @ Nu ) @ I2 )
% 3.08/1.62 = ( finite772340578real_c @ ( produc2010422875real_c @ Nu2 ) @ I2 ) ) )
% 3.08/1.62 & ! [I2: c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ V )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc314122909real_c @ Nu ) @ I2 )
% 3.08/1.62 = ( finite772340578real_c @ ( produc314122909real_c @ Nu2 ) @ I2 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_66__092_060open_062Vagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Iab_M_Abb_J_A_I_N_AsemBV_AI_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_Ax_J_J_A_Imk__xode_AI_AODE_A_Isol_Ax_J_J_A_IsemBV_AI_AODE_J_092_060close_062,axiom,
% 3.08/1.62 ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( produc394644079real_c @ ab @ bb ) @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ( denota1997846518gree_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) @ ( denota1896987029_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ ( denota1293057250_a_b_c @ i @ oDEa ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_67_concrete__v_Osimps,axiom,
% 3.08/1.62 ( denota310462944_a_b_c
% 3.08/1.62 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Nu: produc190496183real_c,Sol2: finite1398487019real_c] :
% 3.08/1.62 ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ Sol2 @ ( produc2010422875real_c @ Nu ) ) @ I2 ) )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ I5 @ ODE2 ) ) @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) @ ( produc314122909real_c @ Nu ) ) @ I2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_68_concrete__v_Oelims,axiom,
% 3.08/1.62 ! [X: denota231621370t_unit,Xa: oDE_a_c,Xb: produc190496183real_c,Xc: finite1398487019real_c,Y: produc190496183real_c] :
% 3.08/1.62 ( ( ( denota310462944_a_b_c @ X @ Xa @ Xb @ Xc )
% 3.08/1.62 = Y )
% 3.08/1.62 => ( Y
% 3.08/1.62 = ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ I2 ) @ ( denota1293057250_a_b_c @ X @ Xa ) ) @ Xc @ ( produc2010422875real_c @ Xb ) ) @ I2 ) )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( finite772340578real_c @ ( if_Fin36944805real_c @ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ I2 ) @ ( denota1293057250_a_b_c @ X @ Xa ) ) @ ( denota1275485728_a_b_c @ X @ Xa @ Xc ) @ ( produc314122909real_c @ Xb ) ) @ I2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_69_Pair__le,axiom,
% 3.08/1.62 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 3.08/1.62 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 3.08/1.62 = ( ( ord_le775706699real_c @ A @ C )
% 3.08/1.62 & ( ord_le775706699real_c @ B @ D ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_70_Pair__le,axiom,
% 3.08/1.62 ! [A: real,B: real,C: real,D: real] :
% 3.08/1.62 ( ( ord_le1342644953l_real @ ( produc705216881l_real @ A @ B ) @ ( produc705216881l_real @ C @ D ) )
% 3.08/1.62 = ( ( ord_less_eq_real @ A @ C )
% 3.08/1.62 & ( ord_less_eq_real @ B @ D ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_71_sem,axiom,
% 3.08/1.62 ! [Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 3.08/1.62 ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ ( static_FVF_a_b_c @ p ) )
% 3.08/1.62 => ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ i @ p ) )
% 3.08/1.62 = ( member1895684704real_c @ Nu4 @ ( denota968303861_a_b_c @ i @ p ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_72_aaba,axiom,
% 3.08/1.62 ( ( produc394644079real_c @ aa @ ba )
% 3.08/1.62 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_73_add_Oinverse__neutral,axiom,
% 3.08/1.62 ( ( uminus_uminus_real @ zero_zero_real )
% 3.08/1.62 = zero_zero_real ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_74_neg__0__equal__iff__equal,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( zero_zero_real
% 3.08/1.62 = ( uminus_uminus_real @ A ) )
% 3.08/1.62 = ( zero_zero_real = A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_75_neg__equal__0__iff__equal,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ( uminus_uminus_real @ A )
% 3.08/1.62 = zero_zero_real )
% 3.08/1.62 = ( A = zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_76_equal__neg__zero,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( A
% 3.08/1.62 = ( uminus_uminus_real @ A ) )
% 3.08/1.62 = ( A = zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_77_neg__equal__zero,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ( uminus_uminus_real @ A )
% 3.08/1.62 = A )
% 3.08/1.62 = ( A = zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_78_neg__le__iff__le,axiom,
% 3.08/1.62 ! [B: real,A: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 3.08/1.62 = ( ord_less_eq_real @ A @ B ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_79_uminus__Pair,axiom,
% 3.08/1.62 ! [A: finite1398487019real_c,B: finite1398487019real_c] :
% 3.08/1.62 ( ( uminus17964590real_c @ ( produc394644079real_c @ A @ B ) )
% 3.08/1.62 = ( produc394644079real_c @ ( uminus1737280820real_c @ A ) @ ( uminus1737280820real_c @ B ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_80_uminus__Pair,axiom,
% 3.08/1.62 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( uminus1225118734um_c_c @ ( produc1439061071um_c_c @ A @ B ) )
% 3.08/1.62 = ( produc1439061071um_c_c @ ( uminus1381786404um_c_c @ A ) @ ( uminus1381786404um_c_c @ B ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_81_vector__uminus__component,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,I3: c] :
% 3.08/1.62 ( ( finite772340578real_c @ ( uminus1737280820real_c @ X ) @ I3 )
% 3.08/1.62 = ( uminus_uminus_real @ ( finite772340578real_c @ X @ I3 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_82_fst__uminus,axiom,
% 3.08/1.62 ! [X: produc190496183real_c] :
% 3.08/1.62 ( ( produc2010422875real_c @ ( uminus17964590real_c @ X ) )
% 3.08/1.62 = ( uminus1737280820real_c @ ( produc2010422875real_c @ X ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_83_snd__uminus,axiom,
% 3.08/1.62 ! [X: produc190496183real_c] :
% 3.08/1.62 ( ( produc314122909real_c @ ( uminus17964590real_c @ X ) )
% 3.08/1.62 = ( uminus1737280820real_c @ ( produc314122909real_c @ X ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_84_neg__less__eq__nonneg,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 3.08/1.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_85_less__eq__neg__nonpos,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 3.08/1.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_86_neg__le__0__iff__le,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 3.08/1.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_87_neg__0__le__iff__le,axiom,
% 3.08/1.62 ! [A: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 3.08/1.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_88_allT,axiom,
% 3.08/1.62 ! [S2: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ zero_zero_real @ S2 )
% 3.08/1.62 => ( ( ord_less_eq_real @ S2 @ t )
% 3.08/1.62 => ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ S2 ) ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_89_iff__to__impl,axiom,
% 3.08/1.62 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,A4: formula_a_b_c,B4: formula_a_b_c] :
% 3.08/1.62 ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 3.08/1.62 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) )
% 3.08/1.62 = ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 3.08/1.62 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) )
% 3.08/1.62 & ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) )
% 3.08/1.62 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_90_le__imp__neg__le,axiom,
% 3.08/1.62 ! [A: real,B: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ A @ B )
% 3.08/1.62 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_91_minus__le__iff,axiom,
% 3.08/1.62 ! [A: real,B: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 3.08/1.62 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_92_le__minus__iff,axiom,
% 3.08/1.62 ! [A: real,B: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 3.08/1.62 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_93_agree__supset,axiom,
% 3.08/1.62 ! [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c,Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ B4 @ A4 )
% 3.08/1.62 => ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ A4 )
% 3.08/1.62 => ( denota1997846518gree_c @ Nu3 @ Nu4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_94_agree__sub,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 3.08/1.62 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B4 )
% 3.08/1.62 => ( denota1997846518gree_c @ Nu3 @ Omega @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_95_mk__v__exists,axiom,
% 3.08/1.62 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,ODE: oDE_a_c,Sol: finite1398487019real_c] :
% 3.08/1.62 ? [Omega2: produc190496183real_c] :
% 3.08/1.62 ( ( denota1997846518gree_c @ Omega2 @ Nu3 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ I @ ODE ) ) )
% 3.08/1.62 & ( denota1997846518gree_c @ Omega2 @ ( denota1896987029_a_b_c @ I @ ODE @ Sol ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_96_uminus__vec__def,axiom,
% 3.08/1.62 ( uminus1737280820real_c
% 3.08/1.62 = ( ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( uminus_uminus_real @ ( finite772340578real_c @ X3 @ I2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_97_uminus__prod__def,axiom,
% 3.08/1.62 ( uminus17964590real_c
% 3.08/1.62 = ( ^ [X3: produc190496183real_c] : ( produc394644079real_c @ ( uminus1737280820real_c @ ( produc2010422875real_c @ X3 ) ) @ ( uminus1737280820real_c @ ( produc314122909real_c @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_98_uminus__prod__def,axiom,
% 3.08/1.62 ( uminus1225118734um_c_c
% 3.08/1.62 = ( ^ [X3: produc214722967um_c_c] : ( produc1439061071um_c_c @ ( uminus1381786404um_c_c @ ( produc1983230011um_c_c @ X3 ) ) @ ( uminus1381786404um_c_c @ ( produc1132019837um_c_c @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_99_mk__v__agree,axiom,
% 3.08/1.62 ! [I: denota231621370t_unit,ODE: oDE_a_c,Nu3: produc190496183real_c,Sol: finite1398487019real_c] :
% 3.08/1.62 ( ( denota1997846518gree_c @ ( denota161327353_a_b_c @ I @ ODE @ Nu3 @ Sol ) @ Nu3 @ ( uminus1381786404um_c_c @ ( denota1293057250_a_b_c @ I @ ODE ) ) )
% 3.08/1.62 & ( denota1997846518gree_c @ ( denota161327353_a_b_c @ I @ ODE @ Nu3 @ Sol ) @ ( denota1896987029_a_b_c @ I @ ODE @ Sol ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_100_mk__xode_Oelims,axiom,
% 3.08/1.62 ! [X: denota231621370t_unit,Xa: oDE_a_c,Xb: finite1398487019real_c,Y: produc190496183real_c] :
% 3.08/1.62 ( ( ( denota1896987029_a_b_c @ X @ Xa @ Xb )
% 3.08/1.62 = Y )
% 3.08/1.62 => ( Y
% 3.08/1.62 = ( produc394644079real_c @ Xb @ ( denota1275485728_a_b_c @ X @ Xa @ Xb ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_101_mk__xode_Osimps,axiom,
% 3.08/1.62 ( denota1896987029_a_b_c
% 3.08/1.62 = ( ^ [I5: denota231621370t_unit,ODE2: oDE_a_c,Sol2: finite1398487019real_c] : ( produc394644079real_c @ Sol2 @ ( denota1275485728_a_b_c @ I5 @ ODE2 @ Sol2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_102_zero__reorient,axiom,
% 3.08/1.62 ! [X: real] :
% 3.08/1.62 ( ( zero_zero_real = X )
% 3.08/1.62 = ( X = zero_zero_real ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_103_agree__refl,axiom,
% 3.08/1.62 ! [Nu3: produc190496183real_c,A4: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_104_agree__comm,axiom,
% 3.08/1.62 ! [A4: produc190496183real_c,B4: produc190496183real_c,V2: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( denota1997846518gree_c @ A4 @ B4 @ V2 )
% 3.08/1.62 => ( denota1997846518gree_c @ B4 @ A4 @ V2 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_105_Pair__mono,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,X5: finite1398487019real_c,Y: finite1398487019real_c,Y6: finite1398487019real_c] :
% 3.08/1.62 ( ( ord_le775706699real_c @ X @ X5 )
% 3.08/1.62 => ( ( ord_le775706699real_c @ Y @ Y6 )
% 3.08/1.62 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X5 @ Y6 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_106_Pair__mono,axiom,
% 3.08/1.62 ! [X: real,X5: real,Y: real,Y6: real] :
% 3.08/1.62 ( ( ord_less_eq_real @ X @ X5 )
% 3.08/1.62 => ( ( ord_less_eq_real @ Y @ Y6 )
% 3.08/1.62 => ( ord_le1342644953l_real @ ( produc705216881l_real @ X @ Y ) @ ( produc705216881l_real @ X5 @ Y6 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_107_fst__mono,axiom,
% 3.08/1.62 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le850691415real_c @ X @ Y )
% 3.08/1.62 => ( ord_le775706699real_c @ ( produc2010422875real_c @ X ) @ ( produc2010422875real_c @ Y ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_108_snd__mono,axiom,
% 3.08/1.62 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le850691415real_c @ X @ Y )
% 3.08/1.62 => ( ord_le775706699real_c @ ( produc314122909real_c @ X ) @ ( produc314122909real_c @ Y ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_109_less__eq__prod__def,axiom,
% 3.08/1.62 ( ord_le850691415real_c
% 3.08/1.62 = ( ^ [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le775706699real_c @ ( produc2010422875real_c @ X3 ) @ ( produc2010422875real_c @ Y3 ) )
% 3.08/1.62 & ( ord_le775706699real_c @ ( produc314122909real_c @ X3 ) @ ( produc314122909real_c @ Y3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_110_less__eq__prod__def,axiom,
% 3.08/1.62 ( ord_le1342644953l_real
% 3.08/1.62 = ( ^ [X3: produc957004601l_real,Y3: produc957004601l_real] :
% 3.08/1.62 ( ( ord_less_eq_real @ ( produc1422991709l_real @ X3 ) @ ( produc1422991709l_real @ Y3 ) )
% 3.08/1.62 & ( ord_less_eq_real @ ( produc1407670175l_real @ X3 ) @ ( produc1407670175l_real @ Y3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_111_ODE__vars__lr,axiom,
% 3.08/1.62 ! [X: c,I: denota231621370t_unit,ODE: oDE_a_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ X ) @ ( denota1293057250_a_b_c @ I @ ODE ) )
% 3.08/1.62 = ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ X ) @ ( denota1293057250_a_b_c @ I @ ODE ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_112__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Aab_A_061_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
% 3.08/1.62 ( ( osafe_a_c @ oDEa )
% 3.08/1.62 => ( ( fsafe_a_b_c @ phi )
% 3.08/1.62 => ( ( ode = oDEa )
% 3.08/1.62 => ( ( p = phi )
% 3.08/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 3.08/1.62 => ( ( ( produc394644079real_c @ aa @ ba )
% 3.08/1.62 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 3.08/1.62 => ( ( initia1631504802real_c @ sol
% 3.08/1.62 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 3.08/1.62 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 3.08/1.62 @ ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 3.08/1.62 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [Uu: c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 3.08/1.62 => ( ab
% 3.08/1.62 = ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_113__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_A_061_Amk__v_AI_AODE_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_A0_A_E_Ai_Aelse_Aab_A_E_Ai_M_Abb_J_A_I_092_060chi_062i_O_Aif_Ai_A_092_060in_062_AFVO_AODE_Athen_Asol_At_A_E_Ai_Aelse_Aab_A_E_Ai_J_092_060close_062,axiom,
% 3.08/1.62 ( ( osafe_a_c @ oDEa )
% 3.08/1.62 => ( ( fsafe_a_b_c @ phi )
% 3.08/1.62 => ( ( ode = oDEa )
% 3.08/1.62 => ( ( p = phi )
% 3.08/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 3.08/1.62 => ( ( ( produc394644079real_c @ aa @ ba )
% 3.08/1.62 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 3.08/1.62 => ( ( initia1631504802real_c @ sol
% 3.08/1.62 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 3.08/1.62 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 3.08/1.62 @ ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 3.08/1.62 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [Uu: c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 3.08/1.62 => ( ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) )
% 3.08/1.62 = ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ t ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_114__092_060open_062_092_060lbrakk_062osafe_AODE_059_Afsafe_A_092_060phi_062_059_AODE_____A_061_AODE_059_AP_A_061_A_092_060phi_062_059_A0_A_092_060le_062_At_059_A_Iaa_M_Aba_J_A_061_Amk__v_AI_AODE_A_Iab_M_Abb_J_A_Isol_At_J_059_A_Isol_Asolves__ode_A_I_092_060lambda_062a_O_AODE__sem_AI_AODE_J_J_A_1230_O_Ot_125_A_123x_O_Amk__v_AI_AODE_A_Iab_M_Abb_J_Ax_A_092_060in_062_Afml__sem_AI_A_092_060phi_062_125_059_AVSagree_A_Isol_A0_J_Aab_A_123uu___O_AInl_Auu___A_092_060in_062_ABVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AInl_A_096_AFVO_AODE_A_092_060or_062_AInl_Auu___A_092_060in_062_AFVF_A_092_060phi_062_125_092_060rbrakk_062_A_092_060Longrightarrow_062_A0_A_092_060le_062_At_092_060close_062,axiom,
% 3.08/1.62 ( ( osafe_a_c @ oDEa )
% 3.08/1.62 => ( ( fsafe_a_b_c @ phi )
% 3.08/1.62 => ( ( ode = oDEa )
% 3.08/1.62 => ( ( p = phi )
% 3.08/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ t )
% 3.08/1.62 => ( ( ( produc394644079real_c @ aa @ ba )
% 3.08/1.62 = ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ t ) ) )
% 3.08/1.62 => ( ( initia1631504802real_c @ sol
% 3.08/1.62 @ ^ [X6: real] : ( denota1275485728_a_b_c @ i @ oDEa )
% 3.08/1.62 @ ( set_or656347191t_real @ zero_zero_real @ t )
% 3.08/1.62 @ ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) )
% 3.08/1.62 => ( ( denota256060419gree_c @ ( sol @ zero_zero_real ) @ ab
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [Uu: c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_BVO_a_c @ oDEa ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( static_FVO_a_c @ oDEa ) ) )
% 3.08/1.62 | ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ Uu ) @ ( static_FVF_a_b_c @ phi ) ) ) ) )
% 3.08/1.62 => ( ord_less_eq_real @ zero_zero_real @ t ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_115_mkV,axiom,
% 3.08/1.62 ( member1321351885real_c @ sol
% 3.08/1.62 @ ( pi_rea1111636068real_c @ ( set_or656347191t_real @ zero_zero_real @ t )
% 3.08/1.62 @ ^ [Uu: real] :
% 3.08/1.62 ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1895684704real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ X3 ) @ ( denota968303861_a_b_c @ i @ phi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_116_compl__le__compl__iff,axiom,
% 3.08/1.62 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ X ) @ ( uminus1381786404um_c_c @ Y ) )
% 3.08/1.62 = ( ord_le1772180283um_c_c @ Y @ X ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_117_iff__sem,axiom,
% 3.08/1.62 ! [Nu3: produc190496183real_c,I: denota231621370t_unit,A4: formula_a_b_c,B4: formula_a_b_c] :
% 3.08/1.62 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ ( equiv_a_b_c @ A4 @ B4 ) ) )
% 3.08/1.62 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ A4 ) )
% 3.08/1.62 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I @ B4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_118_double__compl,axiom,
% 3.08/1.62 ! [X: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( uminus1381786404um_c_c @ ( uminus1381786404um_c_c @ X ) )
% 3.08/1.62 = X ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_119_compl__eq__compl__iff,axiom,
% 3.08/1.62 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ( uminus1381786404um_c_c @ X )
% 3.08/1.62 = ( uminus1381786404um_c_c @ Y ) )
% 3.08/1.62 = ( X = Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_120_VSagree__sub,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c,Nu3: finite1398487019real_c,Omega: finite1398487019real_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 3.08/1.62 => ( ( denota256060419gree_c @ Nu3 @ Omega @ B4 )
% 3.08/1.62 => ( denota256060419gree_c @ Nu3 @ Omega @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_121_VSagree__supset,axiom,
% 3.08/1.62 ! [B4: set_c,A4: set_c,Nu3: finite1398487019real_c,Nu4: finite1398487019real_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ B4 @ A4 )
% 3.08/1.62 => ( ( denota256060419gree_c @ Nu3 @ Nu4 @ A4 )
% 3.08/1.62 => ( denota256060419gree_c @ Nu3 @ Nu4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_122_VSagree__refl,axiom,
% 3.08/1.62 ! [Nu3: finite1398487019real_c,A4: set_c] : ( denota256060419gree_c @ Nu3 @ Nu3 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_123_VSagree__def,axiom,
% 3.08/1.62 ( denota256060419gree_c
% 3.08/1.62 = ( ^ [Nu: finite1398487019real_c,Nu2: finite1398487019real_c,V: set_c] :
% 3.08/1.62 ! [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ V )
% 3.08/1.62 => ( ( finite772340578real_c @ Nu @ X3 )
% 3.08/1.62 = ( finite772340578real_c @ Nu2 @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_124_compl__mono,axiom,
% 3.08/1.62 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ X @ Y )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ Y ) @ ( uminus1381786404um_c_c @ X ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_125_compl__le__swap1,axiom,
% 3.08/1.62 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ Y @ ( uminus1381786404um_c_c @ X ) )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ X @ ( uminus1381786404um_c_c @ Y ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_126_compl__le__swap2,axiom,
% 3.08/1.62 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ Y ) @ X )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ X ) @ Y ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_127_image__uminus__atLeastAtMost,axiom,
% 3.08/1.62 ! [X: real,Y: real] :
% 3.08/1.62 ( ( image_real_real @ uminus_uminus_real @ ( set_or656347191t_real @ X @ Y ) )
% 3.08/1.62 = ( set_or656347191t_real @ ( uminus_uminus_real @ Y ) @ ( uminus_uminus_real @ X ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_128_atLeastatMost__subset__iff,axiom,
% 3.08/1.62 ! [A: real,B: real,C: real,D: real] :
% 3.08/1.62 ( ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
% 3.08/1.62 = ( ~ ( ord_less_eq_real @ A @ B )
% 3.08/1.62 | ( ( ord_less_eq_real @ C @ A )
% 3.08/1.62 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_129_Compl__subset__Compl__iff,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ A4 ) @ ( uminus1381786404um_c_c @ B4 ) )
% 3.08/1.62 = ( ord_le1772180283um_c_c @ B4 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_130_Compl__anti__mono,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( uminus1381786404um_c_c @ B4 ) @ ( uminus1381786404um_c_c @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_131_image__eqI,axiom,
% 3.08/1.62 ! [B: c,F: c > c,X: c,A4: set_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ B @ ( image_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_132_image__eqI,axiom,
% 3.08/1.62 ! [B: c,F: sum_sum_c_c > c,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_133_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: c > sum_sum_c_c,X: c,A4: set_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_134_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: c > sum_sum_c_d,X: c,A4: set_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_135_image__eqI,axiom,
% 3.08/1.62 ! [B: c,F: sum_sum_c_d > c,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_136_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_137_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d,X: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_138_image__eqI,axiom,
% 3.08/1.62 ! [B: real > finite1398487019real_c,F: c > real > finite1398487019real_c,X: c,A4: set_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ B @ ( image_1226855921real_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_139_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_140_image__eqI,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,X: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_141_subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ X4 @ B4 ) )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ A4 @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_142_subsetI,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ X4 @ B4 ) )
% 3.08/1.62 => ( ord_less_eq_set_c @ A4 @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_143_subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ X4 @ B4 ) )
% 3.08/1.62 => ( ord_le764260924um_c_d @ A4 @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_144_subsetI,axiom,
% 3.08/1.62 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c] :
% 3.08/1.62 ( ! [X4: produc190496183real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ X4 @ A4 )
% 3.08/1.62 => ( member1895684704real_c @ X4 @ B4 ) )
% 3.08/1.62 => ( ord_le977353143real_c @ A4 @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_145_subsetI,axiom,
% 3.08/1.62 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c] :
% 3.08/1.62 ( ! [X4: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ X4 @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ X4 @ B4 ) )
% 3.08/1.62 => ( ord_le35002188real_c @ A4 @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_146_Compl__eq__Compl__iff,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ( uminus1381786404um_c_c @ A4 )
% 3.08/1.62 = ( uminus1381786404um_c_c @ B4 ) )
% 3.08/1.62 = ( A4 = B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_147_Compl__iff,axiom,
% 3.08/1.62 ! [C: c,A4: set_c] :
% 3.08/1.62 ( ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) )
% 3.08/1.62 = ( ~ ( member_c @ C @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_148_Compl__iff,axiom,
% 3.08/1.62 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) )
% 3.08/1.62 = ( ~ ( member_Sum_sum_c_d @ C @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_149_Compl__iff,axiom,
% 3.08/1.62 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) )
% 3.08/1.62 = ( ~ ( member1895684704real_c @ C @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_150_Compl__iff,axiom,
% 3.08/1.62 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) )
% 3.08/1.62 = ( ~ ( member1321351885real_c @ C @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_151_Compl__iff,axiom,
% 3.08/1.62 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) )
% 3.08/1.62 = ( ~ ( member_Sum_sum_c_c @ C @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_152_ComplI,axiom,
% 3.08/1.62 ! [C: c,A4: set_c] :
% 3.08/1.62 ( ~ ( member_c @ C @ A4 )
% 3.08/1.62 => ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_153_ComplI,axiom,
% 3.08/1.62 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ~ ( member_Sum_sum_c_d @ C @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_154_ComplI,axiom,
% 3.08/1.62 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 3.08/1.62 ( ~ ( member1895684704real_c @ C @ A4 )
% 3.08/1.62 => ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_155_ComplI,axiom,
% 3.08/1.62 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 3.08/1.62 ( ~ ( member1321351885real_c @ C @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_156_ComplI,axiom,
% 3.08/1.62 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ~ ( member_Sum_sum_c_c @ C @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_157_Icc__eq__Icc,axiom,
% 3.08/1.62 ! [L: real,H: real,L2: real,H2: real] :
% 3.08/1.62 ( ( ( set_or656347191t_real @ L @ H )
% 3.08/1.62 = ( set_or656347191t_real @ L2 @ H2 ) )
% 3.08/1.62 = ( ( ( L = L2 )
% 3.08/1.62 & ( H = H2 ) )
% 3.08/1.62 | ( ~ ( ord_less_eq_real @ L @ H )
% 3.08/1.62 & ~ ( ord_less_eq_real @ L2 @ H2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_158_atLeastAtMost__iff,axiom,
% 3.08/1.62 ! [I3: produc190496183real_c,L: produc190496183real_c,U: produc190496183real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ I3 @ ( set_or385782508real_c @ L @ U ) )
% 3.08/1.62 = ( ( ord_le850691415real_c @ L @ I3 )
% 3.08/1.62 & ( ord_le850691415real_c @ I3 @ U ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_159_atLeastAtMost__iff,axiom,
% 3.08/1.62 ! [I3: real > finite1398487019real_c,L: real > finite1398487019real_c,U: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ I3 @ ( set_or1308937537real_c @ L @ U ) )
% 3.08/1.62 = ( ( ord_le584953750real_c @ L @ I3 )
% 3.08/1.62 & ( ord_le584953750real_c @ I3 @ U ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_160_atLeastAtMost__iff,axiom,
% 3.08/1.62 ! [I3: real,L: real,U: real] :
% 3.08/1.62 ( ( member_real @ I3 @ ( set_or656347191t_real @ L @ U ) )
% 3.08/1.62 = ( ( ord_less_eq_real @ L @ I3 )
% 3.08/1.62 & ( ord_less_eq_real @ I3 @ U ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_161_imageI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,F: c > c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( image_c_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_162_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_163_imageI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,F: c > sum_sum_c_c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_164_imageI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,F: c > sum_sum_c_d] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_165_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_166_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_666880337um_c_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_167_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_675141842um_c_d @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_168_imageI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,F: c > real > finite1398487019real_c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X ) @ ( image_1226855921real_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_169_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_170_imageI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_171_image__iff,axiom,
% 3.08/1.62 ! [Z2: sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ Z2 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 = ( ? [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( Z2
% 3.08/1.62 = ( F @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_172_image__iff,axiom,
% 3.08/1.62 ! [Z2: sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ Z2 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 = ( ? [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( Z2
% 3.08/1.62 = ( F @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_173_bex__imageD,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ? [X7: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X7 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X7 ) )
% 3.08/1.62 => ? [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_174_bex__imageD,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ? [X7: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X7 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 & ( P @ X7 ) )
% 3.08/1.62 => ? [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_175_image__cong,axiom,
% 3.08/1.62 ! [M: set_c,N: set_c,F: c > sum_sum_c_c,G: c > sum_sum_c_c] :
% 3.08/1.62 ( ( M = N )
% 3.08/1.62 => ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ N )
% 3.08/1.62 => ( ( F @ X4 )
% 3.08/1.62 = ( G @ X4 ) ) )
% 3.08/1.62 => ( ( image_c_Sum_sum_c_c @ F @ M )
% 3.08/1.62 = ( image_c_Sum_sum_c_c @ G @ N ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_176_image__cong,axiom,
% 3.08/1.62 ! [M: set_c,N: set_c,F: c > sum_sum_c_d,G: c > sum_sum_c_d] :
% 3.08/1.62 ( ( M = N )
% 3.08/1.62 => ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ N )
% 3.08/1.62 => ( ( F @ X4 )
% 3.08/1.62 = ( G @ X4 ) ) )
% 3.08/1.62 => ( ( image_c_Sum_sum_c_d @ F @ M )
% 3.08/1.62 = ( image_c_Sum_sum_c_d @ G @ N ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_177_ball__imageD,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 => ( P @ X4 ) )
% 3.08/1.62 => ! [X7: c] :
% 3.08/1.62 ( ( member_c @ X7 @ A4 )
% 3.08/1.62 => ( P @ ( F @ X7 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_178_ball__imageD,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 => ( P @ X4 ) )
% 3.08/1.62 => ! [X7: c] :
% 3.08/1.62 ( ( member_c @ X7 @ A4 )
% 3.08/1.62 => ( P @ ( F @ X7 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_179_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,B: c,F: c > c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_c @ B @ ( image_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_180_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: c,F: sum_sum_c_c > c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_181_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,B: sum_sum_c_c,F: c > sum_sum_c_c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_182_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,B: sum_sum_c_d,F: c > sum_sum_c_d] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_183_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: c,F: sum_sum_c_d > c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_184_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_185_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_c,A4: set_Sum_sum_c_c,B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_186_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: c,A4: set_c,B: real > finite1398487019real_c,F: c > real > finite1398487019real_c] :
% 3.08/1.62 ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member1321351885real_c @ B @ ( image_1226855921real_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_187_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_188_rev__image__eqI,axiom,
% 3.08/1.62 ! [X: sum_sum_c_d,A4: set_Sum_sum_c_d,B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( ( B
% 3.08/1.62 = ( F @ X ) )
% 3.08/1.62 => ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_189_Collect__mono__iff,axiom,
% 3.08/1.62 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 3.08/1.62 ( ( ord_le1327118209real_c @ ( collec230941376real_c @ P ) @ ( collec230941376real_c @ Q ) )
% 3.08/1.62 = ( ! [X3: finite1398487019real_c] :
% 3.08/1.62 ( ( P @ X3 )
% 3.08/1.62 => ( Q @ X3 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_190_Collect__mono__iff,axiom,
% 3.08/1.62 ! [P: c > $o,Q: c > $o] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ ( collect_c @ P ) @ ( collect_c @ Q ) )
% 3.08/1.62 = ( ! [X3: c] :
% 3.08/1.62 ( ( P @ X3 )
% 3.08/1.62 => ( Q @ X3 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_191_Collect__mono,axiom,
% 3.08/1.62 ! [P: finite1398487019real_c > $o,Q: finite1398487019real_c > $o] :
% 3.08/1.62 ( ! [X4: finite1398487019real_c] :
% 3.08/1.62 ( ( P @ X4 )
% 3.08/1.62 => ( Q @ X4 ) )
% 3.08/1.62 => ( ord_le1327118209real_c @ ( collec230941376real_c @ P ) @ ( collec230941376real_c @ Q ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_192_Collect__mono,axiom,
% 3.08/1.62 ! [P: c > $o,Q: c > $o] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( P @ X4 )
% 3.08/1.62 => ( Q @ X4 ) )
% 3.08/1.62 => ( ord_less_eq_set_c @ ( collect_c @ P ) @ ( collect_c @ Q ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_193_subset__iff,axiom,
% 3.08/1.62 ( ord_le1772180283um_c_c
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 3.08/1.62 ! [T2: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ T2 @ A5 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ T2 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_194_subset__iff,axiom,
% 3.08/1.62 ( ord_less_eq_set_c
% 3.08/1.62 = ( ^ [A5: set_c,B5: set_c] :
% 3.08/1.62 ! [T2: c] :
% 3.08/1.62 ( ( member_c @ T2 @ A5 )
% 3.08/1.62 => ( member_c @ T2 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_195_subset__iff,axiom,
% 3.08/1.62 ( ord_le764260924um_c_d
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 3.08/1.62 ! [T2: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ T2 @ A5 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ T2 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_196_subset__iff,axiom,
% 3.08/1.62 ( ord_le977353143real_c
% 3.08/1.62 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 3.08/1.62 ! [T2: produc190496183real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ T2 @ A5 )
% 3.08/1.62 => ( member1895684704real_c @ T2 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_197_subset__iff,axiom,
% 3.08/1.62 ( ord_le35002188real_c
% 3.08/1.62 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 3.08/1.62 ! [T2: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ T2 @ A5 )
% 3.08/1.62 => ( member1321351885real_c @ T2 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_198_subset__eq,axiom,
% 3.08/1.62 ( ord_le1772180283um_c_c
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 3.08/1.62 ! [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ A5 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_199_subset__eq,axiom,
% 3.08/1.62 ( ord_less_eq_set_c
% 3.08/1.62 = ( ^ [A5: set_c,B5: set_c] :
% 3.08/1.62 ! [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A5 )
% 3.08/1.62 => ( member_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_200_subset__eq,axiom,
% 3.08/1.62 ( ord_le764260924um_c_d
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 3.08/1.62 ! [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ A5 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_201_subset__eq,axiom,
% 3.08/1.62 ( ord_le977353143real_c
% 3.08/1.62 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 3.08/1.62 ! [X3: produc190496183real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ X3 @ A5 )
% 3.08/1.62 => ( member1895684704real_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_202_subset__eq,axiom,
% 3.08/1.62 ( ord_le35002188real_c
% 3.08/1.62 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 3.08/1.62 ! [X3: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ X3 @ A5 )
% 3.08/1.62 => ( member1321351885real_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_203_subsetD,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,C: sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ C @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ C @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_204_subsetD,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c,C: c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member_c @ C @ A4 )
% 3.08/1.62 => ( member_c @ C @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_205_subsetD,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d,C: sum_sum_c_d] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ A4 @ B4 )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ C @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ C @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_206_subsetD,axiom,
% 3.08/1.62 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c,C: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le977353143real_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member1895684704real_c @ C @ A4 )
% 3.08/1.62 => ( member1895684704real_c @ C @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_207_subsetD,axiom,
% 3.08/1.62 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c,C: real > finite1398487019real_c] :
% 3.08/1.62 ( ( ord_le35002188real_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member1321351885real_c @ C @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ C @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_208_in__mono,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c,X: sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ X @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_209_in__mono,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c,X: c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ X @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_210_in__mono,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,B4: set_Sum_sum_c_d,X: sum_sum_c_d] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ A4 @ B4 )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ X @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_211_in__mono,axiom,
% 3.08/1.62 ! [A4: set_Pr1389752855real_c,B4: set_Pr1389752855real_c,X: produc190496183real_c] :
% 3.08/1.62 ( ( ord_le977353143real_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member1895684704real_c @ X @ A4 )
% 3.08/1.62 => ( member1895684704real_c @ X @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_212_in__mono,axiom,
% 3.08/1.62 ! [A4: set_re2066790124real_c,B4: set_re2066790124real_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( ord_le35002188real_c @ A4 @ B4 )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ X @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_213_double__complement,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( uminus1381786404um_c_c @ ( uminus1381786404um_c_c @ A4 ) )
% 3.08/1.62 = A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_214_ComplD,axiom,
% 3.08/1.62 ! [C: c,A4: set_c] :
% 3.08/1.62 ( ( member_c @ C @ ( uminus_uminus_set_c @ A4 ) )
% 3.08/1.62 => ~ ( member_c @ C @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_215_ComplD,axiom,
% 3.08/1.62 ! [C: sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ C @ ( uminus373867045um_c_d @ A4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ C @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_216_ComplD,axiom,
% 3.08/1.62 ! [C: produc190496183real_c,A4: set_Pr1389752855real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ C @ ( uminus232257166real_c @ A4 ) )
% 3.08/1.62 => ~ ( member1895684704real_c @ C @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_217_ComplD,axiom,
% 3.08/1.62 ! [C: real > finite1398487019real_c,A4: set_re2066790124real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ C @ ( uminus946614837real_c @ A4 ) )
% 3.08/1.62 => ~ ( member1321351885real_c @ C @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_218_ComplD,axiom,
% 3.08/1.62 ! [C: sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ C @ ( uminus1381786404um_c_c @ A4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ C @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_219_imageE,axiom,
% 3.08/1.62 ! [B: c,F: c > c,A4: set_c] :
% 3.08/1.62 ( ( member_c @ B @ ( image_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_220_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ B @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_221_imageE,axiom,
% 3.08/1.62 ! [B: c,F: sum_sum_c_c > c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( member_c @ B @ ( image_Sum_sum_c_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_222_imageE,axiom,
% 3.08/1.62 ! [B: c,F: sum_sum_c_d > c,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( member_c @ B @ ( image_Sum_sum_c_d_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_223_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ B @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_224_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ B @ ( image_666880337um_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_225_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_c,F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ B @ ( image_1558941394um_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_226_imageE,axiom,
% 3.08/1.62 ! [B: c,F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c] :
% 3.08/1.62 ( ( member_c @ B @ ( image_266490115al_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: real > finite1398487019real_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member1321351885real_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_227_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ B @ ( image_675141842um_c_d @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_228_imageE,axiom,
% 3.08/1.62 ! [B: sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,A4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ B @ ( image_1567202899um_c_d @ F @ A4 ) )
% 3.08/1.62 => ~ ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( B
% 3.08/1.62 = ( F @ X4 ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ X4 @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_229_image__image,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_c,G: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( image_666880337um_c_c @ F @ ( image_c_Sum_sum_c_c @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_230_image__image,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_d,G: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( image_675141842um_c_d @ F @ ( image_c_Sum_sum_c_c @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_231_image__image,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > sum_sum_c_c,G: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( image_1558941394um_c_c @ F @ ( image_c_Sum_sum_c_d @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_232_image__image,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > sum_sum_c_d,G: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( image_1567202899um_c_d @ F @ ( image_c_Sum_sum_c_d @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_233_image__image,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,G: c > c,A4: set_c] :
% 3.08/1.62 ( ( image_c_Sum_sum_c_c @ F @ ( image_c_c @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_234_image__image,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,G: c > c,A4: set_c] :
% 3.08/1.62 ( ( image_c_Sum_sum_c_d @ F @ ( image_c_c @ G @ A4 ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: c] : ( F @ ( G @ X3 ) )
% 3.08/1.62 @ A4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_235_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: c > c,A4: set_c,P: c > $o] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ ( image_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_c_c @ F
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_236_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_c @ F
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_237_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_c_Sum_sum_c_d @ F
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_238_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: c > finite1398487019real_c,A4: set_c,P: finite1398487019real_c > $o] :
% 3.08/1.62 ( ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ( ( member1261661570real_c @ X3 @ ( image_687300774real_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_687300774real_c @ F
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_239_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,P: c > $o] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ ( image_Sum_sum_c_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_Sum_sum_c_c_c @ F
% 3.08/1.62 @ ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_240_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,P: c > $o] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ ( image_Sum_sum_c_d_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_Sum_sum_c_d_c @ F
% 3.08/1.62 @ ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_241_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: finite1398487019real_c > c,A4: set_Fi1407883041real_c,P: c > $o] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ ( image_1260608398al_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_1260608398al_c_c @ F
% 3.08/1.62 @ ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ( ( member1261661570real_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_242_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ ( image_666880337um_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_666880337um_c_c @ F
% 3.08/1.62 @ ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_243_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ ( image_1558941394um_c_c @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_1558941394um_c_c @ F
% 3.08/1.62 @ ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_244_Compr__image__eq,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ ( image_675141842um_c_d @ F @ A4 ) )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 = ( image_675141842um_c_d @ F
% 3.08/1.62 @ ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_245_less__eq__set__def,axiom,
% 3.08/1.62 ( ord_le1772180283um_c_c
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_c,B5: set_Sum_sum_c_c] :
% 3.08/1.62 ( ord_le1315653386_c_c_o
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A5 )
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_246_less__eq__set__def,axiom,
% 3.08/1.62 ( ord_less_eq_set_c
% 3.08/1.62 = ( ^ [A5: set_c,B5: set_c] :
% 3.08/1.62 ( ord_less_eq_c_o
% 3.08/1.62 @ ^ [X3: c] : ( member_c @ X3 @ A5 )
% 3.08/1.62 @ ^ [X3: c] : ( member_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_247_less__eq__set__def,axiom,
% 3.08/1.62 ( ord_le764260924um_c_d
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_d,B5: set_Sum_sum_c_d] :
% 3.08/1.62 ( ord_le2143422793_c_d_o
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A5 )
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_248_less__eq__set__def,axiom,
% 3.08/1.62 ( ord_le977353143real_c
% 3.08/1.62 = ( ^ [A5: set_Pr1389752855real_c,B5: set_Pr1389752855real_c] :
% 3.08/1.62 ( ord_le1132241894al_c_o
% 3.08/1.62 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A5 )
% 3.08/1.62 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_249_less__eq__set__def,axiom,
% 3.08/1.62 ( ord_le35002188real_c
% 3.08/1.62 = ( ^ [A5: set_re2066790124real_c,B5: set_re2066790124real_c] :
% 3.08/1.62 ( ord_le818951225al_c_o
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A5 )
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ B5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_250_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ord_le1772180283um_c_c
% 3.08/1.62 @ ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_251_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,P: sum_sum_c_d > $o] :
% 3.08/1.62 ( ord_le764260924um_c_d
% 3.08/1.62 @ ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_252_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 3.08/1.62 ( ord_le977353143real_c
% 3.08/1.62 @ ( collec1643251106real_c
% 3.08/1.62 @ ^ [X3: produc190496183real_c] :
% 3.08/1.62 ( ( member1895684704real_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_253_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_re2066790124real_c,P: ( real > finite1398487019real_c ) > $o] :
% 3.08/1.62 ( ord_le35002188real_c
% 3.08/1.62 @ ( collec913357835real_c
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_254_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_Fi1407883041real_c,P: finite1398487019real_c > $o] :
% 3.08/1.62 ( ord_le1327118209real_c
% 3.08/1.62 @ ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ( ( member1261661570real_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_255_Collect__subset,axiom,
% 3.08/1.62 ! [A4: set_c,P: c > $o] :
% 3.08/1.62 ( ord_less_eq_set_c
% 3.08/1.62 @ ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 & ( P @ X3 ) ) )
% 3.08/1.62 @ A4 ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_256_Collect__neg__eq,axiom,
% 3.08/1.62 ! [P: finite1398487019real_c > $o] :
% 3.08/1.62 ( ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ~ ( P @ X3 ) )
% 3.08/1.62 = ( uminus102402154real_c @ ( collec230941376real_c @ P ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_257_Collect__neg__eq,axiom,
% 3.08/1.62 ! [P: c > $o] :
% 3.08/1.62 ( ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ~ ( P @ X3 ) )
% 3.08/1.62 = ( uminus_uminus_set_c @ ( collect_c @ P ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_258_Collect__neg__eq,axiom,
% 3.08/1.62 ! [P: sum_sum_c_c > $o] :
% 3.08/1.62 ( ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ~ ( P @ X3 ) )
% 3.08/1.62 = ( uminus1381786404um_c_c @ ( collect_Sum_sum_c_c @ P ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_259_Compl__eq,axiom,
% 3.08/1.62 ( uminus373867045um_c_d
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_d] :
% 3.08/1.62 ( collect_Sum_sum_c_d
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] :
% 3.08/1.62 ~ ( member_Sum_sum_c_d @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_260_Compl__eq,axiom,
% 3.08/1.62 ( uminus232257166real_c
% 3.08/1.62 = ( ^ [A5: set_Pr1389752855real_c] :
% 3.08/1.62 ( collec1643251106real_c
% 3.08/1.62 @ ^ [X3: produc190496183real_c] :
% 3.08/1.62 ~ ( member1895684704real_c @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_261_Compl__eq,axiom,
% 3.08/1.62 ( uminus946614837real_c
% 3.08/1.62 = ( ^ [A5: set_re2066790124real_c] :
% 3.08/1.62 ( collec913357835real_c
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] :
% 3.08/1.62 ~ ( member1321351885real_c @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_262_Compl__eq,axiom,
% 3.08/1.62 ( uminus102402154real_c
% 3.08/1.62 = ( ^ [A5: set_Fi1407883041real_c] :
% 3.08/1.62 ( collec230941376real_c
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] :
% 3.08/1.62 ~ ( member1261661570real_c @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_263_Compl__eq,axiom,
% 3.08/1.62 ( uminus_uminus_set_c
% 3.08/1.62 = ( ^ [A5: set_c] :
% 3.08/1.62 ( collect_c
% 3.08/1.62 @ ^ [X3: c] :
% 3.08/1.62 ~ ( member_c @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_264_Compl__eq,axiom,
% 3.08/1.62 ( uminus1381786404um_c_c
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_c] :
% 3.08/1.62 ( collect_Sum_sum_c_c
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] :
% 3.08/1.62 ~ ( member_Sum_sum_c_c @ X3 @ A5 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_265_uminus__set__def,axiom,
% 3.08/1.62 ( uminus373867045um_c_d
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_d] :
% 3.08/1.62 ( collect_Sum_sum_c_d
% 3.08/1.62 @ ( uminus916499104_c_d_o
% 3.08/1.62 @ ^ [X3: sum_sum_c_d] : ( member_Sum_sum_c_d @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_266_uminus__set__def,axiom,
% 3.08/1.62 ( uminus232257166real_c
% 3.08/1.62 = ( ^ [A5: set_Pr1389752855real_c] :
% 3.08/1.62 ( collec1643251106real_c
% 3.08/1.62 @ ( uminus32155087al_c_o
% 3.08/1.62 @ ^ [X3: produc190496183real_c] : ( member1895684704real_c @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_267_uminus__set__def,axiom,
% 3.08/1.62 ( uminus946614837real_c
% 3.08/1.62 = ( ^ [A5: set_re2066790124real_c] :
% 3.08/1.62 ( collec913357835real_c
% 3.08/1.62 @ ( uminus1756072592al_c_o
% 3.08/1.62 @ ^ [X3: real > finite1398487019real_c] : ( member1321351885real_c @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_268_uminus__set__def,axiom,
% 3.08/1.62 ( uminus102402154real_c
% 3.08/1.62 = ( ^ [A5: set_Fi1407883041real_c] :
% 3.08/1.62 ( collec230941376real_c
% 3.08/1.62 @ ( uminus23580315al_c_o
% 3.08/1.62 @ ^ [X3: finite1398487019real_c] : ( member1261661570real_c @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_269_uminus__set__def,axiom,
% 3.08/1.62 ( uminus_uminus_set_c
% 3.08/1.62 = ( ^ [A5: set_c] :
% 3.08/1.62 ( collect_c
% 3.08/1.62 @ ( uminus_uminus_c_o
% 3.08/1.62 @ ^ [X3: c] : ( member_c @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_270_uminus__set__def,axiom,
% 3.08/1.62 ( uminus1381786404um_c_c
% 3.08/1.62 = ( ^ [A5: set_Sum_sum_c_c] :
% 3.08/1.62 ( collect_Sum_sum_c_c
% 3.08/1.62 @ ( uminus88729697_c_c_o
% 3.08/1.62 @ ^ [X3: sum_sum_c_c] : ( member_Sum_sum_c_c @ X3 @ A5 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_271_image__mono,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c,F: c > sum_sum_c_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ ( image_c_Sum_sum_c_c @ F @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_272_image__mono,axiom,
% 3.08/1.62 ! [A4: set_c,B4: set_c,F: c > sum_sum_c_d] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ A4 @ B4 )
% 3.08/1.62 => ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ ( image_c_Sum_sum_c_d @ F @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_273_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_less_eq_set_c @ ( image_c_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_274_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_less_eq_set_c @ ( image_Sum_sum_c_c_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_275_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_276_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_277_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_less_eq_set_c @ ( image_Sum_sum_c_d_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_278_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( image_666880337um_c_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_279_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le764260924um_c_d @ ( image_675141842um_c_d @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_280_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: set_re2066790124real_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le35002188real_c @ ( image_1226855921real_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_281_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le1772180283um_c_c @ ( image_1558941394um_c_c @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_282_image__subsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( ord_le764260924um_c_d @ ( image_1567202899um_c_d @ F @ A4 ) @ B4 ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_283_subset__imageE,axiom,
% 3.08/1.62 ! [B4: set_Sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ B4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 => ~ ! [C2: set_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ C2 @ A4 )
% 3.08/1.62 => ( B4
% 3.08/1.62 != ( image_c_Sum_sum_c_c @ F @ C2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_284_subset__imageE,axiom,
% 3.08/1.62 ! [B4: set_Sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ B4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 => ~ ! [C2: set_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ C2 @ A4 )
% 3.08/1.62 => ( B4
% 3.08/1.62 != ( image_c_Sum_sum_c_d @ F @ C2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_285_image__subset__iff,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F @ A4 ) @ B4 )
% 3.08/1.62 = ( ! [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_286_image__subset__iff,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F @ A4 ) @ B4 )
% 3.08/1.62 = ( ! [X3: c] :
% 3.08/1.62 ( ( member_c @ X3 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_287_subset__image__iff,axiom,
% 3.08/1.62 ! [B4: set_Sum_sum_c_c,F: c > sum_sum_c_c,A4: set_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ B4 @ ( image_c_Sum_sum_c_c @ F @ A4 ) )
% 3.08/1.62 = ( ? [AA: set_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ AA @ A4 )
% 3.08/1.62 & ( B4
% 3.08/1.62 = ( image_c_Sum_sum_c_c @ F @ AA ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_288_subset__image__iff,axiom,
% 3.08/1.62 ! [B4: set_Sum_sum_c_d,F: c > sum_sum_c_d,A4: set_c] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ B4 @ ( image_c_Sum_sum_c_d @ F @ A4 ) )
% 3.08/1.62 = ( ? [AA: set_c] :
% 3.08/1.62 ( ( ord_less_eq_set_c @ AA @ A4 )
% 3.08/1.62 & ( B4
% 3.08/1.62 = ( image_c_Sum_sum_c_d @ F @ AA ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_289_repd_Oelims,axiom,
% 3.08/1.62 ! [X: produc190496183real_c,Xa: c,Xb: real,Y: produc190496183real_c] :
% 3.08/1.62 ( ( ( denotational_repd_c @ X @ Xa @ Xb )
% 3.08/1.62 = Y )
% 3.08/1.62 => ( Y
% 3.08/1.62 = ( produc394644079real_c @ ( produc2010422875real_c @ X )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [Y3: c] : ( if_real @ ( Xa = Y3 ) @ Xb @ ( finite772340578real_c @ ( produc314122909real_c @ X ) @ Y3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_290_repd_Osimps,axiom,
% 3.08/1.62 ( denotational_repd_c
% 3.08/1.62 = ( ^ [V3: produc190496183real_c,X3: c,R: real] :
% 3.08/1.62 ( produc394644079real_c @ ( produc2010422875real_c @ V3 )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [Y3: c] : ( if_real @ ( X3 = Y3 ) @ R @ ( finite772340578real_c @ ( produc314122909real_c @ V3 ) @ Y3 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_291_image__subset__iff__funcset,axiom,
% 3.08/1.62 ! [F2: c > sum_sum_c_c,A4: set_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ( ord_le1772180283um_c_c @ ( image_c_Sum_sum_c_c @ F2 @ A4 ) @ B4 )
% 3.08/1.62 = ( member_c_Sum_sum_c_c @ F2
% 3.08/1.62 @ ( pi_c_Sum_sum_c_c @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_292_image__subset__iff__funcset,axiom,
% 3.08/1.62 ! [F2: c > sum_sum_c_d,A4: set_c,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ( ord_le764260924um_c_d @ ( image_c_Sum_sum_c_d @ F2 @ A4 ) @ B4 )
% 3.08/1.62 = ( member_c_Sum_sum_c_d @ F2
% 3.08/1.62 @ ( pi_c_Sum_sum_c_d @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_293_image__subset__iff__funcset,axiom,
% 3.08/1.62 ! [F2: real > finite1398487019real_c,A4: set_real,B4: set_Fi1407883041real_c] :
% 3.08/1.62 ( ( ord_le1327118209real_c @ ( image_327677598real_c @ F2 @ A4 ) @ B4 )
% 3.08/1.62 = ( member1321351885real_c @ F2
% 3.08/1.62 @ ( pi_rea1111636068real_c @ A4
% 3.08/1.62 @ ^ [Uu: real] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_294_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > c,B4: c > set_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_295_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_real,F: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 3.08/1.62 ( ! [X4: real] :
% 3.08/1.62 ( ( member_real @ X4 @ A4 )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_296_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: sum_sum_c_c > set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_297_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_c,B4: c > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_298_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_d,B4: c > set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_299_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: sum_sum_c_d > set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_300_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_301_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: sum_sum_c_c > set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_302_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: c > set_re2066790124real_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_303_Pi__I,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: sum_sum_c_d > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_304_PiE,axiom,
% 3.08/1.62 ! [F: c > c,A4: set_c,B4: c > set_c,X: c] :
% 3.08/1.62 ( ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_305_PiE,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,B4: c > set_Sum_sum_c_c,X: c] :
% 3.08/1.62 ( ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_306_PiE,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_c,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_307_PiE,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_c,X: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_308_PiE,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,B4: c > set_Sum_sum_c_d,X: c] :
% 3.08/1.62 ( ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_309_PiE,axiom,
% 3.08/1.62 ! [F: real > finite1398487019real_c,A4: set_real,B4: real > set_Fi1407883041real_c,X: real] :
% 3.08/1.62 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member1261661570real_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_real @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_310_PiE,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_311_PiE,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_Sum_sum_c_c,X: sum_sum_c_d] :
% 3.08/1.62 ( ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_d @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_312_PiE,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c,B4: ( real > finite1398487019real_c ) > set_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member527957930al_c_c @ F @ ( pi_rea1228756413al_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_c @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member1321351885real_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_313_PiE,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_d,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) )
% 3.08/1.62 => ( ~ ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) )
% 3.08/1.62 => ~ ( member_Sum_sum_c_c @ X @ A4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_314_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > c,B4: c > set_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_315_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_real,F: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 3.08/1.62 ( ! [X4: real] :
% 3.08/1.62 ( ( member_real @ X4 @ A4 )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_316_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: sum_sum_c_c > set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_317_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_c,B4: c > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_318_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_d,B4: c > set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_319_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: sum_sum_c_d > set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_320_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_321_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: sum_sum_c_c > set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_322_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: c > set_re2066790124real_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_323_Pi__I_H,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: sum_sum_c_d > set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ ( B4 @ X4 ) ) )
% 3.08/1.62 => ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_324_Pi__iff,axiom,
% 3.08/1.62 ! [F: real > finite1398487019real_c,I: set_real,X8: real > set_Fi1407883041real_c] :
% 3.08/1.62 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ I @ X8 ) )
% 3.08/1.62 = ( ! [X3: real] :
% 3.08/1.62 ( ( member_real @ X3 @ I )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X3 ) @ ( X8 @ X3 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_325_Pi__mem,axiom,
% 3.08/1.62 ! [F: c > c,A4: set_c,B4: c > set_c,X: c] :
% 3.08/1.62 ( ( member_c_c @ F @ ( pi_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_326_Pi__mem,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_c,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c_c @ F @ ( pi_Sum_sum_c_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_327_Pi__mem,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_c,A4: set_c,B4: c > set_Sum_sum_c_c,X: c] :
% 3.08/1.62 ( ( member_c_Sum_sum_c_c @ F @ ( pi_c_Sum_sum_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_328_Pi__mem,axiom,
% 3.08/1.62 ! [F: c > sum_sum_c_d,A4: set_c,B4: c > set_Sum_sum_c_d,X: c] :
% 3.08/1.62 ( ( member_c_Sum_sum_c_d @ F @ ( pi_c_Sum_sum_c_d @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_329_Pi__mem,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_c,X: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d_c @ F @ ( pi_Sum_sum_c_d_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_330_Pi__mem,axiom,
% 3.08/1.62 ! [F: real > finite1398487019real_c,A4: set_real,B4: real > set_Fi1407883041real_c,X: real] :
% 3.08/1.62 ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_real @ X @ A4 )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_331_Pi__mem,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_c,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_c,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member1326674048um_c_c @ F @ ( pi_Sum253006871um_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_332_Pi__mem,axiom,
% 3.08/1.62 ! [F: sum_sum_c_c > sum_sum_c_d,A4: set_Sum_sum_c_c,B4: sum_sum_c_c > set_Sum_sum_c_d,X: sum_sum_c_c] :
% 3.08/1.62 ( ( member318754689um_c_d @ F @ ( pi_Sum261268376um_c_d @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_333_Pi__mem,axiom,
% 3.08/1.62 ! [F: c > real > finite1398487019real_c,A4: set_c,B4: c > set_re2066790124real_c,X: c] :
% 3.08/1.62 ( ( member469531344real_c @ F @ ( pi_c_r41638571real_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_c @ X @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_334_Pi__mem,axiom,
% 3.08/1.62 ! [F: sum_sum_c_d > sum_sum_c_c,A4: set_Sum_sum_c_d,B4: sum_sum_c_d > set_Sum_sum_c_c,X: sum_sum_c_d] :
% 3.08/1.62 ( ( member71251457um_c_c @ F @ ( pi_Sum1145067928um_c_c @ A4 @ B4 ) )
% 3.08/1.62 => ( ( member_Sum_sum_c_d @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ ( B4 @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_335_Pi__cong,axiom,
% 3.08/1.62 ! [A4: set_real,F: real > finite1398487019real_c,G: real > finite1398487019real_c,B4: real > set_Fi1407883041real_c] :
% 3.08/1.62 ( ! [W: real] :
% 3.08/1.62 ( ( member_real @ W @ A4 )
% 3.08/1.62 => ( ( F @ W )
% 3.08/1.62 = ( G @ W ) ) )
% 3.08/1.62 => ( ( member1321351885real_c @ F @ ( pi_rea1111636068real_c @ A4 @ B4 ) )
% 3.08/1.62 = ( member1321351885real_c @ G @ ( pi_rea1111636068real_c @ A4 @ B4 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_336_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member_c_c @ F
% 3.08/1.62 @ ( pi_c_c @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_337_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_real,F: real > finite1398487019real_c,B4: set_Fi1407883041real_c] :
% 3.08/1.62 ( ! [X4: real] :
% 3.08/1.62 ( ( member_real @ X4 @ A4 )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member1321351885real_c @ F
% 3.08/1.62 @ ( pi_rea1111636068real_c @ A4
% 3.08/1.62 @ ^ [Uu: real] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_338_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member_Sum_sum_c_c_c @ F
% 3.08/1.62 @ ( pi_Sum_sum_c_c_c @ A4
% 3.08/1.62 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_339_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_c @ F
% 3.08/1.62 @ ( pi_c_Sum_sum_c_c @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_340_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member_c_Sum_sum_c_d @ F
% 3.08/1.62 @ ( pi_c_Sum_sum_c_d @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_341_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > c,B4: set_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member_Sum_sum_c_d_c @ F
% 3.08/1.62 @ ( pi_Sum_sum_c_d_c @ A4
% 3.08/1.62 @ ^ [Uu: sum_sum_c_d] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_342_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member1326674048um_c_c @ F
% 3.08/1.62 @ ( pi_Sum253006871um_c_c @ A4
% 3.08/1.62 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_343_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_c,F: sum_sum_c_c > sum_sum_c_d,B4: set_Sum_sum_c_d] :
% 3.08/1.62 ( ! [X4: sum_sum_c_c] :
% 3.08/1.62 ( ( member_Sum_sum_c_c @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member318754689um_c_d @ F
% 3.08/1.62 @ ( pi_Sum261268376um_c_d @ A4
% 3.08/1.62 @ ^ [Uu: sum_sum_c_c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_344_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_c,F: c > real > finite1398487019real_c,B4: set_re2066790124real_c] :
% 3.08/1.62 ( ! [X4: c] :
% 3.08/1.62 ( ( member_c @ X4 @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member469531344real_c @ F
% 3.08/1.62 @ ( pi_c_r41638571real_c @ A4
% 3.08/1.62 @ ^ [Uu: c] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_345_funcsetI,axiom,
% 3.08/1.62 ! [A4: set_Sum_sum_c_d,F: sum_sum_c_d > sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 3.08/1.62 ( ! [X4: sum_sum_c_d] :
% 3.08/1.62 ( ( member_Sum_sum_c_d @ X4 @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X4 ) @ B4 ) )
% 3.08/1.62 => ( member71251457um_c_c @ F
% 3.08/1.62 @ ( pi_Sum1145067928um_c_c @ A4
% 3.08/1.62 @ ^ [Uu: sum_sum_c_d] : B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_346_funcset__mem,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > sum_sum_c_c,A4: set_re2066790124real_c,B4: set_Sum_sum_c_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member354622481um_c_c @ F
% 3.08/1.62 @ ( pi_rea1500330408um_c_c @ A4
% 3.08/1.62 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_c @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_347_funcset__mem,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > c,A4: set_re2066790124real_c,B4: set_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member527957930al_c_c @ F
% 3.08/1.62 @ ( pi_rea1228756413al_c_c @ A4
% 3.08/1.62 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member_c @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_348_funcset__mem,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > sum_sum_c_d,A4: set_re2066790124real_c,B4: set_Sum_sum_c_d,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1494186770um_c_d @ F
% 3.08/1.62 @ ( pi_rea1508591913um_c_d @ A4
% 3.08/1.62 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member_Sum_sum_c_d @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_349_funcset__mem,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > produc190496183real_c,A4: set_re2066790124real_c,B4: set_Pr1389752855real_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member954762593real_c @ F
% 3.08/1.62 @ ( pi_rea1379668980real_c @ A4
% 3.08/1.62 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member1895684704real_c @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_350_funcset__mem,axiom,
% 3.08/1.62 ! [F: ( real > finite1398487019real_c ) > real > finite1398487019real_c,A4: set_re2066790124real_c,B4: set_re2066790124real_c,X: real > finite1398487019real_c] :
% 3.08/1.62 ( ( member1851015714real_c @ F
% 3.08/1.62 @ ( pi_rea1386151481real_c @ A4
% 3.08/1.62 @ ^ [Uu: real > finite1398487019real_c] : B4 ) )
% 3.08/1.62 => ( ( member1321351885real_c @ X @ A4 )
% 3.08/1.62 => ( member1321351885real_c @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(fact_351_funcset__mem,axiom,
% 3.08/1.62 ! [F: real > finite1398487019real_c,A4: set_real,B4: set_Fi1407883041real_c,X: real] :
% 3.08/1.62 ( ( member1321351885real_c @ F
% 3.08/1.62 @ ( pi_rea1111636068real_c @ A4
% 3.08/1.62 @ ^ [Uu: real] : B4 ) )
% 3.08/1.62 => ( ( member_real @ X @ A4 )
% 3.08/1.62 => ( member1261661570real_c @ ( F @ X ) @ B4 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 3.08/1.62 ! [X: real,Y: real] :
% 3.08/1.62 ( ( if_real @ $false @ X @ Y )
% 3.08/1.62 = Y ) ).
% 3.08/1.62
% 3.08/1.62 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 3.08/1.62 ! [X: real,Y: real] :
% 3.08/1.62 ( ( if_real @ $true @ X @ Y )
% 3.08/1.62 = X ) ).
% 3.08/1.62
% 3.08/1.62 thf(help_If_3_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 3.08/1.62 ! [P: $o] :
% 3.08/1.62 ( ( P = $true )
% 3.08/1.62 | ( P = $false ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.08/1.62 ( ( if_Fin36944805real_c @ $false @ X @ Y )
% 3.08/1.62 = Y ) ).
% 3.08/1.62
% 3.08/1.62 thf(help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_T,axiom,
% 3.08/1.62 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.08/1.62 ( ( if_Fin36944805real_c @ $true @ X @ Y )
% 3.08/1.62 = X ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_0,hypothesis,
% 3.08/1.62 member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( static_FVF_a_b_c @ phi ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_1,hypothesis,
% 3.08/1.62 member_c @ i2 @ ( denota540094197_a_b_c @ i @ oDEa ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_2,hypothesis,
% 3.08/1.62 ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_3,hypothesis,
% 3.08/1.62 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 3.08/1.62 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ zero_zero_real ) @ i2 ) ) )
% 3.08/1.62 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_4,hypothesis,
% 3.08/1.62 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ~ ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ i2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_5,hypothesis,
% 3.08/1.62 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc314122909real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ bb @ i2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_6,hypothesis,
% 3.08/1.62 ( ( ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 & ~ ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ bb @ i2 ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_7,hypothesis,
% 3.08/1.62 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 3.08/1.62 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ i2 ) ) ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 3.08/1.62 & ( ~ ( member_c @ i2 @ ( static_FVO_a_c @ oDEa ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc2010422875real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ab @ i2 ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_8,hypothesis,
% 3.08/1.62 ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc314122909real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c
% 3.08/1.62 @ ( denota1275485728_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ i2 ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c
% 3.08/1.62 @ ( produc314122909real_c
% 3.08/1.62 @ ( denota161327353_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( produc394644079real_c
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ zero_zero_real ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) )
% 3.08/1.62 @ bb )
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) ) )
% 3.08/1.62 @ i2 )
% 3.08/1.62 = ( finite772340578real_c
% 3.08/1.62 @ ( denota1275485728_a_b_c @ i @ oDEa
% 3.08/1.62 @ ( finite557796307c_real
% 3.08/1.62 @ ^ [I2: c] : ( if_real @ ( member_c @ I2 @ ( static_FVO_a_c @ oDEa ) ) @ ( finite772340578real_c @ ( sol @ x ) @ I2 ) @ ( finite772340578real_c @ ab @ I2 ) ) ) )
% 3.08/1.62 @ i2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_9,hypothesis,
% 3.08/1.62 ( ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_c @ ( sum_Inl_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc2010422875real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_10,hypothesis,
% 3.08/1.62 ( ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inl_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) )
% 3.08/1.62 & ( ( member_Sum_sum_c_c @ ( sum_Inr_c_c @ i2 ) @ ( image_c_Sum_sum_c_c @ sum_Inr_c_c @ ( denota540094197_a_b_c @ i @ oDEa ) ) )
% 3.08/1.62 => ( ( finite772340578real_c @ ( produc314122909real_c @ ( denota161327353_a_b_c @ i @ oDEa @ ( produc394644079real_c @ ab @ bb ) @ ( sol @ x ) ) ) @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( denota1275485728_a_b_c @ i @ oDEa @ ( sol @ x ) ) @ i2 ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(conj_11,conjecture,
% 3.08/1.62 ( ( finite772340578real_c @ ab @ i2 )
% 3.08/1.62 = ( finite772340578real_c @ ( sol @ x ) @ i2 ) ) ).
% 3.08/1.62 ------------------------
% 3.08/1.65 % (22247)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_22144 for (2999ds/2Mi)
% 3.08/1.65 % (22247)Instruction limit reached!
% 3.08/1.65 % (22247)------------------------------
% 3.08/1.65 % (22247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (22247)Termination reason: Unknown
% 3.08/1.65 % (22247)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (22247)Memory used [KB]: 1535
% 3.08/1.65 % (22247)Time elapsed: 0.002 s
% 3.08/1.65 % (22247)Instructions burned: 2 (million)
% 3.08/1.65 % (22247)------------------------------
% 3.08/1.65 % (22247)------------------------------
% 3.08/1.65 % (22243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/183Mi)
% 3.08/1.65 % (22244)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_22144 for (2999ds/4Mi)
% 3.08/1.65 % (22244)Instruction limit reached!
% 3.08/1.65 % (22244)------------------------------
% 3.08/1.65 % (22244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (22244)Termination reason: Unknown
% 3.08/1.65 % (22244)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (22244)Memory used [KB]: 1663
% 3.08/1.65 % (22244)Time elapsed: 0.003 s
% 3.08/1.65 % (22244)Instructions burned: 5 (million)
% 3.08/1.65 % (22244)------------------------------
% 3.08/1.65 % (22244)------------------------------
% 3.08/1.65 % (22245)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_22144 for (2999ds/27Mi)
% 3.08/1.65 % (22246)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/2Mi)
% 3.08/1.65 % (22248)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_22144 for (2999ds/275Mi)
% 3.08/1.65 % (22249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/18Mi)
% 3.08/1.66 % (22246)Instruction limit reached!
% 3.08/1.66 % (22246)------------------------------
% 3.08/1.66 % (22246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (22246)Termination reason: Unknown
% 3.08/1.66 % (22246)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (22246)Memory used [KB]: 1535
% 3.08/1.66 % (22246)Time elapsed: 0.003 s
% 3.08/1.66 % (22246)Instructions burned: 2 (million)
% 3.08/1.66 % (22246)------------------------------
% 3.08/1.66 % (22246)------------------------------
% 3.08/1.66 % (22250)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/3Mi)
% 3.08/1.66 % (22250)Instruction limit reached!
% 3.08/1.66 % (22250)------------------------------
% 3.08/1.66 % (22250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (22250)Termination reason: Unknown
% 3.08/1.66 % (22250)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (22250)Memory used [KB]: 1535
% 3.08/1.66 % (22250)Time elapsed: 0.002 s
% 3.08/1.66 % (22250)Instructions burned: 3 (million)
% 3.08/1.66 % (22250)------------------------------
% 3.08/1.66 % (22250)------------------------------
% 3.08/1.66 % (22251)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_22144 for (2999ds/37Mi)
% 3.08/1.66 % (22249)Instruction limit reached!
% 3.08/1.66 % (22249)------------------------------
% 3.08/1.66 % (22249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (22249)Termination reason: Unknown
% 3.08/1.66 % (22249)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (22249)Memory used [KB]: 1791
% 3.08/1.66 % (22249)Time elapsed: 0.013 s
% 3.08/1.66 % (22249)Instructions burned: 18 (million)
% 3.08/1.66 % (22249)------------------------------
% 3.08/1.66 % (22249)------------------------------
% 3.08/1.67 % (22253)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_22144 for (2999ds/3Mi)
% 3.08/1.67 % (22253)Instruction limit reached!
% 3.08/1.67 % (22253)------------------------------
% 3.08/1.67 % (22253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (22253)Termination reason: Unknown
% 3.08/1.67 % (22253)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (22253)Memory used [KB]: 1535
% 3.08/1.67 % (22253)Time elapsed: 0.003 s
% 3.08/1.67 % (22253)Instructions burned: 6 (million)
% 3.08/1.67 % (22253)------------------------------
% 3.08/1.67 % (22253)------------------------------
% 3.08/1.67 % (22245)Instruction limit reached!
% 3.08/1.67 % (22245)------------------------------
% 3.08/1.67 % (22245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (22245)Termination reason: Unknown
% 3.08/1.67 % (22245)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (22245)Memory used [KB]: 1918
% 3.08/1.67 % (22245)Time elapsed: 0.018 s
% 3.08/1.67 % (22245)Instructions burned: 27 (million)
% 3.08/1.67 % (22245)------------------------------
% 3.08/1.67 % (22245)------------------------------
% 3.08/1.67 % (22251)Instruction limit reached!
% 3.08/1.67 % (22251)------------------------------
% 3.08/1.67 % (22251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (22251)Termination reason: Unknown
% 3.08/1.67 % (22251)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (22251)Memory used [KB]: 2302
% 3.08/1.67 % (22251)Time elapsed: 0.013 s
% 3.08/1.67 % (22251)Instructions burned: 38 (million)
% 3.08/1.67 % (22251)------------------------------
% 3.08/1.67 % (22251)------------------------------
% 3.08/1.67 % (22252)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_22144 for (2999ds/15Mi)
% 3.08/1.68 % (22255)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/7Mi)
% 3.08/1.68 % (22254)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_22144 for (2999ds/1041Mi)
% 3.08/1.68 % (22257)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_22144 for (2999ds/3Mi)
% 3.08/1.68 % (22255)Instruction limit reached!
% 3.08/1.68 % (22255)------------------------------
% 3.08/1.68 % (22255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (22255)Termination reason: Unknown
% 3.08/1.68 % (22255)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (22255)Memory used [KB]: 1663
% 3.08/1.68 % (22255)Time elapsed: 0.004 s
% 3.08/1.68 % (22255)Instructions burned: 9 (million)
% 3.08/1.68 % (22255)------------------------------
% 3.08/1.68 % (22255)------------------------------
% 3.08/1.68 % (22257)Instruction limit reached!
% 3.08/1.68 % (22257)------------------------------
% 3.08/1.68 % (22257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (22257)Termination reason: Unknown
% 3.08/1.68 % (22257)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (22257)Memory used [KB]: 1535
% 3.08/1.68 % (22257)Time elapsed: 0.003 s
% 3.08/1.68 % (22257)Instructions burned: 3 (million)
% 3.08/1.68 % (22257)------------------------------
% 3.08/1.68 % (22257)------------------------------
% 3.08/1.68 % (22252)Instruction limit reached!
% 3.08/1.68 % (22252)------------------------------
% 3.08/1.68 % (22252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (22252)Termination reason: Unknown
% 3.08/1.68 % (22252)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (22252)Memory used [KB]: 1791
% 3.08/1.68 % (22252)Time elapsed: 0.011 s
% 3.08/1.68 % (22252)Instructions burned: 15 (million)
% 3.08/1.68 % (22252)------------------------------
% 3.08/1.68 % (22252)------------------------------
% 3.08/1.69 % (22256)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/16Mi)
% 3.08/1.69 % (22258)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_22144 for (2999ds/3Mi)
% 3.08/1.69 % (22259)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/7Mi)
% 3.08/1.69 % (22258)Instruction limit reached!
% 3.08/1.69 % (22258)------------------------------
% 3.08/1.69 % (22258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (22258)Termination reason: Unknown
% 3.08/1.69 % (22258)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (22258)Memory used [KB]: 1535
% 3.08/1.69 % (22258)Time elapsed: 0.003 s
% 3.08/1.69 % (22258)Instructions burned: 5 (million)
% 3.08/1.69 % (22258)------------------------------
% 3.08/1.69 % (22258)------------------------------
% 3.08/1.69 % (22259)Instruction limit reached!
% 3.08/1.69 % (22259)------------------------------
% 3.08/1.69 % (22259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (22259)Termination reason: Unknown
% 3.08/1.69 % (22259)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (22259)Memory used [KB]: 1663
% 3.08/1.69 % (22259)Time elapsed: 0.005 s
% 3.08/1.69 % (22259)Instructions burned: 9 (million)
% 3.08/1.69 % (22259)------------------------------
% 3.08/1.69 % (22259)------------------------------
% 3.12/1.70 % (22256)Instruction limit reached!
% 3.12/1.70 % (22256)------------------------------
% 3.12/1.70 % (22256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (22256)Termination reason: Unknown
% 3.12/1.70 % (22256)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (22256)Memory used [KB]: 1791
% 3.12/1.70 % (22256)Time elapsed: 0.012 s
% 3.12/1.70 % (22256)Instructions burned: 17 (million)
% 3.12/1.70 % (22256)------------------------------
% 3.12/1.70 % (22256)------------------------------
% 3.12/1.70 % (22260)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/3Mi)
% 3.12/1.70 % (22243)Instruction limit reached!
% 3.12/1.70 % (22243)------------------------------
% 3.12/1.70 % (22243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (22243)Termination reason: Unknown
% 3.12/1.70 % (22243)Termination phase: Saturation
% 3.12/1.70
% 3.12/1.70 % (22243)Memory used [KB]: 7419
% 3.12/1.70 % (22243)Time elapsed: 0.055 s
% 3.12/1.70 % (22243)Instructions burned: 183 (million)
% 3.12/1.70 % (22243)------------------------------
% 3.12/1.70 % (22243)------------------------------
% 3.12/1.70 % (22261)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/4Mi)
% 3.12/1.70 % (22260)Instruction limit reached!
% 3.12/1.70 % (22260)------------------------------
% 3.12/1.70 % (22260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (22260)Termination reason: Unknown
% 3.12/1.70 % (22260)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (22260)Memory used [KB]: 1535
% 3.12/1.70 % (22260)Time elapsed: 0.004 s
% 3.12/1.70 % (22260)Instructions burned: 3 (million)
% 3.12/1.70 % (22260)------------------------------
% 3.12/1.70 % (22260)------------------------------
% 3.12/1.70 % (22261)Instruction limit reached!
% 3.12/1.70 % (22261)------------------------------
% 3.12/1.70 % (22261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (22261)Termination reason: Unknown
% 3.12/1.70 % (22261)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (22261)Memory used [KB]: 1663
% 3.12/1.70 % (22261)Time elapsed: 0.003 s
% 3.12/1.70 % (22261)Instructions burned: 6 (million)
% 3.12/1.70 % (22261)------------------------------
% 3.12/1.70 % (22261)------------------------------
% 3.12/1.70 % (22262)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/18Mi)
% 3.12/1.71 % (22248)First to succeed.
% 3.12/1.71 % (22264)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22144 for (2999ds/6Mi)
% 3.12/1.71 % (22262)Instruction limit reached!
% 3.12/1.71 % (22262)------------------------------
% 3.12/1.71 % (22262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (22262)Termination reason: Unknown
% 3.12/1.71 % (22262)Termination phase: shuffling
% 3.12/1.71
% 3.12/1.71 % (22262)Memory used [KB]: 1791
% 3.12/1.71 % (22262)Time elapsed: 0.008 s
% 3.12/1.71 % (22262)Instructions burned: 18 (million)
% 3.12/1.71 % (22262)------------------------------
% 3.12/1.71 % (22262)------------------------------
% 3.12/1.71 % (22248)Refutation found. Thanks to Tanya!
% 3.12/1.71 % SZS status ContradictoryAxioms for DTF2THF_22144
% 3.12/1.71 % SZS output start Proof for DTF2THF_22144
% 3.12/1.71 thf(type_def_5, type, formula_a_b_c: $tType).
% 3.12/1.71 thf(type_def_7, type, denota231621370t_unit: $tType).
% 3.12/1.71 thf(type_def_8, type, oDE_a_c: $tType).
% 3.12/1.71 thf(type_def_9, type, finite1398487019real_c: $tType).
% 3.12/1.71 thf(type_def_10, type, set_c: $tType).
% 3.12/1.71 thf(type_def_11, type, produc190496183real_c: $tType).
% 3.12/1.71 thf(type_def_12, type, set_Sum_sum_c_c: $tType).
% 3.12/1.71 thf(type_def_13, type, set_Pr1389752855real_c: $tType).
% 3.12/1.71 thf(type_def_14, type, c: $tType).
% 3.12/1.71 thf(type_def_15, type, real: $tType).
% 3.12/1.71 thf(type_def_16, type, set_re2066790124real_c: $tType).
% 3.12/1.71 thf(type_def_17, type, set_re1692486081real_c: $tType).
% 3.12/1.71 thf(type_def_18, type, set_re844416664real_c: $tType).
% 3.12/1.71 thf(type_def_19, type, set_re366411824um_c_c: $tType).
% 3.12/1.71 thf(type_def_20, type, set_Sum_sum_c_d: $tType).
% 3.12/1.71 thf(type_def_21, type, set_re1812065969um_c_d: $tType).
% 3.12/1.71 thf(type_def_22, type, set_re141277793al_c_c: $tType).
% 3.12/1.71 thf(type_def_23, type, set_real: $tType).
% 3.12/1.71 thf(type_def_24, type, set_Fi1407883041real_c: $tType).
% 3.12/1.71 thf(type_def_25, type, sum_sum_c_c: $tType).
% 3.12/1.71 thf(type_def_26, type, set_Su1710027039um_c_c: $tType).
% 3.12/1.71 thf(type_def_27, type, set_Su1008197536um_c_d: $tType).
% 3.12/1.71 thf(type_def_28, type, set_Sum_sum_c_c_c: $tType).
% 3.12/1.71 thf(type_def_29, type, sum_sum_c_d: $tType).
% 3.12/1.71 thf(type_def_30, type, set_Su1997276704um_c_c: $tType).
% 3.12/1.71 thf(type_def_31, type, set_Sum_sum_c_d_c: $tType).
% 3.12/1.71 thf(type_def_32, type, set_c_655950471real_c: $tType).
% 3.12/1.71 thf(type_def_33, type, set_c_Sum_sum_c_c: $tType).
% 3.12/1.71 thf(type_def_34, type, set_c_Sum_sum_c_d: $tType).
% 3.12/1.71 thf(type_def_35, type, set_c_c: $tType).
% 3.12/1.71 thf(type_def_36, type, produc214722967um_c_c: $tType).
% 3.12/1.71 thf(type_def_37, type, produc957004601l_real: $tType).
% 3.12/1.71 thf(type_def_38, type, d: $tType).
% 3.12/1.71 thf(func_def_0, type, set_re844416664real_c: $tType).
% 3.12/1.71 thf(func_def_1, type, set_re1692486081real_c: $tType).
% 3.12/1.71 thf(func_def_2, type, set_Pr1389752855real_c: $tType).
% 3.12/1.71 thf(func_def_3, type, produc190496183real_c: $tType).
% 3.12/1.71 thf(func_def_4, type, set_re1812065969um_c_d: $tType).
% 3.12/1.71 thf(func_def_5, type, set_re366411824um_c_c: $tType).
% 3.12/1.71 thf(func_def_6, type, produc214722967um_c_c: $tType).
% 3.12/1.71 thf(func_def_7, type, set_c_655950471real_c: $tType).
% 3.12/1.71 thf(func_def_8, type, set_re141277793al_c_c: $tType).
% 3.12/1.71 thf(func_def_9, type, set_re2066790124real_c: $tType).
% 3.12/1.71 thf(func_def_10, type, denota231621370t_unit: $tType).
% 3.12/1.71 thf(func_def_11, type, set_Su1997276704um_c_c: $tType).
% 3.12/1.71 thf(func_def_12, type, set_Su1008197536um_c_d: $tType).
% 3.12/1.71 thf(func_def_13, type, set_Su1710027039um_c_c: $tType).
% 3.12/1.71 thf(func_def_14, type, set_Fi1407883041real_c: $tType).
% 3.12/1.71 thf(func_def_15, type, set_c_Sum_sum_c_d: $tType).
% 3.12/1.71 thf(func_def_16, type, set_c_Sum_sum_c_c: $tType).
% 3.12/1.71 thf(func_def_17, type, set_Sum_sum_c_d_c: $tType).
% 3.12/1.71 thf(func_def_18, type, set_Sum_sum_c_c_c: $tType).
% 3.12/1.71 thf(func_def_19, type, finite1398487019real_c: $tType).
% 3.12/1.71 thf(func_def_20, type, produc957004601l_real: $tType).
% 3.12/1.71 thf(func_def_21, type, set_Sum_sum_c_d: $tType).
% 3.12/1.71 thf(func_def_22, type, set_Sum_sum_c_c: $tType).
% 3.12/1.71 thf(func_def_23, type, formula_a_b_c: $tType).
% 3.12/1.71 thf(func_def_24, type, sum_sum_c_d: $tType).
% 3.12/1.71 thf(func_def_25, type, sum_sum_c_c: $tType).
% 3.12/1.71 thf(func_def_26, type, set_c_c: $tType).
% 3.12/1.71 thf(func_def_27, type, oDE_a_c: $tType).
% 3.12/1.71 thf(func_def_28, type, set_real: $tType).
% 3.12/1.71 thf(func_def_29, type, set_c: $tType).
% 3.12/1.71 thf(func_def_30, type, real: $tType).
% 3.12/1.71 thf(func_def_31, type, d: $tType).
% 3.12/1.71 thf(func_def_32, type, c: $tType).
% 3.12/1.71 thf(func_def_33, type, coinci501627771_a_b_c: formula_a_b_c > $o).
% 3.12/1.71 thf(func_def_34, type, denota1275485728_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_35, type, denota540094197_a_b_c: denota231621370t_unit > oDE_a_c > set_c).
% 3.12/1.71 thf(func_def_36, type, denota256060419gree_c: finite1398487019real_c > finite1398487019real_c > set_c > $o).
% 3.12/1.71 thf(func_def_37, type, denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o).
% 3.12/1.71 thf(func_def_38, type, denota310462944_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c).
% 3.12/1.71 thf(func_def_39, type, denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c).
% 3.12/1.71 thf(func_def_40, type, denota161327353_a_b_c: denota231621370t_unit > oDE_a_c > produc190496183real_c > finite1398487019real_c > produc190496183real_c).
% 3.12/1.71 thf(func_def_41, type, denota1896987029_a_b_c: denota231621370t_unit > oDE_a_c > finite1398487019real_c > produc190496183real_c).
% 3.12/1.71 thf(func_def_42, type, denotational_repd_c: produc190496183real_c > c > real > produc190496183real_c).
% 3.12/1.71 thf(func_def_43, type, denota1293057250_a_b_c: denota231621370t_unit > oDE_a_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_44, type, finite557796307c_real: (c > real) > finite1398487019real_c).
% 3.12/1.71 thf(func_def_45, type, finite772340578real_c: finite1398487019real_c > c > real).
% 3.12/1.71 thf(func_def_46, type, pi_rea1386151481real_c: set_re2066790124real_c > ((real > finite1398487019real_c) > set_re2066790124real_c) > set_re1692486081real_c).
% 3.12/1.71 thf(func_def_47, type, pi_rea1379668980real_c: set_re2066790124real_c > ((real > finite1398487019real_c) > set_Pr1389752855real_c) > set_re844416664real_c).
% 3.12/1.71 thf(func_def_48, type, pi_rea1500330408um_c_c: set_re2066790124real_c > ((real > finite1398487019real_c) > set_Sum_sum_c_c) > set_re366411824um_c_c).
% 3.12/1.71 thf(func_def_49, type, pi_rea1508591913um_c_d: set_re2066790124real_c > ((real > finite1398487019real_c) > set_Sum_sum_c_d) > set_re1812065969um_c_d).
% 3.12/1.71 thf(func_def_50, type, pi_rea1228756413al_c_c: set_re2066790124real_c > ((real > finite1398487019real_c) > set_c) > set_re141277793al_c_c).
% 3.12/1.71 thf(func_def_51, type, pi_rea1111636068real_c: set_real > (real > set_Fi1407883041real_c) > set_re2066790124real_c).
% 3.12/1.71 thf(func_def_52, type, pi_Sum253006871um_c_c: set_Sum_sum_c_c > (sum_sum_c_c > set_Sum_sum_c_c) > set_Su1710027039um_c_c).
% 3.12/1.71 thf(func_def_53, type, pi_Sum261268376um_c_d: set_Sum_sum_c_c > (sum_sum_c_c > set_Sum_sum_c_d) > set_Su1008197536um_c_d).
% 3.12/1.71 thf(func_def_54, type, pi_Sum_sum_c_c_c: set_Sum_sum_c_c > (sum_sum_c_c > set_c) > set_Sum_sum_c_c_c).
% 3.12/1.71 thf(func_def_55, type, pi_Sum1145067928um_c_c: set_Sum_sum_c_d > (sum_sum_c_d > set_Sum_sum_c_c) > set_Su1997276704um_c_c).
% 3.12/1.71 thf(func_def_56, type, pi_Sum_sum_c_d_c: set_Sum_sum_c_d > (sum_sum_c_d > set_c) > set_Sum_sum_c_d_c).
% 3.12/1.71 thf(func_def_57, type, pi_c_r41638571real_c: set_c > (c > set_re2066790124real_c) > set_c_655950471real_c).
% 3.12/1.71 thf(func_def_58, type, pi_c_Sum_sum_c_c: set_c > (c > set_Sum_sum_c_c) > set_c_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_59, type, pi_c_Sum_sum_c_d: set_c > (c > set_Sum_sum_c_d) > set_c_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_60, type, pi_c_c: set_c > (c > set_c) > set_c_c).
% 3.12/1.71 thf(func_def_61, type, uminus1756072592al_c_o: ((real > finite1398487019real_c) > $o) > (real > finite1398487019real_c) > $o).
% 3.12/1.71 thf(func_def_62, type, uminus23580315al_c_o: (finite1398487019real_c > $o) > finite1398487019real_c > $o).
% 3.12/1.71 thf(func_def_63, type, uminus32155087al_c_o: (produc190496183real_c > $o) > produc190496183real_c > $o).
% 3.12/1.71 thf(func_def_64, type, uminus88729697_c_c_o: (sum_sum_c_c > $o) > sum_sum_c_c > $o).
% 3.12/1.71 thf(func_def_65, type, uminus916499104_c_d_o: (sum_sum_c_d > $o) > sum_sum_c_d > $o).
% 3.12/1.71 thf(func_def_66, type, uminus_uminus_c_o: (c > $o) > c > $o).
% 3.12/1.71 thf(func_def_67, type, uminus1737280820real_c: finite1398487019real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_68, type, uminus17964590real_c: produc190496183real_c > produc190496183real_c).
% 3.12/1.71 thf(func_def_69, type, uminus1225118734um_c_c: produc214722967um_c_c > produc214722967um_c_c).
% 3.12/1.71 thf(func_def_70, type, uminus_uminus_real: real > real).
% 3.12/1.71 thf(func_def_71, type, uminus946614837real_c: set_re2066790124real_c > set_re2066790124real_c).
% 3.12/1.71 thf(func_def_72, type, uminus102402154real_c: set_Fi1407883041real_c > set_Fi1407883041real_c).
% 3.12/1.71 thf(func_def_73, type, uminus232257166real_c: set_Pr1389752855real_c > set_Pr1389752855real_c).
% 3.12/1.71 thf(func_def_74, type, uminus1381786404um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_75, type, uminus373867045um_c_d: set_Sum_sum_c_d > set_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_76, type, uminus_uminus_set_c: set_c > set_c).
% 3.12/1.71 thf(func_def_77, type, zero_z109254132real_c: finite1398487019real_c).
% 3.12/1.71 thf(func_def_78, type, zero_z1506780526real_c: produc190496183real_c).
% 3.12/1.71 thf(func_def_79, type, zero_z659284464l_real: produc957004601l_real).
% 3.12/1.71 thf(func_def_80, type, zero_zero_real: real).
% 3.12/1.71 thf(func_def_81, type, if_Fin36944805real_c: $o > finite1398487019real_c > finite1398487019real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_82, type, if_real: $o > real > real > real).
% 3.12/1.71 thf(func_def_83, type, initia1631504802real_c: (real > finite1398487019real_c) > (real > finite1398487019real_c > finite1398487019real_c) > set_real > set_Fi1407883041real_c > $o).
% 3.12/1.71 thf(func_def_84, type, ord_le818951225al_c_o: ((real > finite1398487019real_c) > $o) > ((real > finite1398487019real_c) > $o) > $o).
% 3.12/1.71 thf(func_def_85, type, ord_le1132241894al_c_o: (produc190496183real_c > $o) > (produc190496183real_c > $o) > $o).
% 3.12/1.71 thf(func_def_86, type, ord_le584953750real_c: (real > finite1398487019real_c) > (real > finite1398487019real_c) > $o).
% 3.12/1.71 thf(func_def_87, type, ord_le1315653386_c_c_o: (sum_sum_c_c > $o) > (sum_sum_c_c > $o) > $o).
% 3.12/1.71 thf(func_def_88, type, ord_le2143422793_c_d_o: (sum_sum_c_d > $o) > (sum_sum_c_d > $o) > $o).
% 3.12/1.71 thf(func_def_89, type, ord_less_eq_c_o: (c > $o) > (c > $o) > $o).
% 3.12/1.71 thf(func_def_90, type, ord_le775706699real_c: finite1398487019real_c > finite1398487019real_c > $o).
% 3.12/1.71 thf(func_def_91, type, ord_le850691415real_c: produc190496183real_c > produc190496183real_c > $o).
% 3.12/1.71 thf(func_def_92, type, ord_le1342644953l_real: produc957004601l_real > produc957004601l_real > $o).
% 3.12/1.71 thf(func_def_93, type, ord_less_eq_real: real > real > $o).
% 3.12/1.71 thf(func_def_94, type, ord_le35002188real_c: set_re2066790124real_c > set_re2066790124real_c > $o).
% 3.12/1.71 thf(func_def_95, type, ord_le1327118209real_c: set_Fi1407883041real_c > set_Fi1407883041real_c > $o).
% 3.12/1.71 thf(func_def_96, type, ord_le977353143real_c: set_Pr1389752855real_c > set_Pr1389752855real_c > $o).
% 3.12/1.71 thf(func_def_97, type, ord_less_eq_set_real: set_real > set_real > $o).
% 3.12/1.71 thf(func_def_98, type, ord_le1772180283um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > $o).
% 3.12/1.71 thf(func_def_99, type, ord_le764260924um_c_d: set_Sum_sum_c_d > set_Sum_sum_c_d > $o).
% 3.12/1.71 thf(func_def_100, type, ord_less_eq_set_c: set_c > set_c > $o).
% 3.12/1.71 thf(func_def_101, type, produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 3.12/1.71 thf(func_def_102, type, produc705216881l_real: real > real > produc957004601l_real).
% 3.12/1.71 thf(func_def_103, type, produc1439061071um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > produc214722967um_c_c).
% 3.12/1.71 thf(func_def_104, type, produc2010422875real_c: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_105, type, produc1422991709l_real: produc957004601l_real > real).
% 3.12/1.71 thf(func_def_106, type, produc1983230011um_c_c: produc214722967um_c_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_107, type, produc314122909real_c: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_108, type, produc1407670175l_real: produc957004601l_real > real).
% 3.12/1.71 thf(func_def_109, type, produc1132019837um_c_c: produc214722967um_c_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_110, type, collec913357835real_c: ((real > finite1398487019real_c) > $o) > set_re2066790124real_c).
% 3.12/1.71 thf(func_def_111, type, collec230941376real_c: (finite1398487019real_c > $o) > set_Fi1407883041real_c).
% 3.12/1.71 thf(func_def_112, type, collec1643251106real_c: (produc190496183real_c > $o) > set_Pr1389752855real_c).
% 3.12/1.71 thf(func_def_113, type, collect_Sum_sum_c_c: (sum_sum_c_c > $o) > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_114, type, collect_Sum_sum_c_d: (sum_sum_c_d > $o) > set_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_115, type, collect_c: (c > $o) > set_c).
% 3.12/1.71 thf(func_def_116, type, image_266490115al_c_c: ((real > finite1398487019real_c) > c) > set_re2066790124real_c > set_c).
% 3.12/1.71 thf(func_def_117, type, image_1260608398al_c_c: (finite1398487019real_c > c) > set_Fi1407883041real_c > set_c).
% 3.12/1.71 thf(func_def_118, type, image_327677598real_c: (real > finite1398487019real_c) > set_real > set_Fi1407883041real_c).
% 3.12/1.71 thf(func_def_119, type, image_real_real: (real > real) > set_real > set_real).
% 3.12/1.71 thf(func_def_120, type, image_666880337um_c_c: (sum_sum_c_c > sum_sum_c_c) > set_Sum_sum_c_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_121, type, image_675141842um_c_d: (sum_sum_c_c > sum_sum_c_d) > set_Sum_sum_c_c > set_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_122, type, image_Sum_sum_c_c_c: (sum_sum_c_c > c) > set_Sum_sum_c_c > set_c).
% 3.12/1.71 thf(func_def_123, type, image_1558941394um_c_c: (sum_sum_c_d > sum_sum_c_c) > set_Sum_sum_c_d > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_124, type, image_1567202899um_c_d: (sum_sum_c_d > sum_sum_c_d) > set_Sum_sum_c_d > set_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_125, type, image_Sum_sum_c_d_c: (sum_sum_c_d > c) > set_Sum_sum_c_d > set_c).
% 3.12/1.71 thf(func_def_126, type, image_1226855921real_c: (c > real > finite1398487019real_c) > set_c > set_re2066790124real_c).
% 3.12/1.71 thf(func_def_127, type, image_687300774real_c: (c > finite1398487019real_c) > set_c > set_Fi1407883041real_c).
% 3.12/1.71 thf(func_def_128, type, image_c_Sum_sum_c_c: (c > sum_sum_c_c) > set_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_129, type, image_c_Sum_sum_c_d: (c > sum_sum_c_d) > set_c > set_Sum_sum_c_d).
% 3.12/1.71 thf(func_def_130, type, image_c_c: (c > c) > set_c > set_c).
% 3.12/1.71 thf(func_def_131, type, set_or1308937537real_c: (real > finite1398487019real_c) > (real > finite1398487019real_c) > set_re2066790124real_c).
% 3.12/1.71 thf(func_def_132, type, set_or385782508real_c: produc190496183real_c > produc190496183real_c > set_Pr1389752855real_c).
% 3.12/1.71 thf(func_def_133, type, set_or656347191t_real: real > real > set_real).
% 3.12/1.71 thf(func_def_134, type, static_BVO_a_c: oDE_a_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_135, type, static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c).
% 3.12/1.71 thf(func_def_136, type, static_FVO_a_c: oDE_a_c > set_c).
% 3.12/1.71 thf(func_def_137, type, sum_Inl_c_c: c > sum_sum_c_c).
% 3.12/1.71 thf(func_def_138, type, sum_Inl_c_d: c > sum_sum_c_d).
% 3.12/1.71 thf(func_def_139, type, sum_Inr_c_c: c > sum_sum_c_c).
% 3.12/1.71 thf(func_def_140, type, sum_Inr_d_c: d > sum_sum_c_d).
% 3.12/1.71 thf(func_def_141, type, equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c).
% 3.12/1.71 thf(func_def_142, type, fsafe_a_b_c: formula_a_b_c > $o).
% 3.12/1.71 thf(func_def_143, type, osafe_a_c: oDE_a_c > $o).
% 3.12/1.71 thf(func_def_144, type, member1851015714real_c: ((real > finite1398487019real_c) > real > finite1398487019real_c) > set_re1692486081real_c > $o).
% 3.12/1.71 thf(func_def_145, type, member954762593real_c: ((real > finite1398487019real_c) > produc190496183real_c) > set_re844416664real_c > $o).
% 3.12/1.71 thf(func_def_146, type, member354622481um_c_c: ((real > finite1398487019real_c) > sum_sum_c_c) > set_re366411824um_c_c > $o).
% 3.12/1.71 thf(func_def_147, type, member1494186770um_c_d: ((real > finite1398487019real_c) > sum_sum_c_d) > set_re1812065969um_c_d > $o).
% 3.12/1.71 thf(func_def_148, type, member527957930al_c_c: ((real > finite1398487019real_c) > c) > set_re141277793al_c_c > $o).
% 3.12/1.71 thf(func_def_149, type, member1321351885real_c: (real > finite1398487019real_c) > set_re2066790124real_c > $o).
% 3.12/1.71 thf(func_def_150, type, member1326674048um_c_c: (sum_sum_c_c > sum_sum_c_c) > set_Su1710027039um_c_c > $o).
% 3.12/1.71 thf(func_def_151, type, member318754689um_c_d: (sum_sum_c_c > sum_sum_c_d) > set_Su1008197536um_c_d > $o).
% 3.12/1.71 thf(func_def_152, type, member_Sum_sum_c_c_c: (sum_sum_c_c > c) > set_Sum_sum_c_c_c > $o).
% 3.12/1.71 thf(func_def_153, type, member71251457um_c_c: (sum_sum_c_d > sum_sum_c_c) > set_Su1997276704um_c_c > $o).
% 3.12/1.71 thf(func_def_154, type, member_Sum_sum_c_d_c: (sum_sum_c_d > c) > set_Sum_sum_c_d_c > $o).
% 3.12/1.71 thf(func_def_155, type, member469531344real_c: (c > real > finite1398487019real_c) > set_c_655950471real_c > $o).
% 3.12/1.71 thf(func_def_156, type, member_c_Sum_sum_c_c: (c > sum_sum_c_c) > set_c_Sum_sum_c_c > $o).
% 3.12/1.71 thf(func_def_157, type, member_c_Sum_sum_c_d: (c > sum_sum_c_d) > set_c_Sum_sum_c_d > $o).
% 3.12/1.71 thf(func_def_158, type, member_c_c: (c > c) > set_c_c > $o).
% 3.12/1.71 thf(func_def_159, type, member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o).
% 3.12/1.71 thf(func_def_160, type, member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o).
% 3.12/1.71 thf(func_def_161, type, member_real: real > set_real > $o).
% 3.12/1.71 thf(func_def_162, type, member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o).
% 3.12/1.71 thf(func_def_163, type, member_Sum_sum_c_d: sum_sum_c_d > set_Sum_sum_c_d > $o).
% 3.12/1.71 thf(func_def_164, type, member_c: c > set_c > $o).
% 3.12/1.71 thf(func_def_165, type, i: denota231621370t_unit).
% 3.12/1.71 thf(func_def_166, type, ode: oDE_a_c).
% 3.12/1.71 thf(func_def_167, type, oDEa: oDE_a_c).
% 3.12/1.71 thf(func_def_168, type, p: formula_a_b_c).
% 3.12/1.71 thf(func_def_169, type, phi: formula_a_b_c).
% 3.12/1.71 thf(func_def_170, type, aa: finite1398487019real_c).
% 3.12/1.71 thf(func_def_171, type, ab: finite1398487019real_c).
% 3.12/1.71 thf(func_def_172, type, ba: finite1398487019real_c).
% 3.12/1.71 thf(func_def_173, type, bb: finite1398487019real_c).
% 3.12/1.71 thf(func_def_174, type, i2: c).
% 3.12/1.71 thf(func_def_175, type, sol: real > finite1398487019real_c).
% 3.12/1.71 thf(func_def_176, type, t: real).
% 3.12/1.71 thf(func_def_177, type, x: real).
% 3.12/1.71 thf(func_def_193, type, sK0: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_194, type, sK1: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_195, type, sK2: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.12/1.71 thf(func_def_196, type, sK3: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.12/1.71 thf(func_def_197, type, sK4: (sum_sum_c_c > $o) > set_c > (c > sum_sum_c_c) > c).
% 3.12/1.71 thf(func_def_198, type, sK5: (c > sum_sum_c_c) > set_c > sum_sum_c_c > c).
% 3.12/1.71 thf(func_def_199, type, sK6: finite1398487019real_c > (c > real) > c).
% 3.12/1.71 thf(func_def_200, type, sK7: (c > sum_sum_c_c) > (c > sum_sum_c_c) > set_c > c).
% 3.12/1.71 thf(func_def_201, type, sK8: (sum_sum_c_c > $o) > (c > sum_sum_c_c) > set_c > sum_sum_c_c).
% 3.12/1.71 thf(func_def_202, type, sK9: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_203, type, sK10: produc190496183real_c > finite1398487019real_c).
% 3.12/1.71 thf(func_def_204, type, sK11: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.12/1.71 thf(func_def_205, type, sK12: (produc190496183real_c > $o) > finite1398487019real_c).
% 3.12/1.71 thf(func_def_206, type, sK13: set_c > (c > sum_sum_c_c) > sum_sum_c_c > c).
% 3.12/1.71 thf(func_def_208, type, ph15: !>[X0: $tType]:(X0)).
% 3.12/1.71 thf(f1255,plain,(
% 3.12/1.71 $false),
% 3.12/1.71 inference(subsumption_resolution,[status(thm)],[f1254,f1162])).
% 3.12/1.71 thf(f1162,plain,(
% 3.12/1.71 ((member_c @ i2 @ (static_FVO_a_c @ oDEa)) != $true)),
% 3.12/1.71 inference(cnf_transformation,[status(thm)],[f1001])).
% 3.12/1.71 thf(f1001,plain,(
% 3.12/1.71 ((member_c @ i2 @ (static_FVO_a_c @ oDEa)) != $true)),
% 3.12/1.71 inference(flattening,[status(thm)],[f497])).
% 3.12/1.71 thf(f497,plain,(
% 3.12/1.71 ~((member_c @ i2 @ (static_FVO_a_c @ oDEa)) = $true)),
% 3.12/1.71 inference(fool_elimination,[status(thm)],[f496])).
% 3.12/1.71 thf(f496,plain,(
% 3.12/1.71 ~(member_c @ i2 @ (static_FVO_a_c @ oDEa))),
% 3.12/1.71 inference(rectify,[status(thm)],[f360])).
% 3.12/1.71 thf(f360,axiom,(
% 3.12/1.71 ~(member_c @ i2 @ (static_FVO_a_c @ oDEa))),
% 3.12/1.71 file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',conj_2)).
% 3.12/1.71 thf(f1254,plain,(
% 3.12/1.71 ((member_c @ i2 @ (static_FVO_a_c @ oDEa)) = $true)),
% 3.12/1.71 inference(trivial_inequality_removal,[status(thm)],[f1253])).
% 3.12/1.71 thf(f1253,plain,(
% 3.12/1.71 ($true != $true) | ((member_c @ i2 @ (static_FVO_a_c @ oDEa)) = $true)),
% 3.12/1.71 inference(superposition,[status(thm)],[f1096,f1132])).
% 3.12/1.71 thf(f1132,plain,(
% 3.12/1.71 ((member_c @ i2 @ (denota540094197_a_b_c @ i @ oDEa)) = $true)),
% 3.12/1.71 inference(cnf_transformation,[status(thm)],[f423])).
% 3.12/1.71 thf(f423,plain,(
% 3.12/1.71 ((member_c @ i2 @ (denota540094197_a_b_c @ i @ oDEa)) = $true)),
% 3.12/1.71 inference(fool_elimination,[status(thm)],[f422])).
% 3.12/1.71 thf(f422,plain,(
% 3.12/1.71 (member_c @ i2 @ (denota540094197_a_b_c @ i @ oDEa))),
% 3.12/1.71 inference(rectify,[status(thm)],[f359])).
% 3.12/1.71 thf(f359,axiom,(
% 3.12/1.71 (member_c @ i2 @ (denota540094197_a_b_c @ i @ oDEa))),
% 3.12/1.71 file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',conj_1)).
% 3.12/1.71 thf(f1096,plain,(
% 3.12/1.71 ( ! [X2 : oDE_a_c,X0 : c,X1 : denota231621370t_unit] : (((member_c @ X0 @ (denota540094197_a_b_c @ X1 @ X2)) != $true) | ((member_c @ X0 @ (static_FVO_a_c @ X2)) = $true)) )),
% 3.12/1.71 inference(cnf_transformation,[status(thm)],[f1047])).
% 3.12/1.71 thf(f1047,plain,(
% 3.12/1.71 ! [X0 : c,X1 : denota231621370t_unit,X2 : oDE_a_c] : (((member_c @ X0 @ (denota540094197_a_b_c @ X1 @ X2)) != $true) | ((member_c @ X0 @ (static_FVO_a_c @ X2)) = $true))),
% 3.12/1.71 inference(ennf_transformation,[status(thm)],[f451])).
% 3.12/1.71 thf(f451,plain,(
% 3.12/1.71 ! [X0 : c,X1 : denota231621370t_unit,X2 : oDE_a_c] : (((member_c @ X0 @ (denota540094197_a_b_c @ X1 @ X2)) = $true) => ((member_c @ X0 @ (static_FVO_a_c @ X2)) = $true))),
% 3.12/1.71 inference(fool_elimination,[status(thm)],[f450])).
% 3.12/1.71 thf(f450,plain,(
% 3.12/1.71 ! [X0 : c,X1 : denota231621370t_unit,X2 : oDE_a_c] : ((member_c @ X0 @ (denota540094197_a_b_c @ X1 @ X2)) => (member_c @ X0 @ (static_FVO_a_c @ X2)))),
% 3.12/1.71 inference(rectify,[status(thm)],[f1])).
% 3.12/1.71 thf(f1,axiom,(
% 3.12/1.71 ! [X0 : c,X1 : denota231621370t_unit,X2 : oDE_a_c] : ((member_c @ X0 @ (denota540094197_a_b_c @ X1 @ X2)) => (member_c @ X0 @ (static_FVO_a_c @ X2)))),
% 3.12/1.71 file('/export/starexec/sandbox/tmp/tmp.eewb5jcYKE/DTF2THF_22144.p',fact_0_ode__to__fvo)).
% 3.12/1.71 % SZS output end Proof for DTF2THF_22144
% 3.12/1.71 % (22248)------------------------------
% 3.12/1.71 % (22248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (22248)Termination reason: Refutation
% 3.12/1.71
% 3.12/1.71 % (22248)Memory used [KB]: 7036
% 3.12/1.71 % (22248)Time elapsed: 0.057 s
% 3.12/1.71 % (22248)Instructions burned: 97 (million)
% 3.12/1.71 % (22248)------------------------------
% 3.12/1.71 % (22248)------------------------------
% 3.12/1.71 % (22242)Success in time 0.08 s
%------------------------------------------------------------------------------